Rock Quality, Seismic Velocity, Attenuation and Anisotropy

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ROCK QUALITY, SEISMIC VELOCITY, ATTENUATION AND ANISOTROPY

BALKEMA – Proceedings and Monographs in Engineering, Water and Earth Sciences

ROCK QUALITY, SEISMIC VELOCITY, ATTENUATION AND ANISOTROPY NICK BARTON

LONDON / LEIDEN / NEW YORK / PHILADELPHIA / SINGAPORE

Taylor & Francis is an imprint of the Taylor & Francis Group, an informa business © 2007 Taylor & Francis Group, London, UK This edition published in the Taylor & Francis e-Library, 2007. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”

All rights reserved. No part of this publication or the information contained herein may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, by photocopying, recording or otherwise, without written prior permission from the publishers. Although all care is taken to ensure the integrity and quality of this publication and the information herein, no responsibility is assumed by the publishers nor the author for any damage to property or persons as a result of operation or use of this publication and/or the information contained herein. Published by: Taylor & Francis/Balkema P.O. Box 447, 2300 AK Leiden, The Netherlands e-mail: [email protected] www.balkema.nl, www.taylorandfrancis.co.uk, www.crcpress.com Library of Congress Cataloguing-in-Publication Data Barton, Nick, 1944– Rock quality, seismic velocity, attenuation, and anisotropy/Nick Barton. p. cm. ISBN 0-415-39441-4 (hardcover: alk. paper) 1. Soil-structure interaction. 2. Earthquake engineering. I. Title. TA711.5.B37 2006 624.1
51—dc22 2006005909 ISBN 0-203-96445-4 Master e-book ISBN

ISBN10: 0-415-39441-4 (Hbk) ISBN13: 978-0-415-39441-3 (Hbk)

Table of contents Preface

XIII

Introduction The multi-disciplinary scope of seismic and rock quality Revealing hidden rock conditions Some basic principles of P, S and Q Q and Q Limitations of refraction seismic bring tomographic solutions

XIX XIX XX XX XXI XXII

Nomenclature

XXIII

PART I 1 Shallow seismic refraction, some basic theory, and the importance of rock type 1.1 The challenge of the near-surface in civil engineering 1.2 Some basic aspects concerning elastic body waves 1.2.1 Some sources of reduced elastic moduli 1.3 Relationships between Vp and Vs and their meaning in field work 1.4 Some advantages of shear waves 1.5 Basic estimation of rock-type and rock mass condition, from shallow seismic P-wave velocity 1.6 Some preliminary conversions from velocity to rock quality 1.7 Some limitations of the refraction seismic velocity interpretations 1.8 Assumed limitations may hide the strengths of the method 1.9 Seismic quality Q and apparent similarities to Q-rock

3 3 4 5 6 7 9 12 13 16 17

2 Environmental effects on velocity 2.1 Density and Vp 2.2 Porosity and Vp 2.3 Uniaxial compressive strength and Vp 2.4 Weathering and moisture content 2.5 Combined effects of moisture and pressure 2.6 Combined effects of moisture and low temperature

19 19 24 25 27 30 32

3 Effects of anisotropy on Vp 3.1 An introduction to velocity anisotropy caused by micro-cracks and jointing 3.2 Velocity anisotropy caused by fabric 3.3 Velocity anisotropy caused by rock joints 3.4 Velocity anisotropy caused by interbedding 3.5 Velocity anisotropy caused by faults

35 35 38 40 45 47

4 Cross-hole velocity and cross-hole velocity tomography 4.1 Cross-hole seismic for extrapolation of properties 4.2 Cross-hole seismic tomography in tunnelling 4.3 Cross-hole tomography in mining 4.4 Using tomography to monitor blasting effects 4.5 Alternative tomograms 4.6 Cross-hole or cross-well reflection measurement and time-lapse tomography

49 49 52 58 61 64 66

VI

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5 Relationships between rock quality, depth and seismic velocity 5.1 Some preliminary relationships between RQD, F, and Vp 5.2 Relationship between rock quality Q and Vp for hard jointed, near-surface rock masses 5.3 Effects of depth or stress on acoustic joint closure, velocities and amplitudes 5.3.1 Compression wave amplitude sensitivities to jointing 5.3.2 Stress and velocity coupling at the Gjøvik cavern site 5.4 Observations of effective stress effects on velocities 5.5 Integration of velocity, rock mass quality, porosity, stress, strength, deformability

69 69 74 77 83 88 88 92

6 Deformation moduli and seismic velocities 6.1 Correlating Vp with the ‘static’ moduli from deformation tests 6.2 Dynamic moduli and their relationship to static moduli 6.3 Some examples of the three dynamic moduli 6.4 Use of shear wave amplitude, frequency and petite-sismique 6.5 Correlation of deformation moduli with RMR and Q

97 97 104 109 110 111

7 Excavation disturbed zones and their seismic properties 7.1 Some effects of the free-surface on velocities and attenuation 7.2 EDZ phenomena around tunnels based on seismic monitoring 7.3 EDZ investigations in selected nuclear waste isolation studies 7.3.1 BWIP – EDZ studies 7.3.2 URL – EDZ studies 7.3.3 Äspö – EDZ studies 7.3.4 Stripa – effects of heating in the EDZ of a rock mass 7.4 Acoustic detection of stress effects around boreholes

117 117 119 124 124 127 131 133 136

8 Seismic measurements for tunnelling 8.1 Examples of seismic applications in tunnels 8.2 Examples of the use of seismic data in TBM excavations 8.3 Implications of inverse correlation between TBM advance rate and Vp 8.4 Use of probe drilling and seismic or sonic logging ahead of TBM tunnels 8.5 In-tunnel seismic measurements for looking ahead of the face 8.6 The possible consequences of insufficient seismic investigation due to depth limitations

139 139 148 149 151 152 154

9 Relationships between Vp, Lugeon value, permeability and grouting in jointed rock 9.1 Correlation between Vp and Lugeon value 9.2 Rock mass deformability and the Vp-L-Q correlation 9.3 Velocity and permeability measurements at in situ block tests 9.4 Detection of permeable zones using other geophysical methods 9.5 Monitoring the effects of grouting with seismic velocity 9.6 Interpreting grouting effects in relation to improved rock mass Q-parameters

159 159 162 165 169 170 172

PART II 10 Seismic quality Q and attenuation at many scales 10.1 Some basic aspects concerning attenuation and Q seismic 10.1.1 A preliminary discussion of the importance of strain levels 10.1.2 A preliminary look at the attenuating effect of cracks of larger scale 10.2 Attenuation and seismic Q from laboratory measurement 10.2.1 A more detailed discussion of friction as an attenuation mechanism

181 181 183 184 186 187

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10.2.2 Effects of partial saturation on seismic Q 10.3 Effect of confining pressure on seismic Q 10.3.1 The four components of elastic attenuation 10.3.2 Effect on Q p and Q s of loading rock samples towards failure 10.4 The effects of single rock joints on seismic Q 10.5 Attenuation and seismic Q from near-surface measurements 10.5.1 Potential links to rock mass quality parameters in jointed rock 10.5.2 Effects of unconsolidated sediments on seismic Q 10.5.3 Influence of frequency variations on attenuation in jointed and bedded rock 10.6 Attenuation in the crust as interpreted from earthquake coda 10.6.1 Coda Q c from earthquake sources and its relation to rock quality Q c 10.6.2 Frequency dependence of coda Q c due to depth effects 10.6.3 Temporal changes of coda Q c prior to earthquakes 10.6.4 Possible separation of attenuation into scattering and intrinsic mechanisms 10.6.5 Changed coda Q during seismic events 10.6.6 Attenuation of damage due to acceleration 10.6.7 Do microcracks or tectonic structure cause attenuation 10.6.8 Down-the-well seismometers to minimise site effects 10.6.9 Rock mass quality parallels 10.7 Attenuation across continents 10.7.1 Plate tectonics, sub-duction zones and seismic Q 10.7.2 Young and old oceanic lithosphere 10.7.3 Lateral and depth variation of seismic Q and seismic velocity 10.7.4 Cross-continent Lg coda Q variations and their explanation 10.7.5 Effect of thick sediments on continental Lg coda 10.8 Some recent attenuation measurements in petroleum reservoir environments 10.8.1 Anomalous values of seismic Q in reservoirs due to major structures 10.8.2 Evidence for fracturing effects in reservoirs on seismic Q 10.8.3 Different methods of analysis give different seismic Q 11 Velocity structure of the earth’s crust 11.1 An introduction to crustal velocity structures 11.2 The continental velocity structures 11.3 The continental margin velocity structures 11.3.1 Explaining a velocity anomaly 11.4 The mid-Atlantic ridge velocity structures 11.4.1 A possible effective stress discrepancy in early testing 11.4.2 Smoother depth velocity models 11.4.3 Recognition of lower effective stress levels beneath the oceans 11.4.4 Direct observation of sub-ocean floor velocities 11.4.5 Sub-ocean floor attenuation measurements 11.4.6 A question of porosities, aspect ratios and sealing 11.4.7 A velocity-depth discussion 11.4.8 Fracture zones 11.5 The East Pacific Rise velocity structures 11.5.1 More porosity and fracture aspect ratio theories 11.5.2 First sub-Pacific ocean core with sonic logs and permeability tests 11.5.3 Attenuation and seismic Q due to fracturing and alteration 11.5.4 Seismic attenuation tomography across the East Pacific Rise 11.5.5 Continuous sub-ocean floor seismic profiles

VII

189 190 193 195 197 202 202 205 207 209 209 210 212 213 214 218 219 221 224 226 226 228 228 230 231 232 235 236 238 241 241 244 254 256 261 263 265 266 267 268 270 271 272 273 276 277 279 281 283

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Table of contents

11.6 Age effects summary for Atlantic Ridge and Pacific Rise 11.6.1 Decline of hydrothermal circulation with age and sediment cover 11.6.2 The analogy of pre-grouting as a form of mineralization

287 289 291

12 Rock stress, pore pressure, borehole stability and sonic logging 12.1 Pore pressure, over-pressure, and minimum stress 12.1.1 Pore pressure and over-pressure and cross-discipline terms 12.1.2 Minimum stress and mud-weight 12.2 Stress anisotropy and its intolerance by weak rock 12.2.1 Reversal of Ko trends nearer the surface 12.3 Relevance to logging of borehole disturbed zone 12.4 Borehole in continuum becomes borehole in local discontinuum 12.5 The EDZ caused by joints, fractures and bedding-planes 12.6 Loss of porosity due to extreme depth 12.7 Dipole shear-wave logging of boreholes 12.7.1 Some further development of logging tools 12.8 Mud filtrate invasion 12.9 Challenges from ultra HPHT

295 295 295 296 297 299 301 302 306 311 312 315 316 320

13 Rock physics at laboratory scale 13.1 Compressional velocity and porosity 13.2 Density, Vs and Vp 13.3 Velocity, aspect ratio, pressure, brine and gas 13.4 Velocity, temperature and influence of fluid 13.5 Velocity, clay content and permeability 13.6 Stratigraphy based velocity to permeability estimation 13.6.1 Correlation to field processes 13.7 Velocity with patchy saturation effects in mixed units 13.8 Dynamic Poisson’s ratio, effective stress and pore fluid 13.9 Dynamic moduli for estimating static deformation moduli 13.10 Attenuation due to fluid type, frequency, clay, over-pressure, compliant minerals, dual porosity 13.10.1 Comparison of velocity and attenuation in the presence of gas or brine 13.10.2 Attenuation when dry or gas or brine saturated 13.10.3 Effect of frequency on velocity and attenuation, dry or with brine 13.10.4 Attenuation for distinguishing gas condensate from oil and water 13.10.5 Attenuation in the presence of clay content 13.10.6 Attenuation due to compliant minerals and microcracks 13.10.7 Attenuation with dual porosity samples of limestones 13.10.8 Attenuation in the presence of over-pressure 13.11 Attenuation in the presence of anisotropy 13.11.1 Attenuation for fluid front monitoring 13.12 Anisotropic velocity and attenuation in shales 13.12.1 Attenuation anisotropy expressions ,  and  13.13 Permeability and velocity anisotropy due to fabric, joints and fractures 13.13.1 Seismic monitoring of fracture development and permeability 13.14 Rock mass quality, attenuation and modulus

323 323 324 326 328 331 332 334 335 337 339

14 P-waves for characterising fractured reservoirs 14.1 Some classic relationships between age, depth and velocity

369 369

341 341 341 342 343 345 346 348 350 351 352 354 356 357 359 365

Table of contents

14.2 14.3

14.4 14.5 14.6 14.7

14.8 14.9 14.10 14.11 14.12 14.13

Anisotropy and heterogeneity caused by inter-bedded strata and jointing 14.2.1 Some basic anisotropy theory Shallow cross-well seismic tomography 14.3.1 Shallow cross-well seismic in fractured rock 14.3.2 Cross-well seismic tomography with permeability measurement 14.3.3 Cross-well seismic in deeper reservoir characterization Detecting finely inter-layered sequences 14.4.1 Larger scale differentiation of facies Detecting anisotropy caused by fractures with multi-azimuth VSP 14.5.1 Fracture azimuth and stress azimuth from P-wave surveys 14.5.2 Sonic log and VSP dispersion effects and erratic seismic Q Dispersion as an alternative method of characterization AVO and AVOA using P-waves for fracture detection 14.7.1 Model dependence of AVOA fracture orientation 14.7.2 Conjugate joint or fracture sets also cause anisotropy 14.7.3 Vp anisotropy caused by faulting 14.7.4 Poisson’s ratio anisotropy caused by fracturing 4C four-component acquisition of seismic including C-waves 4D seismic monitoring of reservoirs 14.9.1 Possible limitations of some rock physics data 14.9.2 Oil saturation mapping with 4D seismic 4D monitoring of compaction and porosity at Ekofisk 14.10.1 Seismic detection of subsidence in the overburden 14.10.2 The periodically neglected joint behaviour at Ekofisk Water flood causes joint opening and potential shearing Low frequencies for sub-basalt imaging Recent reservoir anisotropy investigations involving P-waves and attenuation

15 Shear wave splitting in fractured reservoirs and resulting from earthquakes 15.1 Introduction 15.2 Shear wave splitting and its many implications 15.2.1 Some sources of shear-wave splitting 15.3 Crack density and EDA 15.3.1 A discussion of ‘criticality’ due to microcracks 15.3.2 Temporal changes in polarization in Cornwall HDR 15.3.3 A critique of Crampin’s microcrack model 15.3.4 90°-flips in polarization 15.4 Theory relating joint compliances with shear wave splitting 15.4.1 An unrealistic rock simulant suggests equality between ZN and ZT 15.4.2 Subsequent inequality of ZN and ZT 15.4.3 Off-vertical fracture dip or incidence angle, and normal compliance 15.4.4 Discussion of scale effects and stiffness 15.5 Dynamic and static stiffness tests on joints by Pyrak-Nolte 15.5.1 Discussion of stiffness data gaps and discipline bridging needs 15.5.2 Fracture stiffness and permeability 15.6 Normal and shear compliance theories for resolving fluid type 15.6.1 In situ compliances in a fault zone inferred from seismic Q 15.7 Shear wave splitting from earthquakes 15.7.1 Shear-wave splitting in the New Madrid seismic zone 15.7.2 Shear-wave splitting at Parkfield seismic monitoring array

IX

372 373 374 377 377 378 379 380 382 382 386 386 388 391 392 394 394 394 397 397 397 398 400 401 402 403 404 407 407 408 410 411 412 413 415 415 416 417 419 419 421 422 424 425 425 427 428 428 429

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15.7.3 Shear-wave splitting recorded at depth in Cajon Pass borehole 15.7.4 Stress-monitoring site (SMS) anomalies from Iceland 15.7.5 SW-Iceland, Station BJA shear wave anomalies 15.7.6 Effects of shearing on stiffness and shear wave amplitude 15.7.7 Shear-wave splitting at a geothermal field 15.7.8 Shear wave splitting during after-shocks of the Chi-Chi earthquake in Taiwan 15.7.9 Shear-wave splitting under the Mid-Atlantic Ridge 15.8 Recent cases of shear wave splitting in petroleum reservoirs 15.8.1 Some examples of S-wave and PS-wave acquisition methods 15.8.2 Classification of fractured reservoirs 15.8.3 Crack density and shearing of conjugate sets at Ekofisk might enhance splitting 15.8.4 Links between shear wave anisotropy and permeability 15.8.5 Polarization-stress alignment from shallow shear-wave splitting 15.8.6 Shear-wave splitting in argillaceous rocks 15.8.7 Time-lapse application of shear-wave splitting over reservoirs 15.8.8 Temporal shear-wave splitting using AE from the Valhall cap-rock 15.8.9 Shear-wave splitting and fluid identification at the Natih field 15.9 Dual-porosity poro-elastic modelling of dispersion and fracture size effects 15.9.1 A brief survey of rock mechanics pseudo-static models of jointed rock 15.9.2 A very brief review of slip-interface, fracture network and poro-elastic crack models 15.9.3 Applications of Chapman model to Bluebell Altamont fractured gas reservoir 15.9.4 The SeisRox model 15.9.5 Numerical modelling of dynamic joint stiffness effects 15.9.6 A ‘sugar cube’ model representation 15.10 A porous and fractured physical model as a numerical model validation 16 Joint stiffness and compliance and the joint shearing mechanism 16.1 Some important non-linear joint and fracture behaviour modes 16.2 Aspects of fluid flow in deforming rock joints 16.2.1 Coupled stress-flow behaviour under normal closure 16.2.2 Coupled stress-flow behaviour under shear deformation 16.3 Some important details concerning rock joint stiffnesses Kn and Ks 16.3.1 Initial normal stiffness measured at low stress 16.3.2 Normal stiffness at elevated normal stress levels 16.4 Ratios of Kn over Ks under static and dynamic conditions 16.4.1 Frequency dependence of fracture normal stiffness 16.4.2 Ratios of static Kn to static Ks for different block sizes 16.4.3 Field measurements of compliance ZN 16.4.4 Investigation of normal and shear compliances on artificial surfaces in limestones 16.4.5 The Worthington-Lubbe-Hudson range of compliances 16.4.6 Pseudo-static stiffness data for clay filled discontinuities and major shear zones 16.4.7 Shear stress application may apparently affect compliance 16.5 Effect of dry or saturated conditions on shear and normal stiffnesses 16.5.1 Joint roughness coefficient (JRC) 16.5.2 Joint wall compression strength (JCS) 16.5.3 Basic friction angle b and residual friction angle r 16.5.4 Empirical equations for the shear behaviour of rock joints 16.6 Mechanical over-closure, thermal-closure, and joint stiffness modification 16.6.1 Normal stiffness estimation

432 432 433 435 435 436 436 438 438 440 442 445 447 450 451 454 455 459 460 461 471 475 476 479 480 483 483 486 487 488 492 494 495 497 497 498 499 501 503 505 506 507 508 509 509 511 513 515

Table of contents

16.7

16.8 16.9 16.10 16.11 16.12

16.6.2 Thermal over-closure of joints and some implications 16.6.3 Mechanical over-closure Consequences of shear stress on polarization and permeability 16.7.1 Stress distribution caused by shearing joints, and possible consequences for shear wave splitting 16.7.2 The strength-deformation components of jointed rock masses 16.7.3 Permeability linked to joint shearing 16.7.4 Reservoir seismic case records with possible shearing 16.7.5 The apertures expected of highly stressed ‘open’ joints 16.7.6 Modelling apertures with the BB model 16.7.7 Open joints caused by anisotropic stress, low shear strength, dilation Non-linear shear strength and the critical shearing crust 16.8.1 Non-linear strength envelopes and scale effects Critically stressed open fractures that indicate conductivity 16.9.1 The JRC contribution at different scales and deformations 16.9.2 Does pre-peak or post-peak strength resist the assumed crustal shear stress? Rotation of joint attributes and unequal conjugate jointing may explain azimuthal deviation of S-wave polarization Classic stress transformation equations ignore the non-coaxiality of stress and displacement Estimating shallow crustal permeability from a modified rock quality Q-water 16.12.1 The problem of clay-sealed discontinuities

17 Conclusions

XI

515 517 517 518 520 523 525 526 531 534 536 536 541 544 545 548 552 554 555 559

Appendix A – The Qrock parameter ratings The six parameters defined Combination in pairs Definitions of characterization and classification as used in rock engineering Notes on Q-method of rock mass classification

615 615 615 615 615

Appendix B – A worked example

625

References

627

Index

655

Colour Plates

721

Preface This book traces an accelerating path through an important part of the earth sciences, describing seismic behaviour and rock mechanics interpretation at many scales, to illuminate what lies beneath the earth’s immediate surface. Although geophysics, and the rock mechanics and engineering geology of discontinuous media share the same medium, they have had a mostly separate development – with little cross-referencing in the multitude of journals. Regrettably, we seldom see geophysics colleagues at our rock conferences. This book attempts to bridge this void in strategic locations. Seismic velocity, seismic quality (the inverse of attenuation), and anisotropy are some of the very basics of geophysics, and they depend absolutely on the rock and fluid properties, the rock mass structures, the jointing, the fracturing, the microcracks and the other pore space. These are some of the fundamentals of earth science. All contribute to the resultant dynamic stiffnesses, and to the fluid pressure micro-flow reactions, whether at dam foundation depths, tunnel depths, reservoir-well depths, or earthquake depths. All components of the anisotropic, dynamic, stiffness-velocity-permeability half-space, respond together in a logical pattern. Attempting to understand this pattern is a major objective of this book. The assumed ‘shared earth’ response is revealing itself with increasing speed. Despite the very small strains and displacements involved in seismic wave loading there are inevitable, encouraging parallels, to the rock mechanics of larger strains and displacements. This makes seismic response more understandable and more logical for a wider group of professionals, with contributing areas of expertise. In synthetic modelling in geophysics, there is now much interest in the rock joint or rock fracture compliances that may hold part of the secret of fractured reservoir description. These same properties, when inverted, are used over much larger displacements, in rock stability and deformation modelling. Remarkably, the dynamic compliance and static stiffness of fractures and joints have mostly had a compartmentalized development in the different disciplines. A dynamic, micro-strain-based normal compliance of 1013 m/Pa1 derived from shear-wave anisotropy measurement in the sub-surface, is of recognisable magnitude when inverted, to compare with the pseudo-static ‘macro-strain’ joint normal stiffness (i.e. 10,000 MPa/mm or 10 MPa/micron) obtained from incremental loading tests on similar rock joints at similar high stress levels. The level of rock stress, the joint wall roughness, and the joint wall compressive strength, which are also important components of aperture and permeability, provide estimates of these physical properties, not just the diagonal members of a stiffness matrix. Here we have a classic reason for a disconnect between part of the earth sciences, which can be bridged with advantage. Attenuation and rock quality, another area of disconnect, can also be linked, but not quite so simply as taking the inverse of attenuation and calling it seismic quality. The universally used seismic quality Q of geophysics, that we will often call Q seis, shows some qualitative and quantitative connections to rock mass quality, also called Q, and widely used in rock engineering since the 1970’s. The rock mass quality (Q), which we will often call Q rock, is composed of several attenuation-causing parameters, that are directly equivalent to block size, inter-block friction and a rough measure of effective stress and permeability. There are clear, broad links between Q rock and Q seis, due to the discovery of a mutual connection to the empirically derived and stress-dependent deformation modulus of rock masses. This connection is despite the fact that only micro-strains, micro-displacements, and micro-flows (squirt) occur with the passage of dynamic waves. Rock mass behaviour is non-linear and scale-dependent. Load-deformation curves have different gradients at different stress levels. Dynamic waves seem to sense this non-linearity, and they apparently sense some of the scale effect too. This book is dedicated to making some of these cross-discipline empirical connections, in a simple non-mathematical way, so that the people who see a lot of rock in their daily endeavours (geologists, engineering geologists, rock mechanics and rock engineers), and those who see, and interpret, and model complex seismic results, from

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Preface

earthquakes, from fractured petroleum reservoirs, and from laboratory rock physics reservoir simulations, can more easily communicate in the common anisotropic stiffness-velocity-permeability half-space that is earth science. Communication in words and diagrams, rather than through complex formulae and matrices. At least half of the people working in the earth sciences are not as good at mathematics as the other half may have assumed.

Acknowledgements First and foremost this book is an acknowledgement to the many thousands of earth scientists working with geophysical interpretation of the near-surface, the sub-ocean, and the seismic shallow crust. Their dedication and interesting publications have made this book a possibility. This volume is a well-illustrated documentation of just some of their excellent work. The journey through their contributions has been one of increasing excitement. Efforts have been made to reproduce the physical essence of reviewed work with suitable choice of author’s figures. Ricardo and Marcelo Abrahão have excelled in the expert redrawing of such figures, and are sincerely thanked for their painstaking work. The writer’s summaries of key aspects of reviewed work are interspersed with personal and rock mechanics based interpretations with which authors need not be in full agreement. Material contributions, in the form of inaccessible articles, figures and data, and some valuable discussions and improved insight, have kindly been provided by Dr. Enru Liu, Dr. Eda Quadros, Dr. Baotang Shen, Dr. Axel Makurat, Prof. Stavros Bandis, Dr. Karstein Monsen, Prof. Michael King, Dr. Stuart Crampin, Dr. Heloise Lynn, Harald Westerdahl, Dr. Sonja Maultzsch, Dr. Paul Chapman, Dr. Rudi Lubbe, Dr. Tor Arne Johansen, Dr. Barry New, Dr. Saul Denekamp and Dr. Tore Lasse By, who enthusiastically introduced the writer to cross-hole seismic tomography in 1986. Part I of this book was mostly completed while the writer was Visiting Professor in the University of São Paulo Polytechnic (USP). The writer’s kind neighbour in the Mining Department, Prof. Lineu Ayres da Silva, was indirectly responsible for the five years extension involved in starting and completing Part II of this book. A recently purchased volume by Kearey and Vine, 1996 lay open on his desk. A plate tectonics section of a plunging sub-ducting crust with labels ‘low Q’, ‘high Q’ caught the writer’s rock-engineering attention. What did this ‘Q’ mean? Some of the complex answers, and a simple one showing promise, will be found in Part II. My final acknowledgements are firstly to Pat Coughlin, who has ensured a smooth-running and expert manuscript production over a long period of endeavour. This started with the deciphering of handwriting and ended with countless explanations of Microsoft’s hidden logic. The enthusiastic team at Taylor & Francis, Germaine Seijger and Lukas Goosen and the Charon Tec team have produced a work to be proud of. The reader can be the judge of this. Finally my thanks and apologies to a tolerant and loving wife Eda, who also ensured some key insights into rock-fluid interactions.

Permissions to Reproduce Figures The nature of this book, specifically a wide-reaching literature review, involving some 830 references from some forty different journals and publishing houses, has made obtaining permissions to reproduce figures a daunting and sometimes impossible task regarding author-permissions, due to the several hundreds of first authors, and thousands of multiple authorships. There are instances where we have been unable to trace or contact the copyright holder. If notified, the publisher will be pleased to rectify any errors or omissions at the earliest opportunity. Many key authors are retired, regrettably some have died, including Bengt Sjögren, who’s published work from 1979, 1984 and 2000 was an important source for key figures in several chapters of Part I. The most prominent authors have kindly given permission for multiple reproduction of figures from my limited selection from their important contributions. All publishers as listed below, have kindly given their permission for multiple reproduction of the numerous figures reproduced in this reference volume. Their joint permissions, and those of contacted authors, and the contribution of all authors that could not be contacted for whatever reason, are gratefully acknowledged. Their excellent work, reproduced in this book, is a sincere acknowledgement of their contributions to geophysics.

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XV

Acoustical Society of America (ASA): Journal of the Acoustical Society of America: Figure 13.42 American Association of Petroleum Geologists (AAPG): Figure 15.36 American Geophysical Union (AGU): Journal of Geophysical Research: Figures 2.8, 3.1, 5.33, 5.34, 5.35, 10.14, 10.21, 10.25, 10.27, 10.28, 10.33, 10.37, 10.38, 10.41, 10.43, 10.44, 10.47, 10.48, 10.52, 10.53, 10.55, 10.58–10.60, 11.1, 11.6, 11.7, 11.8, 11.9ab, 11.10–11.21, 11.24–11.30, 11.31a, 11.32, 11.33, 11.35, 11.36, 11.38, 11.40–11.42, 11.48, 11.49, 11.52, 11.54–11.64, 11.66–11.71, 12.11, 12.22, 12.23, 13.2, 13.5a, 13.25, 13.29, 13.32, 13.33, 13.46, 14.16, 14.25, 14.26, 15.8, 15.11, 15.14, 15.18, 15.63. Figure Part II; Tables: 10.5, 10.6, 11.2, 15.2, 15.3, 16.5, 16.6 American Institute of Mining, Metallurgical and Petroleum Engineers (AJME): 16.42, 16.68 American Institute of Physics (AIP): Figure 10.21 American Physical Society (APS): Physical Review E: Figure 10.64 American Society of Civil Engineering (ASCE): Journal of Geotechnical Engineering: Figure 2.15 American Society of Mechanical Engineers (ASME): Transactions of the American Society of Mechanical Engineering: 12.6; Journal of Applied Mechanics: 2.9 Blackwell Publishing: Geophysical Prospecting: Figures 1.3, 1.5, 1.7, 1.8, 1.10, 1.11, 3.9, 4.3, 5.2–5.4, 5.10, 5.11, 6.11, 6.17, 8.12, 9.2, 10.65, 10.67, 13.24, 13.25, 13.36–13.41, 13.44, 13.48, 13.61, 14.15, 15.5, 15.6, 15.22, 15.28, 15.39, 15.40–15.42, 15.47, 15.48, 15.51–15.53, 15.55, 16.20–16.22; Geophysical Journal International (Geophys. J. Int.): 10.22–10.24, 15.1a, 15.3, 15.4, 10.67; Other sources: Figures Part II, 11.1, 11.2, 11.18; Table 11.1 Cambridge University Press: Figures 11.3, 13.1, 13.2, 13.5 and 14.4 Centek Publishers, Luleå: Figure 16.13 Comité Francais de Géologie de l’Ingénieur et de l’Environnement (CFGI): Paris: Figures 5.6, 5.7, 8.5; Tables 8.1, 8.2 Coyne et Bellier: Figures 7.7, 6.19, 6.21 Elsevier: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts: Figures 2.1, 3.2, 3.8, 4.7ab, 4.13, 4.14, 4.17, 4.20, 5.29, 5.30ab, 6.9, 6.20, 7.18, 7.20, 7.25, 7.26, 7.31, 7.32, 8.2–8.4, 9.6, 15.9, 13.53–13.55, 13.58, 15.17, 16.2, 16.4, 16.6, 16.7, 16.9, 16.12, 16.16, 16.17, 16.44, 16.46, 16.69, 16.73, 16.74; Table 4.1; Engineering Geology: Figures 5.17, 5.19, 15.26, 14.39; Journal of Applied Geophysics: 14.15, 15.5a, 15.56, 15.57; Table 16.8; Tectonophysics: Figures 11.31b, 11.53, 16.64, 16.65, 16.76. Other sources: Figures 1.1, 1.6, 2.18, 4.12, 4.21, 5.13, 10.57, 11.5, 11.34, 15.23; Tables 2.2, 5.2, 11.1 European Association of Geoscientists and Engineers (AEGE): First Break: Figure 15.31; Other sources: Figures 10.2, 10.3, 10.10; 10.20, 10.21, 10.31, 10.36, 13.24, 14.37, 14.38, 15.27, 15.31, 15.37, 15.38, 15.43, 15.45, 15.46, 15.54; Table 13.2 Geophysical Research Letters: Figures: 4.9, 10.52, 11.51, 11.56, 15.44, 16.19; Other sources: Figures 9.7, 12.7, 12.8, 11.39, 11.46, 11.54, 13.11, Table 11.3 Geological Society of America (GSA): Geology: Figures 3.13, 10.6, 16.11, 16.56, 16.63; Figure 1.4 Geological Society: The Quarterly Journal of Engineering Geology: Figures 3.7, 3.10, 5.15, 5.16; Other sources: 2.12, 11.47, 13.56, 13.57, 15.16, 16.23 Imperial College, London: Figure 16.6 Imprime Adosa, Madrid: Figure 3.3, 5.1, 5.8, 5.9, 8.16 Institut du Bâtiment et des Travaux Publics; Annales d’ITBTP: Figure 6.20 Institut Français du Pétrole (JFP): Oil & Gas Science and Technology: Figures 3.5, 14.32, 14.33

XVI

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International Association for Engineering Geology and the Environment (IAEG): Figures 3.3, 5.1, 5.6–5.9, 8.5, 8.16; Tables 8.1, 8.2, 16.7 International Commission on Large Dams (ICOLD), Paris: Various sources: Figures 3.6, 6.7, 7.4, 9.1, Table 6.3. International Society for Rock Mechanics (ISRM): ISRM News Journal: Figures 7.2, 7.3, 6.18, 8.21–8.23, Table 12.1 Ishikawa Soil Incorporated Association: Figure 2.13 Japan Tunnelling Association (JTA); Tunnels and Underground: Figure 8.6 John Wiley & Sons: Figures 7.30, 6.23 Kansas Society of Petroleum Engineering: Figures 13.2, 13.5ab Laboratório Nacional de Engenharia Civil (LNEC), Lissabon: Figures 2.2, 6.1, 6.15, 6.22, 6.23 Nagra; Nagra Bulletin: Figure 9.1 National Academy Press, Washington: Figures 6.2, 6.3, 6.8, 7.1, 7.8, 9.11; Table 6.2 Norwegian Petroleum Society (NFP): Figures 14.29, 14.30, 15.36 Office of Nuclear Waste Isolation (ONWI), Columbus: 16.10, 16.14, 16.15, 16.29–16.33, 16.46, 16.67 Österreichischen Gesellschaft für Geomechanik (ÖGG), Felsbau: Figure 6.4 Oyo Corporation: Figure 2.12 Royal Astronomical Society (RAS): Quarterly Journal of the Royal Astronomical Society: Figures 11.5, 11.37, 11.50 Schlumberger: Oilfield Reviews: Figures 12.24–12.26, 14.15, 15.1b, 15.19, 15.36, 15.1b; Other sources: 4.10 Seismological Society of America (SSA): Bulletin of the Seismological Society of America: Figures: 10.39, 10.40, 10.46, 10.52, 10.61, Table 10.7 SGE Editoriali, Padova: Figure 2.13 SKB, Stockholm: Figure 7.23 Society for Mining, Metallurgy and Exploration (SME): Various sources: Figures 2.4–2.7, 5.1a, 6.12, 7.12–7.15, 7.28, 15.7, 15.25, 16.27, 16.75 Society of Exploration Geophysicists (SEG): Geophysics: Figures 2.11, 2.19, 2.21, 3.11, 3.16, 4.15, 7.27, 10.1, 10.4–10.11, 10.13, 10.15ab, 10.16–10.19, 10.29, 10.30, 10.34, 10.35, 10.52, 10.64, 10.66, 10.68–10.72, 11.22, 11.23ab, 11.43, 11.48, 12.27, 13.3, 13.4, 13.6–13.8, 13.11–13.13, 13.17–13.23, 13.26–13.31, 13.34, 13.35, 13.42–13.45, 13.50–13.52, 14.1–14.3, 14.6–14.15, 14.18–14.24, 14.28, 14.31, 15.11, 15.29, 15.30, 15.60, 16.64. Tables: 10.10, 14.1–14.3, 15.1; The Leading Edge: Figures: 12.1a–d, 12.2a–d, 13.10, 13.14a–b, 13.15, 13.16, 14.33–14.36, 14.38, 15.15, 15.24, 15.35, 15.60; Canadian Journal Exploration Geophysics: Figures 10.63, 15.12–15.14, 15.32; Other sources: Figures 12.3, 12.30, 14.1, 15.5c, 15.10, 15.29, 15.44, 15.54, 15.65abc, 15.66, 16.6 Society of Petroleum Engineers (SPE): SPE Journal: Figures 13.2, 13.5ab, 14.32, 14.33; Other sources: Figures 12.12, 12.13, 12.29 Southern Africa Institute of Mining and Metallurgy (SIAMM): Figure 15.46 Springer Science and Business Media: Rock Mechanics: Figures 2.10, 16.10, 16.26, 16.41, 16.54ab, 16.57ab, 16.58; Pure and Applied Geophysics – Pageophysik: 7.22ab, 10.12, 10.49ab, 10.50ab, 10.51, 10.52, 10.54; Other Sources: Figures 10.42, 13.1, 16.60; Table 3.1 Stanford Rock Physics & Borehole Geophysics (SRB): Figures 13.2, 13.5ab

Preface

Swedish National Science Council: Figure 1.45 Tapir Academic Press, Trondheim: Figure 15.25 Thomas Telford: Geotechnique: Figures 12.5, 12.9, 12.10, 15.2, 16.2, 16.8, 16.53, 16.75 Other sources: Figure 4.4, Tables 1.2, 1.3 University of California Berkeley: Figure 16.46 Wilmington: Tunnel & Tunnelling International: Figure 9.13 PhD Theses: S. Bandis, 1980, University of Leeds (Fig. 16.3?, 16.16, 16.18, 16.40, 16.47, 16.52, 16.66, Tbl. 16.2, 16.3); T. Cadoret, 1993, University of Paris (Fig. 13.2, 13.5ab, 13.20); D. Han, 1986, Stanford University (Fig. 13.2, 13.4, 13.5e); K. Iwai, 1976, University of California Berkeley (Fig. 16.46); D.L. Jizba, 1991, Stanford University (Fig. 13.5d); Y.-Q. Liu, 2003, University of Edinburgh (Fig. 14.15b); R. Lubbe, 2005, Oxford University (Fig. 16.20, 16.23); N. Lucet, 1989, University of Paris (Fig. 13.2, 13.5ab); E. Quadros, 1982 (Msc), University of São Pualo (Fig. 16.6); A. Shakeel, 1995, Imperial College, Univ. London (Fig. 13.58); J.C. Sharp, 1970, University of London (Fig. 16.6); C. Slater, 1997, University of Edinburgh (Fig. 15.20, 15.34, 15.35); S.R. Tod, 2002, University of Cambridge (Fig. 15.44); J. Yan, 2003, University of Edinburgh (Fig. 13.14); J. Yuan, 2001, University of Edinburgh (Fig. 14.27).

XVII

Introduction The multi-disciplinary scope of seismic and rock quality Seismic, sonic and ultrasonic measurements are utilised by a large number of geo-science, geo-engineering and georesource disciplines. Their use is so widespread in the earth-sciences, that it should be of no surprise to us that such techniques are also used to register such diverse subjects as osteoporosis in cows, and the control of ‘crispiness in breaded fried chicken nuggets’. The latter was a thesis in Biological Systems Engineering. Since rock engineers tackle different problems from petroleum engineers and geophysicists, who in turn tackle different problems from tectonophysicists, there has been an understandable yet regrettable compartmentalisation between the disciplines. Both practitioners and researchers in each of these major fields, generally go to different conferences and read and publish in different journals, as there are ‘too many’ choices of each in each discipline, even in each speciality where we earn our living. The luxury of cross-discipline interaction, occasionally experienced with great interest and resulting stimulation, is usually defeated by time, cost and also in part, by technical-language barriers, and even mathematics. An interesting example of partial ‘compartmentalization’ is stiffness and compliance. Each have followed almost separate development since the late 1960s in rock mechanics, and since the early 1980s in geophysics. Each are essential to each subject; for numerical modelling of stability and deformability in rock engineering; for improved interpretation of attenuation, anisotropy and shear wave splitting in the geophysics of fractured petroleum reservoirs. Yet the dynamically measured, micro-deformation fracture compliances in geophysics (in the normal and shear directions), are numerically close to the inverse of incrementally-loaded joint stiffnesses in rock mechanics, at least when rock quality is high. The frequently illustrated material in this book has been assembled as a result of an interest in a variety of civil, mining, petroleum, geophysics and earth-science fields. The common denominator has been rock mass and rock joint behaviour as presumably impacting the seismic interpretation. An interesting and very large selection of seismic velocity and seismic quality related data, from practitioners working in widely varied disciplines, has been assembled. Much has obviously been left out or not yet seen. Much is still under development. The chapters of Part I are mostly civil engineering related with strong links to the interpretation of rock conditions at both laboratory and field-scale, with their impact on engineering of tunnels and dams and planned nuclear waste repositories. The chapters of Part II go deeper both figuratively and literally, and consider much larger scale uses of seismic attributes, from hydrocarbon reservoirs and the use of multiple dynamic energy sources, to the interpretation of mid-ocean spreading-ridges, to crustal conditions interpreted from natural earthquake hypocentres. The phenomen of seismic anisotropy, known already in the nineteenth century to give lower stiffness perpendicular to layering than parallel, is now in widespread use for investigating fractured rock at depth. Features of the rock mass, though of sub-seismic-wave size, can be detected at many kilometers depth, due to shear wave splitting, giving polarization parallel and perpendicular to dominant jointing. Different time delays for the fast and slow shear wave components vary with fracture properties and with frequency, giving frequency-dependent anisotropy. Efforts have been made to seek out and to reproduce in brief, with helpful figures, the seismic measurements and interpretations which have a clear or potential rock quality content, at whatever scale. Clearly the term ‘rock quality’ conceals various techniques and scales of measurement, and varied interests in ‘rock quality’ per se. A rock mass with high velocity and high rock quality (i.e., exhibiting low attenuation) would make life less profitable for machine bored tunnellers due to slow progress and frequent cutter-changes. Aggregate producers would need more drilling and explosives per ton, and would seek other quarries. The very existence of hydrocarbon reservoirs and their productivity would be severely prejudiced if either ‘rock quality’ or ‘seismic quality’ was too high. Others would welcome good ‘rock quality’ characteristics, for example producers of dimension stone and clients expecting cheap drill-andblasted tunnels requiring little rock support.

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Revealing hidden rock conditions At the beginning of most rock engineering projects we are operating ‘blind’, and any help to ‘see’ what may lie below our dam foundation, or ahead of our tunnel, saves schedules, budgets and sometimes lives as well. The beauty of seismic, sonic or ultra-sonic investigations is that they can be applied over a virtually unlimited range of scales, to ‘see’ micro-cracks closing under stress in the laboratory, or to ‘see’ fluctuations in effective stress across a regional fault caused by changes of reservoir level, and to monitor the effects of water-flooding in a fractured petroleum reservoir. Already in 1917, Fessenden had proposed (and patented) the use of a cross-hole seismic technique to locate ore bodies. The scale of investigation can be increased by orders of magnitude to ‘earth-scale’, when illuminating the seismic structure of the earth’s crust, and further again to depths of 5000 km or more, to the solid iron core of the earth, as a result of global-station analyses following large earthquakes. Sjøgren, 1984, gave the civil engineering (near-surface) profession a particularly useful guide in the use of shallow seismic refraction techniques for those involved in shallow sub-surface projects. The fundamental principle is that seismic waves propagate with significantly different velocities in different near-surface geotechnical and geological strata, due to the seismic visibility of weathered, low-stressed materials in general. This also means that the velocities tend to increase rapidly with depth, which must not be misinterpreted as meaning better quality per se. Intermediate high-speed layers, or hidden low velocity layers obviously disturb this simplified picture, and velocity anomalies and incorrect depth interpretations result unless separate analysis i.e., downhole vertical seismic profiling (VSP), or coring is performed. Fundamental difficulties in the context of rock engineering (and in all other disciplines too) are that the means of access, superficial or along boreholes, are often limited by the geometry of the problem, by the (urban or sub-sea) location, and by the cost. The freedom to choose optimal experimental layouts is therefore limited. As pointed out by Cosma, 1995, this may cause blind zones, even in the immediate vicinity of the observation points. In the case of soil or weathered rock horizons, seismic velocity interpretation readily distinguishes the water table from a lithological boundary by inspection of the shear or transverse wave velocity (Vs). If this remains constant across the region of changing water content, while Vp changes, a groundwater surface is indicated, since the shear waves do not respond to changing water content due to the lack of shear stiffness. If Vs also changes, a geotechnical or geological layer will have been crossed. Typical ranges of Vp for a variety of near-surface sediments and rocks are reviewed in Chapter 1. One of the historic and important applications of refraction seismic in civil engineering, has been at dam sites, which were investigated in great numbers, especially in the 1950s, 60s and 70s. Rock quality, permeability, and deformation modulus were of fundamental importance. Associated hydropower tunnels such as headrace and tailrace tunnels have been the subject of countless thousands of kilometres of seismic refraction spreads, not to mention all the power house foundations and high pressure penstock locations. The seismic spreads at the ground surface should if possible be set out in optimal directions to investigate suspected sub-surface anomalies. Since the ray paths are essentially following sub-horizontal paths, steeply dipping or vertical features such as faults or deeply weathered zones can be readily located and given a characteristic seismic signature. Localised P-wave velocities of 2 or 3 or 5 km/s have distinct engineering implications for near-surface tunnelling or foundation stripping. Their interpretation in relation to rock type (uniaxial strength and porosity) and in relation to the depth of measurement, or to stress level and stress-induced anisotropy, will be reviewed in detail in this book, with the help of a quantitative rock mass quality description.

Some basic principles of P, S and Q The P-wave is a longitudinal wave, in which the direction of particle motion coincides with the wave propagation. It is often termed the first arrival or compressional wave. By contrast, the lower velocity transverse S-wave has particle motion in the plane perpendicular to the direction of wave propagation. An S-wave is of two possible basic types: the SH-wave in which particle motion is parallel to a boundary, usually the ground surface, and the SV-wave which has particle motion perpendicular to both the wave propagation direction, and to the particle motion of the SH-wave.

Introduction

XXI

When passing through anisotropically fractured petroleum reservoirs, a shear wave will likely split into fast (qS1) and slower (qS2) polarized components, giving clues about the fracturing character and perhaps the principal stress direction. The latter coupling may be more complex than convention suggests however, due to adverse stress-closure-permeability behaviour in reservoir rocks, unless they are strong enough to tolerate tens of megapascals of effective normal stress across their ‘open’ joints or fractures. Slight shearing and dilation may actually be needed on conjugate joint or fracture sets, to explain permeability and production from fractures in weaker reservoir rocks, and to explain the ‘surprising’ maintenance of permeability deep into the crust. There is a ‘problem’ of frequency dependence for all the component velocities of P- and S-waves, but in fact in the problem lies the more accurate interpretation. There are exciting current developments in these dispersive, frequencydependent interpretations of velocities and attenuation, and in their relation to anisotropy, where rock mechanics knowledge of ‘joint stiffnesses’, or their dynamic micro-strain-based near-inverses: the geophysicist’s ‘fracture compliances’, are proving extremely important supplements to the earlier focus on the elliptic aspect ratios of microcracks, and the larger-scale – and smaller magnitudes – of the aspect ratios of almost closed fractures.

Q and Q Seismologists have had a long tradition of utilising a quality factor Q-seismic (with numerous sub-sets such as the basic Qp, Qs, and Qc , the latter from the coda or tail-end of a dynamic wave sequence). Q-seismic was popularized by a famous Knopoff, 1964 paper with the briefest possible title: ‘Q’. We will see the possibility of a Q-seismic relation with another quality descriptor called the ‘Q-value’, from rock engineering, not directly, but via a mutual apparent relation to the stress-dependent pseudo-static deformation modulus: surprisingly not to the dynamic modulus, at least not in the top kilometre or so. Q-seismic is a dimensionless factor whose inverse (Q 1 seis) indicates, if simply stated, the percentage loss of energy of a single wave length due to various (and sometimes disputed) mechanisms of attenuation in the rock mass at many possible scales. Reduction in wave amplitude is the most obvious effect. The attenuation is caused by scattering from geo-structures of different scales, and by absorption in intrinsic micro-mechanisms like normal and shear micro-displacements across microcracks and joints, therefore involving friction to some degree, and relative micromovement of fluids between the pore-space, the micro-cracks and the jointing or fracturing. As a result of the passage of the very slightly deforming seismic waves there will be a lot of references to ‘squirt flow’ losses in Part II of this book, in connection with anisotropic attenuation, which is one of several properties of the fluid conducting structures of fractured or naturally jointed hydrocarbon reservoirs. In parallel but previously almost unrelated endeavours, a prominent engineering geologist (Deere, 1964) developed a simple empirical rock quality factor RQD, related with the degree of jointing or fracturing in drill-core. In the 1970s, with no knowledge of Qseis, the rock quality Q-value was developed, which includes RQD as one of the six parameters. The rock engineering rock quality Q-value describes the degree of jointing (as relative block size) and important ‘internal’ joint properties like roughness and clay-filling (giving the inter-block friction coefficient). It also incorporates estimates of the permeability and the stress-to-strength ratio. Frequent use will be made of the Barton et al., 1974 and Barton 2002 rock quality Q-value and Qc-value in various parts of this book. It provides a simple link to seismic velocity, and it probably has the potential for explaining some attenuation mechanisms as well. The rock quality Q-value has a six orders of magnitude scale of quality (from 0.001 to 1000), and it predicts a two to three orders of magnitude range of deformation modulus. Completely unjointed, massive rock masses, with Q
1000, will clearly show almost no attenuation. At many kilometres depth, Qseis values are of similar magnitude. Completely decomposed, near-surface, faulted rock with Q
0.01–0.001 will obviously give complete attenuation (i.e. effectively lower than the theoretically lowest possible Qseis and highest possible Q 1 seis – each probably beyond measurement limits). It is expected that future graphs of Q (seismic quality factor) versus Q (rock quality factor) in rock masses (as opposed to lab-samples), can show strong correlations in the future, when geophysics data is reported in parallel with rock quality data. Each of the ‘Q-factors’ will be described in greater detail later in this book. We will also see the ‘problem’ of frequency-dependence, and the ‘problem’ of anisotropy, but both these problem areas are obviously

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concealing the potential for improved interpretation of the structures beneath the earth’s surface, both shallow and deep.

Limitations of refraction seismic bring tomographic solutions Refraction seismic methods have been used for at least fifty years, but have some fundamental limitations that include masking of lower velocity layers under higher velocity materials, such as basalts above petroleum reservoirs, and difficulties with multiple velocity layers in close proximity. Some unexpectedly costly tunnelling has resulted from mistakes in interpretation, due to such features. However, as with most limitations, there are various solutions, and geophysicists have been extremely creative, and also willing to modify and apply techniques from other well-funded fields like medicine. While P-wave and S-wave measurement between two points can be expressed as average wave velocities (or give a rather unhelpful ‘average’ picture of a patients brain), there is the possibility of using more comprehensive multiple source and receiver positions in separate multiple-boreholes, thereby giving positional (2D or 3D) tomographic imaging. A tumour in an unfortunate patient, and real-time scanning of brain-wave activity, as illuminated in medicine, have their engineering-scale equivalents. A fault zone delaying a tunnel, and four-dimensional fluidmigration-imaging in a producing reservoir would be approximate, large-scale geophysics equivalents. The most basic imaging analogy has been practiced for many years by geophysicists, who use earthquake sources and global monitoring stations to deduce the structure of the whole earth. So perhaps geo-physicists actually helped to inspire medical imaging of the human body? In intermediate-scale, near-surface civil engineering, the strategic positioning of pairs of boreholes across complex zones or faults can be used for optimal characterization of these features, if they appear to be a threat to progress of a tunnel, or to dam foundation integrity. In special cases cross-hole tomography measurements may lead to the avoidance of collapse, as more reliable decisions can be taken concerning the need for strengthening by pre-grouting, or the need for special pre-installed ground support, or perhaps even ground-freezing. Tunnels with inadequate overburden or severe water leakage potential such as inundation by rivers or lakes, or local inflows that would allow pore pressure draw-down compaction in soft clays beneath important buildings, can also benefit greatly from seismic-based decisions for special treatment of the ground. Part I which occupies the first third of this book, will be found to contain mostly civil-engineering and tunnel engineering treatments of the velocity-quality links that are helpful when interpreting near-surface conditions.The complementary laboratory testing that has often accompanied geophysics investigations of the near-surface, will also have emphasis on lower stress. Because of this, the effect of weathering and alteration and excavation on seismic attributes, will each be emphasised. Despite the obvious challenges of seismic interpretation in fractured and faulted petroleum reservoirs at many kilometers depth, or of mid-ocean ridge investigations beneath three kilometers of ocean, many geophysicists insist that obtaining high resolution images from ground level to just 50 m depth, is still one of the major challenges of modern geophysics. This happens to be the layer of the subsurface closest to most of our civil engineering endeavours, from tunnels, to dams, to the foundations for high buildings. Part II of this book tackles greater depths, greater scales, and more subtle geophysical detail, as benefits this rapidly developing field. Geophysics has been in ‘rapidly developing’ phases many times in the past. The latest phase is due to many parallel developments, not least an acceptance of the benefits of three-dimensional surveys, of monitoring reservoir changes over time (4D), each requiring the ever-developing power of modern computers for the complex processing of huge amounts of digital data. Investment in geophysics is growing further, due to the inestimable advantages of improved information. The continued search for reliable earthquake precursors, and the pressures to find more hydrocarbons in more heterogeneous reservoirs, and improve the recovery from those already being depleted, are each driving the developments in this remarkable field. In the future, more geophysical investments may also be used to aid in the search for potable water, which already far exceeds the price of gasoline in many locations.

Nomenclature

    v h m1

c h min H max r v 1 2 3   max  min

  b c peak r  ANDRA AR AVO AVOA BB BEM BGS BHA BHC BHTV BISQ BP BWIP c CBTF CC CDR CSFT

angle subtended between a discontinuity and the major principal stress s1 rock mass density (t/m3) shear-wave anisotropy parameter change in value (e.g. e, E applying to changes in joint or fracture apertures) vertical component of deformation horizontal component of deformation frequency of joints (or fractures) per meter (also F m1) shear modulus uniaxial compression strength (MPa) minimum horizontal component of stress maximum horizontal component of stress radial stress around an excavation in rock vertical component of principal stress principal stresses tangential stress around a (circular) opening maximum tangential stress minimum tangential stress shear stress (in a direct shear test) friction angle of joint, fracture, filled discontinuity, fault (geomechanics) fractional porosity (rock physics) basic friction angle, flat unweathered surfaces, low stress critical state line defining s1 = 3s3 peak friction angle of a joint, fracture residual friction angle of a joint, fracture, fault axial modulus Agence Nationale pour la gestion des Déchets Radioactifs advance rate (TBM, actual weekly, monthly rate) amplitude variation with offset amplitude variation with offset and azimuth Barton-Bandis constitutive model for rock joints, used with UDEC as UDEC-BB boundary element method of numerical modelling British Geological Survey bottom hole assembly borehole compensated sonic logging tool borehole televiwer Biot and squirt flow model British Petroleum Basalt Waste Isolation Project, Hanford, Washington, USA cohesion of intact rock, joint, fracture, or rock mass Conoco Borehole Test Facility cohesive component of rock mass (from Q-value) compensated dual resistivity log coupled stress/shear flow test/temperature, for HM, HTM testing of joints

XXIV

Nomenclature

CSM md, d DEM D-H-M e E Edyn Ee EF dyn FL dyn Emass e E EDA EDZ Mini-EDZ EOR F m1 FEM FC FLAC FLAC3D FM, FMS FRACOD FZI GRM HDR HPHT HRSN HSP HTI HTM i I50 IPT ISONIC ISRM Ja JCS Jn Jr JRC Jv Jw K,k K Kint Kmax Kmin Kn

Colorado School of Mines, Idaho Springs experimental mine facility Darcy-based unit of permeability (md, d for milli-, micro-darcies) distinct element modelling dynamic-hydraulic-mechanical coupling change of hydraulic aperture (joint, fracture: interpret from flow test) change of (mean) physical aperture (joint, fracture: interpret from deformation) dynamic axial or Young’s modulus from VP and VS measurement modulus of elasticity (pseudo-static unloading stiffness: plate load test) (as Edyn but field-scale, based on seismic measurements, shortened to EF) (as Edyn, lab-scale, based on ultrasonic measurements, shortened to EL) pseudo-static modulus of deformation (also D, Ed and M) from loading stiffness of rock mass hydraulic aperture of a joint or fracture (kintrinsic laminar flow, defined as e2/12) mean physical aperture of joint or fracture (empirical JRC-estimated, or BB-model) extensive dilatancy anisotropy excavation disturbed/damaged zone ( typically around tunnels) ‘alteration zone’ typically around boreholes or wells enhanced oil recovery frequency of fractures (or joints) per meter finite element method of numerical modelling frictional component of rock mass (from Q-value) two-dimensional continuum code for modelling small or large deformations in rock or soil 3D continuum code for modelling small or large deformations in rock or soil formation micro-scanner fracture mechanics boundary element code for modelling fracturing process in rock flow zone indicator generalized reciprocal method hot dry rock high pressure high temperature (well) high resolution seismic network, Parkfield, California horizontal (in-tunnel) seismic reflection profiling as TIH, transversely isotropic, horizontal axis of symmetry hydro-thermal-mechanical (coupling) (also MHT) with  or  implies dilation or contraction when loaded in shear point load index for 50 mm size samples Institute of Technological Research (S~ao Paulo) sonic while drilling tool International Society of Rock Mechanics rating for joint alteration, discontinuity filling in Q-calculation joint wall compression strength (MPa) rating for number of joint sets in Q-calculation rating for joint surface roughness in Q-calculation joint roughness coefficient (dimensionless: range 0 to 20) volumetric joint count (sum of frequencies for different sets) rating for water softening, inflow and pressure effects in Q-calculation permeability (intrinsic: units of length2, engineering: units of m/s) bulk modulus (also Kbulk) intermediate principal permeability maximum principal permeability minimum principal permeability normal stiffness (of joint or fracture: strongly non-linear, sample dependent)

Nomenclature

Kn dyn Ko KS Ks dyn L Lg LOFS LSS LWD M M1,2 MAR MHF MIT MPBX MWD n n% NAFZ ND NGI NMO NPF OC O/R OBC OBS P Pg Pn Pr PR Q Qrock Qc QE Qe Qk Qo QP Qs QS Qc Qo Qseis, Qtbm QVO r,R REV RMR

dynamic normal stiffness (of joint or fracture) ratio of rock stresses sh min/sv shear stiffness (of joint or fracture: non-linear, sample dependent, scale dependent) dynamic shear stiffness (of joint or fracture) Lugeon unit of water injection (l/min/m of borehole/1MPa excess pressure  107 m/s) coda waves, tail of seismogram life of field seismic long-spaced sonic tool logging while drilling deformation modulus (pseudo-static loading stiffness: plate load test. Also Emass, D) dynamic elastic moduli at frequencies f1 and f2 mid-Atlantic ridge massive hydraulic fracturing Massachusets Institute of Technology multiple position borehole extensometer measurement while drilling effective stress coefficient (Biot) porosity of matrix North Anatolian Fault Zone, Turkey natural directivity Norwegian Geotechnical Institute, Oslo, Norway normal moveout Norsk Petroleumsforening (Norwegian Petroleum Society) over-closure of joints, mechanical or thermal open/rock-to-rock sections of shearing joint, opposite rotation ocean bottom cable ocean bottom seismometers volumetric stress direct (P-) wave (crustal scale studies) refracted (P-) wave (crustal scale studies) support pressure, radial capacity of support in a tunnel penetration rate (TBM, uninterrupted boring) rock mass quality rating (‘Q-value’ range 103 to 103, dimensionless) rock mass quality rating, distinguish from Qseis, seismic quality, inverse of attenuation seismic quality of coda wave seismic quality in extensional resonance mode seismic quality component (Young’s mode of elastic excitation) seismic quality component (bulk mode of elastic excitation) seismic quality, Lg coda at 1 Hz seismic quality of P-wave (through given medium) seismic quality component (shear mode of elastic excitation) seismic quality of S-wave (through given medium) rock mass quality rating (Q or Qrock normalized by c/100) Q (or Qc or Qrock) calculated with RQDo, oriented in the loading or measurement direction seismic quality factor (‘Q’), inverse of attenuation, also for QP or QS, or the coda wave Qc rock-machine quality factor for TBM tunnel boring machines based partly on Q-value Q(seismic) versus offset Schmidt hammer rebound % on wet joint surfaces, dry intact samples, respectively representative elemental volume rock mass rating developed by Bieniawski

XXV

XXVI

Nomenclature

RQD RQDo RQI SAFZ SCV S(fr) S/C ratio SKB SRF TBM 3DEC TIH TIV TSP TSX UCS UDEC (3DEC) URL Vp VS VSP WAP WIPP w.r.t. ZEDEX ZN ZT

rock quality designation developed by Deere (modified core recovery %) RQD oriented in the loading or measurement direction reservoir quality index San Andreas Fault Zone Site Characterization and Validation, SKB project in Stripa mine, Sweden steel fibre reinforced sprayed concrete ratio of subsidence to compaction magnitudes, above and within reservoirs Swedish Nuclear Fuel Co. (Stockholm) rating for faulting, strength/stress ratios, squeezing, swelling: 6th parameter in Q-value tunnel boring machine three-dimensional distinct element code for modelling jointed rock masses transversely isotropic, horizontal axis of symmetry (also HTI) transversely isotropic, vertical axis of symmetry (in-tunnel) seismic reflection profiling tunnel sealing experiment uniaxial compressive strength of rock cylinder universal distinct element code, for modelling jointed, fractured rock in 2D three-dimensional distinct element code, for modelling jointed, fractured rock in 3D) Underground Research Laboratory, Manitoba, Canada P-wave seismic velocity (km/s) S-wave seismic velocity (km/s) vertical seismic profiling wide aperture profile Waste Isolation Pilot Plant, New Mexico with respect to (index only) Zone of EXcavation Disturbance Experiment, SKB project, Äspö, Sweden dynamic compliance (of joint or fracture) ( 1/Kn dyn) dynamic compliance (of joint or fracture) ( 1/Ks dyn)

Cross-discipline differences and connections • • • • •

effective stress  total stress minus pore pressure in geomechanics differential stress  shear stress caused by 1 – 3 application in geomechanics differential pressure  confining pressure minus pore pressure in rock physics compliance  (dynamic stiffness)1, compliance  (pseudo-static stiffness)1 Qseis  1/attenuation, Qrock  Qseis, but Qrock provides estimate of Emass  Qseis

Part I

1

Shallow seismic refraction, some basic theory, and the importance of rock type ‘Nature has left us an incomplete and often well-concealed record of her activities, and no ‘as constructed’ drawings!’ (Stapledon and Rissler, 1983) ‘Tenders for the Tay pipeline crossing did not allow time for boreholes to locate bedrock. Seismic refraction took one day to confirm that the trench would not encounter rock. The pipeline was laid in sediments.’ (Gardener, 1992) ‘The time may come when the various relations between geophysical parameters and rock properties can be usefully combined into a single classification system.’ (Darracott and Orr, 1976)

1.1

The challenge of the near-surface in civil engineering

Refraction seismics is by far the oldest method used in exploration seismology, with its origin traced to R. Mallet from 1848. Shallow refraction seismic measurements using first arrival, compressional P-wave velocities close to the surface often give a remarkable picture of near surface conditions due to some fortuitous interactions of physical phenomena. Firstly, weathering and the usual lack of significant stress near the surface has allowed joint systems, shear zones and faults to be exaggerated in both their extent and severity. Secondly, stress levels are low enough to allow joints and discontinuities to be seismically visible due to their measurable apertures. So-called acoustic closure occurs at greater depths than those usually penetrated by conventional hammer seismic, unless rock strengths are rather low (e.g., New and West, 1980; Hudson et al., 1980). (At this juncture, we need to differentiate between two ‘J.A. Hudson’ authors, one in geophysics, the other in rock engineering, and both very prominent in their chosen fields. We will occasionally refer to ‘rock’ Hudson in Part I, and later in Part II to ‘seismic’ Hudson). Since micro-fractures and rock joints are sensitive to stress levels, the more closed state of the discontinuities

that are perpendicular to the major stress, and the more open state of those that are parallel will give the rock mass anisotropic stiffness. Consequently the rock mass will frequently display anisotropic seismic velocities. By implications, hydraulic conductivities and deformation moduli that show anisotropic distributions will be, at least in part, detectable by seismic measurements. Anisotropy will also be caused by layered inter-beds, foliation and schistocity, and of course by a dominant joint set. Simple examples of (azimuthal) anisotropy, applicable in civil engineering, will be given in Chapter 3, while largerscale examples of anisotropy detection will be described in much greater detail, and from various fields of the earthsciences, in Chapters 13, 14 and 15 in Part II. Despite the obvious challenges of seismic interpretation in fractured and faulted petroleum reservoirs at many kilometers depth, or of mid-ocean ridge investigations beneath three kilometers of ocean, many geophysicists insist that obtaining high resolution images from ground level to just 50 m depth, is still one of the major challenges of modern geophysics. This happens to be the layer of the subsurface closest to most of our civil engineering endeavours, from tunnels, to dams, to the foundations for high buildings. Undoubtedly, the ‘0 to 50 m’ challenge is mainly due to the extreme variability of the near-surface, resulting from the contrasting geological materials and weathering

4

Rock quality, seismic velocity, attenuation and anisotropy

grades that are often present. There is also a velocity gradient that is extreme compared to anything found at greater crustal depths, where consolidation effects smooth out some of the differences. The first 5 m of unconsolidated dry beach sand may see velocity increase from 150 m/s to 300 m/s, (Bachrach et al., 2000), giving a gradient of 30 s-1, which may be an order of magnitude higher than the gradient over the next 50 to 100 m, where weathered and jointed rock may typically be found. There are an infinite number of challenges in the nearsurface. Some of the worse may be karst phenomena in limestones, or the ‘inverse’ problems of core-stone anomalies in the case of sparsely jointed but deeply weathered granites and gneisses. These features have caused tunnelling surprises in numerous countries, with nearly as numerous arbitrations as a result. Although completely weathered Grade V is an expected feature beneath the Grade VI soil in tropical terrains, Grade V saprolite sometimes confusingly swaps places with the usually deeper, and almost unjointed Grade I or II. (Saprolite is a weak, water sensitive, weathered in-place, sometimes beautifully structured and coloured relic of the rock). If this reversal of weathering grades appears in a tunnel arch beneath massive, high velocity core-stones, or if there is a generally very undulating rock surface, with frequent tunnel penetrations into weathered materials, there can be major delays. A tunnel collapse is difficult to avoid when water is present, unless preparations have been made, as a result of the more frequent exploratory drilling demanded when seismic anomalies such as these are suspected. Pre-injection ahead of the tunnel face, and heavier tunnel support, would be the very basic requirements in a drill-and-blasted tunnel. (This is one of the purposes of the ‘Q-system’ of rock mass characterization and tunnel support selection). In the case of a TBM (tunnel boring machine) excavation, a change to a closed mode in the case of a hybrid machine with earth-pressurebalance (EPB) would be needed, especially if the weathered depressions in the bedrock contained water, as is usually the case. Best advice of all, as a direct result of a seismic refraction survey, would be to drive a deeper tunnel from the start. It is easy to imagine subway station construction under such heterogeneous conditions. It could be extremely time-consuming, and even dangerous. The cost of deeper access to the stations, via longer escalators, would be a small price to pay for much reduced tunnelling and station costs.

Sjøgren, 2000 suggested the following list of essential information expected from near-surface seismic surveys, performed for civil engineering geotechnical investigations: ●

●

●

●

● ●

●

●

The velocities of the overburden layers, including the upper, less consolidated rock layers. The thickness of the various overburden velocity layers, and the total depth to the main refractor. A detailed determination of the velocity distribution in the main refractor. An estimate of the uncertainty of the velocity and depth determinations. An analysis of the (velocity-) depth structure. An assessment of velocities in vertical and lateral directions in relation to the geology. Seismic results in relation to results from other investigations, if available. Conclusions and recommendations resulting from the investigation that are of importance to the project.

Although reflection methods have eventually dominated the field of exploration seismics due to the various needs involved with deeper exploration, there is ‘universal’ use of shallow refraction seismic in sub-surface investigations for civil engineering projects around the world, due to its apparent simplicity and low cost. Furthermore, refraction seismics can be used to remove (from the more deeply focussed reflection data), the ‘adverse’ effect of the first meters or tens of meters of the heterogeneous weathered layer, where differences in the original rock quality may cause tens of meters of sub-surface ‘topography’ in the case of on-land exploration.

1.2

Some basic aspects concerning elastic body waves

It is usually assumed that the strains associated with the passage of a seismic wave are of minute, sub-micron magnitude, and except in the neighbourhood of the source, the strains are generally assumed to be elastic. Based on this assumption, the velocities of propagation of seismic waves are determined by the appropriate elastic moduli and densities of the materials passed through. The general form of the classic equations linking these three quantities is V  (E/) ⁄ . Compressional bodywaves (primary or P-waves) propagate by alternating compression and dilation (Figure 1.1 a) in the direction of the waves. 1 2

Shallow seismic refraction, some basic theory, and the importance of rock type

5

The third important elastic modulus influencing the conversion between dynamic properties is the bulk modulus (K), defined as the ratio of the volumetric stress (P) and the volumetric strain (v/v). Since the three moduli are linked by the equation   K  4/3 , it follows that Vp can also be expressed as:  K  4 /3   Vp     

1

2

(1.3)

This equation therefore demonstrates the fundamentally faster nature of Vp in relation to Vs. The ratio of these two dynamic properties are also linked by the dynamic Poisson’s ratio for the material, as will be shown in the next section, which contains some standard equations. 1.2.1

Figure 1.1 Elastic deformations and particle motions associated with the propagation of body waves: a) P-wave, b) S-wave. Based on Bott, 1982.

The oscillating uniaxial strain involved in the case of a confined body, means that the axial modulus () controls the velocity of propagation, thus:  Vp      

1

2

(1.1)

Shear bodywave waves, termed secondary, transverse or S-waves propagate by a sinusoidal pure shear strain (Figure 1.1 b) in a direction perpendicular to the direction of the waves. The shear modulus ( ), which is given by the ratio of shear stress ( ) divided by the shear strain (tan ), will therefore control the (lower) velocity of propagation, thus:   Vs      

1

2

(1.2)

Some sources of reduced elastic moduli

In the case of micro-cracked, fractured, or jointed rock masses, there is a correspondingly reduced set of moduli in relation to the undisputed elastic nature of the intact matrix, because of micro (and probably elastic) displacements in normal and/or shear directions across and/ or along the micro-cracks, fractures or joints. These represent an important part of the source of attenuation of the seismic waves in the dry state, due both to various scales of wave scattering and due to the intrinsic microdeformations. Added losses are incurred if these microor macro-discontinuities are partly saturated, since there is communication with the pores and eventual pore fluid, and minute flows may be initiated to equilibrate pressures. These micro-imbalances will only be equilibrated when the frequency is sufficiently low. The above mechanisms mean that dynamic properties, such as the velocities, Poisson’s ratio and attenuation tend in practice to be dispersive, or frequency dependent. They are also of course rock quality and environmentdependent, in the broadest possible meanings of these words. As rock quality declines, or the surface is approached, there develops a serious discrepancy between the dynamic or elastic properties of the intact matrix and the dynamic properties of the (partly discontinuous) medium. The ratio between the dynamic properties of the (partly discontinuous) medium and the static deformation properties, such as the (rock mechanics) deformation moduli and joint stiffnesses (the inverse of compliances), may rise into double figures in this

6

Rock quality, seismic velocity, attenuation and anisotropy

complex region, where velocity-depth gradients are often extreme. At depth, under high confinement, and if rock quality is high, it is assumed that there will be only small discrepancies between the dynamic properties of the matrix and the dynamic properties of the rock mass. The ‘static’ crack and joint stiffnesses, being so high, will be close to the dynamic (inverted) crack and joint compliances. There is controversy however, about the ratio of the dynamic normal and shear compliances, and the (inversed) ratio of the ‘static’ normal and shear stiffnesses. There is even controversy over whether friction is a valid attenuation mechanism, at the level of these microdisplacements. In the rock mechanics of ‘static’, ‘macro-deformations’, we are familiar with a significant mismatch between the high normal stiffness, and the much lower (and scaledependent) shear stiffness. Concerning the ratio of dynamic compliances, geophysicists seem not to be so sure, a dilemma that also probably affects whether friction is, after all, to be a valid attenuation mechanism, as assumed in much of the geophysics literature, virtually up to the present day. 1.3

Relationships between Vp and Vs and their meaning in field work

The advantages of using both P-wave and S-wave data to interpret seismic results in hard rock was strongly emphasised by Sjøgren, 1984. This has been reinforced by the successively easier acquisition of multi-component, multichannel data, and rapidly developing PC analysis capabilities. In addition to many other sets of data, some of which will be referred to later, Sjøgren, 1984 presented average Vp/Vs ratios from 93 rock sections from 5 different sites in igneous and metamorphic rocks. These are reproduced in Figure 1.2. P-wave velocities ranged from 3.3 to 5.7 km/s, and S-wave velocities from 1.6 to 3.4 km/s. On average, Vp/Vs ratios were 1.89 in the rock mass with lower velocities (heavier jointing) and 1.80 in the rock mass with higher velocities (sparser jointing). These two ratios of Vp/Vs imply rock mass quality Q-values of roughly 1 to 10, and 10 to 100 respectively, according to the following near-surface, hard rock Vp–Q relationship (Barton,1991). Vp ≈ 3.5  log10 Q

(1.4)

Figure 1.2 Mean Vp and Vs statistics from 4 km of seismic profiles in metamorphic and igneous rocks. Sjøgren, 1984.

The rock mass quality Q-value, mentioned earlier in the introduction, is composed of parameter pairs (RQD/ Jn, Jr/Ja and Jw/SRF – see Appendix A for descriptions and ratings). These effectively describe relative block size, the inter-block friction coefficient, and an active stress. This rock quality term will be utilised in various places in this book, not least as a possible interpretation of seismic quality Q (the inverse of attenuation). (Improvements to equation 1.4 will be developed in Chapter 5, to allow for its application to weaker and more porous rock types, and to adjust it for depth or stress effects). A rock quality Q-value of 1 tends to be heavily jointed, containing some clay, while values 1, are tending towards better quality, with wider spacing of joints, less joint sets, and no clay. (Q may reach values of about 1000 to 2000 in the case of massive, unjointed rock masses, confined at depths of say 500 m or more). The ratio Vp/Vs depends on dynamic Poisson’s ratio () according to the following: Vp Vs



2  2 1  2

(1.5)

Shallow seismic refraction, some basic theory, and the importance of rock type

From equation 1.5 one can derive the value of dynamic Poisson’s ratio as follows: 

( Vp / Vs )2  2

(1.6)

2( Vp / Vs )2  1

– The ratio Vp/Vs is about 3 for hard (zero-porosity) rocks, for which 
0.25. However, in the case of unconsolidated sediments, the ratio Vp/Vs can even reach values of 20 to 40 for near surface material, for which  is commonly greater than 0.45. Later in this chapter, high values of (dynamic) Poisson’s ratio for a near-surface fault zone will also be seen, for similar reasons to the above. A rock quality interpretation, linking these dynamic parameters, can be added here, by taking Sjøgren’s (1984) P- and S-wave results from 4.1 km of seismic profiles for hard but sometimes weathered metamorphic and igneous rocks (Figure 1.2). The mean value of Vp/Vs  1.89 in the more heavily jointed rocks (perhaps a rock quality Q
1–10), and the mean value of Vp/Vs 1.80 in sparsely jointed rocks (perhaps a rock quality Q
10–100), can be used to calculate dynamic Poisson’s ratios of 0.30 and 0.28 respectively. As lower rock quality Q-values are approached in shear zones and faulted zones (e.g. rock quality Q
0.1), the ratio Vp/Vs increases to about 2.0, corresponding to a calculated value of dynamic Poisson’s ratio of about 0.33. The corresponding Q-value (from equation 1.4, using minimum Vp data from Figure 1.2) is indeed about 0.1. Extremely low Q-values, for example Q  0.01–0.001 (when Vp
1.5–2.5 km/s) will be needed before dynamic Poisson’s ratio values become as large as 0.45 (as indicated for near-surface shear zones, in a later section of this chapter). Further basic equations linking Vp, Vs, dynamic Poisson’s ratio (), density () and dynamic Young’s modulus Edyn. are as follows (Darracott and Orr, 1976):  Edyn.(1   )   Vp     (1   )(1  2 )    Edyn.  Vs       2(1   )  Edyn.  Vs2   

1

1

2

(1.7)

2

3( Vp / Vs )2  4 ( Vp / Vs )2  1

(1.8)

(1.9)

7

In the case of massive rocks of low porosity, the static and dynamic values of the elastic constants (e.g., the elastic moduli Estat. and Edyn.) are quite close, while for heavily fractured and clay bearing zones, large differences between Estat and Edyn are seen (e.g. Cosma, 1995). Rock mass quality descriptions such as Q or RMR or RQD, which are described in more detail later, correlate better with static moduli than with dynamic moduli. Numerous relations between these moduli will be given in Chapter 6.

1.4

Some advantages of shear waves

In addressing the challenge of resolving the 0–50 m resolution problem, Dasios et al., 1999 reported multicomponent investigations at four shallow sites (thick clays, clay/sand sequences over chalk, mudstone overlying granodiorite bedrock, and landfill), using a combination of both compressional and shear wave seismic. The authors of course admit that there is a higher level of effort required to conduct multi-component seismic, requiring a three-component source configuration, and three-component geophones, but otherwise conventional multi-channel seismic recording systems, and PC-based processing software. Obviously the surveys are more difficult and more time consuming than compression-wave refraction or reflection, but the level of geophysical information is that much more useful. They varied the acquisition geometry to optimize results. They found that under all the conditions, shearwaves penetrated with less attenuation than compressional waves, also being unaffected by water saturation. Shear-wave reflections from shallow interfaces were in some cases less affected by noise compared with the equivalent compressional-wave reflections. They offered the following simple explanation of why shear-waves offer better vertical resolution than compressional-waves, particularly in shallow, unconsolidated sediments. The dominant reason is that the shear-wave velocities in such cases, are only a fraction (sometimes less than one fifth) of the compressional-wave velocities. This results in very small wavelengths, despite the fact that the dominant frequency of shear wave data is generally lower than is the case for compressional wave data. In order to obtain the same level of resolution with P-waves, energy of very high dominant frequency has to be generated, and this is correspondingly more attenuated in the low seismic Q sub-surface.

8

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

Figure 1.3 a) Shear-wave velocities (km/s) and Vp/Vs ratios versus depth. b) Shear-wave velocities (km/s) and dynamic Poisson’s ratio versus depth for a clay-over-mudstone-above-basement sequence, with an interpreted water table at 4.7 m depth. Results of multicomponent seismic at one of four shallow sites described by Dasios et al., 1999.

Since shear-waves are not attenuated at the water table, and are little affected by changes in fluid saturation, they can more easily detect lithological changes with correspondingly less ambiguous velocity contrasts. The authors found that under conditions of full water saturation, P-wave velocity contrasts between lithologies were small, whereas the shear-wave velocities reflected the true lithological changes. In this brief summary, the results from a site they investigated in Crewekerne, Dorset will be reproduced. Their results give a good illustration of the subtle interaction

of Vp, Vs and the dynamic Poisson’s ratio, in the presence of a water table, and also show the effect of increasing depth in a uniform sedimentary rock. At their site, thin clays overlayed mudstone, with a basement of granodiorite at 70 m depth. Figure 1.3 shows multi-component plots of shear-wave velocity versus the ratio of Vp/Vs, and of shear-wave velocity versus (dynamic) Poisson’s ratio, each as a function of depth to the basement rock at 70 m depth. Analysis of the P-wave first arrivals gave velocities of 496 m/s and 1,766 m/s for the unsaturated and saturated

Shallow seismic refraction, some basic theory, and the importance of rock type

layers, and indicated a depth of 4.7 m for the top of the saturated zone. The dynamic Poisson’s ratio showed a small decrease close to the surface as a result of the consolidation, then a sharp increase as a result of the water saturation, followed by a steady decrease with depth within the uniform water-saturated mudstones. As expected from the theoretical calculation of the dynamic Poisson’s ratio, there is a certain accentuation of the above trends for the case of the ratio Vp/Vs, except that this ratio reduces faster at shallow depth (rather than when deeper), due to the strong Vp gradient. The authors point out that the P-wave velocity was not available at the greatest depths, due to attenuation, so the data was extrapolated to 70 m. There were indications of shear-wave anisotropy in the uppermost meters of clay, but whether due to desication fractures or some form of layering is not certain. Although outside the usual range of Vp/Vs (about 1.4 to 2.0) for water saturated rocks, it is of interest to see details of the development of Vp/Vs ratios in unconsolidated (e.g., subsea) sediments, by noting the progression from soft soils through compacted soils, to rocks. Hamilton, 1979 gave comprehensive Vp-depth, Vs-depth and Vp/Vs-depth data for silty clays, turbidites and mudstones to 1 km depth. Vp values increased slowly from about 1.5 to 2.3 km/s as porosity reduced with increased depth, while Vs increased rapidly from only .05 km/s close to the surface, to 0.15 km/s at depth. Vp/Vs ratios therefore reduced very rapidly from double figures down to about 2.5 at 1000 metres depth. The dynamic values of Poisson’s ratio decreased, as a result, from about 0.49 near the surface to 0.41 at 1000 m depth. In connection with these high values of Poisson’s ratio for sediments, it is significant to note the relatively high values of (dynamic) Poisson’s ratio that tend to be recorded in shear zones and fault zones at much shallower rock engineering projects. Gardener, 1992, calculated the values of Poisson’s ratio from Vp and Vs measurements at the Transfynydd power station in Wales, estimating 0.45 for the shear zones, where the Vp velocity range was 1.6–2.7 km/s. The higher values of Poisson’s ratio for shear zones have pseudo-static parallels to the special feature of heavily jointed rock masses, which can show ‘expansion ratios’ or pseudo-Poisson’s ratios far in excess of 0.5, and even in excess of 1.0 as (shear) failure is approached (Barton and Bandis, 1982). Elastic continuum theory is of course ‘violated’ by the shear displacements tending to occur on the failing joint surfaces.

1.5

9

Basic estimation of rock-type and rock mass condition, from shallow seismic P-wave velocity

When first investigating the bedrock for suitability for near-surface tunnelling or other relatively shallow construction in rock, the preliminary use of shallow refraction seismic is very typical, where surface access (including noise) do not present major problems. As a minimum, the information gives a Vp – depth profile of inestimable value for further planning of the sub-surface investigation, in particular the optimal siting of boreholes for future core-logging and permeability testing. Figure 1.4 reproduces four examples of shallow refraction results from Sjøgren 1984, demonstrating the helpful information about the location, width and depth of zones of lower velocity. Later in this chapter, and in subsequent chapters, we will be seeing the many ways of interpreting such velocities in terms of rock quality and degree of fracturing, each tempered by the effect of rock type, density, porosity, depth (or stress level), and of course the possible anisotropy (or directional dependence) of the result in relation to an anisotropic jointing frequency, and horizontal stress anisotropy. The seismic refraction survey provides numerous depth to bedrock and quality of bedrock assessments at a small fraction of the cost and time needed for drilling. Depths are given at the impact points (hammer or shallow explosive source) and at the detector points (geophones or 3D seismometers), so a close spacing of detectors gives the equivalent of a large number of soundings or borings. Sjøgren, 1984, gives the example of 5 m detector and 25 m source separations for a 10 m deep bedrock investigation. A 100 m profile gives the equivalent of 250 m of soundings, and a complete distribution of relative quality beneath the profile. With the 10 m source and 50 m detector separations needed for a deeper survey to 50 m depth, the equivalent of 650 m of soundings per 100 m profile is given. The knowledge and experience of the geophysical team is essential in setting out optimal profiles in relation to the geology and structural geology, in particular in relation to anisotropic, layered media, and in relation to fault and shear zones. ‘Correct’ interpretation of the calculated information cannot be divorced from the geology, since a given velocity (Vp or Vs or dynamic Poisson’s ratio) is not unique to any one material but part of a scale or gradation in the specific geological profile at the site, and reflects

10

Rock quality, seismic velocity, attenuation and anisotropy

Figure 1.4 Seismic refraction results illustrating the wealth of potential information obtained concerning near surface conditions. Sjøgren, 1984.

Shallow seismic refraction, some basic theory, and the importance of rock type

11

Figure 1.5 Typical ranges of Vp for sediments and for little weathered, moderately fractured rocks. Sjøgren, 1984.

various ‘environmental’ factors acting on each rock domain, as will be demonstrated in subsequent chapters. The later geological and rock quality interpretation of core recovered from boreholes drilled close to the seismic profiles is the domain of engineering geologists, who besides identifying rock type, will perform careful logging of RQD, joint or fracture spacing, joint roughness and discontinuity mineral filling identification (or testing). The performance of rock quality characterization of drillcore is also standard practice for civil engineering and many mining projects, using the Q-value (Barton et al., 1974, Barton, 2002) and RMR (Bieniawski, 1989) as a minimum. Although these two methods have similarities, and common goals, there are differences, and care is needed in converting Q to RMR and visa versa, e.g. Barton, 1995. Typical ranges of velocities for relatively competent (little weathered moderately fractured) rocks are given in Figure 1.5. Much lower velocities, covering most of the lower diagonal space between 1 km/s and 6 km/s are seen with extremes of weathering, jointing and fault related fracturing. The following is an example of the effects of weathering for just one rock type, from Sjøgren, 1984:

A similar range of values from the SSDS Project granites in Hong Kong (Gardener, 1992) gives a useful qualitative impression of variations caused by weathering and jointing in the same rock type. Table 1.2 Typical range of Vp (km/s) for granite (Gardener, 1992). Decomposed granite (soil) Fracture zones Jointed granite Intact granite

At the hazardous second Severn Estuary crossing between England and Wales, tidal currents are so strong that 85% of the crossing had continuous rock outcrops between low and high tide. Sonar buoys and bottom drag cable gave the following relatively tight ranges of velocities for five rock types that were confirmed with boreholes, enabling the rocks to be identified across the site. Table 1.3 P-wave velocities at the Second Severn Crossing (Gardener, 1992). Rock description

Table 1.1

Typical range of Vp for gneiss (Sjøgren, 1984).

500 m/s 1700 m/s 2800 m/s 3500 m/s 4900–5400 m/s

Soil (above water table) Highly weathered biotite gneiss Weathered biotite gneiss Jointed biotite/granitic gneiss Sound biotite gneiss

1.6–1.8 2.8–3.5 3.5–4.5 4.5–6.5

Triassic mudstone Triassic siltstone Triassic sandstone Carboniferous siltstone and sandstone Carboniferous sandstone

Average velocity (km/s)

Velocity range (km/s)

2.1 2.4 2.6

1.7–2.3 2.2–2.6 1.8–3.1

3.0 4.0

2.5–4.4 3.0–4.4

12

Rock quality, seismic velocity, attenuation and anisotropy

Figure 1.6 Typical ranges of Vp for common rock types. Griffiths and King, 1987.

Griffiths and King, 1987, also give typical Vp ranges for common rock types. These are reproduced in Figure 1.6, as a source of cross-referencing. Fractured, faulted and heavily jointed zones extend the six major ranges for these rocks far to the left on occasion. Note the extremely high velocities of the dense, ultramafic rocks, which lie outside the common range of 1 to 6 km/s. A comprehensive set of in situ seismic Vp values, and some Vs values for common rock types, is also shown in Table 1.4. The data are given by Press, 1966. The wide ranges of velocity for sandstone, shale, limestone and dolomite are mainly due to the wide ranges of porosity (and density) for these materials. The surprisingly high range for gneiss is due to the wide range of mineralogical composition (and density) for this rock. The marked variation of velocities that are measured in superficial deposits (0.5 to 2.0 km/s in Figure 1.5) are partly caused by location either above or below the water table, as shown by Sjøgren’s 1984 data set. The list given in Table 1.4 shows 0.2 to 2.0 km/s just for the case of sand, mostly for this reason. The following is perhaps a good example of the influence of particle size in river born sediments. The last line of Table 1.5 (for cobbles and boulders) differs significantly from the range 1.3 to 1.9 km/s for ‘river boulders’ given by Dhawan et al., 1983, presumably due to differences in porosities. In the latter case, the ‘silty sand matrix’ is presumably absent. These last

Table 1.4

A list of typical Vp and Vs values from Press, 1966.

Material

Vp (m/s)

Alluvium Clay Sand Glacial Till Sandstone Shale, Slate Limestone Soft Hard Crystalline Dolomite Granite, Granodiorite Diabase Gabbro Basalt Schist Gneiss Water Air

500–2100 1100–2500 200–2000 400–1700 1400–4500 2300–4700 1700–4200 2800–6400 5700–6400 3500–6900 4600–6000 5800–6000 6400–6700 5400–6400 4200–4900 3500–7500 1450 335

Vs (m/s)

2800–3200 3400–3600 2700–3200 2500–3200 3300–3700

Table 1.5 P-wave velocities for different horizons in a river bank terrace (Sen and Bandyoadhyay, 1990). 0.7–0.8 km/s 1.7–1.8 km/s 2.1–2.2 km/s

Clayey and silty soil with pebbles Pebbles/cobbles in silty sand matrix Cobbles/boulders in silty sand matrix

Table 1.6 P-wave velocities for phyllites at a Himalayan dam site (Dhawan et al., 1983). Overburden/weathered phyllites Unweathered phyllites

925–1200 2520–4500

authors also give data for phyllites, which do not appear on the foregoing figures or tables of Vp data. 1.6

Some preliminary conversions from velocity to rock quality

Due to the seismic ‘visibility’ of jointing in the upper 25 to 30 metres or so, Sjøgren et al., 1979 and Sjøgren, 1984 and others, have been able to record significant correlations between Vp, RQD and joint frequency. These authors compared the results from a total of 113 km of P-wave profiles from fifteen sites, with the results of 2.85 km of core-logging from seventy four drill holes at eight of the hard rock sites. (They also had 5 km of S-wave surveys at five of the sites).

Shallow seismic refraction, some basic theory, and the importance of rock type

The range of rocks occurring at the measured locations, mostly in Norway, were: amphibolite, granite, gneiss, meta-anorthosite, pegmatite, porphyry, quartzite and mylonite. The authors were careful to emphasise that the correlations they derived between P-wave velocity and jointing descriptions such as mean RQD and mean frequency F(m1) were relevant only to unweathered igneous and metamorphic rocks, and generally for the upper 20 to 30 metres.

Figure 1.7 reproduces Sjøgren et al., 1979 data in the readily absorbed format used by the authors. Mean values for all the parameters apply. The Edyn modulus is the same as the symbol () used to denote the uniaxial or axial modulus in equation 1.1. Since their measurements were shallow, the effect of stress-induced joint closure was minimised. They also effectively removed other sets of variables by generally recording correlations for hard and almost unweathered igneous and metamorphic rocks. The usual variables of depth, porosity, uniaxial compressive strength and density were therefore largely removed. A hard rock, near surface correlation of Vp and the rock quality Q-value was derived by Barton, 1995, on the basis of trial and error fitting to cases known to the writer and also Q-logged. (These will be described in Chapter 5). In Figure 1.8, the important effects of porosity, uniaxial strength and depth are ignored, as for the Sjøgren et al., 1979 data. Note that the RQD and F/m mean data have been smoothly extrapolated beyond both ends of the Sjøgren et al., ‘data-base’ represented by Figure 1.7. 1.7

Figure 1.7 Mean values of physical and dynamic properties for hard, unweathered igneous and metamorphic rocks, based on shallow refraction seismics. Sjøgren et al., 1979. Q-Scale added by Barton, 1995.

13

Some limitations of the refraction seismic velocity interpretations

The seismic refraction method has some important limitations. One is that the horizontal or sub-horizontal ray

Figure 1.8 RQD and Fm1 trends from Sjøgren et al., 1979. Q-scale, (as also in Figure 1.7) added by Barton, 1995. These results and approximate correlations to seismic-frequency Vp are relevant for hard, low porosity, unweathered, near-surface rock masses.

14

Rock quality, seismic velocity, attenuation and anisotropy

paths record only the upper part of each seismic layer. A thin high-speed layer can mask underlying material, while a low-velocity intermediate layer will not be recognised for similar reasons. Depth calculations to underlying refractors will be erroneous. The hidden low velocity zones can of course be detected by up-hole shooting from a borehole to the seismic spread (i.e. VSP), or by inspection and index testing of core, if available. A useful review of refraction seismic methods and commonly used methods of interpretation is given in Whitely, 1990. Citing Sjøgren, 1984 that low velocity zones are consistently interpreted as being shallower than the borehole confirmation, Whiteley, 1990 went on to compare three interpretation methods of the simple yet frequently occurring situation shown in Figure 1.9. The three solutions were obtained by independent geophysics practitioners. It is clear that control drilling of identified features must be made before making important decisions such as minimum depth of cover over a sub-sea tunnel. Stapledon and Rissler, 1983 emphasised the following potential shortcomings of the seismic method, as related to near-surface investigations for civil engineering projects. 1. Minor geological defects such as weathered seams or minor faults may govern the engineering behaviour of a site, especially if their orientation is unfavourable. The seismic method ‘generally is unable to detect such defects’. Is this pessimism justified or is it entirely correct? 2. P-waves are first to arrive at the geophones ‘and must take the shortest path through the best rock’. Will this mean that they do not represent the average local quality but the best local quality? Both shallow and deep refraction seismic are subject to velocity anomalies, causing time-distortion and therefore depth anomalies, as we have seen in the above shallow example. Although the following case of Armstrong et al., 2001 is strictly speaking a deeper reservoir case, it provides such a nice illustration of the hazards of depth interpretation that it will be referred to in this first chapter. As the authors point out, the overburden above a hydrocarbon prospect is often more or less horizontal or perhaps with gently dipping sedimentary layers. It is generally paid little attention, in relation to the focussed investigation of the reservoir target at depth. Clearly, the overburden at typical shallow refraction sites for civil

Figure 1.9 Three independently derived depth estimates for a low velocity zone detected by refraction seismics. Whiteley, 1990.

engineering projects may be far different from these apparently uniform conditions. Yet even the ‘simple’ site may contain velocity anomalies, which reduce the image quality. The time horizons suffer ‘push-down’ beneath slow-velocity anomalies, and ‘pull-up’ beneath fast velocity anomalies. The geological ‘reality’ shown on the left in Figure 1.10 contrasts nicely with the equivalent post-stack seismic time section, shown on the right. There is significant distortion of layer ‘horizons’, and perhaps surprisingly persistent follow-through to depth. Armstrong et al., 2001 describe a method for compensating for these discrete overburden velocity anomalies. (Their warning about possible miss-calculation of reserves, or misspositioning of infill wells, or by-passing of incremental reserves in relation to petroleum engineering, can clearly apply in other contexts to shallow civil engineering projects, where for example there are buried sedimentfilled channels that have been known to plague certain tunnel projects, due to high water storage, and ‘constant’ inflow pressure). Also concerning the possibility of depth estimation error, it was emphasised by Bradford and Sawyer, 2002, in the context of shallow seismic reflection measurements, that larger depth and layer thickness estimates would occur when using conventional velocity analysis, if in the presence of the extreme velocity gradient close to the drysaturated transition, (usually fairly close to the surface in temperate climates).

Shallow seismic refraction, some basic theory, and the importance of rock type

(a)

15

(b)

Figure 1.10 Schematic cross-section through an overburden containing velocity anomalies of different geological age. The idealized vertical section is shown on the left, and the contrasting, time-horizon distortions, post stacking, are shown on the right. Armstrong, et al., 2001.

The authors indicated (as also seen earlier), that the P-wave velocity could increase by a factor of four or more at this transition, in the case of unconsolidated sediments changing from dry, through partial saturation, to full saturation – which may occur just above the water table, due to the action of capillary forces. A large velocity gradient (e.g. 400 m/s to 1600 m/s from 1 to 10 m depth) apparently violates many of the assumptions made in conventional reflection data processing schemes. In a recent paper, Sjøgren, 2000, evaluated several standard methods for interpreting travel time curves. He utilised the ABC method (originating from 1931), the ABEM correction method (early 1950s, detailed in Sjøgren, 1984), the mean-minus-T method (mid-fifties, also adopted in the ABEM method), and the Hales method (1958), in order to critically evaluate a more recent (1980) generalized reciprocal method (GRM) of Palmer, in particular Palmer, 1991.

Sjøgren, 2000 expressed concern about the usefulness of the GRM method for near-surface geotechnical investigations, where details of the various overburden layers are required since they may have important consequences for the subsequent geotechnical design. A relatively more recent technique for modelling of travel times and travel time inversion in refraction seismics is the so-called Eikonal solver. In principle, this involves the calculation of travel times on a regular velocity grid. Early versions, originating from the late 1980s were restricted to a plane topography for the recording surface. Lecomte et al., 2000, describe a first order Eikonal solver that can incorporate the exact topography of the surface terrain, and any arbitrary lateral variation of velocity. There is no restriction on the velocity contrast. In effect, the model is built up layer by layer, with the refractor imaging, and the velocity mapping being performed for each identified refractor at a time, as seen

16

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c)

Figure 1.11 An arbitrarily chosen model for demonstrating a new method of refraction seismic inversion. Lecomte et al., 2000 used this synthetic model for demonstrating some basic elements of the Eikonal solver, which calculates the travel time of the fastest wave at any point of a regular velocity grid, using the head waves generated in refraction seismics. The three stages of modelling shown here are: a) Wave-fronts and raypaths at receivers along the surface, when considering the whole model (but minus the acoustic wave velocity in the air, which was omitted for clarity. b) Wave-fronts and raypaths at receivers along the surface, when masking the deepest layer. c) Wave-fronts and raypaths at receivers along the surface, when masking the two deepest layers.

schematically in one of their illustrative figures, reproduced here in Figure 1.11.

1.8

Assumed limitations may hide the strengths of the method

In later chapters the numerous factors influencing seismic velocities such as joint frequency, porosity, rock (and joint wall) strength, density, depth, stress, stress anisotropy, degree of saturation, type of saturating fluid, will each be reviewed. This will be done in order to emphasise that the seismic method has numerous complications, but also inestimable advantages, and that some of the assumed shortcomings can be due to misinterpretations (often an over-simplification, or perhaps even a pre-conceived opinion about ‘seismic’ limitations).

Consider for example the jointed chalk marl at the Chinnor Tunnel in the UK, where jointing in this weak material were seismically closing at about 15 metres depth, to give a stable 1.6 km/s field velocity, despite changes in the degree of jointing (‘rock’ Hudson et al., 1980). This can be contrasted with the jointed gneiss at the Gjøvik cavern in Norway, which gave a continuous rise in velocity from 3.5 to 5.5 km/s in the first 50 metres depth due to increased stress, yet had almost unchanged rock quality. The joint frequency, RQD and rock quality Q-values did not show an improvement with depth (Barton et al., 1994). Both the above observations could be interpreted as ‘limitations’ of the method. In fact they are demonstrating specific and quite logical physical laws of behaviour. The latter is an example of the need to interpret seismic velocity with knowledge of depth and/or stress level, since a rock quality Q-value increase from perhaps 1 to 100 might otherwise be assumed in these first 50 metres,

Shallow seismic refraction, some basic theory, and the importance of rock type

based on a ‘hard rock’, ‘stress-less’ interpretation (i.e. equation 1.4, and Figure 1.8). The interpretation cannot be divorced from consideration of what is actually occurring in a rock mass as depth increases, i.e. joint normal stiffness increases, joint aperture reduces, joint frequency reduces (usually), and the clay content in the joints reduces (usually). The list can be lengthened considerably by adding that the stress increases, the deformation modulus increases, the permeability reduces, the pore pressure increases. Since there may be changes of lithology with depth increase, the provision ‘usually’ should really be added to each of the above. When considering the possibility of relating seismic velocity to a rock quality descriptor such as the rock quality Q-value, another quite basic problem must also be considered. A velocity of 2.5 km/s for massive chalk marl of high porosity, as in the better parts of the UK-France Channel Tunnel, will have entirely different engineering consequences to that of a regional fault-zone of the same 2.5 km/s velocity, crossing a Japanese high-speed rail tunnel excavation, and delaying progress by months. In this best quality chalk marl, near-world record speeds of (TBM) tunnel boring were achieved. The natural velocity of the unjointed rock under in situ conditions (Sjøgren et al., 1979), and the contrast seen in low velocity zones is the main index of difficulty, since an order of magnitude reduction in the rock quality Q-value will generally accompany each 1.0 km/s reduction in seismic velocity, according to the simplified model shown in Figure 1.8. Low velocity and potentially high permeability zones will be the natural focus of attention in most sub-surface civil engineering projects. However, in a TBM (machinebored) tunnelling project, there will be serious delays if there is too much high velocity rock, due to the slow progress made in hard, sparsely jointed rock. This would give a ‘reversed’ Vp–rock quality indication, due specifically to poor borability and the need for frequent cutter changes. A Q-value based ‘Qtbm’ rock-machine quality factor has been developed for this specific problem (Barton, 2000), which also allows for the fact that more jointing is good for progress – up to some limit, when other problems may arise. (More tunnel support is needed, there could be gripper-setting problems, the cutter head could even be jammed). In the case of drill-and-blasted tunnels, the drillability and blastability components of the cycle time for one

17

round of advance would also be demonstrating a ‘reversed’ Vp-quality behaviour. However, the more dominant effect of a reduced need for time consuming rock support would be consistent with the normal ‘high velocity  high quality’ concept. Since it is more logical that Vp increases should accompany rock quality or Q-value increases, such cases of ‘reversed’ quality must be treated as separate, method-specific cases.

1.9

Seismic quality Q and apparent similarities to Q-rock

A fundamental feature of the propagation of stress waves in all materials is the absorption of energy and the resulting change in shape of the transient waves. Non-linear friction has traditionally been assumed to be one of the dominant attenuation mechanisms (Kjartansson, 1979), but as will be discussed in Part II, there are a large number of mechanisms that can explain the different degrees of attenuation in different rock masses, including scattering due to structure, and squirt flow. Geophysicists commonly characterise seismic attenuation by the seismic quality factor Q, which of necessity has been termed Q seis throughout this book, to distinguish it from the rock mass quality Q. Intuitively Q seis is related to, but no relation of, the rock mass quality Q of Barton et al., 1974, which is a ‘quality number’ also widely used in civil and mining engineering in the last several decades. The seismic quality Q seis is often defined as the maximum energy (Emax) stored during a cycle, divided by the energy lost (E) during a cycle: Q seis 

2  E max E

(1.10)

For dry rocks, Q seis has been claimed to be independent of frequency over a reasonable frequency range (McKenzie et al., 1982). However, as will be seen in Part II, Q seis is a remarkably sensitive indicator of anisotropy, and is frequency dependent in the case of saturated or partly saturated conditions. When attenuation (Q1 seis) is high, Q seis obviously has a low value. Chapter 10 in Part II, will address Q seis in detail, and also draw some tentative parallels between ‘Q and Q’, via a common link to deformation properties. Intuitively, the rock mass quality Q (of Barton et al., 1974) which has a high value in high-modulus, highvelocity rock masses (i.e., Q  100, Vp  5.5 km/s,

18

Rock quality, seismic velocity, attenuation and anisotropy

Emass
45 GPa) would seem likely to have high energy storage and low energy loss under such conditions, and therefore qualify for a high value of Q seis and a low value of attenuation (Q1 seis). Conversely, in a rock mass characterized by many joint sets with clay coatings and fillings on many joints (i.e., Q  0.1, Vp  2.5 km/s, Emass  5 GPa), both low energy storage and high energy loss per cycle would be expected. (Q seis is low and attenuation Q1 seis is correspondingly high.)

Further discussion of Q seis is given in Chapter 4, based on recent seismic attenuation tomography (see alternative tomograms). However, a much fuller treatment of Q seis is given of both lab-scale and in situ scale attenuation phenomena, in Part II, chapter 10, and in relevant parts of Chapters 13 and 15.

2

Environmental effects on velocity

In this chapter, the effects of near-surface weathering on the seismic velocity Vp will be reviewed. This automatically introduces the separate, but closely integrated effects of density, porosity, uniaxial compressive strength, and the depth and degree of saturation. Depth and stress effects will only be superficially reviewed here; that discussion belongs in later chapters of Part I dealing with anisotropy and rock-burst or stress-slabbing in deep excavations, and is of course a fundamental aspect of all the deep or high pressure seismic results reviewed in Part II. The review will be loosely organised into subsections, on density, porosity, uniaxial strength and water content, but overlap will inevitably occur within each sub-section. Weathering and depth effects are inseparable from the general presentation of reviewed data. The key result of the inter-relationships in this nearsurface environment, is a velocity-depth gradient even in one rock type, that can easily climb into two and three figures, for example 2 km/s increase in the space of 20 m. The dual effects of rock mass strength and quality improvement, and of vertical and horizontal stress increase, are usually responsible. 2.1

Density and VP

The strong influence of density on P-wave velocity, and the stabilisation of density below the weathered zone are nicely demonstrated in Figure 2.1 (Ikeda, 1993). The marked fluctuations in velocity at depth were interpreted by the author as due to high shear stresses, which were interpreted from hydraulic fracturing conducted in the same holes. (Presumably the elastic isotropic estimate of H max, based on the ‘3P-Q’ model was several times the magnitude of the measured H min). Note the typical rapid increase in velocities in the 25 to 75 m depth zone, which partly mirror density increases and are partly related to joint closure and less frequent jointing. In the case of a range of rock types including marl and peridotite, Kujundzíc and Grujíc, 1966 found a linear relation Vp  4.75 – 7.3 (r  0.88) for Vp in km/s,

and density  in gm/cm3. Seismic velocities ranged from 2.3 to 6.5 km/s, and densities from 2.1 to 3.0 gm/cm3. Early Bulgarian experiences with seismic registration of weathering effects are provided by Iliev, 1966. Fresh and weathered monzonite were shown to have the following ranges of properties, and linear relationships between Vp–n% and Vp– (gm/cm3). (See Figure 2.2)

Fresh monzonite Weathered monzonite

Vp km/s

E (GPa)

 (gm/cm3)

n%

5.0 1.4

50 6

2.61 2.34

2 12

The linear Vp–n% and Vp– relationships conceal a non-linear Vp–uniaxial compressive strength trend. When a reduction in Vp due to c and due to n% are assumed, the strength of the porosity relationship as above, needs modification. Iliev, 1966, noted that a weathering coefficient could usefully be defined as the ratio (Vpo–Vpw)/ Vpo where sub-scripts (o) and (w) signify fresh and weathered. The coefficient approaches values of 0 and 1 at opposite ends of the weathering scale. Many of the long span bridges in Japan have been constructed in soft rock such as Tertiary mudstones and sandstones, or weathered Tertiary granites. The long span bridges of the Honshu - Shikoku Bridge system described by Yamamoto et al., 1995, and Ishikawa et al., 1995, had foundation sizes in the 50 to 100 m range but nevertheless had contact pressures as high as 1 to 2 MPa. For this reason, Japanese authorities devised comprehensive routines for geological and geotechnical investigations. Seismic methods, in situ deformability, strength and classification schemes were used extensively, especially when trying to extrapolate the results of in situ testing at more convenient onshore sites, to the actual undersea locations of the pier foundations. The data given in Figure 2.3 shows in situ seismicvelocity-based rock classes, porosities, densities and degree of saturation, each intimately linked. This remarkable, and useful diagram covers all the sub-titles of this

20

Rock quality, seismic velocity, attenuation and anisotropy

chapter, but has been included at the beginning, together with density, to indicate the integrated nature of these measures of rock mass quality (or lack of quality). Other useful data sets include Vp versus deformation modulus,

seismic rock class versus shear strength, and deformation modulus versus RQD and uniaxial strength. Most of the data was obtained from measurements in medium to lower quality, weathered granites.

Figure 2.1 Influences of weathering, depth of measurement and density on Vp and resistivity. Ikeda, 1993.

Environmental effects on velocity

The authors used an extended version of the Tanaka and Japan Highways classification (which involved the six classes A, B, CH, CM, CL and D where subscripts mean high, medium and low), and included three

Figure 2.2 Effects of weathering on Vp of monzonite are seen in linear Vp-n% and Vp- relationships. Iliev, 1966.

21

classes at the lowest end of the scale (DH, DM, DL) for rock masses with velocities in the range 1.5 to 2.7 km/s. Table 2.1 shows the scheme adopted, which cross-correlates with deformation modulus, density, porosity and resistivity. A large collection of laboratory Vp– (gm/cm3), and Vp–n% data is given by Kelsall et al., 1986, for the case of basalts from California and dolerites from S.W. England. Data that fall outside the general trend for the intact rock are ascribed to fissured and persistently microcracked rock, shown by the black data points in Figures 2.4 and 2.5. The lower seismic velocity of the fissured samples is accentuated by the air-dried state of these samples. When plotted on a log-linear scale, the uniaxial strength is seen to broadly correlate with the air-dry Vp value. The data set given in Figure 2.6 goes to

Figure 2.3 Inter-relationships between rock class, Vp, porosity, density and degree of saturation at the Honshu - Shikoku Bridge project in Japan. Ishikawa et al., 1995. Table 2.1 Extended (low velocity) Japanese classification scheme used at Honshu-Shikoku Bridges, showing cross-correlation of parameters. Note extreme range of densities due to weathering. Yamamoto et al., 1995. Rock class

Vpr (km/s)

Rt ( • m)

Esb (GPa)

c (103 kg/m3)

R (103 kg/m3)

nc (%)

nR (%)

DL DM DH CL CM CH

1.5–1.8 1.8–2.2 2.2–2.7 2.7–3.3 3.3–4.0 4.0–4.8

1–4 4–7 7–12 12–20 20–50 50–120

0.05–0.3 0.3–0.8 0.8–1.5 1.5–3.0 3.0–6.0 6.0–12.0

1.7–2.1 2.1–2.3 2.3–2.5 2.5–2.55 2.55–2.6 2.6–2.65

1.55–1.75 1.75–2.0 2.0–2.15 2.15–2.3 2.3–2.4 2.4–2.5

33–58 19–33 11–19 6–11 3.5–6 2.0–3.5

50–64 37–50 27–37 20–27 15–20 11–15

Note: Vpr: P-wave velocity of rock mass; Rt: resistivity of rock mass; Esb: deformation modulus from pressure meter; c: density of core; R: density of rock mass; nc: porosity of core; nR: porosity of rock mass.

22

Rock quality, seismic velocity, attenuation and anisotropy

Figure 2.4 Effects of dry density on Vp for air-dry samples of dolerites. Note increased density of fissured samples, presumably indicating a subtle change in composition. Kelsall et al., 1986.

unusually high levels of strength (500 MPa) and velocity (7.5 km/s); the latter a direct function of the high density (2.9–3.1 gm/cm3) of the dolerites. Note the ratio of Vp (air-dry) to Vp (saturated) given in Figure 2.7. The samples with the pre-existing fissures show greatest contrast in these velocities, due to the positive effect of wave transmission through water filled fissures (or joints). Before leaving this section on (mostly) Vp and density trends, caused by weathering, it is instructive to also look at extreme Vp values due to exceptionally high densities, both from natural causes and from the influence

Figure 2.5 Effects of porosity variations on Vp for air-dry samples of dolerites. Note increased density of the fissured samples, presumably indicating a change in composition. Kelsall et al., 1986.

of high stresses (1000 MPa or 10 kbars). The velocity of a variety of high density rocks such as dunite and serpentinite are shown in Figure 2.8. For densities in the range of 2.5 to 4.5 gm/cc, velocities ranged from 6 to more than 9 km/s at these extremely high pressures (Birch, 1961). Velocity (and of course density), have been used with success for identifying minerals from host rocks. Salisbury et al., 2000, used seismic imaging of known ore bodies in central and eastern Canada, together with high pressure laboratory tests, using what they termed a ‘crack closure pressure’ of 200 MPa confining pressure. They drew various envelopes in velocity-density space, to distinguish commonly occurring sulphide ores, and

Environmental effects on velocity

23

Figure 2.7 Air-dry and saturated Vp values for intact and fissured samples of dolerite. Kelsall et al., 1986.

Figure 2.6 Vp–c relation for high strength and weathered rocks. Kelsall et al., 1986.

typical silicate host rocks. We may select some contrasting combinations: density  5.0 gm/cm3 (the extreme member) density  4.6 gm/cm3 density  4.1 gm/cm3 density  2.4 to 2.9 gm/cm3 (host rock)

Figure 2.8 Extreme Vp-density data for crustal rocks at 1000 MPa confinement. Birch, 1961. (Numbers: next to open circles  mean atomic weights; on diagonal lines  constant mean atomic weights (approx.)).

At the shallowest depths of the earth’s crust, namely the soil cover, specific depth-density-Vp relationships are also evident. Brandt, 1955, developed a theory for the influence of pressure and porosity (and saturation) on the seismic velocity in porous granular media. His

elasticity-based, Hertz contact theory predicted that Vp should be proportional to the 1/6 power of the effective stress. He then compared (in Figure 2.9) this Vp-depth gradient with test data for soil, clay and gravel measured by Nasu, 1940. The slopes of the test data plotted

Pyrite:

Vp  8.0 km/s

Pyrrhotite: Vp  4.7 km/s Chalcopyrite: Vp  5.5 km/s Serpentinite: Vp  5 to 7 km/s

24

Rock quality, seismic velocity, attenuation and anisotropy

Figure 2.9 Effect of depth of burial on Vp values of soils in relation to theory. The gradient 1/6 is drawn from the origin, signifying only the Vp-depth relation, not the velocity magnitude, which can vary widely depending on the composition of the soil. Brandt, 1955.

on log (Vp)–log (depth) scales, ranged from 1/2 to 1/7, bracketing his theoretical gradient prediction of 1/6. In practice this data and the accompanying theory can help to explain the virtual seismic ‘disappearance’ of heavily stressed, faulted gouge at great depth or at large induced stress levels. Such was experienced, for example, ahead of a stuck TBM in an 800 m deep tunnel where cross-hole tomography was designed to investigate a known fault (Contract report, NGI, 1998).

2.2

Porosity and VP

There is a wealth of data in the literature concerning the effect of the rock matrix porosity on the P-wave velocity. This is found in most abundance in the rock physics investigations to do with petroleum reservoirs, and will be reviewed in Part II, Chapter 13, and elsewhere. In general, an approximate inverse proportionality is found between velocity and porosity, but there are many subtle variations bought about by, for example claycontent in sandstones. High pressure data (from Chapter 13) suggests a fairly strongly curved, concave relation for porous (30 to 80%) marine sediments, with velocities falling rapidly at first, with a plateau of about 1.5 km/s

Figure 2.10 Vp – porosity data for limestones, sandstones and (jointed, weathered) granites. Fourmaintraux, 1975.

beyond extreme porosities of about 50%. Something nearly approaching linearity is seen in the case of sandstones. A simple, illustrative set of experimental data, applicable in civil engineering is that provided by Fourmaintraux, 1975, which is reproduced in Figure 2.10. Remarkable linearity is shown in these three cases. The strong influence of the porosity of the matrix in rocks such as limestone and sandstone, and the linear nature of the Vp–n% inverse relationship is clearly demonstrated. In the case of the granites, where joint porosity and presumably weathering of the matrix, are the chief sources of porosity, the reduction of velocity is even more marked. The uniaxial compressive strength is also strongly related to matrix porosity in the case of porous rocks such as limestones and sandstones. It may therefore be logical to allow for the influence of both c and n% when seeking an integrated Vp– rock quality – deformability chart, to be developed in subsequent chapters. Wilkens et al., 1984, found that the percentage of clay content in sandstones had a marked effect on the P-wave velocity of dry samples. Although this particular data set was related to petroleum reservoirs, and confining pressure was consequently very high (50 MPa), the data will be included in this chapter, as it gives a good illustration of the adverse influence of clay-content, which is a particularly relevant aspect of the near-surface, due to weathering effects on some constituent minerals.

Environmental effects on velocity

25

Figure 2.11 Effect of % clay content on the variation of Vp for dry sandstones, for given values of porosity. (Note: high pressure data, for illustration of relative effects. See Part II, Chapter 13 for high pressure rock physics data). Wilkens et al., 1984.

Clearly the higher velocities given in the figure will not be so closely approached in the case of near-surface claybearing sandstones, but the relative effects of claycontent are illustrative. For a given porosity, say 20%, Vp was shown to range from 3.5 to 4.5 km/s due to clay content reducing from 15% to 5% (approx.). Figure 2.11 shows Vp–n% data for dry sandstones, with the % of clay displayed next to the data.

2.3

Uniaxial compressive strength and VP

Classification of uniaxial strength by means of seismic velocity alone is obviously suspect since porosity, density and grain size will also be important to differing degrees. However, if envelopes are used to separate the major rock groups, then c–Vp relationships become somewhat clearer, as illustrated by Ohkubo and Teresaki, 1977, and Won and Raper, 1997, in Figure 2.12. The open circles are data for basalt, tuffs and agglomerates from investigations at a tunnel and highway cutting site in Australia. Note the trend lines (c
Vp3 and c
0.25 Vp3) whose 4:1 range is still insufficient to encompass the range of data produced in the Japanese study (Ohkubo and Teresaki, 1977 Oyo Corporation. Technical Note RP-479).

Figure 2.12 c–Vp trends from Ohkubo and Teresaki, 1977, with data from a tunnel site in basalt, tuffs and agglomerates. Won and Raper, 1997.

Evangelista and Pellegrino, 1990, referred to extensive Japanese data assembled by Ogawa, 1986, in also citing the potential link between porosity and uniaxial compressive strength. Figure 2.13 shows the enormous influence that porosity has on uniaxial strength, indicating a bi-linear trend in a semi-log plot. The influence of porosity on density, and the influence of uniaxial strength on stiffness, means that several inter-related physical properties play their role in increasing or decreasing seismic velocity. Microcracking, jointing, stress level and degree of saturation (including type of fluid) add to the complexity, as will be extensively demonstrated in later chapters, both in Part I and Part II. Several hundred uniaxial compression strength tests on flysch sandstones were conducted by Pininska, 1977, in three orthogonal directions. The following general trend can be seen in their c–Vp plot: Vp  2.0 c  10

3.0 20

4.0 40

5.0 80

5.5 100

(6.0) est. (160) est.

km/s (MPa)

However, the scatter of data was very large, and one could refer to ranges of the above velocities of as much as 1.5 km/s in the enclosed region of the above tabulation. The doubling of strength for each 1 km/s increase

26

Rock quality, seismic velocity, attenuation and anisotropy

Figure 2.13 The inter-relationship between porosity and uniaxial compressive strength. Ogawa, 1986 from Evangelista and Pellegrino, 1990.

Figure 2.14 Poor correlation of Vp,  and c is evident for shale, due in part, to the similar densities of component minerals. Lashkaripour and Passaris, 1995.

in Vp is a good mean trend. We can add this to another general trend, namely that the rock mass quality Q-value increases 10-fold for each 1 km/s increase in Vp for the case of hard, low porosity rocks at shallow depth.

Index tests such as the point load test and Schmidt hammer test (with density included in the interpretation) are known to correlate reasonable closely with uniaxial compressive strength. For this reason, Wei and Liu, 1990,

Environmental effects on velocity

27

strength (1 MPa to 10 MPa) for 1 km/s increase in velocity (i.e., 1.5 km/s to 2.5 km/s). The ‘decade’ rule-ofthumb, referred above, was again demonstrated for much of the data. The Japanese data shows slightly lower strengths (i.e., 5 MPa compared to 10 MPa) for a velocity of 2 km/s, though as with Pininska, 1977, the scatter of data is large when porosity variations are not shown.

2.4

Figure 2.15 Vp-c data for Tertiary mudstones and sandstones from Japan. Aydan et al., 1992 and Sato et al., 1995.

used Vp, Schmidt rebound value (R) and point load test (I50) to evaluate the weathering grade of four igneous rocks. Their database was very large (1069 I50 tests, 499 Vp tests, and 1330 Schmidt hammer tests) and gave, as one might expect, strong correlation to the predetermined weathering grades. In the case of shale, with its mixed content of similar density minerals, i.e. quartz (  2.66 gm/cm3), illite and montmorillonite (  2.61 gm/cm3), the correlation of compressive strength and density is inevitably poorer than for most rocks (Lashkaripour and Passaris, 1995). Since seismic velocity usually correlates well with density, it is perhaps inevitable that in the case of shales, P-wave velocity is not a sensitive indicator of compressive strength, as shown by the large spread of data in Figure 2.14 from the same authors. Water content on the other hand correlates extremely closely with uniaxial strength for shales, e.g., c
90e(0.5w) (w  water content), based on the mean of data from two coalmines. The porosity and compressive strength were linked in a strongly non-linear manner. At the extreme low end of the Vp-c spectrum (c  1 MPa to 10 MPa), the laboratory data for Tertiary mudstones and sandstones from Japan given in Figure 2.15 shows roughly an order of magnitude increase in

Weathering and moisture content

Effects of weathering on the physical and seismic properties of four rock types from a dam site (quartz diorite) and from three quarries (andesite, basalt and dacite) were reported by Saito, 1981. This very comprehensive study, involving hundreds of samples with different weathering grades and porosities, gives a very useful picture of some key trends between strength, hardness, porosity, degree of water saturation and P-wave velocity. These behavioural trends are fundamental to an understanding of the in situ behaviour, where the addition of joints to the cracks and pores tested here, adds another layer of complexity. Saito, 1981, collected numerous block samples of the different rocks and weathering grades and cast these in regular shaped concrete blocks, before coring cylindrical samples for his tests. Schmidt (N-hammer) tests were made on these larger blocks. Figure 2.16a illustrates and describes the typical weathered zones (1 to 5), and an idea of the ranges of compression strengths (dry samples) and porosities are given in Figure 2.16b and 2.16c. The very different porosities of the three volcanic rocks compared to the crystalline quartz diorite are well reflected in the clear separation of the Vp values shown in Figure 2.16c. The extended Vp range of 1 km/s to almost 6 km/s was the result of the huge range of porosities (57% to 1%). When only uniaxial strength and velocity were plotted (Figure 2.16d) the fundamental differences in porosity were not seen due to the relatively high strength of the three volcanic rock types. Figure 2.16e shows how Saito’s Schmidt (N) hammer rebound data related to Vp in a quite linear manner, not showing the same ‘plateau’ effect seen with Vp versus c. This is an encouraging aspect of this ultra-simple test method, which was adopted for registering the compressive strength of (fresh or weathered) rock-joint walls (JCS) in the shear strength criterion of Barton and Choubey, 1977.

28

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c)

(d)

(e)

Figure 2.16 (a to e) Effects of weathering at four sites in Japan cause huge ranges of porosity, strength and P-wave velocity. Saito, 1981.

Environmental effects on velocity

(a)

29

(b)

(c)

Figure 2.17 Top: a), b) effect of water saturation on Vp. Bottom: c) Dry Vs/Vp trend over a wide range of Vp. Saito, 1981.

The significant differences of behaviour caused by porosity reappear when degree of water saturation and its effect on Vp are shown side-by-side in Figure 2.17a and 2.17b. The higher porosities corresponding to higher weathering grades show very strong (even 200–300%) increases in Vp from initial low values, as saturation exceeds about 85%. Much less sensitivity to saturation (just a weak linear effect) was seen for the fresher, low porosity, high Vp samples, where Vp increased from just 5 km/s to 5.5 km/s with saturation, in the case of a low porosity sample.

The Vp/Vs ratios that Saito derived from many hundreds of data are shown in Figure 2.17c. These particular data are for dry samples. Vp/Vs ratios are seen to reduce from about 2.0 at low velocity to about 1.6 at high velocity, broadly following the trends discussed in Chapter 1. An example of the effect of saturation is given a simple theoretical basis by Grainger et al., 1973. Their evaluation of chalk foundation qualities at the proposed site for a proton accelerator facility in Norfolk, England revealed one anomalous result, when low quality chalk (grade V), which was normally sampled above the water

30

Rock quality, seismic velocity, attenuation and anisotropy

table (Vp
0.7 km/s) showed a velocity of 1.95 km/s at one location. The grade V chalk was described by the authors as a structureless melange of angular fragments set in a matrix of deeply-weathered, remoulded chalk. A matrix version of the time average equation of Wyllie et al., 1956, was used by the authors to explain this anomaly as follows:  1 1    V Vfl Vsd

(2.1)

where Vfl  velocity in fluid, Vsd  velocity in solid, and   ratio of the path length in the fluid to the total path length (i.e. the ‘porosity’) The authors assumed Vsd  2.3 km/s for the intact chalk fragments, and first assumed dry conditions with Vfl  Vair  0.33 km/s, when substituting the measured value for grade V  0.7 km/s in equation 2.1, to give   0.29. Returning to the assumed saturated conditions, using the calculated ‘porosity’ of 0.29 and Vfl  Vwater  1.44 km/s, the authors calculated a P-wave velocity for the saturated chalk of 1.97 km/s, close to that measured by the shallow refraction seismic. An interesting variant of the above time average equation is illustrated for the case of jointed rock, by the manner in which joints are assumed to change the seismic velocity. McDowell, 1993, presented the classic equation of Wyllie et al., in the form: L nw L  nw   Vp (rock mass) Vp (joint filler) Vp (rock matrix) (2.2) where L is the path length n is the number of joints w is the average width of the joints In practice the velocity through dry jointed rock is lower than given by the above, even when the velocity through air (Vp  330 m/s) is taken into account. This is because an air-filled joint will tend to act as an acoustic barrier, except round its ends or across points of contact. The actual travel distance has increased, but (L) has not been corrected in the above equation. In the case of water-filled (Vp  1.44 km/s) or clayfilled joints, the formula is likely to be more correct, due to the improved coupling across the joint walls. The saturated condition was successfully modelled by the matrix version of the time average equation, in the above

structureless melange of angular fragments set in a matrix of deeply-weathered, remoulded chalk, analysed by Grainger et al., 1973.

2.5

Combined effects of moisture and pressure

We have seen from Saito’s 1981 data, the importance of the degree of saturation on Vp in the absence of pressure (Figure 2.17a,b). In fact, the combined effect of degree of saturation and stress level have significant influence in rock engineering projects due to the common ‘environmental changes’ that are introduced when we excavate a tunnel, slope or foundation, causing changes of stress (especially unloading) and changes in the pore pressures and drainage routes in the so-called ‘excavation disturbed zone’ (EDZ), which will be reviewed in detail in Chapter 7. The excavation process (blasting, boring, ripping, etc.) causes stress redistribution and the release of radial stresses. Monitoring of Vp in such zones sometimes shows areas of increase, but more usually significant reductions in velocity, especially when the rock mass is significantly jointed or damaged by the high tangential stresses, and by the excavation process itself, particularly if by less careful versions of drilling-and-blasting. It is usually assumed that the release of radial stress and the formation of new fractures by blast gasses are the two chief causes of velocity (and modulus) reductions in the EDZ. However, the results of tests on the effect of saturation in weathered and micro-cracked materials (Saito, 1981 and Kelsall et al., 1986) seen in Figures 2.7 and 2.17, obviously suggest a third mechanism of velocity reduction, namely drying out. The presence or absence of stress and the dry or saturated state create the largest ‘environmental’ changes to Vp besides weathering state (n%, , c). Nur and Simmons, 1969, classic experiment with repeated measurements of Vp on a sample of Chelmsford granite (n
1%) showed a reduction of Vp from 5.4 km/s (when the sample was saturated) to a value of about 3.9 km/s after four days at room temperature, while drying out. The rapid change in the first 5 hours, even though the rock is of low porosity, is seen in Figure 2.18. Nur and Simmons, 1969, data also show very strong sensitivity to confining stress, especially in the case of dry samples, which would mean that an unloaded tunnel wall (r  0) in a dried-out rock mass would tend to show significantly lower velocities than if still saturated.

Environmental effects on velocity

If velocity reductions appear to exceed what one would expect in relation to reasonable modulus reductions in an EDZ (from Chapter 7), then drying out seems to be a distinct possibility. The tabulations below, that also belong with high stress data from Part II, show the potential strength of such effects, in comparing dry and saturated samples. (Data extracted from Nur and Simmons tabulations, and rounded). The very fine grain size in the Solenhofen limestone (0.01 mm) compared to the millimetre-size, or several millimetre-size grains of the other rocks, and its complete lack of crack porosity is the reason for the almost complete lack of pressure sensitivity for this rock. Micro-cracks are presumably the chief cause of the above sensitivities to pressure and degree of saturation in the case of the

Figure 2.18 Slow air-drying of a saturated sample of granite reduces Vp by 1.5 km/s. Nur and Simmons, 1969.

Table 2.2

crystalline rocks (upper half of Table 2.2). A large-scale parallel would be the effect of ‘environment’ (stress and degree of saturation) on jointed rock which we will see in other data sets in later chapters, in particular the data connected with EDZ experiments (Chapter 7). To conclude this section on the combined effects of moisture and pressure, some data sets will be ‘borrowed’ from future topics in this book, namely the higher pressure world of Part II, relevant to petroleum reservoirs and earthquake related tectonophysics. An idea of the eventual non-linear nature of Vp-stress data, is given in some early King, 1966, experiments with hydrostatic loading of sandstones, shown in Figure 2.19 with classic psi and ft/sec units. The watersaturated and dry states show classic ‘knee’ shapes, and velocities that begin to converge at high stress, due to closure of microcracks. The improved coupling with water, still gives the highest velocity in the saturated state. The maximum pressures in King’s experiments were about 35 MPa. The strong effect of extreme confining pressure, especially when these pressures go far beyond the uniaxial strength of the rocks, is typically illustrated by classic ‘knee’ shaped Vp–3 curves. Figure 2.20 shows a variety of behaviours from high pressure laboratory test results on dry samples, given by Wepfer and Christensen, 1991. A compressible shale (3.0 to 5.7 km/s) and a porous sandstone (2.2 to 4.0 km/s) show strongest effects of confining pressure, while low porosity sandstone, dolomite and limestone show only 200 to 300 m/s increases. The authors refer to velocity hysteresis; the effect of pressure in closing cracks in the stress range 0–200 MPa (0–2 kb) is

Confining pressure and dry/saturation effects on the Vp (km/s) of some hard rocks (Nur and Simmons, 1969). Confining Pressure (MPa)

Vp km/s

Rock type

dry saturated dry saturated dry saturated dry saturated dry saturated dry saturated

Casco granite

0.7%

Westerly granite

0.9%

Troy granite

0.2%

Webatuck dolomite

0.7%

Solenhofen limestone

4.7%

Bedford limestone

Porosity

12.3%

31

0

5

10

20

40

3.3 5.3 3.8 5.5 4.5 5.7 5.0 6.4 5.6 5.6 2.6 4.5

4.2 5.8 4.5 5.6 5.7 6.2 5.9 6.6 5.6 5.6 2.8 4.6

5.1 6.0 5.0 5.7 5.9 6.2 6.4 6.7 5.6 5.6 3.0 4.7

5.7 6.1 5.3 5.8 6.2 6.3 6.7 6.8 5.6 5.7 3.4 4.8

6.0 6.3 5.6 5.9 6.3 6.4 6.9 6.9 5.6 5.7 3.8 4.8

32

Rock quality, seismic velocity, attenuation and anisotropy

not matched by equal crack opening when unloading occurs in this region, and velocity hysteresis results. 2.6

Figure 2.19 Effect of dry and water-saturated states on Vp-versusstress, for a sandstone, King, 1966. (Note: an intermediate curve for kerogen, lying just below the water-saturated curve, has been removed since not relevant to Part I).

Combined effects of moisture and low temperature

This chapter on ‘environmental’ effects on Vp would not be complete without reference to the influence of low temperature and ice formation on Vp. Construction in permafrost, and monitoring of the ground-freezing method, for tunnelling though unstable water bearing areas under environmentally-sensitive areas such as city streets, could each benefit from seismic monitoring to determine the progression or regression of the ice front. Data given by Timur, 1968, show velocity increases upon freezing that vary from about 20 to 50% for many saturated porous rocks, as compared to their P-wave velocities at room temperature. In general, the largest increases are for the most porous rocks. A shale showed only 8% increase. Dry rock samples are hardly affected by cooling below 0°C. The enormously contrasted temperature-velocity graphs for the dry and saturated states, for the first few

Figure 2.20 High pressure effects on Vp (500 to 1000 MPa) for a variety of rock types. Wepfer and Christensen, 1991.

Environmental effects on velocity

33

(a)

(b)

Figure 2.21 Contrasting effects of low temperature on Vp for Berea sandstone in the dry and wet state, with 1  31.3 MPa in each case. Timur, 1968.

degrees below 0°C, is nicely demonstrated in Figure 2.21. This contrast is due to the different rates of freezing in pore volumes that have different area/volume ratios. Surprisingly perhaps, the author explains that the smallest pores actually freeze later due to less favourable area/ volume ratios. In the ‘macro-discontinuity’ world

of jointed rock, one would expect that the smaller, finer tips of cracks and joints would freeze first, due to the more stationary conditions, making ‘ice-wedging’ such an effective mechanism of weathering in mountainous terrain, and in more northerly and southerly climates.

3

Effects of anisotropy on Vp

In this chapter the ‘simple’ approach to anisotropy caused by micro-cracks or jointing will be taken, considering principally P-wave, azimuthal anisotropy, and anisotropy caused by stress difference. Besides micro-cracks that may be aligned due to tectonic history or due to existing or applied stress anisotropy, there will be fundamental reasons for velocity anisotropy in foliated, schistose, layered or inter-bedded rocks with unequal layer stiffness. When jointing and faulting are included, with the special effects of stress anisotropy on these larger scale features, the potential causes of velocity anisotropy will be numerous. Although velocity anisotropy complicates interpretation, at the same time it also provides important information for a rock engineering project, and of course for a fractured petroleum reservoir, if correctly interpreted. It will be seen that the classic alignment of a dominant joint set with the maximum horizontal stress direction is often a cause of a double-anisotropy effect. Both the near-surface and high stress treatment of P-wave anisotropy, as introduced in this chapter, will be supplemented in Chapter 14, by studies at considerably greater depth, principally in fractured reservoirs. In Chapter 15 the anisotropy information found in shear waves will finally be the focus of attention, as a lot more information is contained in waves that polarize in parallel (fast qS1), and (slow qS2) perpendicular directions relative to the discontinuities. These shear wave components show dispersive, frequency dependent levels of anisotropy, caused, in principle, by the dimensions, density and stiffnesses of the fracturing and jointing. There are also those who attribute the shearwave anisotropy at depth mostly to micro-cracks.

3.1

An introduction to velocity anisotropy caused by micro-cracks and jointing

It is reported that Maurycy Rudzki, the first Professor of Geophysics at a university in Cracow, stated his intention to do research on the propagation of seismic waves in anisotropic media, in 1896. (Helbig and Szaraniec, 2000). It has also been recognised since early in the 1900s that compressive stress affects the elastic properties of rock,

and that change of properties are related to the behaviour of the micro-cracks under load. In Chapter 2 it was seen how micro-cracked and fissured samples were particularly sensitive to the degree of saturation, since they are seismically much more visible when dry and unloaded, than when saturated and strongly loaded. Nur and Simmons, 1969, reported important results of stress-induced anisotropy, noting that the largest velocity change took place in the direction of the applied stress. Prior to loading, isotropic velocity was usually recorded. Nur, 1971, showed how the observed velocity anisotropy caused by stress effects on crack closure could be modelled, in fair to good agreement with experimental results. Figure 3.1 shows the relative effects of hydrostatic stress (0 to 50 MPa), and uniaxial stress (0 to 40 MPa) on the compressional wave velocity Vp. Here we are also looking ahead into levels of stress appropriate to Part II. Under uniaxial stress, the velocity increase parallel to the stress direction is much greater than the velocity increase perpendicular to the stress, due to preferential closure of those micro-cracks that are aligned more or less perpendicular to the applied stress. The effect may be enhancing in situ velocity anisotropy effects since Hmax often tends to be parallel or sub-parallel to major jointing, and velocity parallel to these joints is highest, independent of the above ‘intact’ rock effects. Similarly to these microcracks, minor joint sets in situ tend to be closed by the major principal stress, giving a further reason for stressinduced velocity anisotropy at larger scale. Holt et al., 1997, suggested that stress dependent velocity (caused by micro-cracks) seen in cores taken from great depth may be mainly a result of coring damage caused by the release of anisotropic stresses. This stress dependent behaviour is particularly pronounced at low stresses compared to the virgin stress, such as in a triaxial test performed below the original stress state. Above the previous stress state, the sensitivity to stress change was less. Holt et al., 1996 and 1997, observed that there was little or no stress dependence when no cracks were formed in the recovery process, nor was there stress dependence when the rock was loaded (or unloaded) near the original stress state. In a limited stress regime around the original stress state, the rock behaved as a linear elastic substance.

36

Rock quality, seismic velocity, attenuation and anisotropy

Figure 3.1 Velocity anisotropy under stress (I hydrostatic, II measured parallel to uniaxial, III measured perpendicular to uniaxial), due to micro-crack closure perpendicular to stress. Nur, 1971.

A comprehensive in situ and laboratory study was reported by Engelder and Plumb, 1984, using shallow boreholes at in situ sites that were free of joints and above the water table. Dried core from the same holes

was also utilised. Systematic measurements were made along different azimuths to check for anisotropic velocities as a result of anisotropic in situ stresses. The stressrelieved cores showed azimuth dependent velocity reductions of as much as 20% in granite and as low as 1% in limestone. In the case of the granite, the maximum anisotropy was consistent with the in situ stress orientation. Significantly, the difference between Vp (in situ, stressed) and Vp (core, unstressed) was usually less than 0.5 km/s when the in situ stress difference (1–3) was limited to about 10 MPa. These velocity differences tended to be between 0.5 and 1.5 km/s when the stress difference (1–3) was as large as 20 to 40 MPa in situ. The dilation and brittle fracturing that occurs when rock is highly stressed was found by Rummel et al., 1978, to be a significant source of P-wave anisotropy. They utilised a biaxial loading arrangement with fastreacting servo-control, to study the development of dilation adjacent to the shear failure surfaces developed in granite. They found that the P-wave velocity increased continuously in the direction of maximum compression in the pre-peak region. In the post-failure region the P-wave velocity decreased almost reversibly with reducing compression. By comparison, the minimum and intermediate principal stress directions suffered a marked reduction of P-wave velocity (recorded as travel time increases), after fracturing was initiated. As they pointed out, enhanced permeability would be a related phenomen of such dilation: this would presumably occur mostly in the 1 direction. The authors mentioned the need to be aware of the possibility for increasing velocity anisotropy, when interpreting field seismic data in crustal regions where large tectonic stresses are assumed to be operating. Failure processes in intact rock (Berea sandstone) up to and beyond the brittle ductile transition, with simultaneous monitoring of axial and lateral P-wave and S-wave signatures were reported by Scott et al., 1993. Confining pressures of 20 to 138 MPa were used. Slight P-wave anisotropy at the start of each test (due to a weak bedding fabric) were strongly enhanced at increasing axial strains, as micro-cracks tended to close perpendicular to 1, and open parallel to 1. At failure in the brittle regime, the shear fracture formation caused a small break in the P-wave signal, followed by constant Vp (axial) and Vp (lateral) velocities as shown in Figure 3.2a. During ductile deformation at much higher stresses, the P-wave anisotropy continued to increase, presumably due to a more pervasive micro-crack and grain crushing development. By comparison, the shear fractures

Effects of anisotropy on Vp

37

Figure 3.2 a) P- and S-wave anisotropy as a function of confining pressure level for Berea sandstone samples. Note the effect on the velocities of the onset of dilatancy, and the fracturing event. b) As the ratio of differential stress to ultimate strength rises, the P-wave anisotropy is seen to increase, but high confinement removes this anisotropy. Scott et al., 1993.

38

Rock quality, seismic velocity, attenuation and anisotropy

developed at lower confining pressure were only surrounded by a limited zone of micro-cracks. Scott et al., show an interesting plot of P-wave velocity anisotropy in relation to confining pressure and differential stress level (Figure 3.2b) that nicely demonstrates the increasing anisotropy of Vp (axial) and Vp (lateral) close to failure (at least 30% drop in Vp lateral) and the reduction of this anisotropy at high stress levels.

3.2

Velocity anisotropy caused by fabric

Intact specimens of rock that exhibit strongly anisotropic or orthotropic tendencies such as slate, show significant velocity differences when measured parallel to foliation (e.g., 5.2 km/s) and perpendicular to foliation (e.g., 4.2 km/s). Duellmann and Heitfeld, 1978, show that this anisotropy varies smoothly as the angle of incidence to the foliation is varied from 0° to 90°, as shown for loading and unloading cases in Figure 3.3. The minor velocity hysteresis seen on unloading is presumably due to loaddeformation hysteresis of the fabric, or of eventual

Figure 3.3 Velocity anisotropy of intact samples of slate due to cleavage. Duellmann and Heitfeld, 1978.

micro-cracks. It is a slightly stronger effect when loadingunloading occurs perpendicular to the fabric, as one might expect. A extensive collection of laboratory data that show the clear effect of the measurement direction in relation to the foliation (0°, 45° or 90°) was given by Tsidzi, 1997. He used the ultrasonic pulse transmission technique to derive Vp data for intact samples of amphibolite, gneiss, hornfels, phyllite, schist, slate and quartzite (the latter only weakly or very weakly foliated). Both dry and unsaturated conditions were tested. The effects of loading were not reported. Tsidzi, 1997, suggested that ‘strongly’, ‘moderately’ and ‘weakly’ foliated rocks could be expected to show velocity anisotropies of 40–20%, 20–6% and 6–2% respectively. In Table 3.1, some results have been selected from the much larger set of data given by the author. Strongly foliated gneiss from the Nagra project in Switzerland showed even stronger anisotropy, giving, in the dry state, a parallel-to-schistocity Vp value of 4.4 km/s, and only 3.1 km/s perpendicular to this direction (Hesler et al., 1996). Figure 3.4 shows that both these extremes were achieved at the lowest axial stress of about 2 MPa, while the application of more than 25 MPa appeared to largely remove the velocity anisotropy; the slow perpendicular direction converging to the fast parallel direction above this stress level. This convergence is in direct contrast to the microcrack related divergent (increasing anisotropy) behaviour shown by Nur’s (1971) results, in Figure 3.1. As noted in Chapter 2, the effect of saturation is to remove much of the effect of load increase on velocity, and the same appears to be the case for anisotropy caused by fabric. Figure 3.4 shows only slight velocity anisotropy in the case of saturated samples of gneiss, though the data set is limited. An important contribution to the understanding of the three-dimensional anisotropy of dense shales was reported by Zinszner et al., 2002. They used ultrasonic techniques in the laboratory, to measure the multi-directional P-wave

Table 3.1 A selection of Vp anisotropy data, showing the effect of foliation, schistocity and cleavage, and the dry or saturated state, when the velocity measurement direction is parallel, at 45°, or perpendicular to the particular planar fabric. Tsidzi, 1997. Rock Type

  0°

  45°

  90°

  0°

  45°

  90°

Condition Gneiss (SW) Phyllite (F) Schist (SW) Slate (F)

Dry 5102 6010 6641 5913

Dry 4211 5130 5802 5074

Dry 3956 5090 5151 4893

Saturated 5918 6050 6706 5745

Saturated 5237 5417 5932 4722

Saturated 5081 5307 5378 4283

Effects of anisotropy on Vp

velocity across a 666 cm, 18-sided truncated cube of the Tournemire shale, whose format is illustrated in Figure 3.5a, using a slate example. Their interpretation of qP velocities is shown in the form of a Wulff ’s stereogram, in Figure 3.5b. As may be noted, the minimum velocity of approx. 3,200 m/s is recorded perpendicular to the bedding (Z-axis), while the maximum of approx. 4,250 m/s is parallel to the bedding (X, Y, etc.)

39

The authors also gave the results of velocity measurements under uniaxial stress levels from 0 to 20 MPa, which show a remarkable lack of stress sensitivity: the Vp – stress curves giving almost horizontal straight lines between the seven different stress levels applied. However, the directional effect was marked, possibly accentuated by a tendency for slight shear in ‘diagonal’ directions of loading relative to the bedding. The lowest velocities were in the ZXX, YZY, ZXZ, YZZ and ZYZ (sub-perpendicular to bedding) directions giving velocities of only 1,700 to 1,800 m/s, while in the XXX, YYX, YYY, XXZ, YYX and YYZ (sub-parallel to bedding) directions, velocities were as high as 4,200 to 4,300 m/s. Under the level of compression applied, and with presumed careful preservation of the samples, the ZZZ

(a)

(b)

Figure 3.4 Effect of schistocity in a strongly anisotropic gneiss, loaded to 40 MPa, parallel or perpendicular to the fabric. Hesler et al., 1996.

Figure 3.5 Ultrasonic measurements on a truncated cube of dense shale recovered from the Tournemire experimental tunnel, south of Aveyron, in France. a) Truncated cube model of slate, showing axes. b) Interpolation of qP velocity measurements for a sample of the shale, from the west gallery. Zinszner et al., 2002.

40

Rock quality, seismic velocity, attenuation and anisotropy

direction gave intermediate velocities in this case, roughly 3,200 to 3,300 m/s. These were similar to in situ P-wave velocities calculated from seismic tomography, where in the vertical direction they recorded 3,125 m/s, with some reduction to 2,950 m/s in a tectonically disturbed area near a sub-vertical fault. 3.3

Velocity anisotropy caused by rock joints

Masuda, 1964, gave a simple but illustrative example of the effect of jointing and joint direction on the anisotropic velocity of blocks of granite at the Kurobe IV dam site in Japan. Figure 3.6 shows P-wave velocities in the dry and saturated state, for three orthogonal measurement directions. Velocity anisotropy was significant and sometimes amounted to 20% or even 25% difference in velocity. The slowest direction was of course when crossing the joints, the fastest when parallel. The loading state of the blocks was not referred to, but judging by the extreme effect of the dry or wet state, possibly the blocks were under low or zero load when these velocity measurements were made. A massive granitic site in Cornwall, England, with one set of predominant jointing striking ESE–WNW, (note rotated axis), caused seismic velocities to be quite anisotropic, with maximum velocities of 5.5 km/s parallel

Figure 3.6 Effects of measurement direction (and saturation) on Vp values across jointed blocks of rock, at Kurobe IV dam site in Japan. Masuda, 1964.

with this jointing and minimum values of 5.1 km/s more or less perpendicular to the jointing (New, 1985). The velocity rosette shown in Figure 3.7 is a convenient way of representing the anisotropy, but the possible reasons for some of the other features on the rosette, for example the marked reduction between 30° and 40° (not exactly perpendicular to the 120–130° joint orientations) was not given. Perhaps the principal stress had rotated some 20° to 30° to 140–150°, giving a low velocity perpendicular to h (minimum), or shear stress effects were involved. Noting the complexity of describing jointed rock masses and their physical anisotropy in relation to deformability and seismic velocity, Oda et al., 1986, developed a crack tensor technique which they compared with laboratory tests on artificially jointed samples, and with in situ tests on jointed granite. The artificial samples of gypsum plaster were cast with artificial, deformable cracks made of deformable greased paper. In Figure 3.8a, it will be noted that the cracks have either a random distribution or an ordered ‘N-S’ distribution. The squared velocity ratio (V/Vo)2 which is the measured ultrasonic velocity normalised by that of the intact sample (Vo), showed corresponding isotropic or anisotropic distributions.

Figure 3.7 Vp anisotropy at a massive granite site in Cornwall, England. Vp(max) was parallel to the single set of joints. New, 1985.

Effects of anisotropy on Vp

(i)

b

(ii)

Figure 3.8 Velocity anisotropy of gypsum samples with flaws, and of two jointed granite sites in Japan. Oda et al., 1986.

41

42

Rock quality, seismic velocity, attenuation and anisotropy

Figure 3.9 Azimuthal Vp anisotropy in jointed limestones at a ‘dry’ (left) and saturated site (right). Bamford and Nunn, 1979.

The graphic results of these authors’ in situ tests are shown in Figure 3.8b. Both granite sites were anisotropic and the intensity of jointing differed, as clearly shown by the magnitude of the squared velocity ratio (Vo for granite samples was 4.5 km/s). The authors’ crack-tensor calculation showed remarkably good agreement with the seismic anisotropy measurements. The orientations of the velocity distributions are clearly dominated by the two ‘fast’ velocity directions sub-parallel to the relevant joint set directions. As seen in Figure 3.8a, small uniformly distributed random cracks cause seismic velocities to be isotropically reduced in relation to an uncracked matrix. Attenuation is increased isotropically, and Vp/Vs ratios are also changed. In contrast, most jointing shows some overall alignment, and ensures anisotropic seismic response. An analysis of the seismic refraction tests at regularly jointed sites in limestones (Bamford and Nunn, 1979) given by Crampin et al., 1980, indicated that the velocity anisotropy (shown in Figures 3.9a and 3.9b) was also very sensitive to the degree of saturation of the joints. The two maxima (at about 40° and 120°) were clearly related to two sets of joints that intersected at about 80°. Details of similar seismic refraction tests to those referred to in Figure 3.9 are given by Nunn et al., 1983.

They used radial (20° interval) geophone spreads at a total of four sites in chalk in Lincolnshire, England. The chalk was not exposed at the seismic measurement locations, but two quarries in the area were mapped to obtain joint orientation data. Strong velocity anisotropy was measured at three of the four sites (Figure 3.10), and maxima at between 5° and 25° were found to correspond with dominant near-vertical joints which were perpendicular to the axis of a major monocline, which had a predominant direction of 15°  7°. The velocity anisotropy of all four sites is compared in Figure 3.10a, and a comparison of velocity anisotropy and resistivity anisotropy for site CFR is given in Figure 3.10b. For the case of site RGQ, Vmax. and Vmin. were 2.85 and 1.75 km/s, giving a total velocity anisotropy (Vmax.  Vmin.)/Vmax.  0.38, i.e., approximately 20% around the mean of 2.25 km/s. Resistivity anisotropy (Figure 3.10b) was greater than seismic anisotropy for the case compared, possibly due to the strong contribution of a fluid bearing joint set. An in-depth investigation of anisotropy caused by persistent sub-vertical jointing at a geothermal site in the USA (Beaver County, Utah) was described by Leary and Henyey, 1985. The authors analysed in detail why, if a significant number of vertical joints remained open (due

Effects of anisotropy on Vp

43

Figure 3.10 a) Azimuthal Vp anisotropy at jointed limestone sites in Lincolnshire, England. b) A comparison of Vp and resistivity anisotropy at one of the four sites (see diamond symbols), is also given. Nunn et al., 1983.

to horizontal stress anisotropy), the elastic properties and hence the seismic velocities would be anisotropic. Compressional waves travelling perpendicular to the joints would obviously be slowed more than those travelling parallel to the joints. However, the authors cautioned that minor geologic structure and mineral fabric could also influence the measured velocity anisotropy. Following earlier work by Garbin and Knopoff, Crampin, and McGonigle and Bamford, Leary and Henyey, 1985, gave simplified equations for the effect of cracks (or joints) on seismic velocity, and the effect of the dominant direction of the cracks (or joints). The following two equations are given for the dry and saturated states. Ignoring higher order terms: 1) For dry cracks: VP2  VP20 (1  71/21e  8/3e cos 2  e/21 cos 4 )

(3.1)

2) For saturated cracks: VP2  VP20 (1  8/21e  8/21e cos 4 )

(3.2)

where:   Nr3/V is the crack (or joint) density of N cracks of radius r in a volume V, and is the angle of

incidence relative to the crack plane normals, where   1. Vpo is the velocity without cracks. At the geothermal site in question, the authors used 22 clusters of shots (sources) each located within 1 km of the wellhead, and used geophones downhole at depths ranging from 30 m to about 700 m. The source clusters were at about 160 m, 280 m and 370 m from the wellhead along six radial lines. The close-in shots were far enough from the wellhead that casing or tube waves did not obscure first arrivals. The results of these tests are shown in Figure 3.11. They demonstrate both azimuthal velocity anisotropy and velocity-depth effects. The two sets of data shown in the figure, represent average P-wave velocity for seismic waves originating 370 m from the wellhead, which were received at two depth ranges in the well (0–300 m, shown as triangles and 460–520 m, shown as squares). The 1.5 to 2.0 km/s increase in velocity is surprisingly large for an average depth increase of only about 350 m. However, Barton et al., 1994, showed a similar velocity increase even in the first 50 m at the Gjøvik cavern site in Norway, due to several MPa increase in stress in rock that had more or less unchanged frequency of jointing and RQD and rock quality Q, in these first 50 metres. In other words, the increased stress acting on the joints (3 to 5 MPa in this case),

44

Rock quality, seismic velocity, attenuation and anisotropy

Figure 3.12 Ultrasonic and longer wave length seismic investigation of four joint sets in dolomitic limestones, which had greater frequency (sets I and II), or lesser frequency (sets III and IV). The strengths of the velocity anisotropy of the different frequencies of jointing are distinguished in a logical manner. Lykoshin et al., 1971.

Figure 3.11 Effects of joint set anisotropy on velocities, with depth effects superimposed, based on an ‘areal well shoot’ or 3-D VSP measurements at a borehole. Vp anisotropy results are shown in the lower diagram, for receivers at depth ranges of 0–300 m (lower, averagevelocity curves) and 460–520 m (higher, averagevelocity curves). Leary and Henyey, 1985.

rather than reduced joint frequency, was the reason for the velocity increase of 2 km/s at a site saturated nearly to the surface. The important effect of stress on joint closure and seismic ‘visibility’ is not treated in the above

equations (3.1 and 3.2). This topic will be treated fully in Chapter 5. When jointing intensity is quite different between the different sets of joints, the use of different seismic wave lengths may be important in distinguishing the behaviour in different orientations. Lykoshin et al., 1971, describe the use of ultrasonic measurement with wave lengths of 0.8 to 0.1 m, and the seismic method with wave lengths of 8 to 15 m, for distinguishing the velocity anisotropy caused by the closely spaced joints (S
0.1 to 0.2 m), from the velocity anisotropy caused by the much wider spaced joints. The results of this interesting, and quite early dual-scale velocity anisotropy measurement are shown in Figure 3.12. Sets I and II correspond to the joints with the closest spacing, and Sets III and IV which had lower frequency, were separately logged by this method. A helpful diagram of jointing, ‘broken down’ into its component sets, was presented by Olson and Pollard, 1989. This is shown in Figure 3.13. The figure was used by Schoenberg and Sayers, 1995 to illustrate their building of a stiffness matrix for a rock mass. This they did by summing the compliance tensor of an unjointed background rock and the compliance tensors for each set of parallel or aligned joints. This they inverted into the form of a stiffness tensor, which they suggested was more

Effects of anisotropy on Vp

45

and shear stiffnesses, i.e. Kn  Ks, even for the case of small laboratory samples of rock joints, whether under low or high normal stress. This is because Kn and Ks are entirely different physical deformation processes, involving the normal deformation of a stiff compressed joint, and the less stiff shearing deformation along the same joint. The ‘macro-displacement’ stiffness anisotropy increases further with increased block size. (Barton and Bandis, 1982). However, it is at present uncertain to which degree this fundamental rock mechanics aspect influences the dynamic rock physics aspect of micro-displacements that are presumably elastic in nature. There is controversy on this aspect, and even on whether friction along joints is a valid attenuation mechanism, as assumed for so long. We will attempt to resolve some of these questions in the more comprehensive chapters of Part II. 3.4

Figure 3.13 a) Joint traces from a 1 m thick bed of limestone, ‘disaggregated’ in b) and c) into their two component sets. Olson and Pollard, 1989.

useful in the consideration of elastic wave propagation through rock masses, than the compliance, which is the inverse of stiffness (as commonly used in rock mechanics). Schoenberg and Sayers went on to apply their rock mass stiffness matrix to the interpretation of shear-wave anisotropy, which is strictly the topic of Chapter 15. An aspect that will reduce the predicted anisotropy when applying the Schoenberg and Sayers stiffness matrix, is the fact that they assumed equal shear and normal compliances, based on seismic imaging of some perhaps not ideally suited, roughened ‘lucite-sheet’ models. (These will also be discussed in Chapter 15). Compliance is the inverse of stiffness. In the ‘macrodisplacement’ world of rock mechanics, there is a one to two order of magnitude difference between the normal

Velocity anisotropy caused by interbedding

The commonly occurring interbedding (alternation) of sedimentary strata of different stiffness, such as sandstone, shale and mudstone; layers which also have different porosity, density and uniaxial strength, causes anisotropy of all the major mechanical parameters and also affects all the components of velocity. (In relation to petroleum reservoirs, the reader is directed to Part II, Chapter 14, for a fuller discussion of this fundamental topic). In this section, some observations of the effects of inter-bedding on near-surface civil engineering projects will be presented. Fine layering of sedimentary strata means that the dominant wavelength of a seismic pulse is long compared to the thickness of individual layers. The medium will then exhibit effective (and real) anisotropy, with a vertical symmetry axis in the case of horizontal layering. In the presence of hydrocarbons this layered medium may show substantial attenuation and velocity dispersion. The combination of effective anisotropy and attenuation means Qseis anisotropy and anisotropic velocities (Carcione, 2000) as we shall see later. Oberti et al., 1979, reported a very instructive set of in situ near-surface measurements that involved downhole sonic logging, cross-hole logging and comparison with deformation moduli determined at different depths below plate loading tests. The latter were performed parallel and perpendicular to the strata, and could therefore be compared with the anisotropic velocities.

46

Rock quality, seismic velocity, attenuation and anisotropy

Figure 3.14 Seismic cross-hole and downhole investigations of marl-sandstone interbedded strata, at a dam site in Italy. Oberti et al., 1979.

Figure 3.15 Correlated anisotropy for the velocity and ‘static’ deformation moduli, as recorded in the interbedded marl-sandstone sequences shown in the previous figure. Oberti et al., 1979.

The rhythmically layered sandstone and marl, with a dip of 27°, formed the foundation for an arch-gravity dam in the Apennines in Italy. Figure 3.14 illustrates the geological sequence and location of boreholes. The exploratory tunnel used for the plate loading tests, shown in Figure 3.15, was at 30 to 35 m depth, and ran parallel to the strike of the inter-bedded strata. The three boreholes (A1 to A3) were parallel and spaced at 3 m centres. Sonic and cross-hole logs are shown sequentially in Figure 3.14. The mean velocity

anisotropy in this orthotropic rock mass was 4.3 km/s (perpendicular to the layers) and 5.0 km/s (parallel to the layers). Differences can be noted between the higher velocities in the sandstones and the lower velocities in the marl. Figure 3.15 shows a comparison of the sonic measurements performed in central boreholes beneath each plate loading location, where deformations were also recorded with extensometers, so that ‘static’ deformation moduli could be calculated at different depths. The lower static moduli and lower velocities of the disturbed near-surface

Effects of anisotropy on Vp

47

re-visited in several contexts in Part II, particularly regarding frequency dependent and stress dependent attenuation, described in Chapter 10.

3.5

Figure 3.16 Inter-bedded limestones, shales and sandstones in a 230 m deep well, Sams, 1995. Resolution of detail in finely interlayered sequences.

rock are evident, especially that of the marl in the invert, where moisture content perhaps had increased. As can be seen in Chapter 5, the deformation moduli and velocities measured in these tests correlate quite closely with the ‘Vp–Q–M’ model, where the rock quality Q-value, or the velocity, are both seen to correlate with the ‘static’ deformation modulus (M), provided that appropriate corrections are made for porosity, rock strengths and depth. A case intermediate between the near-surface and petroleum reservoir interpretation was presented by Sams, 1995, for inter-bedded limestone, shale, sandstone sequences in a 230 m deep (and subsequently additional) research well. The combined use of a borehole compensated (BHC) sonic logging tool, a compensated formation density tool, and a Formation Micro Scanner (FM) was capable of resolving much of the detail of finely interlayered rock sequences. This research will be

Velocity anisotropy caused by faults

A final category of anisotropy that will be described in this chapter is that caused by major faulting. An instructive example is provided from Japan, where Ikeda et al., 1981, describe some of the extensive Japanese high-speed railway (Shinkansen) tunnel investigations in major fault zones. They show characteristic variations in velocity in a major 300 m wide faulted zone in the Rokkô Tunnel, with three zones of velocities as low as 2.2 km/s (Figure 3.17a, b, c). Extensive investigation galleries enabled the authors to investigate the effect of the angle between the fault boundary and the seismic investigation line. When the angle is very acute, and if the fault is also dipping at a shallow angle ( in Figure 3.17b), a false high velocity (V
) may be registered, or it becomes impossible to register the fault. The authors also assembled seismic data from 100 rail tunnels, with emphasis on fault zones, and heavily fractured rock. In Figure 3.17c, Vc is the higher velocity of the competent rock surrounding the heavily fractured zone, which is given a velocity classification A to F in the table shown in this lower figure. The heavily fractured zone has the lower velocity V. They observed that the clay core of fault zones could have velocities as low as 0.8 to 2.5 km/s. It is of interest to note that the two parallel fault zones depicted in Figure 3.17a, which have a minimum velocity of 2.2 km/s, created many months of delay in tunnelling, as can be judged by the profusion of investigation adits into this regional Otsuki Fault zone. In another rock type, on the other side of the globe, the same seismic velocity of about 2.0 to 2.5 km/s allowed tunnelling progress (with TBM) of up to 1500 metres per month, the reason being the high porosity of an entirely different, easily excavated, and relatively stable rock type, when not heavily jointed. The UK-France Channel Tunnel chalk marl had a porosity n
27%, and an easily cuttable strength of only 4 to 9 MPa. The Q–Vp relationship (Vp
3.5  log10 Q) for hard, non-porous, near-surface rocks presented in Chapter 1, would normally predict a Q-value as low as 0.003 to 0.01 (exceptionally poor) for such low velocities: as if the low

48

Rock quality, seismic velocity, attenuation and anisotropy

Figure 3.17 Seismic investigations of fault zones at Japanese rail tunnels. Ikeda et al., 1981. a) Plan view of fault zone crossing the tunnels. b) False high velocity (V
) caused by too acute angle of the seismic investigation line relative to the fault zone. Width of fractured zone has small effect. c) Integrated results from 100 rail tunnels giving a velocity ratio expression for the low fault zone velocity (V) in relation to the surrounding competent rock (Vc).

velocity represented a fault zone. But in the chalk marl in question, Q-values were in the range 10 to 20 where these record tunnelling speeds were achieved. The missing corrections for a low uniaxial strength (i.e. c
5 MPa)

and a high porosity (i.e. n
27%) will be described in Chapter 5. They are essential for integrating rock quality Q and Vp – in softer rocks.

4

Cross-hole velocity and cross-hole velocity tomography

Cross-hole and between-gallery seismic work has been performed for many years at major dam projects, particularly at the sites of arch dams, where the deformation moduli of the rock foundation and valley walls are of most concern. Unfortunately, the large number of dams constructed from the 1960s to the early 1980s did not have the benefit of tomographic imaging, in which not just the average velocity between source and receiver, but also the approximate location and velocity could be displayed, following inversion of the multi-source-multireceiver-position data. The use of pairs of boreholes (or multiple holes), for direct access to a ‘hidden plane’ (or planes), on which representative velocities and their location could be calculated has many advantages for assessing the severity of fault zones, the need for treatment of the ground, or even in some cases the avoidance of bad ground. In this chapter, a wide variety of cross-hole seismic tomographic imaging of the sub-surface will be reviewed, from tunnels and caverns, to mining pillars, blasting-effect analysis, excavation disturbed zone mapping, and analysis of grouting efficiency.

4.1

Cross-hole seismic for extrapolation of properties

In the initial stages of site description for a civil engineering project, geological mapping of major structures may be followed by imaging of these features, using large scale reflection techniques. As emphasised by Cosma et al., 2001, subsequent access in a very limited number of holes will normally suggest VSP measurements, with sources at the ground surface. When the construction phase is begun, access via a larger number of boreholes, even those drilled from shafts or tunnel walls will allow a combination of smaller scale VSP, and direct cross-hole tomography, giving velocity and location. Later in this chapter we will see some exceptional applications of ‘close-in’ seismic tomography. A classic example of cross-hole and between-gallery seismic is that shown in Figure 4.1 from the 220 m high

Mratinje Dam in Yugoslavia, as reported by Kujundzíc, 1979. This figure shows the separate sites of the deformation tests for determining E (the dynamic elastic modulus), D (the deformation modulus) and Vp (the local value of Vp at the deformability test site). Some of the cross-hole, between gallery and boreholeto-gallery velocity measurements are shown in more detail in Figure 4.2 (from Ivanovíc et al., 1970), where the ‘fans’ of velocity can be readily observed. By relating the velocity at each test site to the moduli, the larger scale cross-hole results could be used to extrapolate the expensive and time-consuming tests to other parts of the foundation. In Chapter 6 we will see some of the inter-relationships that have been developed between Vp, Eintact and D, for comparison with Edynamic which can be derived from Vp, Vs and density, as indicated in Chapter 1. Possible pitfalls when performing cross-hole seismic measurements in low velocity layered media such as clays, which presumably will also affect cross-hole seismic tomography in similar media are illustrated in Figure 4.3. McCann et al., 1975, indicate that there is an apparent decrease in the velocity of the high velocity layers with increasing separation of the boreholes. First arrivals at the common depth of 7.4 m showed velocities of 2.18, 1.97, 1.83, 1.81 and 1.78 km/s with borehole separations increasing successively from 2.9 m to 15.1 m. The high frequency direct first arrival received at small borehole separations was replaced by a long dispersed waveform at the largest separations. Attenuation of the higher frequency, higher velocity part of the wave at increasing distance was apparently occurring. The authors used a high voltage ‘sparker’ source in their measurements. The strongly attenuating properties of the clay were presumably the cause of this result. Various seismic wave characterisation methods were compared at a rock anchor foundation site by Ebisu et al., 1992. Figure 4.4 shows P-wave data interpreted from seismic refraction, downhole logging, cross-hole and surface exploration. The discrepancies between the systems should serve as a warning that many factors need to be

50

Rock quality, seismic velocity, attenuation and anisotropy

Figure 4.1 Cross-hole and gallery-to-gallery seismic tests at the Mratinje Dam in Yugoslavia, for extrapolating deformability tests. Kujundzíc, 1979.

Cross-hole velocity and cross-hole velocity tomography

51

Figure 4.2 Classic example of the use of gallery and cross-hole seismics for extrapolating quality and deformation modulus values at the Mratinje Dam, Yugoslavia. Ivanovíc et al., 1970.

Figure 4.3 Dispersion effects in layered Oxford clay give apparent reduced Vp for stiff layer with increased cross-hole separation. McCann et al., 1975.

evaluated when interpreting the results of a suite of tests. Ebisu et al. prefer the use of the surface wave velocity Vr to correlate with modulus of deformation. They show on a log-log plot of modulus versus Vr, that a consistent

trend is established. A modulus of 0.3 GPa corresponds to Vr
0.5 km/s, 1 GPa corresponds to Vr
0.8 km/s. Usually, when comparing cross-hole and downhole velocity measurements, the downhole sonic probe is considered to give a small-scale, and usually higher velocity than the averaged cross-hole result. However, the small-scale excavation damage zone (EDZ) that may also accompany a borehole in incompetent rock, may presumably be the reason for sometimes measuring a lower velocity at the small scale. In Figure 3.14 in the chapter on anisotropy, the sonic log of Oberti et al., 1979, generally showed about 0.5 km/s lower velocity than the cross-hole result, where the hole spacing was 3 metres. The sonic log also showed greater sensitivity to the layering (marls and sandstone) in this case. The large reduction of the velocity in the ‘withinthe-borehole’ measurement shown in Figure 4.4 (Ebisu et al., 1992) was not discussed by the authors, but is perhaps an expression of damage caused by the drilling/ flushing process in these near-surface weathered materials at the rock anchor foundation in Japan.

52

Rock quality, seismic velocity, attenuation and anisotropy

Figure 4.4 Contrasting P-wave velocities at a rock anchor foundation, using four methods of measurement. Ebisu et al., 1992.

A more ‘normal’ comparison between a downhole sonic log and a cross-hole log is that shown in Figure 4.5 from Whiteley, 1990. Hole spacing was 40 m. The latter shows a smoothed, average behaviour. While general trends are seen to be remarkably similar, details between the two logs clearly differ due to the change of scale and location. 4.2

Cross-hole seismic tomography in tunnelling

The system of seismic data analysis used in tomographic studies was probably adapted from the medical profession, although the use of ‘superficial’ seismic sources (earthquakes) for inversed imaging of the internal structure of the earth seems to be a possible source of inspiration. The efficient data handling and graphic presentation techniques represented by the tomographic method, were rapidly adopted in rock engineering projects since roughly the mid-1980s, and to an increasing degree in petroleum engineering. The simple principle of the method is that a string of receivers (hydrophones or 3D accelerometers) suspended (or pushed into) a borehole at (e.g. 2.5 or 5 m) regular spacing, are used to receive the seismic signals from a

Figure 4.5 Comparison of a sonic log and a cross-hole (mean velocity) log. Whiteley, 1990.

source of dynamic energy in an adjacent hole. The artificial source can be a 1 gm detonator cap, a downhole hammer, a sparker or a piezoelectric high frequency source, which is moved successively down the sender hole. The same spacing of sources and receivers (e.g. 2.5 or 5 m), is normally used. The inversion of the travel times of the multiply crossing ray paths, into velocities, or into other seismic attributes, is organised in principle into a regular grid in which average solutions for the local velocity (or other seismic attribute), are produced. Tomographic plots of velocity, amplitude and velocity difference are commonly employed. Most frequently, the method is used from single pairs or multiple pairs of boreholes drilled from the surface or from the face of a tunnel, to image a pending (or already intersected) fault zone. Increasingly in recent years the method is also being used in mining to delineate highly stressed and burst prone areas, which seem to be most closely associated with steep gradients of velocity, where high shear stresses

Cross-hole velocity and cross-hole velocity tomography

may be present. The seismic tomography method can be used remotely and safely in hostile environments, to image highly stressed regions of a mine or overstressed rock around a deep tunnel. (The interesting use of ‘passive’ sources such as acoustic emission (AE) will be illustrated briefly in Chapter 7, where average velocities can be calculated.) Figure 4.6 show some potential layouts for the borehole arrays. A moving source, for example mining equipment, can also be used to obtain a tomographic image, if a suitable array of receivers is in place, and if measurements are repeated at regular intervals over a suitable length of time. Westman et al., 1996, utilised a long wall shearer in an Appalachian coal mine in the USA, and sampled this source at 1⁄2 to 1 minute intervals during mining shifts, while the shearer was moving. Their receivers were geophones fixed to rock bolts in the mine entry roofs, close to the mining face. They produced attenuation tomograms that changed with time as mining advanced in response to high stress anomalies, stress release phenomena, changed degrees of jointing and stress induced fracturing. The assumption is often made that P-waves have travelled directly from source to receiver, and a straight line tomography program is used. Curved ray path tomography is preferred to allow for velocity anisotropy and for refraction (McDowell, 1993). By, 1987, described a comprehensive layout of vertical boreholes for cross-hole seismic tomography, which was performed in Oslo for a difficult, faulted section of the twin tube, 13 m span Fjellinjen road tunnels (Figure 4.6a). Some 20 m of soft clay underlying downtown Oslo had to be protected from groundwater pressure drawdown. At one location, the rock cover over the arch consisted of only 3 to 5 m of crushed alum shale (damaging to concrete), beneath 20 to 30 m of soft clay, in a major regional fault zone. Selection of freezing for one of the tunnel tubes was made on the basis of the seismic results, which were based on cross-hole measurements from five boreholes of 60 m depth and a total of eight cross-hole sections. In contrast to this layout of vertical holes, Hope et al., 1996, working in chalk, used single holes drilled radially into the wall of a pilot tunnel, and the upper and lower walls of a tunnel, to give two triangular shaped spreads (see Figure 4.6b). They obtained a distribution of velocities ranging from 1.8 to 2.5 km/s between the crown positions (2 m intervals) and the borehole, and 1.9 to 2.3 km/s between the invert positions (2 m intervals) and the borehole. Lower velocity zones were consistent with additional jointing associated with a listric fault cutting through the chalk. This was verified after benching down

53

and widening of the pilot tunnel had been performed, to create a cylindrical oil storage cavern. The initial refraction seismic survey from the pilot tunnel had indicated a range of velocities of approximately 2.3 to 2.6 km/s, representing generally uniform conditions. Laboratory samples of the 10 MPa chalk had indicated a mean P-wave velocity of 2.4 km/s at natural water content (13 to 14%), and 2.5 km/s when fully saturated. An example of the potential benefits obtained from cross-hole seismic tomography at a near-surface cavern site is shown in Figure 4.7a and b. The measurements were performed for the Gjøvik Olympic cavern site investigation in Norway in 1990. The position of the planned, 62 m span, 140,000 m3 cavern was adjusted in order to penetrate as little as possible of the lower velocity, near-surface zone (Vp
4.1 to 4.3 km/s). This was proved in later cavern logging to have rock quality Q-values as low as 2 to 5 at the shallow end of the cavern. This quality results from a low to moderate RQD (frequent smaller pieces of core 10 cm long), up to four joint sets (Jn  12–15), and with some alteration of the joint walls (Ja  2). Positive aspects were considerable joint roughness (Jr  2 to 3), and surprisingly high horizontal stresses. (See Appendix A for Q-parameter ratings.) These moderate velocities fit the hard rock, near-surface relation Vp
3.5  log10 Q presented in Chapter 1 quite closely, for the relevant shallow conditions (approx. 25 m depth). At the other, deeper end of the cavern, Qvalues also fell to 2 or 3. Significantly, this rock quality Q was lower than the Vp values would have indicated, with this shallow seismic relationship. The fundamental need for depth or stress adjustments in a Q–Vp–M (static modulus of deformation) relationship, are discussed in Chapter 5. The details of NGI’s cross-hole tomography, analysed in more detail in Chapter 5, indicate a continuous rise in velocity down the 60 m deep boreholes (approximately from 3.5 km/s to 5.5 km/s), despite more or less constant joint frequency, RQD and rock quality Q-values down the lengths of the recovered rock cores. This is a good example of stress effects on in situ Vp values, since hydraulic fracturing stress measurements had shown h min (and the elastic theory estimate of H max), to be about 3 and 5 MPa respectively, at cavern depth, i.e. equivalent to depths of
100–200 metres, if vertical stress alone had been responsible for the rise in Vp. Shifting to another category of seismic tomography applications for tunnelling, it is interesting to note that deviated boreholes are quite frequently used in combination with sea-bottom hydrophones to obtain

54

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

Figure 4.6 a) Cross-hole tomography arrays to characterise a fault zone at the Oslo Tunnel. By, 1987. b) Some examples of seismic arrays, and a triangular Vp tomogram for chalk at a storage cavern site in Israel. Hope et al., 1996.

Cross-hole velocity and cross-hole velocity tomography

55

Figure 4.7 Cross-hole velocity tomography performed by NGI for the Gjøvik cavern site investigation, Norway. Note the use of different velocity scales, to improve the velocity information a) above the cavern, b) at cavern depth. Barton et al., 1994.

56

Rock quality, seismic velocity, attenuation and anisotropy

Figure 4.8 Sub-fjord borehole to seabed seismic tomography, using differently inclined and deviated 250 to 300 m holes drilled from the land and from an intervening island, and seabed geophones. (Westerdahl and Cosma, priv. comm.1998.)

information about major faults known to be sub-parallel to these deep fjord depressions. There are numerous sub-fjord and sub-sea tunnel sites in Norway, that have utilised seismic tomography for the near-land part of their routes, with sub-sea refraction measurements for the less accessible kilometres of these tunnels. A typical case is shown in Figure 4.8, for planning the 1997–1999 tunnelling under the Oslo Fjord, near Drøbak in southern Norway (pers. comm. Westerdahl, NGI and Cosma, Vibrometric, 1998). In this particular case the 50 to 70 m thick, fjord-bottom sediments, caused some reduction in resolution. The fault zones were correctly predicted and later encountered in the tunnel, but some details of their structure could not be detected as well as expected. Because of uncertainties about the likely quality of difficult pre-grouting into a boulder and clay filled depression in the bedrock, against a back-pressure from more than 100 m of seawater, a deeper by-pass tunnel was excavated to maintain schedule. Penetration of the major zone was prepared with more extensive (but partly unsuccessful) pre-grouting, followed by a timeconsuming freezing, when the full scope of the situation was understood. The quality of pre-grouting (or that of the freezing process) could probably have been detected by means of seismic tomography monitoring. Excellent examples of the use of cross-hole seismic tomography, (‘geotomography’) in mountain tunnelling, are given by Chang and Lee, 2001, who refer to several tunnels in South Korea, surveyed by these and other methods. The authors point out that severe topographic changes and gradational weathering in mountainous terrain, make the use of conventional travel-time refraction

seismic hard to use, as long geophone arrays may receive shortest path direct waves earlier than the refracted head waves. There is also gradational, progressive weathering, rather than distinct layering, with less clear development of head waves. Consequently, the authors report widespread use of tomographic inversion techniques for their tunnels through steep terrain, and use not only of hole-to-hole, but also hole-to-surface and surface-to-surface configurations of sources and receiver strings. The authors also show the parallel use of downhole logging, with Vp and Vs based interpretation of the three elastic moduli and velocity-depth gradients. The additional use of rock quality RMR and Q-value core logging, and the extrapolation and intrapolation of properties afforded by the geophysics, provides a quite reliable basis for tunnel support strategies, with key attention to fault zones and portal areas. Other near-surface uses of cross-hole seismic tomography that can be mentioned in this section are of course the possibilities of using geotomography at dam sites. It is easy to imagine the benefits of correctly located low and high velocity zones in a dam foundation such as that illustrated in Figures 4.1 and 4.2, where at that time, (in the 1960s and 1970s), only average velocities between holes could be determined to extrapolate deformation moduli across the foundations. At dam sites that are located in limestones and marbles, solution cavities can prove extremely difficult to find and treat with conventional drilling and injection. Deep, sediment-filled scour-holes in dam site canyons, extending foundation depths many tens of metres could also be mapped more successfully with cross-hole seismic tomography.

Cross-hole velocity and cross-hole velocity tomography

By et al., 1988, described the use of the technique at a dam site in northern Norway. Small, concentrated low velocity zones of about 3 km/s were observed at numerous locations in the marble-mica schist dam foundations, using cross-hole measurements between seven inclined boreholes. The information formed a fence-like picture across the foundation, enabling decisions to be made about modified grout-curtain designs. Cross-hole seismic tomography from boreholes drilled from the surface can also be performed at greater depth, in order to extrapolate core-logging data to (presently) inaccessible locations, as a means of optimising layouts for mines or nuclear waste repositories, or researchrelated underground laboratories. An early example of cross-hole seismic tomography at the Underground Research Laboratory (URL) site in Manitoba, Canada is given by Wong et al., 1983. They first conducted a form of ‘cross-hole VSP’ by fixing a transmitter in one hole at 100 m depth, while the receiver was moved by 2.25 m intervals in a vertical hole 16 m away. In this case both P and S arrivals were inverted, giving average values of Vp and Vs of 5.5 and 3.1 km/s, and a deduced dynamic Young’s modulus of 65 GPa and a dynamic Poisson’s ratio of 0.245. Due to the relatively coarse resolution achieved when they subsequently conducted cross-hole seismic tomography with a 175 m borehole spacing, they felt the need to plot the so-called residual velocity, to accentuate information levels at the location of one of the now quite well known, and much researched fracture zones. This intersected borehole URL-6 at 275 m, and was proved to be the same zone at 300 m depth in borehole M2a, due to the consistently low velocity between these two locations. The calculation of residual velocity shown in Figure 4.9 was designed to remove background velocity and velocitydepth trends. The authors used piezoelectric transducers as high frequency sources, in order to improve resolution. The authors expressed the residual velocity as: Vp  V
p  5.5  0.002 (z  100)

(4.1)

with depth expressed in metres (for z  100 m). They were thus reducing the measured velocity by 0.2 km/s at 200 m depth, by 0.4 km/s at 300 m depth, making an assumed velocity – depth gradient of 2 s1. A lot of discussion concerning such gradients will be found in Chapter 11, relevant to continental velocity-depth structures, and those derived from mid-ocean, spreading ridge investigations of new basalt crust. At the UK Nirex Ltd Sellafield site in NW England, where it had been proposed to locate a low and intermediate level nuclear waste repository following many

57

Figure 4.9 Residual Vp tomogram between two boreholes at the Underground Research Laboratory (URL), Canada. These were spaced 175 m apart. The calculation of residual velocity was designed to remove background velocity (5.5 km/s) and a measured velocity-depth gradient of 2 s1 seen from equation 4.1. Wong et al., 1983.

years of investigations of the site, cross-hole seismic tomography was performed between some of the 1000 to 1200 metre deep boreholes. The layout of the holes and the results of two of the tomograms are shown in Figure 4.10. Stress levels at 1200 metres depth were as high as 40–50 MPa in the direction BH2 to BH5, and about 20 to 30 MPa in the direction BH2 to BH4. Because of the fault structures sub-parallel to H (max) seen crossing the BH2 to BH4 tomogram, and in view of the lower horizontal stress acting in this direction, one would expect lower average velocities in this tomogram than between BH2 and BH5. This proves not to be the case, and one must therefore question whether the betweenborehole distance of 600 m is giving similar attenuation problems as shown in Figure 4.3 earlier in this chapter. The other possible conclusion to draw from the velocity tomograms is that perhaps a deep zone with different joint orientation caused the lower velocity region at 800 to 1100 metres depth. Whatever the explanation, the

58

Rock quality, seismic velocity, attenuation and anisotropy

Figure 4.10 Deep (1000–1200 m) cross-hole tomography at the UK Nirex Ltd Sellafield site. (Schlumberger GeoQuest, Nirex Report S/94/007, by kind permission.) (See Color Plate 1)

frequently occurring velocities of about 5.2 to 6.2 km/s relate quite poorly with the mean weighted Q-value of about 3 (range 1 to 10) which were logged by the NGI team of engineering geologists. (Barton et al., 1992a). This discrepancy is most likely due to stress effects on Vp in the jointed (ignimbrite and welded tuff ) rock mass (Barton, 1995). This will be discussed further in the next chapter, where effects of depth and stress in jointed media are reviewed in more detail. Correlations are finally developed between depth and velocity for a given rock quality Q, also incorporating uniaxial compressive strength and matrix porosity.

4.3

Cross-hole tomography in mining

Phenomenological results of stress change causing velocity change will be presented in this section, prior to the in depth review of stress effects on velocities in jointed media to be given in Chapter 5. Although the cases reviewed are from mining, it may be useful to start with an interesting high pressure tomography experiment from the laboratory, described by Scott et al., 1994. The effects of their high pressure loading of an intact cylinder of Berea sandstone with a steel indentor, was monitored by 20 acoustic sensors arranged in a ring

Cross-hole velocity and cross-hole velocity tomography

59

Figure 4.11 Ultrasonic tomography to monitor the loading on an indentor on Berea sandstone. a) Experimental set-up, showing acoustic sensors, load application, and data acquisition. b) Cross-section, showing tomographic plane. c) Acoustic tomograms for different indentor stress levels a to h. Scott et al., 1994.

around the sample. The sample had a porosity of 18%. One hundred and thirty ray-paths were analysed to calculate the velocity in 97 individual elements. The experimental set-up is shown in Figure 4.11a,b and the tomographic images for eight load increments (including final unloading) are shown in Figure 4.11c. It was found that the mean velocity of 2.3 km/s for the sample increased to 3.0 km/s a short distance under

the indentor at 20.6 MPa applied stress, and finally to 3.55 km/s at 110 MPa applied stress. The rate of velocity increase declined at higher stresses, presumably due to the already reduced pore space. However, the sample appeared to have remained nearly in the elastic state, and the velocity after final unloading was very similar to that before loading, except for some increase in the area showing the lowest velocity. Slight damage was assumed.

60

Rock quality, seismic velocity, attenuation and anisotropy

Figure 4.12 Cross-pillar seismic tomography showing ray paths and Vp values (km/s) across pillars in the Masua Mine in Italy. The host rock was dolomitic limestone, and the orebody was mineralized limestone. Barla, 1993.

A second experiment involving a vertical plane of measurement, revealed velocity increases as before, but the levels achieved differed from those in the horizontal plane (they were lower) indicating differential stress induced anisotropy. Following this laboratory demonstration of pressure effects on Vp in intact (but porous) rock, we can examine some cases from mining where monitoring of stress changes was carried out at much larger scale. Barla, 1993, describes the use of seismic tomography across three pillars in the ore-body of the Masua Mine in Italy. While there was a general tendency of high velocity (up to 7 km/s) in central parts of the pillars, and lower velocities (3–4 km/s) on the outsides of the pillars, there was however some variation, and in one perhaps highly mineralised zone, the velocities were highest at one edge of a pillar, as shown in Figure 4.12. Friedel et al., 1995, 1996a and 1996b, used seismic velocity tomography both in a coal mine (Foidel Creek, Colorado), and in the deep Homestake gold mine, in South Dakota, USA for monitoring of apparent stress changes and stress gradients as a result of mining. At the coal mine reported by Friedel et al., 1996a, they monitored velocity and velocity changes in two yield pillars alongside active longwall panels.

Figure 4.13 Cross-pillar seismic tomography across a coal pillar, showing the relation between Vp and the perceived stress level in ‘yield pillar A’. Friedel et al., 1996a.

Figures 4.13 and 4.14 show the tomographic test set-up in each case, and below this the velocities (2.25 to 3.75 km/s) and velocity changes (1.5 to 2.5 km/s) as a result of the adjacent longwall panel advance. The one day of advance (some 8 metres) caused reductions in velocity, presumably just as required for a yield pillar function. The local reductions in velocity probably reflect the adverse effect of an increase in the vertical pillar stress (‘1’), which would cause loosening and reduced velocity in horizontal directions (as monitored), where the rock was not well confined. Gas and coal outbursts in Polish mines in the Lower Silesian coal basin, and the difficulty or impossibility of obtaining test samples due to the fineness of the discontinuities, led Poldolski et al., 1990, to use timelapsed tomographic imaging to monitor velocities and related areas of high stress. The authors describe a 70 ton roof fall (and 2600 m3 ejection of methane) and how

Cross-hole velocity and cross-hole velocity tomography

61

McConnell orebody, near Sudbury, Ontario. This is a steeply dipping sulphide, crossed by a number of deviated boreholes, as illustrated in Figure 4.15a. The author described the use of a non-destructive piezoceramic vibrator source which was successively lowered down each of the inclined water-filled holes, with a hydrophone string of detectors in the nearest neighbouring hole. Figures 4.15b and 4.15c show a schematic of the equipment, and 1/5 th of the ray-paths between two of the adjacent holes. The (approximately reproduced) tomogram shown in Figure 4.15d indicated a clearly delineated orebody velocity of about 4.0 to 4.5 km/s, compared to the 5.9 to 6.5 km/s of the host rock. The so-called pixel dimensions for the tomographic imaging and interpretation were only 1.5 m  2.5 m. Dominant frequencies were in the 3–4 kHz range. As a first approximation, a straight ray-path assumption was made to speed the interpretation. As the author pointed out, actual raypaths were likely to curve due to refraction in a non-uniform geologic medium, and could be degraded by false features or artefacts. Checking of the tomogram structure, using independent means, including the recovered core, was therefore advised. Figure 4.14 Vp as a monitor of increasing stress in ‘yield pillar B’, adjacent to a longwall-mining advance in coal. Friedel et al., 1996a.

high seismic velocities in the same area correlated with increased volumes of coal ejection and degassing from blast holes drilled for shooting the longwall face. The link between high stress and high velocity – prior to failure, is clear. Friedel et al., 1995, reported monitoring between two levels of the deep Homestake gold mine in the USA. Their results indicated a sensible correspondence between low velocity zones and back-filled areas, ore chutes, and so on. High velocity gradients were interpreted as locations of potential rock burst. We shall see more examples of the effects of high stress on velocities, when reviewing the work that has been done in excavation disturbed zones (e.g. Cosma et al., 2001) in Chapter 7, and also see the possibilities of using acoustic emission (AE) as a remote method of monitoring high stress gradient problem areas. Cross-hole seismic tomography has also been in use to delineate the detailed structure of orebodies, beyond what can be achieved by intermittent core drilling. A good example was described by Wong, 2000, from the

4.4

Using tomography to monitor blasting effects

Several investigators have used seismic velocity tomography to follow the effects of loosening and void formation caused by blasting. Cumerlato et al., 1988, performed seismic tomographic analysis of pre-blast and post-blast quarrying effects in dolomite, in a lime quarry in the USA, using a modified refraction seismic technique. Figure 4.16 shows pre-blast and post-blast velocity distributions, and clear advantages of a modified blast hole loading factor for controlling fracturing. High velocity zones (Vp  4.5–6.0 km/s) were reduced to low velocity (0 to 3.5 km/s) when blasting performance was unfavourable, due to all the crushing and void formation. Maxwell and Young, 1993, used a velocity difference image technique for analysing the effect of an explosive detonation in a borehole in granite. The experimental set-up is shown in Figure 4.17a and b. The velocity difference images, examples of which are shown in Figure 4.17c and d, are computed from before-and-after-blasting time-delays, along common ray paths. The authors observed extension of the lower velocity zone away from the blast hole, sub-parallel to the trace of assumed

62

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c)

(d)

Figure 4.15 a) Sulphide orebody delineated by boreholes. b) Schematic of equipment and acquisition geometry (shown vertical). c) Onefifth of the total 4,200 raypaths for one pair of holes. d) Approximate velocity tomogram, showing the lower velocity of the sulphide orebody (Vp  4.0–4.5 km/s), compared to the host rock (Vp  5.9–6.5 km/s). Wong, 2000.

Cross-hole velocity and cross-hole velocity tomography

63

Figure 4.16 Pre-blast (left) and post blast velocity tomograms. Cumerlato et al., 1988.

(a)

(b)

(c)

(d)

Figure 4.17 a,b) Cross-hole tomography set-up, for monitoring blasting effects in a borehole in granite. c,d) Velocity difference tomograms showing reduced velocity caused by blasting. Error tomogram on right. Maxwell and Young, 1993.

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Rock quality, seismic velocity, attenuation and anisotropy

joint planes. Secondary changes may have been associated with changes in the water table. Seismic tomography for controlling blast fragmentation results for mine areas where in situ leaching was planned, were described by Thill et al., 1992. The results shown in Figures 4.18 and 4.19 were obtained from crosshole measurements by the US Bureau of Mines at the experimental Edgar Mine in Idaho Springs, Colorado. They found good correlation between pre-blast and post-blast velocities that corresponded to areas where

blast induced fracturing had occurred. These low velocity zones (for example Figure 4.19) showed increases in velocity when fluid was injected. These were also the areas where lost circulation occurred when drilling was performed. The joint aperture changes and new fractures presumably created poor acoustic coupling so were readily detected as velocity reductions, later to be partly recovered when there was resaturation in the area.

4.5

Figure 4.18 Pre-blast ‘fence’ tomogram at the USBM Edgar Mine in Colorado, USA. Thill et al., 1992.

Alternative tomograms

Thill et al., 1992, show a method they developed of constraining the seismic parameters (e.g., velocity) at a common borehole axis, when two non-coplanar tomograms were to be joined in a ‘fence’ type presentation, as illustrated in Figure 4.18. One result that is not immediately obvious is the Vp/Vs ratio tomogram shown in Figure 4.19. Why the post-blast high velocity (undamaged) areas should have the highest Vp/Vs ratios (i.e. 1.88 or higher) while fractured zones with low velocities have the lowest ratios, must presumably be due to the changed saturation, since if each area were saturated the opposite result would be expected, as we saw in Chapter 1.

Figure 4.19 Post-blast tomograms at the stope leaching site, Edgar Mine, Colorado, USA. Thill et al., 1992.

Cross-hole velocity and cross-hole velocity tomography

Another factor also seen in Chapter 1, is the basic, and theoretically determined correspondence between high Vp/Vs ratios and high dynamic Poisson’s ratios. The general form of both these tomograms is seen from Figure 4.19 to be similar, following the theoretical basis given in Chapter 1. In a nice example of the capabilities of alternative tomographic descriptions of a site, using different seismic wave form analyses, Watanabe and Sassa, 1996, give three tomographic plots of the same experimental

65

mining site (the Kamioka Mine in Japan). The geological setting and source and receiver locations are shown in Figure 4.20a and b. The P-wave velocity tomogram shown in Figure 4.20c indicates high velocities, even in locations where ‘fractures’, ‘basic dike’ and ‘fault’ are shown, suggesting high stresses and reduced sensitivity to jointing and faulting. The authors therefore utilised amplitude attenuation tomography (Figure 4.20d) and pulse broadening tomography (Figure 4.20e), which correlated better with the geologic structures.

(c)

(a)

(d)

(b)

(e)

Figure 4.20 a) to e). Three tomograms comparing P-wave velocity, amplitude attenuation and pulse broadening methods of analysis at the Kamioka Mine in Japan. Watanabe and Sassa, 1996.

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Rock quality, seismic velocity, attenuation and anisotropy

Amplitude attenuation was calculated for the first arrival P-wave, and was based on the fact that amplitude decreases by geometrical spreading, and is a function of the distance between the source and receiver. The attenuation coefficient (␣) is given by: 

f QV

(4.2)

where (Q) is the seismic quality factor, (f ) is the frequency and (V) is the velocity. Watanabe and Sassa, 1996, suggested that the seismic Q-value was an inherent parameter of the medium that was independent of frequency in the seismic wave frequency range. At the same mine site they listed the following Vp and Q-seismic values for cores. Table 4.1 Seismic velocity and Q-seismic of rock cores measured in the laboratory (Watanabe and Sassa, 1996).

Gneiss Limestone Skarn Basic dyke

Velocity (m/s)

Q-seismic

5700 5470 4900 5170

79 22 28 36

The gneiss showed the highest Vp (5.7 km/s) and the highest Q-seismic value (79). In situ, the gneiss between points 5 and 20 (Figure 4.20b) had an average velocity of 5.53 km/s and a Q-seismic value of 16. The amplitude attenuation tomography shown in Figure 4.20d gives the Q-seismic values. A dark colour corresponds to high Q-seismic values of low attenuation. Light colours correspond to the low Q-seismic values associated with the fault. Soft limestone and areas oozing water reportedly also showed lower Q-seismic values (i.e., about 10 or less). There seems therefore to be more evidence here of a fairly close implicit relationship between the Q-value (the rock mass quality rating of Barton et al., 1974) and the Q-seismic value. This will be explored in greater detail in Part II, Chapter 10. The final tomographic plot shown in Figure 4.20e is called pulse-broadening tomography. The dark colour denotes a large broadening factor, or low attenuation. The pulse broadening technique is based on the fact that the wavelength lengthens and the frequency reduces as a seismic wave travels in the rock mass. The

rise time or pulse width of the first arrival P-wave is used. 4.6

Cross-hole or cross-well reflection measurement and time-lapse tomography

Although strictly outside the scope of Part I of this book, which deals mostly with civil and mining engineering topics, an exception will be made here, concerning a description of the obvious benefits of using cross-well seismology in the petroleum industry. Paulsson et al., 1993, recommended not only cross-hole tomography but also well-to-well reflection measurements, as shown diagrammatically in Figure 4.21, to obtain a better understanding of the (increasing-as-time-goes-by ?) heterogeneity of reservoirs. They demonstrated how repeated (time-lapsed) surveys could be used to follow the progress of enhanced oil recovery (EOR) programmes, such as steam injection, and also pointed out the advantages of the downhole location of both source and receivers, since the attenuating weathered (or soft-sediment) layer is no longer limiting the high frequencies that can be recorded.

Figure 4.21 Cross-well transmission and reflection tomography for petroleum reservoir definition. Paulsson et al., 1993.

Cross-hole velocity and cross-hole velocity tomography

67

Their results showed the strong correlation between oil saturation and velocity (e.g., 1.5 km/s at 20% oil saturation to 2.7 km/s at 60% oil saturation). They also noted the high velocity zone that developed when injecting cold water, due to resaturation, a result that could presumably locally reverse in a jointed reservoir, if effective stress reductions and joint aperture increases exceeded the otherwise positive effect of resaturation on Vp. In a keynote lecture at the 6th IAEG Congress in Amsterdam, Whiteley, 1990, gave particular emphasis to the high resolution, cross-hole reflection imaging technique. The three diagrams given in Figure 4.22a, b, and c illustrate the basic field set-up and two of the methods (yo-yo and beam steering) for imaging targets from multiple positions. In this particular application from Australia, interest was focussed on the location of shallow coal seams and of unfavourable structural features that would affect mining operations. A modified marine sparker source was lowered in one hole, and an array of closely spaced marine hydrophones were located in an adjacent hole, which could be up to 150 metres away. Borehole depths were up to 300 metres.

Figure 4.22 High resolution, cross-hole reflection imaging technique, showing the yo-yo and beam steering methods, for delineating shallow coal seams in Australia. Whiteley, 1990.

5

Relationships between rock quality, depth and seismic velocity

Efforts to relate rock quality and seismic velocity have been made at intervals, during the development and integration of rock engineering and engineering geology. Included in this review will be RQD, joint or fracture frequency (Fm1), and the Q-value (the ‘static’ rock mass quality rating). Their various relationships to P-wave velocities obtained from shallow refraction seismic, and also from down-hole sonic logging, will be explored. The correlations obtained have had emphasis on hard rocks, with or without weathering, without the complication of matrix porosity variations, or large ranges of strength and density. These preliminary empirical correlations between RQD and velocity ratio, and between Fm1 or the Q-value and Vp, must necessarily include the effect of depth or stress level on Vp, for them to be more widely applied. On the basis of numerous reviews of deeper seismic measurements, a method is developed in this chapter, that includes matrix porosity and rock strength besides all the rock mass attributes of jointing, faulting, weathering and clay. To these are added the all important influence of depth or stress level, causing gradual or rapid closure of many or all of the joint sets. 5.1

Some preliminary relationships between RQD, F, and Vp

Relationships between Vp (lab, therefore intact) and Vp (field, therefore jointed) have been suggested as a seismic measure of degree of jointing for many decades. Deere et al., 1967, found that the ratio Vfield/Vlab. when squared, was numerically very close to the value of RQD (expressed as a ratio rather than a percentage), at least for nearsurface measurements. (RQD is defined as the % of core that has core sticks 10 cm long, for selected structural domains, or for specific lengths of core). The following simple table shows the central trend of this relationship, which however shows considerable scatter. (It should be noted that seismic refraction velocities in

the field are being compared with the higher frequency, typically ultrasonic measurements of the laboratory.)  V 2 RQD%  100  field   Vlab 

(5.1)

Table 5.1 Relationship between rock quality, RQD and velocity index, Deere et al., 1967. (VF  field value of Vp, VL  laboratory value of Vp). Quality description

RQD (%)

Velocity index (VF/VL)2

Very poor Poor Fair Good Excellent

Less than 25 25–50 50–75 75–90 Over 90

0–0.25 0.25–0.5 0.5–0.75 0.75–0.9 Over 0.9

Other authors, reviewed by McDowell, 1993, have suggested the following evaluation of rock quality, as expressed by RQD. Table 5.2 Seismic evaluation of Rock Mass Quality (see McDowell, 1993). The ratios are field-seismic/lab-ultrasonic. Quality description

RQD (%)

Joint frequency (m1)

Very poor Poor Fair Good Excellent

0–25 25–50 50–75 75–90 90–100

18 15–18 8–5 5–1 1

VF VL 0–0.4 0.4–0.6 0.6–0.8 0.8–0.9 0.9–1.0

 V 2  F   V  L

0–0.2 0.2–0.4 0.4–0.6 0.6–0.8 0.8–1.0

The above sets of relationships are only approximate, as too few factors that obviously affect Vp values for the rock mass are actually ‘captured’ in the RQD value alone. RQD on its own is an insufficient descriptor of the rock mass quality. However, as a single parameter it is very effective in heavily jointed rock masses, where

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Rock quality, seismic velocity, attenuation and anisotropy

it is particularly sensitive to the state of weathering or alteration, since the frequent occurrence of clay-fillings in the accentuated near-surface jointing, gives appropriately low values of RQD, for example 10 to 20%. (Note that ‘incompetent’ rock pieces that can be broken by hand are excluded, i.e. local RQD  0%, following Deere’s recommendations.) When joints are tightly closed by effects of depth or horizontal stress, VF will more closely approach the value of VL without RQD being affected. Therefore whether RQD, or the Bieniawski, 1989 RMR, or the Barton et al., 1974 Q-value are used to correlate with seismic velocities, a depth or stress correction is required for use below the superficial penetration of surface refraction measurements, in other words when depths exceed some few tens of metres. In fact a depth correction may be needed at shallower depths, but with RQD, RMR and Q typically increasing rapidly in the first tens of meters, a reliable depth correction is problematic, since three variables are changing at once (quality, depth, velocity). Turk and Dearman, 1986, proposed a seismic fissurization index K that was based on the difference between P-wave velocity of a dry, intact sample loaded to 1/2 c (half the uniaxial strength), and the velocity of the dry rock mass. K 

V /2  Vmass,dry

(5.2)

Vmass,dry

They showed that K was sensitive to increased porosity caused by weathering (e.g., for fresh or weathered andesites: n  1.9%, K  0.21, and for n  9.1%, K  0.68 respectively). When they analysed data from King et al., 1978, concerning Vp and joint frequency measurements from above the water table in andesite, K was shown to vary from about 0.1 to 0.3 with increased joint frequency, while the in situ velocity (for unsaturated conditions) varied from about 6 km/s to 5 km/s. This data and King et al., 1978, source data are shown in Figure 5.1a and b. Karmis et al., 1984, also investigated the effect of fractures (saw-cut or tensile) on the seismic velocity. When F(m1) was plotted against the velocity ratio (V/V0), a linear relationship was given. In approximate terms, the following was found: Fm1

V/V0%

18 9 4.5

50 75 90

(a)

(b) Figure 5.1 Fissuration index K in relation to in situ velocity for dry rock masses. Turk and Dearman, 1986, with andesite data from above the water table, from King et al., 1978.

One of the most thorough analyses of seismic refraction measurements in mostly hard, jointed rock environments was that given by Sjøgren et al., 1979 and Sjøgren, 1984. The authors’ experience from some 113 km of P-wave surveys (15 sites) and 5 km of S-wave surveys (5 sites) were compared with the results of 2.85 km of core from 74 drill holes at 8 of the hard rock sites. The range of rocks occurring at the measured locations, mostly in Norway, were: amphibolite, granite, gneiss, meta-anorthosite, pegmatite, porphyry, quartzite and mylonite. The authors were careful to emphasise that the correlations they derived between P-wave velocity and jointing descriptions such as mean RQD and mean frequency F(m1) were relevant only to unweathered igneous and metamorphic rocks, and generally for the upper 20 to

Relationships between rock quality, depth and seismic velocity

71

Figure 5.3 Mean values of physical and dynamic properties for hard, unweathered igneous and metamorphic rocks, based on shallow refraction seismics. Sjøgren et al., 1979.

Figure 5.2 Curve 1  joints per metre, curve 2  RQD, as a function of Vp, from shallow refraction seismic in hard, unweathered rocks, mostly from Norway. Sjøgren et al., 1979.

30 metres. They also emphasised the differences caused by weathering. Figure 5.2 shows mean numbers of cracks (joints) per metre (Fm) for a given velocity in more or less unweathered Scandinavian rocks. The general trend for mean RQD values versus velocity are also given for this ‘unweathered’ data set. Deviation from these average curves were reported to be about 1 crack/m at the higher velocities, and 1.5–2.0 cracks/m for the lower velocities. Corresponding dispersions of RQD values were 2–3% and 5–6% respectively. The 74 drill holes were as close as possible to, or on the seismic lines, and directed to be as perpendicular as possible to the tectonic structure or foliation. Fm1 values are therefore close to the maximum and RQD values

close to the minimum, when considering a line sample through the rock mass. The general joint frequency and RQD trends for these unweathered jointed rocks, including resulting dynamic moduli are summarised in Figure 5.3. (In this figure k  bulk modulus, and  shear modulus. This data is reproduced at larger scale in a subsequent comparison with Q-values.) Sjøgren et al., 1979, discussed various factors that could alter the proposed mean joint frequency and mean RQD versus Vp trends shown in Figures 5.2 and 5.3. They pointed out that the ‘natural’ velocity of the unjointed (or most massive) rock from site to site could vary due to rock type, mineralogy, etc. (One could also add to this list the inter-related technical terms: porosity, density and uniaxial compressive strength.) Besides these fundamental causes for variation, the effects of weathering and depth of measurement were obviously of particular influence. For this reason the authors addressed most of their attention and derived most of their data from the depth zone of up to 20 or 30 metres. When they conducted subsequent tunnel measurements, they found that a 30 to 50 m depth resulted in a general increase in velocity of about 5 to 15%, greatest for the lower velocity. When Vp was lower than 3 km/s they had observed ‘considerably greater’ increases with depth, and also a common reduction of the widths of the low velocity zones with increased depth (40 to 60% was quoted). In a later publication, Sjøgren, 1984, gave his earlier example of hard rock correlations between mean RQD, mean joint frequency per metre (Fm) and mean P-wave velocity (shown in Figure 5.2) with an additional curve 3 related to the mean trend of RQD in Permian and Triassic sandstones (Figure 5.4). Obviously these sets of measured data cannot all fit the simple relation of Deere et al., 1967, that (V F/V L)2
RQD/100.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 5.5 Data from Sjøgren and co-workers for Fm1 versus Vp for various rock conditions, with increased weathering effect and/or reduced strength, from right (#1) to left (#4). Palmström, 1996. Figure 5.4 Mean RQD and Fm1 as a function of Vp for the previous hard rock sites (curve 1  Fm1, curve 2  RQD), and for Permian and Triassic sandstones. Sjøgren, 1984.

The large reductions in velocity (1.5–2 km/s) are clearly a function of increased porosity (and density) and uniaxial strength (or deformation modulus E). When there is a tendency for weathering, or for matrix porosities higher than normal for hard rocks, then the same joint frequency will be recorded at lower seismic velocities. The four curves from Sjøgren and co-workers, shown in Figure 5.5 represent at the one extreme (curve No. 1) the same data as given in Figure 5.2 for hard, unweathered rocks at shallow depth. The degree of weathering increases, rock strength eventually reduces, and the matrix porosity increases while progressing from curve No. 1 to curve No. 4 in Figure 5.5. The data were assembled from Sjøgren and co-workers, and are derived from measurements in Scandinavia, in

the Andes and in Tanzania. In relation to empirical correlation possibilities, corrections for weathering, porosity and rock strength (or density) are probably needed to explain the range of data. Extensive fracture frequency and velocity data were presented by Niini and Manunen, 1970. The data in Figure 5.6 were derived from 55 vertical or steeply inclined holes drilled into the upper 15 metres of bedrock, along 100 km of seismic traces made for the 120 km long Helsinki water supply tunnel. The possible complication of increased stress, from tectonic causes or from 15 to 30 m of additional soil cover, has apparently meant that high fracture frequencies were recorded even when velocities were as high as 4.5 km/s. Possibly all fractures in the core, and the natural joints, were each included in ‘fractures/m’, since these numbers for Fm1 are significantly larger than the Sjøgren data sets. Fracture frequencies were unusually high (F  26/m for 0–5 m rock depth, F  21/m for 5–10 m rock depth) and seismic velocities were strongly affected as a result.

Relationships between rock quality, depth and seismic velocity

Figure 5.6 Joint frequency and velocity trends from the Helsinki water tunnel. Niini and Manunen, 1970. There appears the possibility that both joints and artificial fractures were counted, in view of the extremely high Fm1 magnitudes, for a given velocity.

73

Figure 5.7 The separation of velocities within fractured zones, and outside the fractured zones, from studies for the 100 km long Helsinki water tunnel. Niini and Manunen, 1970.

The authors gave the following ranges of results for intact rock samples obtained from 31 drillholes in the granites and from 2 drillholes in the mica gneisses.

Granites Mica gneisses

Vp (field) km/s

Vp (lab) km/s

Edyn (lab) GPa

3.4–5.3 3.8–5.2

5.8–5.5 5.5–5.8

61–82 85–96

An unusual set of data for fractured zone widths was also described by Niini and Manunen, 1970. Zone widths were shown in relation to velocities measured within the low velocity zones and also outside the zones. Figure 5.7 shows that fracture zone widths were larger, as one would expect, if the velocity outside the zone was also low. Narrowest zones tended to have lowest internal velocities, and highest external velocities. Developments in logging joint and fracture frequency effects using a downhole acoustic tool that could log in water-filled or dry boreholes were described by King et al., 1978. Figure 5.8a and b show good examples of the relationship between the larger scale downhole velocities and the laboratory velocities from a mining location in andesites and pegmatites. Laboratory conditions of humidity and stress (7 MPa) were matched to the mining stope conditions as far as possible. The data shown in Figure 5.8 can also be taken as a useful example of excavation disturbed zone (EDZ) and drainage effects, although since joint frequency also increases towards the mine opening, the combined effects of Fm1 and % saturation cannot be separated.

Figure 5.8 Examples of joint frequency effects on downhole acoustic log Vp values, with comparison to laboratory velocities under the same stress levels as in situ. King et al., 1978.

The highly fractured and altered zones were, of course, strongly correlated to velocity and amplitude reductions. The same authors also made some useful assessments of the effect of logged fracture (or joint) frequency (Fm1) on velocities in cored 60 m deep boreholes (Figure 5.8), and assembled other near-surface and underground data to investigate correlation of the squared velocity ratio (VF/VL)2 with joint frequency (Fm1). Care was taken to discount the drilling induced fractures. The authors gave the following correlation (see Figure 5.9).

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Rock quality, seismic velocity, attenuation and anisotropy

and Q-logs including a useful set from the Xiaolangdi multi-purpose hydroproject in China, where plate loading tests also provided ‘static’ deformation modulus measurements that showed broad correlation with the Q-values independently logged by the writer. Various hard rocks such as granites, gneisses, volcanic ignimbrite and competent sandstones were also tested in projects in Norway, England and Hong Kong, where first-hand information on Q-logging had been obtained. The proposed relationship, which was briefly introduced in Chapter 1, was as follows: Vp  3.5  log10 Q Figure 5.9 A collection of near-surface and underground data, showing velocity ratio squared (VF/VL)2 as a function of fracture frequency. King et al., 1978.

(VF /VL )2  0.96  0.036F

(5.3)

(Correlation coefficient  0.93)

5.2

Relationship between rock quality Q and Vp for hard jointed, near-surface rock masses

Due to the seismic ‘visibility’ of jointing in the upper 25 to 30 metres, Sjøgren et al., 1979, and Sjøgren, 1984, were able, as we have seen, to record significant correlations between Vp, RQD and joint frequency. Since their measurements were shallow, the effect of stress-induced joint closure was minimised. They also effectively removed other sets of variables by generally recording correlations for hard and almost unweathered igneous and metamorphic rocks. The variables of depth, porosity, uniaxial compressive strength and density were therefore largely removed. This has some advantages for what follows. A hard rock, near surface correlation of Vp and rock quality Q-value can also be derived on the same basis as above, if effects of porosity, uniaxial strength and depth are first ignored, as for the Sjøgren et al., 1979, data shown in Figures 5.2, 5.3 and 5.4. On the basis of the Norwegian Geotechnical Institute’s cross-hole seismic tomography measurements at the Gjøvik (62 m span) cavern site in Norway, shown in Chapter 4, and based on Q-logging of the same boreholes, a preliminary model for a Vp-Q-value relationship was developed by Barton, 1991. This was subsequently confirmed by analysis of several other seismic, cross-hole

(5.4)

This empirical relation is plotted in two different ways together with Sjøgren et al., 1979, trends for RQD and Fm1 (derived from Figure 5.2). Figures 5.10a and b show the result. When the rock quality Q-value is 1.0, midway between the extremes of 0.001 and 1000, Vp  3.5 km/s. The velocity changes by roughly 1 km/s (upwards or downwards) for each ten-fold change in rock quality Q-value. This model has now been tested on sites in several countries where rock quality Q-logging of core has been performed. The fit to measured data is quite good, provided that depths are shallow (i.e. down to 25 m, near the usual limit of shallow refraction seismic surveys performed where depth of weathering is relatively limited). A further necessary condition is that the rocks are non-porous and reasonably hard (i.e. typically with uniaxial strengths of 100 MPa or more). This model for hard rocks, and a modified one for soft porous rocks to be developed later, can be used for initial interpretation of seismic data. The table of data given in Figure 5.11, from Sjøgren et al., 1979, can also be expanded to include the Q-value scale, as shown at the bottom of this figure. As also noted in the figure, depth or stress effects, discussed in detail later, will mean that the Q-scale must be shifted more and more to the right in relation to Vp, as depth increases. The same of course will actually apply to the RQD and Fm1 scales. For the above reasons, the suggested correlations must be strictly applied to nearsurface seismic data (shallow refraction seismic or shallow boreholes) in hard, non-porous, largely unweathered rocks, but of course can apply to heavily fractured and sheared zones, (i.e., faults) containing clay. It is interesting to note the perceived inter-relationships between eight methods of rock mass classification using the Chinese descriptive classes ‘soft rock’, ‘hardpan’,

Relationships between rock quality, depth and seismic velocity

75

Figure 5.10 a) Mean RQD and Fm1 trends for hard, near-surface, low porosity rock masses, from Figure 5.2 Sjøgren et al., 1979, with an estimated extrapolation of the ‘extremes’ (dashed-lines), by the writer. The lower rock quality Q-scale, added by the writer, is also only relevant for hard, unweathered, low porosity, near-surface rock masses. b) Note rearrangement of Q-Vp relationship, with appended RQD and Fm1 data from Sjøgren et al., 1979, after Barton, 1995.

Figure 5.11 Mean RQD, Fm1, Vp and Edyn. data for hard, near-surface, low porosity rock masses, from Sjøgren et al., 1979. The rock quality Q-value scale was added by the writer. Note the need for a shift of the Q-scale to the right, with increasing depth.

‘normal soil’ etc. that was given by Chen, 1982, using the seismic velocity ranges as a reference. Approximate similarity to the empirical model (Vp
3.5  log Q) that was developed ten years later is indicated in Figure 5.12.

Comparison of rock quality Q-values logged in boreholes (or mapped at the surface) and seismic velocity measurements are not yet very common in the rock mechanics literature, though data is available at numerous

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 5.12 Inter-relationships between various rock mass classification schemes, Vp, RQD, and the rock quality Q-value. Chen, 1982.

sites. Chan, 1993, describes the engineering geological investigations performed for the purpose of optimising the location and orientation of a 24 metre span cavern to be used for refuse transfer, at Mount Davis in Hong Kong. General mapping of tuffaceous outcrops using the rock quality Q-system (70% Q  10, 25% Q  10 to 2, 5% Q  2 to 0.1) was supplemented by inclined drill holes and surface refraction seismic measurements. Figure 5.13 compares the results of core-logging (Q range 1 to 100) and an adjacent seismic profile, showing near-surface velocities of 4.5, 4.7 and 5.9 km/s at about 25 m depth. Velocities of only 1.1 and 3.2 km/s were recorded in a weakness zone. Based strictly on the simple Q–Vp relationship for low porosity, hard rocks at shallow depth (Vp
3.5  log10 Q), the following wide range of Q-values can be anticipated from the above velocities: Vp  5.9, Q
250 Vp  4.7, Q
16 Vp  4.5, Q
10 Vp  3.2, Q
0.5 Vp  1.1, Q
0.004

very good quality good quality good quality very poor quality exceptionally poor quality

These appear to be reasonable values for massive rock, good quality rock, and fault zones respectively. However, a basic problem with such comparisons is that the shallow refraction seismic is not penetrating to the same depths as the core-logging. The broad, low velocity

Figure 5.13 Comparison of refraction seismic velocities and corelogged rock quality Q-values at a cavern site in Hong Kong tuffs. Chan, 1993.

zone shown in Figure 5.13 is clearly quite complex at cavern level (50 to 70 m depth) since it has rock quality Q-values of less than 1 (two locations), and Q-values of about 10, 20 and 70 in other parts of the zone. The shallow seismic picks up Vp  1.1 (Q
0.004?) and Vp  3.2 (Q
0.5?) but not the higher quality slabs (?) of rock apparently existing at greater depth within the same fault zone.

Relationships between rock quality, depth and seismic velocity

5.3

Effects of depth or stress on acoustic joint closure, velocities and amplitudes

Bertracchi et al., 1966, gave some early Italian experiences of cross-hole and downhole sonic logging, and noted a consistent tendency for increased velocity with depth (usually 30 to 60 m/s increase per metre) in the depth range 5 to 25 m. However, related core logging results were not given. This increase in velocity gives an extreme gradient of 30 to 60 s1, which is about an order of magnitude greater than in the subsequent few hundred meters. Depth effects on seismic velocity were also reported by Cecil, 1971, from a survey of Swedish tunnels. Velocities at 50 to 60 m depth in high quality rock were up to 17% higher, while for low quality, heavily jointed rock they were up to 38% higher. By comparison Sjøgren et al., 1979, reported 5 to 15% increase at 30 to 50 m depth compared to that at the surface. In both the above cases the comparative rock qualities at the different depths are a factor of uncertainty. There are also cases in the literature where depth effects are, apparently, absent. Bertacchi and Sampaola, 1970, conducted repeated measurements of seismic velocity at four Italian dam sites, using a combination of downhole sonic logging and cross-hole measurements. The deepest measurements (to 100 m depth) were conducted at the 160 m high Alpe Gera dam, founded in serpentine with marked foliation. Measurements were repeated over a four-year period and showed invariance with time, and independence of reservoir storage level. In view of the dependence of Vp on effective stress, it is tempting to assume that the measurements were concentrated downstream of a successful grout curtain and effective drainage. Entirely different experiences are seen at other dam sites, as we shall see in a later chapter. An illustrative set of depth-related data, which nevertheless is inconclusive, is that given by Mouraz Miranda and Mello Mendes, 1987, in Figure 5.14. The objective was to explain the reducing rates of penetration and increased specific energy used when diamond core drilling and downhole hammer drilling in a 22 metre deep profile of weathered granites. Since all the indices of quality used were increasing with depth (i.e. hardness, RQD, density), it is inevitable that a very large increase in Vp (1.0 to 4.5 km/s) should have been registered. Hudson et al., 1980 (‘rock’ Hudson), demonstrated some fundamental effects concerning the influence of rock strength, joint spacing and depth (or stress) on seismic

77

velocity in a weak porous rock. This was due to some fortuitous circumstances at a test tunnel in chalk. Their studies were performed in an experimental machine-bored tunnel in the Lower Chalk at Chinnor in Oxfordshire, England, and also in the laboratory. All the studies were performed in chalk from above the water table, but with a natural water content of about 17 to 20% and a density of 2.2 gm/cm3. Firstly, Figure 5.15a shows the influence of intact strength on Vp values, using penetration tests at ch. 79 m in the tunnel. A similarly strong effect of joint or discontinuity spacing on Vp, from the same location in the tunnel is shown in Figure 5.15b. The most interesting result was the effect of stress level (or tunnel depth) on seismic velocity. Velocity increased from typical values of 1.1–1.3 km/s in the first 30 metres of tunnel, up to 1.5–1.6 km/s between 40 and 60 m inside the tunnel, where overburden had increased to some 15–20 m. This increase in Vp might appear to be as expected, but it actually occurred despite an increase in the frequency of joints and discontinuities in the chalk, as one progressed further into the tunnel (Figure 5.16). Often, Vp-depth data can be ambiguous because velocity increases occur at depth, due also to less frequent jointing. Here the two effects were, by unusually good fortune, separated. New and West, 1980 working on the same problems, also performed loading tests on artificially fractured or sawn interfaces for various rocks, and found that for several different surface roughnesses in the case of the chalk from the Chinnor Tunnel, a stress of about 0.4 MPa was required for ‘acoustic closure’ (Figure 5.17). Significantly, this stress also corresponded to the overburden stress where in situ Vp values had shown a certain flattening out. The maximum in situ Vp values of about 1.6 km/s (influenced by a fracture frequency as high as ten per meter), may be compared with Vp values for intact blocks of 1.95 km/s (range 1.6 to 2.2 km/s). Before leaving the Chinnor Tunnel, it may be of interest that Hudson, Jones and New, 1980, also mentioned very low P-wave velocities (0.6–1.0 km/s) for badly fractured areas of the chalk, and quoted permeability values of 106 to 104 m/s, or approximately 10–1000 Lugeons. According to a rule-of-thumb (L
1/Qc developed in Chapter 9), strength-normalized rock quality Qc -values might then be expected to range from about 0.1 to 0.001, in the absence of complications caused by clay sealing. This range of qualities (where Qc  Q  c/100) is broadly what might be expected from rock quality Q-logging in badly fractured areas of this weak rock, since if one assumes values of uniaxial compressive

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 5.14 Simultaneous increases in hardness, RQD, and density give a cumulative effect on Vp (450%) and drilling rate (75%). Mouraz Miranda and Mello Mendes, 1987.

strength (c) for the chalk from about 10 MPa down to 1 MPa (when weathered), the implied rock quality Q-values would be respectively 1 and 0.1, closely resembling ‘well-jointed’, and ‘heavily jointed and weathered’ rock, respectively. New and West, 1980, also discussed the question of stress level (or tunnel depth) on joint closure. They questioned the applicability of the Deere et al., 1967 relation (i.e., (Vp field/Vp lab)2
RQD/100: see beginning

of this chapter), since they argued that stress could ‘acoustically close’ joints, and joint frequency as expressed by RQD would then prove to have little effect on the velocity. Their experiments on artificial flat surfaces in contact, to simulate smooth joints in various rocks, show the approach of ‘acoustic closure’ at about 2 to 4 (?) MPa normal stress in Figure 5.17. However, these artificial surfaces were probably not responding quite in the usual non-linear manner, in terms of stress-closure, such as

Relationships between rock quality, depth and seismic velocity

Figure 5.15 Penetration strength and discontinuity spacing show a strong influence on the P-wave velocity for partly saturated, porous chalk from the Chinnor Tunnel. Hudson, Jones and New, 1980.

reported by Bandis et al., 1983, and they only represented the behaviour of ‘joints’ that were perpendicular to the principal stress. In Figure 5.18, New and West, 1980, show the insensitivity of Vp to joint frequency changes in a sandstone, as measured along the Kielder aqueduct tunnel, in northern England. However the principal joints were reportedly vertical only (i.e. one set that had responded to the effects of 100 m overburden and previous geological history, and were perhaps tight and closed). In a mudstone section of the same tunnel, calcite filled joints and some heavily jointed and faulted zones showed generally strong effects on velocity, as seen in Figure 5.19. In general, a rock mass with several joint sets is likely to show stress sensitivity to greater depth or stress level than the authors are implying, and if the rock is very weak and porous, volume changes will occur at greater stress giving velocity increases. In a rock like chalk marl, joints may close easily with moderate

79

Figure 5.16 Seismic measurements at the Chinnor Tunnel in England. Increase of overburden stress caused V p to increase (as expected), but this was despite an unusual increase in joint frequency with greater depth. ‘Absolute proof’ of a stress-related increase in Vp is evident from this case, since the matrix did not change. Hudson, Jones and New, 1980.

stress, as shown by the Chinnor experience, but large stress increases will inevitably ‘reactivate’ sensitivity to stress as compaction occurs. ‘Acoustic closure’ studies by Westerman et al., 1982, were based on artificially sawn, ground and then acidetched surfaces of a corallian limestone. Perhaps because of the partial ‘non-mating’ of the etched depressions in each surface they found that normal stress levels as high as 20 MPa were required to reach the seismic velocity (5.6 km/s) of the intact rock. The parabolic-type increase in velocity from 3.9 km/s was quite smooth, and corresponded to a reducing attenuation, the latter stabilising beyond normal stresses of about 10 MPa. The samples were dry as far as can be understood from the results obtained. The ratio of stress to strength, for example the ratio JCS/n used in the shear strength criterion of Barton and Choubey, 1977 may be useful for explaining so-called ‘acoustic closure’, since it is not only the stress level, or depth, but also the rock joint stiffness or strength that determines the contact area needed for the less attenuating

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 5.18 Insensitivity of Vp to vertical joint frequency in sandstone at the Kielder Tunnel, with 100 m overburden. New and West, 1980.

Figure 5.17 Vp increases for flat, dry artificial rock surfaces under normal stress. New and West, 1980.

seismic transmission across joints. The ratio of JCS (joint wall compression strength and n (effective normal stress) is closely related – or perhaps nearly identical – to the ratio of A1 (assumed contact area)/A0 (actual contact area). The ratio A0/A1 is very small for the case of hard unweathered rock joints near the surface, which continue to show velocity increase for many hundreds of metres, while A0/A1 is much larger for the case of a soft porous rock mass like chalk marl, which can show ‘acoustic closure’ at stresses as low as 0.4 MPa according to Hudson, Jones and New, 1980. Tanimoto and Ikeda, 1983, found that Vp was approximately proportional to the normal stress applied to simulated joints over the range 3 to 20 MPa, but that Vp dropped rapidly below stress levels of 3 MPa. A cut-off aperture of about 40 m separated their experimental results, with apparently no influence of Fm1 on Vp

Figure 5.19 Sensitivity of Vp to frequencies of calcite-filled joints in mudstone section of Kielder Tunnel. New and West, 1980.

below this aperture. The above effects and new experimental data are the main reason why Tanimoto and Kishida, 1994, and others are advocating the use of compression wave amplitude as a supplement to velocity data, for better sensitivity to jointing, particularly for the higher stress levels than those usually employed in shallow refraction seismic.

Relationships between rock quality, depth and seismic velocity

81

Figure 5.20 Tests on artificially fractured columns of marble, showing Vp and Vs as a function of normal stress, in the dry state. Stacey, 1977.

Laboratory tests using artificially jointed columns of marble that could be axially loaded and submerged in water were described by Stacey, 1977. These very interesting and instructive tests showed that the commonly used P-wave velocity was not the most sensitive parameter as regards rock quality. ‘Rock quality’ in this set of experiments was simulated by having 0, 1, 2 or up to 8 tension fractures distributed along the 0.46 m length of marble under dry or wet conditions, or with clay in the fractures. The basic P-wave and S-wave velocity responses to different levels of normal loading (0 to 7 MPa) in the dry state are shown in Figure 5.20. The number of fractures corresponds to F values (m1) of about 2, 6, 9, 13 and 17 per metre. The major increases in P-wave velocity (e.g., 2.8 to 4.4 km/s) occur in the first 2 MPa of normal loading, thereafter less rapid increases are seen, but the rise is consistent and nearly constant up to the maximum applied stress of 7 MPa. The number of fractures had much less influence on velocities at stresses above 2 to 3 MPa, in the dry state. Under zero stress levels the number of fractures had the greatest influence. When, by contrast, the tension fractures were wet and clay-coated, their number reportedly had ‘negligible’ effect on P-wave velocity.

Figure 5.21 Tests on artificially fractured columns of marble. a) S-wave frequency. b) relative P-wave amplitude. Stacey, 1977.

Stacey, 1977, went on to demonstrate that shear wave frequency was also very sensitive to the degree of joint closure caused by stress. Frequency increases from about 8 kHz to about 19 kHz were indicated for the case of well compressed, dry tension fractures, with less sensitivity in the case of wet conditions, or with wet clay fillings. These results are shown in Figure 5.21a.

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Rock quality, seismic velocity, attenuation and anisotropy

(There appears to be a possible link here to shear wave splitting, polarization and anisotropy interpretation, for the case of fractured reservoirs with gas or liquid saturation – see Chapters 13 and 15.) Furthermore, the compressional wave amplitude showed great sensitivity to both stress level and the frequency of the tension fractures, as demonstrated in Figure 5.21b. Compressional wave amplitude is of course an indicator of the level of attenuation, which was shown to be maximum in the case of unloaded, multiple-fracture models, and minimum for the case of well confined, single fractures. Attenuation is treated in detail in Part II, Chapter 10. A related though more comprehensive set of experiments was reported by Tanimoto and Ikeda, 1983, using numerous 50 mm diameter cylinders of various rocks (rhyolite, sandstone, granite, granodiorite and tuff ). The rock cylinders had five different lengths, making it possible to represent a ‘line sample’ through and imagined rock mass, with 0, 10, 20, 30 or 40 joints per metre. Filter paper, dry or saturated, was used to produce the desired ‘joint apertures’ and moisture contents. Figure 5.22 shows a schematic of the various ‘line samples’ created by cylinders of different length. In the case of the natural joint sample, both normal and shear load was applied. In Figure 5.23, the authors showed that the ratio k  Vp (jointed)/Vp (intact) was hardly influenced by the frequency or number of the types of ‘joints’. However, they qualified this by indicating that it was their apertures of less than 0.04 mm (or 40 m) that caused the frequency of fractures to have little influence on the P-wave velocity. In the context of numerous seismic surveys underground that they had included in their evaluations, they suggested that apertures were considerably wider than 40 m, therefore allowing fracture or joint frequency (Fm1) to influence the velocity ratio VJ/Vi as follows: Vjointed

 5   Vintact    F  4 

1

2

(5.5)

No reduction in P-wave velocity is predicted with 1 joint per meter, but with 5, 10 or 20 per meter, the ratio k is predicted to show successive reductions to 0.75, 0.6 and 0.5 (to the nearest decimal places). So a hard crystalline rock with Vintact of 5.5 km/s, might show reductions to 4,100, 3,300 and 2,500 km/s respectively. This appears inherently representative of experiences in fractured zones, at least in the near-surface.

Figure 5.22 Schematic of the multi-cylinder ‘line samples’, individual ‘filled-joints’ and a natural joint, that were studied by Tanimoto and Ikeda, 1983.

Figure 5.23 Joint frequency (n), velocity ratio (k), and amplitude ratio A/A0, indicating little influence of ‘joint’ frequency (or Fm1) on the P-wave velocities, but a strong influence on the amplitude ratio. Tanimoto and Ikeda, 1983.

One may perhaps conclude that heavily jointed rock masses have a degree of acoustic coupling that is not as complete as in the (aperture 40 m) laboratory experiments, due to variously oriented joints and lower

Relationships between rock quality, depth and seismic velocity

near-surface stresses, various rock-to-rock contact areas, and various ranges of weathering, mineral coatings and fillings. The contact area ratio A0/A1 referred to earlier in this chapter will obviously change completely in the presence of clay filling under high compressive stresses. As in the case of Stacey, 1977, Tanimoto and Ikeda, 1983 found that compressive wave amplitude gave a very sensitive measurement of the number of ‘joints’. The amplitude ratio A/A0 (A0 for intact rock) is shown in Figure 5.23 (open circles), and shows excellent sensitivity to number of ‘joints’. These authors also found that apertures less than 0.01 mm (10 ␮m) did not have influence on the wave propagation, even when the normal stress was as low as 1–2 MPa. Physical apertures (E) of this size (in contrast to hydraulic apertures (e) which are smaller due to roughness effects), are probably rare in the upper 20–30 metres of rock masses where refraction seismic is carried out, so this result is probably consistent with experience in the field. (One may speculate whether such a finding could have application in the interpretation of so-called ‘open’ fractures in petroleum reservoirs: would these need to be of greater aperture than this order-of-magnitude, before they could cause shear wave splitting?) A combination of permeability testing and index testing of the relevant joints (i.e. roughness JRC, and wall strength JCS) using the methods described by Barton et al., 1985, for converting between hydraulic and physical joint apertures would indicate the rough order of magnitude of the ‘necessary’ hydraulic apertures to satisfy this possible ‘rule-of-thumb’ that E must be 10 m, for having influence on wave propagation. A look ahead to Chapters 15 and 16 where joint properties are discussed in detail, would suggest that hydraulic apertures of about 10, 1.8 and 0.3 m might be operating with E  10 m, if joint roughnesses were respectively 2.5 (quite smooth and nearly planar), 5 (near-planar but some small undulations) and 10 (non-planar with marked inclined asperities). These latter would hardly be considered as ‘open’ joints, and in a reservoir situation are perhaps (as suggested by the Tanimoto and Ikeda, 1983 results) not capable of influencing seismic waves, nor, by implication, shear wave splitting. Tanimoto and Ikeda, 1983, also investigated the effect of larger apertures (or thicknesses of discontinuity fillings) using more sheets of filter paper to give a range of 1 to 3.4 mm thickness. There was strong sensitivity of Vp to stress level (0.3 to 3 MPa) and to the total cumulative joint aperture and moisture condition.

83

Fratta and Santamarina, 2002, also used columns of blocks under stress to demonstrate velocity-stress sensitivity. They studied the effects of varying thicknesses of kaolinite gouge materials, finding that shear wave velocity gave a very sensitive indication of the effect of gouge thickness at even lower stress levels, equivalent to about 1 to 10 m, typical of the weathered zone. For example at 0.25 MPa normal stress, equivalent to about 10 m depth, the conditions a) no gouge, b) 0.5–1 mm of gouge, c) 2.0 mm of gouge, d) 2.5 mm of gouge, gave S-wave velocities of about 850 m/s, 750 m/s, 600 m/s and 450 m/s respectively. The strongly non-linear (convex) Vs – normal stress curves, showed velocities ranging, respectively, as low as 450 to 250 m/s at an equivalent depth of only 1 meter. In hard rocks, such as the numerous cases reported by Sjøgren et al., 1979 and Sjøgren, 1984, there is a significant in situ correlation between Vp and joint frequency (and RQD), due presumably to the fact that this ‘cut-off aperture’ (whatever it may be in different rocks) has not been reached at the moderate (20–30 metres) penetration of shallow refraction seismic surveys. Tanimoto and Ikeda, 1983, found that Vp was proportional to n in the stress range 3–20 MPa, but dropped sharply for n  3 MPa. By chance, or similar physics, in the field case records used to design the empirical Vp–Q–M chart to be shown later (Barton, 1995), Vp and depth are also found to be linearly related from about 200 m to 1000 m depth (5 to 25 MPa), with Vp falling rapidly for depths in the range 25 m to 100 m, i.e., for n or v (or h) 2.5 MPa. 5.3.1

Compression wave amplitude sensitivities to jointing

One of the most thorough studies of the effect of joint parameters on seismic signatures was reported in a subsequent study by Tanimoto and Kishida, 1994 and Kishida, 1999, which was built on these earlier investigations of Tanimoto and Ikeda, 1983. The advantages of compressive wave amplitude compared to Vp for sensing joint frequencies at the higher stress levels was emphasised again, and convincingly demonstrated experimentally. The authors also compared (conventional) seismic velocity tomography (SVT) with seismic amplitude tomography (SAT). The latter reportedly corresponded more closely to jointing observed with a borehole scanner, as compared to the more frequently used (SVT). The studies were made in boreholes at a dam site, using an exploratory adit for further confirmation.

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Rock quality, seismic velocity, attenuation and anisotropy

The extensive laboratory studies reported by Tanimoto and Kishida, 1994, were based on cylindrical rock specimens, with a total of 86 cylinders representing sandstone, rhyolite, shale, granite, granite porphyry and slate. In the case of ‘joint samples’, natural joints were moulded and replicated with hard mortar or plaster, to reproduce the same roughness as in nature. Since the authors were very concerned about the correct measurement of roughness they utilised a non-contact laser scanner micrometer mounted on a 3D, movable stage roughness profiler. They show in Figure 5.24 a relationship between the joint roughness coefficient JRC (from Barton and Choubey, 1977) and ‘Ms’. The latter is derived from a power spectrum versus frequency relation analysed by the so-called ‘maximum entropy method’, which the authors selected in preference to the ‘fast Fourier transform’ method conventionally used. The inter-relationship between ‘Ms’ and JRC shown in Figure 5.24 is needed to interpret the effect of joint roughness variations used in their seismic velocity and seismic amplitude (A/A0 results shown collectively in Figure 5.25 and 5.26. Each horizontal pair of figures compares the sensitivity of Vp and amplitude ratio A/A0 to the following: 1. ‘joint’ frequency (25, 37.5 or 50 m1) and normal stress level (0 to 3 MPa) 2. ‘joint’ aperture (0, 1.05 or 2.10 mm) and normal stress level (0 to 3 MPa) 3. joint roughness (see Ms–JRC relation) and normal stress level (0 to 3 MPa) using joint replicas 4. shear displacement of joint replicas (0 to 7 mm) for three normal stresses (0.2 to 0.6 MPa) 5. dilation (0 to 1 mm) during joint shear at three normal stresses (0.2 to 0.6 MPa) for JRC
13 6. aperture change during normal loading of joint (JRC
8 to
13). These two figures demonstrate why shallow seismic refraction measurements which operate at low stress levels are successful in distinguishing joint frequency and aperture (achieved here with moist filter paper), but why amplitude measurements appear to be much more desirable than velocity measurements at higher stress levels, if joint frequencies and character are still to be distinguished. This emphasises the value of attenuation measurement, or of seismic Q. It reflects richly of the mechanisms involved with seismic detection of joints. Better ‘joint’ inter-locking from increased stress, or an absence of dilation and shear, gave increased

Figure 5.24 Correlation of the parameter Ms used by the authors, with JRC for the natural joints. Tanimoto and Kishida, 1994.

amplitude as expected, and the opposite occurred (loss of energy), in the case of shearing or joint dilation ‘post peak’. These comprehensive results leave one in no doubt about the potential advantages of amplitude measurement compared to velocity measurement. Even such details as joint roughness, which obviously also relates to acoustic coupling and contact area, demonstrates that amplitude measurement has clear sensitivity to the mechanics involved in the joint plane. The ratio A/A0 tends to get smaller (increased attenuation) as roughness increases, which fits with the picture of joint closure difficulties when joints are rough. (See extensive treatment of rock joint behaviour in Chapter 16). The above authors would probably be the first to agree that further studies with real joints would be an advantage, and of course that further field studies using velocity and amplitude tomography, together with comprehensive joint surveys, would be necessary for refining the interpretation of these useful techniques. Since SAT and SVT methods reportedly show good correspondence when filling materials and wider apertures are found (i.e., near surface), an understanding of the interrelationships can perhaps best be obtained in this low stress, weathered, or partly weathered zone, since wide ranges of both Vp and (A/A0) are seen, and the rock mass quality Q-value also varies strongly in this region. Some useful indicators about rock joint closure mechanics can also be obtained from a study reported by Nihei and Cook, 1992. They utilised a combination of acoustic emission (AE) monitoring and P- and S-wave monitoring of artificial tension fractures in sandstone.

Relationships between rock quality, depth and seismic velocity

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Figure 5.25 Parallel comparison (see a and b pairs) of Vp-monitoring, and amplitude ratio monitoring, of loading effects (0 to 3 MPa) with: top) varied ‘joint’ frequency, centre) varied ‘joint’ filling thickness, bottom) varied joint roughness for the natural joints. Tanimoto and Kishida, 1994.

These rough fractures were loaded to 24 MPa in mated and unmated conditions. As a result they produced widely different levels of acoustic emission (Figure 5.27), especially on the first cycle of loading.

The velocity-stress behaviour shown in Figure 5.28 indicated a consistent pattern of behaviour, with increased contact area at higher stress causing marked increases in both the P-wave and S-wave velocities. The

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 5.26 Parallel comparison (see a and b pairs) of Vp-monitoring, and amplitude ratio monitoring of a) shear displacement along a natural joint, b) dilation during shear, c) aperture changes with three joints of different roughness. Tanimoto and Kishida, 1994.

mated fracture more closely approached the intact sample in terms of velocity, showing rapid increases in Vp from about 2.8 km/s (at 2.5 MPa) to 3.4 km/s (at 10 MPa), and thereafter a slower increase of velocity. The unmated fracture showed nearly parallel behaviour,

but at velocities of about 0.2 km/s slower, both for Pwaves and S-waves. It is apparent that rough-walled rock joints with their typically high JRC values (often 15 to 20) are more difficult to close acoustically, so rough joints in

Relationships between rock quality, depth and seismic velocity

87

Figure 5.27 a) Stress-deformation cycles comparing intact, mated, and unmated tension fractures. b) The number of acoustic emission events associated with loading the mated and unmated fractures to 24 MPa. Nihei and Cook, 1992.

Figure 5.28 A comparison of P-wave and S-wave velocities when loading the intact, mated and unmated samples from about 2.5 to 25 MPa. Strong stress sensitivity is shown, due particularly to the dry state. Nihei and Cook, 1992.

hard rocks could be seismically ‘visible’ to significant depths (e.g., 10 MPa or more, corresponding to several hundreds of metres overburden). There are however other factors involved, such as mechanical over-closure, and thermal over-closure, (Barton, 2004), which would give tighter apertures than ‘expected’ from the present depth of burial or exposure. (See Chapter 16). The above closure aspects would contrast with the evidence from some of the experimental work on flat surfaces in weak rock reviewed earlier, for example that of New and West, 1980, which would suggest much lower levels of stress sensitivity in the case of smoother rock joints, except when closer to the surface.

In massive granite at the Underground Research Laboratory (URL) in Manitoba, Canada, micro-seismic EDZ and stress-induced failure sensing reported by Talebi and Young, 1992, showed P-wave velocities ranging from 5.6 to 5.9 km/s, and S-wave velocities ranging from 3.3 to 3.4 km/s for the depth range 310 to 400 metres (approximately) down the 4.6 m diameter shaft. (The ratio of Vp(mean)/Vs(mean) was exactly 1.70 in this massive granite.) Velocities increased by about 0.1 km/s for every 30 m increase in depth, (gradient  3.3 s1), based on the 1 m deep measurements using numerous shallow boreholes drilled into the walls of the shaft. If stressinduced fracturing had been involved, a linkage

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Rock quality, seismic velocity, attenuation and anisotropy

between increased depth and increased velocity would be less certain, as dilation and reduced velocity might equally well occur, with such shallow holes. (Core recovered from different depths at URL showed reduced compressive strength and modulus with increased sampling depth, due to increases in stress-induced microcracking.) 5.3.2

Stress and velocity coupling at the Gjøvik Cavern site

The foregoing review of depth and stress effects on P and S-wave velocities measured across loaded joint assemblies, or at tunnel sites in natural settings, can be concluded by a brief review of the stress effects on velocities that were documented at the Gjøvik Olympic cavern site in Norway. Figure 5.29 is a reminder of some of the cross-hole seismic tomography discussed in Chapter 4. Figure 5.30a shows the stress measurement results at the cavern site, based on hydraulic fracturing and hydraulic jacking of existing joints, performed by Tunbridge, of NGI. Both h min and the estimated H max show rather high values, many times greater than the calculated vertical stress gradient. The jointed gneiss at the site had steeply dipping conjugate jointing with up to four joint sets, but fortunately these were joints with significant roughness and undulation. Based on the evidence shown in the velocity tomograms (Figure 5.29 and other tomograms from Chapter 4), a maximum velocity rise of some 2 km/s (3.5 to 5.5 km/s) occurred in the depth range 10 to 60 metres, over which range, horizontal stresses may have increased by 2 MPa to 4 MPa, depending on direction relative to H max and h min (Figure 5.30a). The above rise of velocity occurred in a rock mass with a typical Q-value of about 8 to 10, with a joint frequency that ranges from about 3 to 10 per metre, and an RQD that ranges from about 60 to 100%. There is no evidence from the four core logs of consistently increasing rock quality with depth, so the velocity increase of nearly 2 km/s occurred mostly as a presumed result of the increase in horizontal stress. The gneissic rock mass at the site was generally saturated to within a few metres of the surface, and Lugeon-type permeability tests in the four investigation boreholes indicated values in the range 1 to 0.01 Lugeons, mostly 0.1. An inversion of the median Lugeon value is close to the mean Q-value, the significance of which will be clarified in Chapter 9.

Figure 5.29 Cross-hole seismic tomography at the Gjøvik cavern site, showing strong increases in velocity with depth, actually caused most by high horizontal stress levels (3 to 6 MPa) in the upper 50 meters. There were velocity-depth gradients as high as 80 s1 in the upper 20 m, and as high as 40 s1 over the first 50 m. Remarkably, the rock quality parameters: RQD, Fm1 and Q, did not improve beyond about 5 m depth. Barton et al., 1994.

5.4

Observations of effective stress effects on velocities

Dam construction represents a significant local source of rock mass loading, in which the total vertical stress initially is increased without necessarily changing the pore pressure, since the reservoir takes time to fill. When grouting of the foundations is very thorough, this assumption is of course suspect and a more complicated picture may arise. When reservoir impounding begins there are likely to be significant reductions in effective stress near the dam, and fluctuations of the latter, usually on a seasonal basis. Savich et al., 1983 noted the above effects when the 270 m high Inguri arch dam was being constructed. A

Relationships between rock quality, depth and seismic velocity

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(a)

(a)

(b) Figure 5.30 a) Hydraulic fracturing based stress estimation at Gjøvik. b) Velocity depth trend next to one of the boreholes where seismic tomography was performed. RQD and Fm1 (and also Q-value) did not show improvement with depth. Kristiansen, 1991 pers. comm., Barton et al., 1994. (b)

sharp change in deformation was noted when impounding of water began. Significantly, Vp values reduced (Vs values also reduced), and there was a reduction in resistivity, each implying reduced effective stresses due to the rise of joint water pressures in spite of the grouting and drainage measures. The most intensive reductions in Vp occurred during periods of water level rise, with weaker reductions, when the water level was constant. Interestingly, the ‘conventional’ effective stress type linkage with Vp was modified, and radically changed in subsequent long term monitoring. Savitch et al., 1987 gave updated and longer term syntheses of the Inguri dam response, following another

Figure 5.31 Vp distribution in Inguri dam abutment, and records of Vp changes with construction, reservoir filling and seasonal fluctuations. Savich et al., 1987.

four years of performance monitoring, since their last referred article (Savitch et al., 1983). Figure 5.31a shows the deeply penetrating lower velocity contours in the left abutment and a joint pole concentration plot. Figure 5.31b shows the complex coupling of Vp and reservoir level response, with predominant gradients showing Vp increasing with reservoir level (H). A nine-year record of Vp, percentage change of Vp, dam load and reservoir level fluctuation shown in Figure 5.32b

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Rock quality, seismic velocity, attenuation and anisotropy

confirms the general, but slightly delayed increase in Vp with reservoir level, following the initial reduction in Vp which appeared to be effective stress related. A more detailed look at Vp–H response, with smoothed-out behavioural trends (Figure 5.32b) shows a small delay. Savitch et al., 1987 interpret the near-synchronous behaviour (after first reservoir filling) as closure of joints or cracks due to the reservoir load on the dam. However, at higher pressures perhaps a widening of large cracks occurs. Reservoir draw-down rate appears to be important since if the draw-down rate exceeds the ‘permeability velocity’, a sharp decrease in Vp occurs, corresponding to the classic effective stress model. Before leaving this chapter on effective stress-depth effects, we will review an interesting set of cases presented by Moos and Zoback, 1983. Seismic velocity measurements in four wells to roughly 1 km depth, can serve as a bridge to the much deeper seismic velocity-depth profiles that are given in Chapter 11. Four wells, varying in depth from 0.6 to 1.2 km were surveyed with borehole televiewer, and sonic logged, which involved measuring vertical travel times over a 1.2 to 1.5 m interval. One of the wells (the Crystallaire well, termed XTLR, was drilled 4 km from the San Andreas fault, in crystalline rocks, in the Mojave Desert area. This well was the subject of three separate seismic investigations using sonic logging (from below the water table), vertical seismic profiling (VSP) using an air gun source, and nearby seismic refraction. The three different frequencies were respectively 2 MHz, 75 Hz and 10 Hz, and these meant three fundamentally different wave lengths in relation to the fractures. Wave lengths were respectively 20 to 60 cm (i.e. similar to the fracture spacing), 60 m (using a 30 m geophone interval) and several hundreds of metres. In addition, laboratory samples were taken at intervals down the core, and were subjected to appropriate confining pressures, based on an assumed effective stress gradient of 16.7 MPa/km, designed to correspond to the effective overburden stress. These four sets of data are compared in Figure 5.33. The majority of the fractures (or joint sets) were steeply dipping. Overall there was remarkable agreement between the three in situ methods, but the ultrasonic measurements on the intact cores gave significantly higher velocities; about 2 km/s higher at shallow depth and about 1 km/s higher at intermediate depths. There was a relatively high degree of fracturing in this well, as shown in Figure 5.34, which also shows the detailed sonic log, and its ‘divergency’ from the lab (intact) data, as the surface is approached.

(a)

(b)

Figure 5.32 Ten years of recording P-wave velocity and reservoir fluctuations at Inguri dam. Top) Ultrasonic, borehole P-wave velocity fluctuations, ‘relative velocities’, and reservoir levels, including filling. Bottom) Seismic Pwave velocity fluctuations show slight ‘inertial delay’ relative to the seasonal reservoir fluctuations. Savich et al., 1987.

Another well reported by Moos and Zoback, 1983, showed reduced depth-dependent velocities in relation to the above, due to the somewhat lower fracture frequency. This was the MONT-1well, from the Monticello reservoir in South Carolina, USA, drilled through granodiorites. Joint or fracture frequencies and P-wave velocities are shown together with Vs and Vp/Vs ratios in Figure 5.35. The solid circles representing the ultrasonic tests on the laboratory samples were in this case very close to the in situ sonic-log data for this sparsely fractured well. These two contrasting wells showed increases of average Vp from about 3.5 to 5.2 km/s (XTLR, Fm1  1 to 4) and 5.4 to 6.1 km/s (MONT-1, Fm1  1 to 2), over the respective 100 to 850 m and 50 to 1100 m depth ranges. Naturally, almost every fracture zone (or joint swarm) was a zone of low velocity.

Relationships between rock quality, depth and seismic velocity

Figure 5.33 Comparison of velocity-depth trends obtained from three different frequencies of field measurement (smoothed sonic log, VSP, refraction seismic) with ultrasonic tests on intact laboratory samples, tested at appropriately increasing effective confining stress levels. XTLR well in crystalline rocks, 4 km from San Andreas fault zone. Moos and Zoback, 1983.

Besides the description of joint frequency, there was relatively little information in Moos and Zoback’s interesting article from which to judge the number of joint sets or the joint character. However, an attempt can be made to match these quite different velocity-depth gradients with a deconvoluted version of Figure 5.36. This is shown in Figure 5.37, and will be explained shortly.

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Figure 5.34 Details of joint frequencies in the XTLR well, showing generally small variations with depth except in upper and lower 50 m, together with the generally increasing trend of the sonic log velocities with depth. Moos and Zoback, 1983.

The average velocity-depth gradients shown in Figures 5.33 (XTLR well) and in Figure 5.35 (MONT-1 well) are as follows:  Vp  5.2  3.5  XTLR    2.3 s1   depth  0.75 mean  Vp  6.1  5.4  MONT  1    0.7 s1  depth  1.05 mean

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Two other wells reported by Moos and Zoback, 1983, showed little, or in one case reversed (negative Vp/depth gradient) due to the increasing frequency of fractures from about 350 to 600 m in the well. Velocities in the top 200 m averaged about 5.5 km/s. When little Vp-depth sensitivity is shown, it suggests few fractures. In fact the range of average Vp for a well named MONT-2 was as high as 5.9 to 6.1 km/s despite medium fracture density. This suggests (in Q-value terms) that there might have been only one set of joints, giving a high Q-value, and further that the joints and rock had characteristics allowing for stiff, possibly smooth-walled apertures.

5.5

Figure 5.35 Velocity-depth trends were less marked in the MONT-1 well, in less jointed granodiorites, where laboratory sample velocities were also close to the field result. Moos and Zoback, 1983.

Integration of velocity, rock mass quality, porosity, stress, strength, deformability

It has been shown in previous sections how the P-wave velocity is sensitive to each of the factors listed in the above sub-title. To this we must also add moisture content (for the matrix) and ground water level (for the rock mass). The assumption will be made in the following development that seismic velocity measurements will most frequently be made in saturated rock masses. The

Figure 5.36 Integration of rock quality Q-Vp-Emass in a model that incorporates depth, porosity and rock strength adjustments. Note that Emass (or M) represents the static modulus of deformation, from plate loading tests and from back-analysis of measured deformations. Vp is the seismic velocity measured from refraction seismic, and from cross-hole seismic tomography, in the case of greater depths. Barton, 1995.

Relationships between rock quality, depth and seismic velocity

correlations developed will be based on this assumption, and systematic errors will of course arise if drainage causes drying out of the matrix and/or joint water. Since velocity–rock quality correlation is a complex task, no hesitation must be made in adding some degrees of sophistication to the simple model Vp  3.5  log10Q proposed earlier (Figure 5.10). Avoidance of mathematics suggests the use of a graphic method for converting the formulation for hard, unweathered, lowporosity, near-surface rock masses (i.e. typical Sjøgren et al., 1979, data) to conditions towards the other end of the seismic and rock quality scale, e.g., low strength, weathered, high porosity, highly stressed (or unstressed) rock masses. The development shown in Figure 5.36 which was introduced by Barton 1995 and 1996a, has opposing corrections for porosity and depth (i.e. stress) since these cause opposing influences on velocity. In addition, an adjustment for uniaxial compression strengths different from a typical hard rock 100 MPa (or more) is made by the following simple normalisation of the rock quality Q-value:

Qc  Q 

c (c expressed in MPa) 100

(5.6)

93

This correction is necessary because the rock quality Q-value was originally developed in 1974, for correlation with tunnel and cavern rock reinforcement and support needs (i.e. rock bolts and sprayed concrete, respectively). The rock quality Q-value only uses the ratio strength/stress (c/1 in the SRF factor – see Appendix A), when major principal stress levels (and their concentration as maximum tangential stress  31 – 3) are causing stress-related fracturing. It is probable that in a tunnel excavation disturbed zone (EDZ), the potentially large values of SRF (that reduce the Q-value directly) can also be used in principal to predict the measured reductions in velocity and deformation modulus that are typically recorded in the walls of deep shafts and tunnels (e.g. Barton and Bakhtar, 1983 who back-calculated moduli of 3.5 GPa in the outer 3 m, or one radius, of a 1,600 m deep shaft in steeply bedded, highly stressed, jointed quartzites, compared to 65 GPa at a depth of two shaft diameters, using multiple position borehole extensometers, or MPBX). In highly stressed cases, c will tend to be high for hard massive rocks subject to dynamic and sometimes explosive stress-slabbing, and c will be low for soft rocks that are subject to a slower, ‘plastic-deformation’ type of squeezing. In equation 5.6, c/100 corrects the

Figure 5.37 Conversion of the Barton, 1995 rock quality Qc-Vp model of Fig. 5.36, into a more familiar velocity-depth format. Note that there will be a tendency for ‘curve-jumping’ (i.e. ‘Q-jumping’), as a near-surface rock quality improves at greater depth. This will be due to the reduced effects of weathering, and due to a tendency for reduced jointing frequency. Note the contrasting directions of the ‘N’ and ‘J’ arrows shown in the figure, together with the s1 (km/s/km or m/s/m) gradients.

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Rock quality, seismic velocity, attenuation and anisotropy

Q-value to an approximately suitable value of Q c to correlate more closely with the rock mass static deformation modulus (M, or Emass) and with the seismic velocity Vp, particularly for the case of softer rocks. The ‘opposed corrections’ given by the two sets of diagonal lines in Figure 5.36 are designed to do the following: 1. A strongly non-linear initial correction for depth gives greater sensitivity to ‘acoustic joint closure’ for weaker and lower quality rock masses. 2. A weakly non-linear porosity correction also gives larger changes of velocity for the weakest rocks. The chart, which should be considered as an approximate engineering guideline, was developed with the hard rock (Vp  3.5  log10Q) relationship (Figure 5.10) as a ‘core’ (see diagonally-aligned black discs in Figure 5.36). Development for soft rocks occurred by a process of trial-and-error fitting of Q, Vp, c, n and depth data from known sites in jointed chalks, (Saul Denekamp, personal communication), jointed chalk marl from the UK end of the Channel Tunnel, sandstones, mudstones, shales, welded tuff and ignimbrite. Data from Israel, England, Japan and China were included. Depths ranged from about 25 meters to more than 1000 metres in the case of tuff/ignimbrite from UK Nirex’s Sellafield site, where cross-hole tomography and laboratory tests could be compared with NGI’s detailed rock quality Q-logging (and joint index testing) of 9 km of drill core (see Chapter 4). The first two empirical relationships listed in the top of Figure 5.36 were derived from extensive field test data for hard rocks (Barton, 1996). Testing with soft rocks has shown that the modified Qc term gives satisfactory fit, which is improved when the porosity and depth corrections are also made. Thus we have the following approximations for general use. Note that both Vp and deformation modulus (M or Emass) are predicted to increase with depth (see detailed discussion in Barton, 2002a). Vp  log10 Q c  3.5 (km/s)

(5.7)

M(mean)  10Q c1 3 (GPa)

(5.8)

Although there is little data for deformation modulus measurement at ‘undisturbed’ depths of hundreds of metres, it will be noted that the predicted static moduli

(Figure 5.36, right-hand column) become closer to seismically derived dynamic E moduli (from Vp, Vs and density, see Chapter 1). If truly undisturbed static modulus testing could be achieved, the normal discrepancy between static deformation modulus and dynamic E modulus might be lessened, despite the fundamentally different levels of strain involved in each case. An illustration of application of the Q–Vp–M method to very soft rocks can be given here, based on Q-logging of tunnels in chalk marl (Terlingham Tunnel, Beaumont Tunnel, and UK sector Channel Tunnels, and selected marine drill core: PB1 to PB8). Details of the rock quality Q-logging are given by Barton and Warren, 1996c. A weighted mean value of Q  8 was obtained from the so-called ‘precedent study’ of nearby tunnels in chalk marl, and from marine drillcore. This Q-value was found to compare closely with the overall mean Q-value recorded in the contractor-owner (Trans Manche Link – EuroTunnel) TBM face logs from the 20–24 km subsea chainage near the English south coast, where an overall mean value of Q  9 was obtained from the three machine bored tunnels. In this zone, significant tunnelling problems were caused by the (salt) water leakage and overbreak, hindering PC-element ring-building, and causing problems with electrical equipment on the TBM. The mean c value for the chalk marl was 6 MPa. Thus from equation 5.6 we have: Q  8, c  6 MPa, Q c  8 

6  0.48 100

This Qc value intersects the central diagonal line (equation 5.7) in Figure 5.36 at Vp  3.2 km/s. Correction for average porosity (n  27.7%) results in a reduction of 1.6 km/s giving 3.2–1.6  1.6 km/s. Tunnel depths of, for example 40 m, bring this value up to about 2.0 or 2.1 km/s. Offshore geophysics carried out during several campaigns indicated P-wave velocities generally in the range 2.0 to 2.6 km/s for the UK chalk marl. A Q-value of about 20 is needed to explain the upper velocity of 2.6 km/s using the above method. This is in line with the otherwise generally good rock mass Q-values, registered outside the 4 km zone with much overbreak. The predicted moduli of M
0.5 GPa (minimum) and 3 GPa (mean) compare with (disturbed) but unjointed laboratory scale moduli of 0.64 GPa (mean) and a range of 0.15 to 4.2 GPa. Deformation measurements

Relationships between rock quality, depth and seismic velocity

in the tunnels were interpreted as indicating an in situ modulus of about 1 to 2.5 GPa for a range of rock qualities, quite consistent with the above. The correction Q c  Q  c/100 can also be applied in the direction of very hard rock, to adjust the value of Q c above that of the logged Q-value. As we shall see in Chapter 7 on EDZ phenomena, this gives a useful hard rock correlation between measured velocities and observed Q-values from greater depths. We will examine predicted and measured velocities and moduli from greater depths in Chapter 7. The sloping lines for depth adjustments that are shown in Figure 5.36 can be converted to velocity-depth gradients, with a format more familiar to geophysicists, as shown in Figure 5.37. Here one may note the marked linearity at depths beyond the first 250 m, and the marked non-linearity in the upper 100 m in particular. With awareness of the different velocity scales, we can compare the velocity-depth trends of the XTLR well near the San Andreas fault (Figure 5.34) with the overall gradients of a rock mass quality of Qc  0.1 in Figure 5.37. This suggests a well tectonised rock mass with several joint sets, and possibly with clay coatings and smooth or slickensided joints. Unfortunately, the detailed condition of core seems seldom to be described in published articles, so whether this ‘picture’ is realistic is uncertain. At the extreme end of the rock mass quality spectrum, one may refer to the seismic studies of a several

95

million cubic meter post-glacial landslide, at Koefels in Austria, which covers a valley over an area of some 10 km2. Brueckl and Parotidis, 2001, found that the landslide mass could be approximated by a Vp-depth model which we can simplify to Vp
400D0.32 m/s. So at 50 m, 100 m, 200 m and 300 m (the average depth), the velocities would, in round figures be approximately as low as 1,400, 1,750, 2,300 and 2,500 m/s, compared to a bedrock of 5.2 km/s. As a first approximation one might view the Qc -Vp – depth model of Figure 5.37 and consider a faultedcrushed-rock Q-value of 0.01, which would reduce to a Q c – estimate of 0.001 if weakened rock of say, 10 MPa uniaxial strength was involved. The relevant Vp – depth curve gives a certain geometric similarity to the above velocity increases down to 300 m depth, but needs a minor ‘parallel shift’ to somewhat lower values. Such could be ‘achieved’ by a) a minor downwards adjustment of velocity, due to a porosity correction (Vp) for slightly altered rock, or b) by a larger downwards adjustment due to the larger mass porosity of the failed materials, e.g. 20%, but then necessarily from a higher Q c value as a starting point. Detective work, preferably aided by local knowledge of the site, may result in improved insight, where a hint concerning the deformation modulus of the slide masses (about 5 GPa) might also need to be used.

6

Deformation moduli and seismic velocities

Although it was not the original intention in this book to explore in detail the ‘static’ deformability of rock masses, a superficial treatment is necessary, in view of the common use of seismic measurements to extrapolate nearsurface deformation or elastic modulus measurements. We saw in the last chapter how the loading of individual joints, or of multiple jointed columns of rock in the laboratory created changes in the P-wave and S-wave velocities and amplitudes. Detailed monitoring of in situ loading tests using sonic logging in boreholes beneath plate loading tests, such as shown in Chapter 3 (Figure 3.15), also shows correlation with the moduli obtained. However, due to the inevitable damage in the unloaded zone around the sites of the tests, the lowest moduli (and lowest velocities) are usually registered closest to the loading plates, flatjacks or pressure chambers, while higher velocities and moduli are registered at greater depth. This is probably due to the more uniform stresses outside the excavation disturbed zone, or EDZ, where shear stresses are less due to the radial stress (r) being higher. There is increasing discrepancy between dynamic and ‘static’ deformation moduli in the near-surface, low quality, weathered zone, that may unfortunately need to be used as a dam or large building foundation. In this chapter there will be detailed treatment and examples of the multitude of ‘moduli’ that have proliferated with the combined use of loading (and unloading) ‘static’ moduli, and the attempts to extrapolate or compare these with the ‘dynamic’ moduli, both from laboratory samples and in situ measurement.

the foundation using larger scale cross-hole, betweengallery, or VSP (hole to surface or tunnel perimeter) velocity measurements. Classic examples of this were shown in Figure 4.1 and 4.2. A useful basic comparison between the ‘static’ modulus of deformation Ed (or M in Figure 5.36) and the so-called modulus of elasticity (Ee) is shown in Figure 6.1. The modulus of elasticity (Ee) is traditionally obtained from the gradient of the unloading curves, which are often similar, and supposedly have elastic character due to the frequent closed state of the stress-deformation loops. These results were given in the 1st ISRM Congress by Kujundzíc and Grujíc, 1966. Three of their figures are reproduced in Figure 6.1. The total deformation measured at the highest load level, after several loading cycles, is the usual basis for the calculation of Ed (Figure 6.1a). Thus defined, Ed may change with stress level, while Ee is considered a constant. Partly for this reason, the inequality Ee  Ed can be quite large, as it depends also on the stress level, which in turn is usually based on the size and type of dam (or other structure) to be located on the particular rock foundation. The basic inequality of Ed and Ee is clearly shown in Figure 6.1b and c. Kujundzíc and Grujíc, 1966, assembled most of their data from tests on limestone foundations at Yugoslavian dam sites carried out in the 1950s and 1960s. As can be seen from the data, the largest inequalities (ratios of 1.5 to 2.5) are seen at the lowest moduli values (5 GPa). The values of Ee and Ed followed approximately the following trend:

6.1

Ee


Correlating Vp with the ‘static’ moduli from deformation tests

The method that is perhaps most common for relating seismic velocity and in situ modulus measurements, is what we may call the seismic characterisation method. The rock mass at, or beneath, the site of a deformability test is logged by downhole, cross-hole or shallow refraction seismic. On the basis of the local Vp value the measured moduli are extrapolated (or interpolated) to other parts of

15.50 Ed 6.45  Ed

(6.1)

where Ee and Ed are expressed in GPa. Let us look at two examples to illustrate the trends of Ee  Ed, with differences reducing when higher quality rock masses are involved. Assuming Ed of 5 and 50 GPa, we see from equation 6.1 that the elastic moduli are predicted to be 8.9 and 57.3 GPa.

98

Rock quality, seismic velocity, attenuation and anisotropy

(a)

Note that these larger differences with Ee  Ed at lower qualities, are largely caused by an increasing hysteresis in the load-unload behaviour of the individual rock joints, as rock mass quality deteriorates, typically due to weathering and unloading effects near the surface. In Chapter 16 we will also see the different shapes of these rock mass loading curves caused by predominance of joint closure (concave type) over shear (convex type). A combination of both components may give a semblance of ‘linearity’. (Barton, 1986). (The above inequality Ee  Ed is in the ‘static’ loading, ultra-low-frequency sphere of geophysics. This behaviour is not directly related to another key inequality in geophysics, namely that the (static) joint stiffnesses become less than the inverse of the (dynamic) joint compliances, as rock mass quality deteriorates. These aspects are discussed in Chapters 15 and 16 in relation to shear-wave splitting). Grujíc, 1974, also reported results of Vp measurements in the galleries at a Yugoslavian dam site, as shown in Figure 6.2. The ability to use Vp measurements to extrapolate flatjack or plate loading test results is obviously an important part of the economy and thoroughness of major foundation studies. In most cases, working hypotheses are established that relate deformation moduli with the seismic velocities. In the case of the Mratinje dam on limestone foundations, Grujíc found the following relationship: Ed  9.1  4.8 (Vp  3.6) GPa

(b)

(c) Figure 6.1 Definition of Ed and Ee, and examples of their differences, from limestone dam foundations in Yugoslavia. Kujundzíc and Grujíc, 1966.

(6.2)

With Vp  4.5 km/s, (an implied nominal 25 m depth rock quality Qc  10), this equation suggests a static deformation modulus Ed of 13.4 GPa. This is midway between the minimum and mean M-values shown in Figure 5.36. The tendency for ‘disturbed zone’, nearvalley-side reductions in Vp and presumed reductions in Ed (or M) can be seen in Figure 6.2. The basis for the above correlation between Vp and Ed, were the so-called polar measurements of Vp surrounding the flatjack (and therefore loaded) locations. These are illustrated in plan and in vertical section, in Figure 6.3. The upper line in Figure 6.3c shows Ee (E), and the lower line shows Ed (D), and their correlations with velocity. These obviously relate to velocities of the flatjack-loaded rock mass, giving a range of Vp, together with rock quality variations, from 1.5 to 5.5 km/s. The rocks involved were variously jointed and weathered Triassic limestones. A very thorough review of inter-relationships between seismic velocity measurements and E-moduli and

Deformation moduli and seismic velocities

99

Figure 6.2 Example of Vp measurements in exploration galleries at a dam site in Yugoslavia. These are used to economically extrapolate deformation modulus test results to other parts of the dam foundation. Grujíc, 1974.

(a)

(b)

(c)

Figure 6.3 Flatjack deformation tests for determining the moduli D(or Ed), and E (or Ee), and correlation with velocity in the Triassic limestones. Grujíc, 1974.

D-moduli obtained from plate loading tests in Italy was given by Ribacchi, 1988. These are shown in Figure 6.4. The particular emphasis of this review article was rock mass deformability, and complexities caused by

anisotropy, which the author nevertheless concluded, was greatest with samples that had been recovered for laboratory tests. The results of in situ investigations at eleven sites were given. These involved several varieties

100

Rock quality, seismic velocity, attenuation and anisotropy

Ee GPa

(a)

Ed GPa

(b)

Ee GPa

(c)

Ed GPa

(d)

Figure 6.4 a,b) Results of in situ deformation tests at eleven sites, showing Ee and Ed correlated with Vp2. c,d) Mean data from each site shows reduced scatter. Note dynamic Poisson’s ratio gradients Ribacchi, 1988.

of limestones, schists, gneisses, granodiorites, mylonites, dolomite, a high porosity (n  30%) calcarenite, and inter-bedded sandstones and mudstones. Both the plate loading tests and the seismic velocity measurements were

conducted perpendicular and parallel to layering, bedding, or schistocity, as appropriate. The author cited examples of sites that showed good correlation between modulus and typical indices

Deformation moduli and seismic velocities

101

of jointing (RQD, and joint frequency Fm1). The scatter of more than 100 data points for modulus E or D versus V2p in Figure 6.4 is quite large for the whole sample, but reportedly showed good correlation for limestones and dolomites. Figures 6.4a and b show all data points for Ee and Ed, while somewhat reduced scatter for the mean data at each site is shown in Figures 6.4c and d. Ribacchi’s data from a limestone and dolomite site are shown in Figures 6.5a and b. Here, modulus is plotted on a log scale, and velocity is not squared as above, thereby showing much narrower scatter. Trend lines for these and other limestones (Yugoslavian) are shown in Figure 6.6. The deformation moduli M(mean) and M(min.) tabulated in the inset to Figure 5.36 (in Chapter 5) are also encompassed by the above trend lines. The loglinear equation given in Figure 5.36 simplifies to: M  10(Vp  0.5)/3 (GPa )

(6.3) (a)

and serves as a mean value for the in situ E-moduli (Ee shown in Figure 6.5a), while it is closer to an upperbound for the in situ deformation moduli (Ed shown in Figure 6.5b). The M(min.) values given in Figure 5.36 independently encompass the minimum Ed trend lines given in Ribbacchi’s Figure 6.6. Kikuchi et al., 1982, also presented a very comprehensive set of modulus and velocity data, this time from investigations at Japanese dam sites. They established a rock grading system based on a combination of seismic refraction data, deformation moduli from plate load tests, Mohr Coulomb parameters from in situ shear tests, and rock rebound hammer (modified to 30 mm impact diameter for soft rocks). Their data extended from weathered or soft rocks with uniaxial strengths as low as 2 MPa up to extremely hard rocks with uniaxial strengths as high as 300 MPa. The in situ P-wave velocities ranged from 0.4 up to 5 km/s. Figure 6.7a and b show examples of their Vp–rock grade, and Vp-D (modulus of deformation) correlations, while Figure 6.7c gives the well-correlated log E–Vp relationship. The elastic (E) modulus and the deformation (D) modulus were defined as tangent and secant gradients at the maximum loading of 7 MPa. Their best-fit trend lines for E and D compare quite closely with envelopes 2 or 3 and 1, respectively in Figure 6.6 (from Ribacchi, 1988). Broad correlations between seismic P-wave velocities and in situ loading test results at dam sites are also demonstrated by Navalón et al., 1987. Investigations at

(b) Figure 6.5 Vp versus logarithm of deformation moduli Ee and Ed, for two Italian dam sites in limestone and dolomite. Ribacchi, 1988.

two similar sites consisting of crystalline limestones and marly limestones with innumerable clayey interlayers of millimetre thickness produced the results shown in Table 6.1 (M  deformation modulus).

102

Rock quality, seismic velocity, attenuation and anisotropy

These three depth zones were defined at each of the two dam sites, and were relevant to foundation testing in the left and right abutments and in the riverbed at each site. Similar geology was involved in each case. The above low velocity data broadly fits the simple empirical equation developed in Chapter 5 (Figure 5.36): D or M
10Q

(a)

(b) Figure 6.6 Vp versus logarithm of deformation moduli Ee and Ed, from Italian, Yugoslavian and American in situ test data. See Ribacchi, 1988 for references.

Table 6.1

1

3

GPa

(6.4)

when Vp values are converted to Q-values using the ‘hard rock’ relation Vp
3.5  log10Q. However, the ‘deep zone’ data with Vp
3.5 km/s have surprisingly high moduli (approx. 14 to 20 GPa) which are higher than that predictable from equation 6.4. For some reason the moduli but not the velocities appear to be increased by the ‘deep zone’ boundary condition (i.e. by higher stress). The process of rock mass loading and even failure under various sizes of plate loading (0.28 to 0.45 m in diameter) was monitored by Savitch et al., 1974, using simultaneous Vp measurement in the first one metre beneath the plates. The testing was performed at the Inguri arch dam in Russia, which is founded on medium and intensely jointed limestones. The range of deformation moduli was 1 to 15.7 GPa. Increments of loading were applied, to final levels of about 10, 20, 30 or 50 MPa (depending on rock quality) which caused characteristic rises and sharp falls of Vp-values (Figure 6.8a, b, c) for various rock qualities, which were sampled by arranging the loading tests at different depths below the surface. The Vp monitoring was performed cross-hole, to 1 m depth below the plates, in boreholes that were located close to the edges of the plates, across a diameter. Figure 6.8 shows small arrows on each set of curves. Those arrows pointing downwards signify ‘failure’ as evaluated by the seismic results, while the arrows below the curves signify failure as assessed by the accelerating

Deformation moduli and velocities from numerous plate load tests. Navalón et al., 1987.

A)

Vp (km/s)

M (GPa)

B)

Vp (km/s)

M (GPa)

C)

Vp (km/s)

M (GPa)

Decompression zones

0.7–2.0 0.9–2.3 1.0–2.4 1.5–2.5

0.4–3.9 0.7–5.9 0.9–6.4 2.0–6.4

Intermediate zones

1.8–2.2 2.6–2.7 2.6 2.6

3.4–4.9 7.4–8.3 7.3 7.4

Deep zones

3.3–3.6 3.5 3.5

17.6–19.7 14.2–16.2 16.2

Deformation moduli and seismic velocities

103

(b)

(a)

(c)

Figure 6.7 Correlations of refraction seismic velocities with weathering grade, deformation modulus and elastic modulus from Japanese dam sites. Kikuchi et al., 1982.

deformation. Consistent relationships between deformation modulus, velocity and the ultimate strengths of the rock masses are shown by the following tabulation: Table 6.2 Plate load tests taken to ultimate failure. Savitch et al., 1974. Test No.

D (GPa)

Vp (km/s)

c (mass) MPa

3 6 4 1 7

0.9 1.0 2.8 3.4 15.4

1.3–2.2 2.2–2.4 3.6–3.9 3.6–3.8 3.9–4.2

2–3 3–5 19–24 22–23 42–78

Coal, which in some ways resembles jointed rock at reduced scale, also shows the expected increases in velocity

with stress increase (uniaxial or triaxial), but Shea and Hanson, 1988, identified two other phases of behaviour as well which resemble those we have just seen in Savitch et al., 1974 plate load tests. Phase I represented the rapid rise in P-wave velocities due to ‘closing of layer cavities’ at quite low levels of loading (MPa assumed). Attenuation also decreased in this phase as shown in Figure 6.9a Phase III marked the decline of these two trends, while Phase II represented the increase in attenuation that probably signified the creation of micro-cracks. There was hardly any increase in P-wave velocity in this phase, although the S-wave velocity continued to increase. Figure 6.9b shows that triaxial conditions (1.7 MPa confinement) caused consistently reducing attenuation in Phase I and II, then a sudden increase in attenuation and reduction in velocity as failure approached in

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 6.8 Effect of stress on Vp values beneath plate load tests at the Inguri arch dam in Russia. Savich et al., 1974.

elastic moduli to rock engineering design will also be addressed. The four standard equations, two of which were introduced earlier in Chapter 1 are reproduced here together, for ready reference (ISRM, 1998). Dynamic Young’s modulus Edyn: E dyn  Vs2

 Vp2

(a)

3( VP / Vs )2  4 ( VP / Vs )2  1

(6.5)

(1  d )(1  2d ) 1  d

(6.6)

Dynamic Poisson’s ratio d: d  (b)

1 ( VP / Vs )2  2 2 ( VP / Vs )2  1

Figure 6.9 a) Uniaxial, and b) triaxial test of coal, showing velocity and attenuation changes caused by cleat and microcrack behaviour. Shea and Hansen, 1988.

Dynamic shear modulus : (also with symbol G)

Phase III. Broadly similar (but inverted) behaviour of the P-waves was also seen.

 Vs2 

6.2

Dynamic bulk modulus Kbulk:

Dynamic moduli and their relationship to static moduli

In this section, which principally concerns dynamic moduli and dynamic Poisson’s ratio, the use of Vp and Vs measurements to derive the four standard dynamic elastic properties of rock masses will be discussed. The validity or otherwise of these dynamic, small-strain,

E dyn 2  2 d

K bulk  ( Vp2  4/3 Vs2 )



E dyn 3  6d

(6.7)

(6.8)

(6.9)

(6.10)

Deformation moduli and seismic velocities

Figure 6.10 Contrasting laboratory and field data for the Vp and Vs values of limestones, with calculated dynamic Poisson’s ratios. Note the over-riding tendency of higher dynamic Poisson’s ratio in the case of the lower velocity in situ data. Ribacchi, 1988.

It will be noted that if the dynamic Poisson’s ratio is estimated (rather than derived from Vp and Vs), the three dynamic moduli can theoretically be estimated from Vp measurement alone. As pointed out later, this can cause significant inaccuracies, and such values given in the literature should be treated with caution. The manner in which Vs and Vp values are distributed in relation to the general quality of the rock mass was illustrated in Chapter 1 (Figure 1.7 from Sjøgren, 1984). Further sets of data, both from laboratory samples and from comparable field data (Ribacchi, 1988) are illustrated in Figure 6.10. Ribacchi’s data shows a particularly clear demarcation between the lower dynamic Poisson’s ratio in the case of the higher velocity laboratory data, and the opposite trend for the lower velocity field data. High dynamic Poisson’s ratio are a clear sign of the influence of jointing. In shear zones and faulted rock, high values of d are common. During ‘static’ flatjack biaxial loading tests of rock masses, ‘static Poisson’s ratios’ (or lateral expansion coefficients) in excess of 0.5 may even be measured. In special

105

Figure 6.11 Ratio of Vp and Vs at a hard igneous rock site in Norway. Vp/Vs
1.8–1.9. The full range of dynamic Poisson’s ratios was from 0.15 to 0.39, with higher values when velocity was lower. Sjøgren et al., 1979.

cases, values in excess of 1.0 have been registered. This occurs as shear failure is approached, in the case of biaxially loaded model rock masses, having two conjugate fracture sets that are under significant levels of shear stress. (Barton and Hansteen, 1979, Barton, 1993a, and Barton, 2004b). Measurements of Vp and Vs at an unweathered site in Norway are shown in Figure 6.11, and indicate ratios of Vp/Vs of about 1.8 to 1.9. The corresponding dynamic Poisson’s ratios were found to lie in a narrow range, more than 80% of the values were between 0.26 and 0.32. The mean value of 0.28 in fact lay close to the maximum RQD and minimum joint frequency trend for this particular site, and corresponded to a ratio Vp/Vs between 1.8 and 1.85. In the rock masses investigated, the authors found that the full range of dynamic Poisson’s ratios was from 0.15 to 0.39. Deere et al., 1967, addressed the important differences between field measurements of EF dyn and laboratory measurements of EL dyn of the intact rock, by utilising their observation that (VField/VLab)2 resembled RQD/ 100. (This was referred to in Chapter 5, Table 5.1.) This was based on the Onodera, 1963, suggestion of using the field/lab velocity ratio VF/VL as a measure of rock quality. The resulting method for estimating EL dyn/EF dyn is shown in Figure 6.12. As can be noted from the spread of

106

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c)

Figure 6.12 Utilising the velocity ratio (squared) or RQD%/100, to estimate the ratio of the dynamic modulus for intact samples (EL dyn), compared to the dynamic field modulus (EF dyn). Deere et al., 1967.

data, the inverted knee-shaped trend does not give a good method for estimating the lowest values of the ratio, as RQD and (VF/VL)2 vary too much in the region EL dyn/ EF dyn
0.1–0.3. In higher quality rock masses however, a more consistent trend is observed, some of the data from the USA even indicating EF dyn
EL dyn , for values of (VF/VL)2 as high as 0.9, or RQD  90% or more. When commenting on the differences between static and dynamic moduli, Wang and Nur, 1992, make the usual observation concerning the different strain amplitudes involved (perhaps 103 and 106 respectively) but also point out that the different moduli are thereby directly caused by the presence of pores, cracks (and joints). These are deformed in static tests, but hardly deformed by dynamic waves, but when stresses are very high and pores, cracks and joints are (almost) closed, the static and dynamic moduli are likely to be very close. The possibility of estimating Edyn values from Vp measurement alone, by just estimating the value of the dynamic Poisson’s ratio (d) instead of measuring both Vp and Vs was referred to earlier. This would involve using equation 6.6 instead of the correct method utilising equation 6.5. In warning against this short-cut, Stacey, 1977, assembled what he called ‘reliable’ Edyn values from the literature. These values are shown in Figure 6.13a. (For the numbered references see Stacey, 1977). Stacey also assembled a large number of Ee-Edyn data (Figure 6.13b) and Ed-Edyn data (Figure 6.13c). These two figures show the apparently irrelevant nature of Edyn in comparison to the standard rock engineering methods of testing deformation modulus for design purposes. The doubt nevertheless remains that most of our large scale methods are testing an excavation disturbed zone, or EDZ, rather than the undisturbed state, with its higher and maybe more isotropic in situ stresses. There is a contrary factor that most rock masses observed or tested, are actually on a major unloading curve due to erosion or due to rock excavation, and may have correspondingly higher joint stiffnesses, than if loaded up without this prior unloading. The mismatch of the static and dynamic moduli in jointed rock masses, except where rock qualities are very high and strains are very small, is probably a universal rule, unless extremely small strains are actually involved in the ‘static’ loading. In the last two decades, it has apparently been recognised in soil engineering that strain levels associated with normal foundation designs are rather small, for example 0.01 to 0.1%, and therefore stiffnesses may be successfully described by the correlations obtained from in situ

Deformation moduli and seismic velocities

(a)

seismic measurements (Matthews et al., 1997). Such measurements also have the great advantage of registering the stiffness of the ground at in situ stress levels and in the undisturbed condition. A corollary to the above is the predicted high deformation moduli for jointed rocks at depth, shown in Figure 6.14 (Barton, 1995). A pre-condition here is that the rock mass is undisturbed and strains are small, corresponding more closely with the higher seismic velocities seen at greater depths in the same rock masses. When a tunnel or test adit is constructed at considerable depth, the EDZ effect will alter the above conditions in a complex way, to a degree that depends on rock quality and the care with which the adit-excavation has been performed. One must expect a certain seismic velocity gradient, a deformation modulus gradient, a deformation gradient and even a permeability gradient and pore pressure gradient, and finally a possible gradient of saturation. The natural complexity of a site may also tend to increase the range of moduli and moduli ratios in relation to those measured in one particular lithology. The Latiyan Dam site in Iran was founded on granites, pegmatites, migmatites and gneiss, and weathered layers of each of these. Lane, 1964, compares four of the basic moduli commonly obtained at dam sites: ●

● ●

●

(b)

(c) Figure 6.13 An extensive collection of ‘reliable’ Edyn. data, and of the ratios Ee/Edyn. and Ed/Edyn.. Stacey, 1977. (See individual references in article).

107

laboratory EL dyn (from laboratory Vp, Vs and Poisson’s ratio) field EF dyn (from field Vp, Vs and Poison’s ratio) field deformation modulus (D, Ed or M) (from plate or flatjack loading) field elastic modulus (Ee) (from plate or flatjack unloading)

and also gives ratios of each, as obtained in three exploratory tunnels in the dam foundations. The surprisingly large ratios of these moduli, for rather poor rock mass qualities (Q mostly  0.1?) are shown in Table 6.3. Link, 1964, also gave a wide-reaching comparison of dynamic and static moduli from projects (usually dams) in many countries. He found that the ratio of EF dyn/D from field tests (category 6 in Table 6.3), ranged from about 1 to 16, with most values of the ratio lying in the range 3 to 7. A large number of the static loading tests were pressure chamber tests from Central European dam sites, and the author pointed out that the seismic measurements (from Vp, Vs and dynamic Poisson’s ratio) were also of quite large scale. As we see from the above table, ratios of EF dyn/D can be even larger than the above when the rock quality is poor, due to the basic inequality

108

Rock quality, seismic velocity, attenuation and anisotropy

Figure 6.14 High values of static deformation modulus Emass (or M) for the rock mass (also referred to as D, or Ed by some authors), are predicted where stresses and rock quality are high. Here Emass approaches EF dyn.. Barton, 1995.

Table 6.3

Ranges of moduli and ratios of moduli at three complex sites (after Lane, 1964).

Modulus 1 Laboratory Dynamic (EL dyn) 2 Field seismic (EF dyn) 3 Average modulus of deformation field loading (D or Ed or M, depending on author) 4 Average modulus of elasticity field unloading (Ee) 5 Ratio laboratory dynamic to field seismic (EL dyn/EF dyn) 6 Ratio field seismic to modulus of deformation (EF dyn/D) 7 Ratio field seismic to unloading modulus of elasticity (EF dyn/Ee) 8 Ratio laboratory dynamic to modulus of deformation (EL dyn/D) 9 Ratio laboratory dynamic to jacking modulus of elasticity (EL dyn/Ee)

of the two static unloading/loading moduli: Ee/Ed (or Ee/D), shown, for example by Kujundzíc and Grujíc, 1966. Link, 1964, made special reference to an extremely high value of EF dyn measured (interpreted) under the lower slopes of the Vajon limestones. The value of 140 GPa was considered the result of high overburden, and/or residual stresses. Graphic presentation of the inequalities between EF dyn and Ee were given by Kujundzíc and Grujíc, 1966. Figure 6.15a and b show the significant inequality of Edyn and Ee for the case of the limestones tested in their

Tunnel 1

Tunnel 3

Tunnel 4

(GPa) (GPa) (GPa)

35.8 17.7 1.8

45.4 25.4 1.3

35.8 16.4 1.3

(GPa)

4.8 2.02 10 3.7 20 7.4

4.6 1.78 20 5.6 36 9.9

3.8 2.18 12 4.4 27 11.5

Yugoslavian dam site tests. A general trend was noted as follows: Ee 

Edyn (5.3  0.05Edyn )

(6.11)

where Ee and Edyn are expressed in GPa. The lower the dynamic modulus the larger the ratio of the dynamic/static moduli. When the inequality of Ee and Ed is also considered, the very large ratios of Edyn/Ed of 10 to 20 given by Lane, 1964, and Link, 1964, are more readily understood.

Deformation moduli and seismic velocities

109

(a)

(b)

Figure 6.15 Inequality between Ee (static unloading) and Edyn. (or EF dyn), for limestones tested at Yugoslavian dam sites. Kujundzíc and Grujíc, 1966.

6.3

Some examples of the three dynamic moduli

Sjøgren et al., 1979, gave average curves for the three dynamic moduli (Young’s, bulk and shear), reproduced in Figure 6.16. These were based on 80 examples from three igneous and metamorphic rock areas (1  dynamic E modulus, 2  bulk modulus K, and 3  shear modulus G). Each are shown in relation to measured values of Vp from refraction seismic, which ranged from 3 to 5.5 km/s. Deviations from the curves occur with changes in the dynamic Poisson’s ratio (d). This is because of the fundamental linkage between Vp and Vs:  1    d     Vs  1 2  d 

Vp

1

2

(6.12)

and because of the elastic equations (6.5 to 6.10) linking Vp and Vs with the dynamic elastic (Edyn), bulk (k bulk) and shear ( ) moduli. Concerning Edyn and , high Poisson’s ratios give values below the curves in Figure 6.16 and low Poisson’s ratios give values above the curves.

Figure 6.16 Average curves for the field-scale dynamic elastic (E: curve 1), bulk (k: curve 2), and shear ( : curve 3) moduli, in relation to refraction seismic Vp, based on 80 examples from igneous and metamorphic areas. Sjøgren, 1984.

The authors found that the dispersion of the dynamic Poisson’s ratio values always increased at lower velocities (e.g., dispersion
0.02 at 5.5 km/s, and
0.065 at 3.5 km/s). In Figure 6.17, their calculated values of dynamic Poisson’s ratios (from equation 6.7) are shown integrated with Vp magnitudes, with calculation of equivalent values of Edyn and k bulk. The reduced moduli where even higher values of dynamic Poisson’s ratio are calculated, can be readily imagined. In this connection it is of interest to refer to the results of Vp and Vs logging of shallow boreholes. Results given by Chang and Lee, 2001 from a Korean tunnelling project, show the elastic ‘constants’ for a 30 m deep borehole. (Figure 6.18a). The Edyn moduli of 0.07 and 0.23 GPa are less than the bulk moduli (k) of 0.15 and 0.38 GPa in the residual soils in the top 10 m of the hole, where the dynamic Poisson’s ratios are as high as 0.43 and 0.40 respectively, and Vp only 0.5 km/s. It is not until the soft rock is reached at 24 m depth, that Edyn of 5.92 GPa becomes greater than k of 5.20 GPa, with Vp increased to 1.85 km/s, and dynamic Poisson’s

110

Rock quality, seismic velocity, attenuation and anisotropy

Figure 6.17 Dynamic moduli Edyn and k bulk, as a function of the calculated dynamic Poisson’s ratio, for different Vp values. The solid curves refer to the appropriate magnitudes of Edyn, and the dashed-curves refer to the k bulk values. Note the reducing values of Edyn at higher values of the dynamic Poisson’s ratios. Sjøgren et al., 1979.

ratio reaching a ‘rock-like’ 0.31. With the harder rock at 30 m depth, the respective values have changed to 24.07 GPa, 18.43 GPa, 3.45 km/s and 0.28. Figure 6.18b shows a similar set of results for a deeper, mountain tunnel borehole, where Vp varied from 5.2 km/s beyond 30 m depth, to 5.5 km/s beyond 150 m depth. Here Edyn increased from 50 GPa to beyond 60 GPa, with corresponding increases in rock density, and reductions in Poisson’s ratio. 6.4

Use of shear wave amplitude, frequency and petite-sismique

In Chapter 5, we saw how S-wave frequency was used by Stacey, 1977, to monitor the closure-under-stress of dry, wet and clay-coated joints. P-wave amplitude was also found by Stacey 1977, Tanimoto and Ikeda, 1983, and Tanimoto and Kishida, 1994, to be particularly sensitive to joint closure and joint shearing mechanisms.

Here we will make a brief, premature digression to large-scale, high stress earthquake environments, to illustrate one of the many uses of shear wave monitoring. Chen et al., 1993, showed in research related to earthquake source mechanisms, that stable sliding and ‘stick-slip’ could be differentiated by interpretation of continuous shear-wave monitoring. Continuous sliding between rock interfaces under pressure reportedly caused a continuous decrease in shear wave amplitude, while stickslip behaviour was detectable by a rapid drop in amplitude prior to or during ‘slip’, and by an increase in amplitude during each ‘stick’ period. The authors suggested this method as an alternative to the classic but possibly unreliable observation that the ratio of Vp/Vs showed a large decrease in earthquake source regions prior to earthquakes (Agarwal et al., 1973). (Anomalies in the amplitude ratio As/Ap have also been reported before earthquakes.) A well known but tragic fact is that Chinese seismologists succeeding in predicting the 1975 Liaoning earthquake due to the decreased Vp/Vs ratio, but failed one year later to predict the 1976 Tangsham earthquake which reportedly killed almost one million people. In rock engineering projects, particularly arch dam sites investigated by French consultants Coyne et Bellier, direct use has been made of the correlation between the ‘frequency of the second arrival’ (the S-wave frequency) and the in situ static modulus of deformation (variously described as Ed D, Emass and M in the foregoing text and referenced figures). Schneider, 1967, and Londe, 1979, were instrumental in developing and publicising the ‘petite-sismique’ method, which was subsequently given some impetus by Bieniawski, 1978, with the additional test data and seismic data from some South African projects. At this time a linear relation between in situ static modulus (D or M) and S-wave frequency (f ) was proposed (D  0.054f9.2), as shown both in Figures 6.19 and 6.20. Subsequently the method, termed SCARABEE (Systeme Complet d’Analyse des Roches d’Appui de Barrages et d’Excavations) was standardised and expanded by Coyne et Bellier and Geodia, 1995, in France. Use was made of a normalised value of the Schmidt rebound (40), a normalised value of the dynamic modulus (44 GPa) and of the S-wave frequency (750 Hz), with a standard gain (45 dB), to give a more comprehensive picture of rock mass conditions. The correlation between D and f is now considered to be of the non-linear form: (D
0.17 f 1.7 ), as shown in Figure 6.21, from Coyne et Bellier, 1998 and Carrère, 1999.

Deformation moduli and seismic velocities

111

(a)

(b)

Figure 6.18 The dynamic elastic moduli compared from down-hole Vp, Vs and density logging, a) for a shallow 30 m deep hole, b) for a 300 m deep mountain tunnel borehole. Chang and Lee, 2001. Note GPa, and symbol conversion, G to .

6.5

Correlation of deformation moduli with RMR and Q

The extensive in situ deformation modulus data presented by Ribacchi, 1988, which was reproduced earlier in this chapter, represents a useful source of field data with which to test how well the standard RMR-deformation modulus

and Q-deformation modulus relationships relate to large scale data. The mean deformation modulus (Ed) data presented in Figure 6.4 for twenty different sites (as Ed versus Vp2) is presented again in Figure 6.22, this time with modulus in relation to RMR, shown as the lower scale. The source of the solid curve of Ed-versus-RMR given in Figure 6.22 is shown in Figure 6.23, where both the

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Figure 6.20 ‘Petite sismique’ method of modulus estimation, with additional, linearly distributed data from South African hydropower projects, from Bieniawski, 1978. Earlier data from Schneider, 1967 is also shown.

(a)

(b) Figure 6.19 The originally assumed, linear correlation between S-wave frequency and tangent modulus of deformation, in the so-called ‘Petite sismique’ method of modulus estimation. Londe, 1979.

(Seraphim and Pereira, 1983) equation and the Q-system equation for ‘static’ deformation modulus prediction, are each shown. It can be seen from Figure 6.23, that the Seraphim and Pereira, 1983, relation is as follows: Ed  M 

10((RMR 10)/40)

(6.13)

Figure 6.21 Updated, non-linear relationship between the static modulus of deformation and the shear wave frequency, from Coyne et Bellier, 1998, Carrère, 1999.

The Q-system based equation for deformation modulus prediction gives a similar trend: 1

E d  M  10Q c 3

(6.14)

where Q c  Q  c/100, so Q c
Q in a typical hard rock situation. This equation is the source of the

Deformation moduli and seismic velocities

113

‘circled-black-dots’ in Figure 6.22, which lie on, or just below, the ‘RMR-curve’. The solid and dashed lines shown in Figure 6.23 are also seen to almost coalesce for Q-values less than 1 and RMR less than 50. If we further assume that Q and RMR can be related by the following simple relation (Barton, 1995): RMR
50  15 log10Q

(6.15)

then we can supply a Q-value scale to the top of Figure 6.22, where in approximate terms: RMR Q

Figure 6.22 RMR – Ed fit to Ribacchi, 1978 data using the empirical Seraphim and Pereira, 1983 equation. The Barton, 1995 RMR to Q conversion: (RMR
15 log Q  50) has been added to give the uppermost Q-scale, together with ‘circled-dots’ representing the M  10Q c⁄ (GPa) relation. 1 3

 5 20 35 50 65 80 95  0.001 0.01 0.1 1.0 10 100 1000

For lower strength rocks, the estimate of static deformation modulus is suitably lower using the Q-based equation 6.14 compared to the RMR-based equation 6.13, and actually more in line with the extremely low moduli that are usually measured, in the case of soft porous rocks. From earlier in this chapter one may note from Figure 6.7b (Kikuchi et al., 1982, Japanese tests) that one third of the deformation moduli lie in the range 0.05 to 1.0 GPa, with correspondingly low P-wave velocities (mostly 0.5 to 2.5 km/s).

Figure 6.23 A comparison of the old and the new RMR – deformation modulus relations (Seraphim and Pereira, 1983, and Bieniawski, 1989), and the more recent formulation involving Q or Qc. Barton, 1995.

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An example application of equation 6.14 may be useful here. Let us suppose that the conventionally logged Qvalue (for tunnel support selection) in a weak sandstone of c
2 MPa is as low as 0.01 due to heavy jointing and low frictional strength. When we correct Q  0.01 to Qc, a value of Qc  Q  c/100, or Qc  0.0002 is obtained. Substitution in equation 6.14 gives a predicted Ed or M value of 0.6 GPa. The RMR equation 6.13 gives a predicted Ed or M value of 1.8 GPa, when Q  0.01 or RMR  20. Such an estimate may be too high for soft rocks. As may be noted from Figure 5.36, in Chapter 5, an additional correction for porosity is also available in the ‘Q-diagram’, to improve fit to Tertiary type, weak, porous sedimentary rocks. In the case of an exceptionally poor quality faulted zone or extremely weathered zone with Q
0.001, with crushed rock pieces having a strength of only 1 MPa (almost a soil) we would need to use a Qc-value of 0.00001 in equation 6.14, which would correspond to an exceptionally low Ed or M value of only 0.2 GPa. This is close to the ‘lowest possible’ M(min.) value tabulated in Figure 6.14, and corresponds apparently (and perhaps realistically) to a P-wave velocity as low as 0.5 km/s. In Figure 6.24, showing Ribacchi, 1988 data from Figures 6.5b and 6.6b, the following relation between — M and Vp is plotted. (This relation was given in Figure 6.14, see inset at top): M  10.10((Vp 3.5) / 3)  10((Vp 0.5) / 3)

(a)

(6.16)

The objective was to again test the relation against the extensive data and data trends for limestones and dolomites given by Ribacchi, 1988. In this figure, the predicted M(mean) values given by this equation are seen to represent upper-bound envelopes in relation to the Ed data given in the figure. The M(min.) tabulation given in Figure 6.14 appears to represent a lower-bound envelope in the case of the five trend lines given in Figure 6.22. It is important to try to understand why such high velocities as, for example, 4.0 to 4.5 km/s can be associated with Ed values as low as 5 to 10 GPa as can be seen in Figure 6.24b. Although the assumed porosities of the limestones and dolomites might affect Ed values more than Vp values, there is much evidence, for example from Figure 2.10 (Chapter 2, Fourmaintraux, 1975) that this cannot be so. Possibly the most likely explanation, which has been raised earlier in this chapter, is that the large scale deformation modulus test as practised at dam sites (plate load,

(b) Figure 6.24 Plate load data for limestones and dolomites (see Figs. 6.5b and 6.6b) from Ribacchi, 1988, and a comparison of the M-Qc model. (Mmean is the solid line: left, Mmin. is the dashed line: right).

Deformation moduli and seismic velocities

flatjack or occasionally pressure chamber) is nearly always testing an excavation disturbed zone (EDZ), in a loading direction parallel to the radial stress (r), while the velocity measurement may be averaging velocities over a larger volume, and may tend to be recording velocities parallel to the  (tangential stress) direction, which is a much higher, maximum local principal stress, compared to the minimum radial stress. The latter obviously approaches zero, due to the effect of excavating a test adit. The stress anisotropy (  r) around an excavation, which can explain higher values of Vp parallel to  than parallel to r, could therefore explain the higherthan-expected Vp values, and the higher-velocity-thanexpected Ed–Vp trend lines seen in Figure 6.24b. In this connection, it is significant that the empirical equations that were introduced in Chapter 5: 1

Vp  3.5  log10 Q c and M  10Q c 3

were developed independently (at different times) from different data sets. The first equation was developed

115

from core logging and refraction seismic, and from deeper cross-hole tomography data. The second equation was developed from large scale modulus of deformation data where either the Q-value was known from independent logging or from approximate conversion from logged RMR values, using equation 6.15. The implied connection between M and Vp (elimination of Q c between the above equations) to give equation 6.16, is a ‘pure’ link, which ignores the potential complication that anisotropic stresses (  r) may cause anisotropic velocities in the EDZ test zones.

7

Excavation disturbed zones and their seismic properties

The existing surface of exposed rock that may be found where soil cover is absent can be considered as nature’s disturbed zone. Steep mountainsides in rocky terrain, steep gorges or valley sides where dams may be founded or glaciated terrain are typical examples. As we have seen earlier the special coincidence of low stress, weathering effects and possibly more frequent jointing (with joint apertures above the limits of ‘acoustic closure’) make such zones extremely ‘visible’ in seismic refraction or sonic logging of shallow boreholes. Velocities may be up to several km/s lower in the near-surface zone than at greater depth, in some cases even when joint frequencies remain unchanged. In an attempt to get away from the weathered zone, investigators of dam sites and deep foundations may often construct adits or shafts for conducting deformability and other geomechanical tests. Unfortunately, however much care is taken, even to the extent of non-blasting methods, a disturbed zone results. The removal of stressed rock and its usual replacement by air at atmospheric pressure (a convenient ‘definition’ of tunnelling), results in a radial stress (r) that approaches zero at the excavation walls. The tangential stress ( ) may assume many values (including negative) depending upon the existing stress anisotropy, joint orientation, rock strength and the disturbance caused by the excavation method.

7.1

Some effects of the free-surface on velocities and attenuation

The problem with the EDZ is that many of the geomechanical properties we are most interested in investigating at large scale are themselves affected by the process of obtaining access. Only a borehole-size intrusion may be considered nearly free of damage, but it will cause local disturbance to the stresses, that may influence permeability measurements and may also influence preliminary load cycles from borehole dilatometers. The ‘skin-effect’ around an excavation adit is far from ‘skin-deep’, and may extend many metres or to one or several radii from the excavation wall, especially in the case of softer rock that is highly stressed. We must assume both a damaged zone and a disturbed zone that together have been given the nomenclature EDZ (excavation damage and disturbed stress zone). ED1D2Z would be more specific, as with e.g. line drilling of an experimental tunnel, as at URL in Canada, we have only ED2Z. An unusual and instructive geophysical monitoring of the Dneiper ship lock excavation, which reached a depth of more than 20 metres, is shown in Figure 7.1. The effect of loosening caused by blasting, stress relief (and presumably inadequate slope reinforcement) is shown very

Figure 7.1 Free-surface effect, and slope excavation (and degradation) effects on P-wave velocities. There is a 1 year delay between measurements c) and d). Savich et al., 1983.

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clearly. There is a one-year delay between diagrams (c) and (d). Savich et al., 1983, refer to a 200–300% reduction in velocity, a 75 to 85% reduction in deformation modulus, and a 1 to 20 times increase in ‘joint voids’. This can be considered an excavation disturbed zone (EDZ) study related to slopes, in which velocity changes were related both to loosening and presumably to water drawdown. The same basic mechanisms may be at work around tunnels, in which EDZ effects are important for may reasons, including increased support needs, reduced deformation modulus, and frequently increased leakage (or permeability) in the case of larger or less stable tunnels. These effects may be remedied by high pressure pre-grouting with micro or ultra-fine cements. This will be discussed later. In the case of very stable rock, and small tunnels, inflow may reduce in relation to expectation. (Olsson, 1992). Price et al., 1970, reported the results of seismic refraction measurements at three sites in the UK where bolting, anchoring and grouting of rock slopes was being designed. Their measurements at Edinburgh Castle in complexly jointed basalt foundations, suggested a 16% increase in Vp as a result of bolting and anchoring (6 to 12 m deep) followed by grouting. At Cheddar Gorge, which cuts through massive, but bedded limestones, an outer layer of about 5 m thickness showed a velocity of 2.9 km/s, while deeper into the walls of the gorge, the velocity was 5.5 km/s. The vertical, pseudo columnar jointing in dolerite at Stirling Castle showed ratios of Vfield/Vlab as low as 0.1 due to stress relieved joints and weathering near the surface. Slope ‘EDZ’ can clearly exceed the EDZ associated with tunnelling, due to the added influence of weathering. The authors also described early trials with a downhole

Figure 7.2 Seismic attenuation compared in broken rock, and in compact rock masses. Young et al., 1985.

seismic probe for easier access to inaccessible locations behind steep slopes. Cross-hole measurements clearly indicated the presence of stress-relieved joints behind the slope faces. The excavation efficiency of large dragline excavators in open cast coal mines as a function of efficient blasting practice was investigated by Young et al., 1985, using what they called ‘seismic spectroscopy’ to quantify the degree of brokenness of the rock before and after blasting. They utilised seismic attenuation and anisotropy diagrams to evaluate the efficiency of the blasting process. Certain frequencies were found to be attenuated due to the effect of fracture size and porosity (and void space). The principle of the method is shown in Figure 7.2. The attenuation spectrum of the broken rock mass differed fundamentally from that of the unbroken, more homogeneous rock. As shown in this most interesting Figure 7.3, attenuation was larger and more irregular for

Figure 7.3 Effect of blasting and depth below surface on the seismic attenuation. Attenuation is greatest near-surface, and at intermediate frequencies. Young et al., 1985.

Excavation disturbed zones and their seismic properties

shallow depths (where fractures open more easily) and more regular and limited at greater depths, where confinement limits fracture or joint opening. Associated compressional wave velocities typically changed from 1.1 and 1.8 km/s (at the surface/at greater depth) prior to blasting, down to 0.6 and 1.1 km/s respectively, after blasting. These excavation disturbance effects were accompanied by rotations of both attenuation anisotropy axes and velocity anisotropy axes, presumably as a result both of disturbance to pre-existing joint patterns and blast-induced fracturing in the proximity of a high wall.

7.2

EDZ phenomena around tunnels based on seismic monitoring

In the years before the 1980s, reports of EDZ investigations in the rock mechanics literature were usually in connection with hydropower projects. An impressively early model for subsequent investigations was provided by Hasselstrøm et al., 1964, at a dam site in Sweden, who compared cross-hole and downhole sonic logging results in an investigation gallery, as shown in Figure 7.4. Velocities were seen to fall from about 5.5 to 3.5 km/s in the outer 1 metre of their 1.5  2 m gallery. The

authors cited the same reasons for the velocity reduction that we hear in more recent times at nuclear waste investigation sites such as Hanford (King et al., 1984), URL (Maxwell and Young, 1996), Äspö (Emsley et al., 1996) and Stripa (Olsson, 1992). Fracture formation, joint disturbance, stress redistribution and possible desiccation of the existing joint system were all listed by Hasselstrøm et al., in 1964, and are equally relevant (and complicated) today. A classic EDZ investigation in relation to pressure tunnel design was reported by Kujundzíc et al., 1970. They performed a trial chamber test for investigating poststressing effects on the concrete liner of their 5 m diameter, circular tunnel. In the course of this study, they utilised numerous grouting boreholes (32 in all) for conducting cross-hole seismic along the tunnel axis at eight different radial positions. Their results are shown in Figure 7.5. They visualised the existence of three zones around the tunnel: 1) the loosened zone (with lowest velocities); 2) the stress bearing ring (with highest tangential stresses and velocities); 3) the uninfluenced zone (with declining velocities and background stresses). Their mean results (Vp  3.5 km/s at the tunnel wall, Vp  5.5 km/s at 1 m radius, and Vp
4.5 km/s in the undisturbed zone) shown in the centre of Figure 7.5 can be interpreted by means of the Vp-stress effect model as discussed in Chapter 5 (Figure 5.36). Significant sophistication was added to the analysis of disturbed zone phenomena by Russian engineers, who analysed a variety of effects, including anisotropic velocities using ultrasonic and seismic methods. They emphasised the need to consider the use of different wave lengths (see Chapter 3, Lykoshin et al., 1971, Figure 3.12). In relation to the EDZ logging of a shaft in diabase, these same authors used a time-average equation to estimate the joint void ratio (e) as a function of depth, as shown in Figure 7.6:

e

Figure 7.4 An early EDZ measurement at a Swedish dam site gallery that compares cross-hole (1) and sonic log (2) results. Hasselstrøm et al., 1964.

119

Va ( Vr  Vm ) Vm ( Vr  Va )

(7.1)

where Va was given the value 345 m/s assuming airfilled joint voids, Vr is the intact rock velocity and Vm the mean velocity at the depth of measurement. For example, we can substitute the P-wave velocities 0.345, 5.0 and 3.5 km/s respectively to obtain an estimated

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Figure 7.5 Pressure tunnel investigations of seismic velocity as a function of radius, and therefore as a function of tangential stress, using cross-hole measurements. Kujundzíc et al., 1970.

joint void ratio of 0.03 (or 3%) at an imagined shallow depth into the wall of an excavation. At greater depth when Vm has increased, for example, to 4.5 km/s, the calculated joint void ratio will have reduced to 0.008 (or 0.8%). If we suppose that greater depth into the excavation wall (or the results of high

stress) cause Vm eventually to equal Vr, then clearly the void space will theoretically vanish. Lykoshin et al., 1971, recommended the use of ultrasonic logging with the minimum transmitter-receiver distance (e.g., 0.1 m) to obtain the relevant velocity distributions in such studies.

Excavation disturbed zones and their seismic properties

121

Figure 7.6 Calculations of joint void ratio (%) in the EDZ surrounding a shaft in diabase, using a time average equation. Lykoshin et al., 1971.

The simple time-average equation given above is a particularly useful theoretical means of investigating the void space created in an EDZ, since we can also investigate the theoretical effects of drying out, by substituting the Va value of 0.345 km/s (as in equation 7.1) in place of a Vw value for water of 1.44 km/s. However, the resultant values of Vr for the intact rock and Vm for the jointed rock will also tend to change due to drying, most rapidly in the case of Vm (because of the influence of Va) and less rapidly in the case of Vr. The example of reducing Vp with time due to gradual drying of an intact sample of granite (Nur and Simmons, 1969, Figure 2.18, Chapter 2) could be referenced at this juncture. Lykoshin et al., 1971, also gave a more complex expression for the velocity of eventual joint filling materials, based on the P-wave velocities Va and Vw, and on three other component velocities of the rock and rock mass. Capozza, 1977, reviewed the results of a large number of EDZ-style investigations of tunnels. These were made using both seismic and cross-hole seismic techniques. Figure 7.7 shows the ratio of velocities V2/V1 in the first few metres depth in numerous tunnel walls.

Figure 7.7 Tunnel EDZ measurements assembled by Capozza, 1977 for a variety of rock types. Tunnel depths (m) are shown in parentheses.

Values in parentheses show the depth of the tunnel in metres. It is typical for Vp to be reduced by 25 to 50% close to the tunnel walls. The 3 m thick ‘skin’ observed in the tunnel with 2100 m of overburden is presumably a result of stress slabbing in the granite. Bernabini and Borelli, 1974, described a variety of early seismic tests performed at hydroelectric projects in Italy in the 1950s, 1960s and early 1970s. In hydropower tunnels in gneiss and granite, they measured EDZ effects using seismic refraction techniques along four lines in each tunnel (two in the arch, and two in the lower walls). There were marked reductions of velocity (at least 50 to 60%) in the measurements made just 100 metres from the tunnel entrance (for example 4.8 to 2.2 km/s) as can be seen in Figure 7.8. Further from the tunnel entrance (300 m and 500 m) the higher quality and higher velocity rock showed less marked reductions in velocity due to excavation disturbance.

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Dhawan et al., 1983, described seismic refraction measurements at a dam site in the Himalayas and attempts to correlate results with 1100 metres of core logging and in situ testing in the same quartzitic and slaty phyllites. The in situ testing was performed in boreholes and in an investigation drift in the dam foundations, shown in Figure 7.9. The values of deformation modulus, ranging from about 0.5 to 3 GPa from plate jacking and flat jack tests, seemed to correlate poorly with the wider range of seismic velocities (1.5 to 4.0 km/s), possibly due to the discrepancy of the plate jacking loading direction (radial) in relation to the perpendicular-to-tangential-stress direction followed by most of the seismic refraction ray-paths. The flat-jack loading could possibly have been performed in

the location of minimum tangential stress, if horizontal slots, rather than vertical slots were cut in the wall, and if horizontal along-the-valley stresses were maximum principal stresses in the location of the tests. The disturbed zone surrounding the drift showed a thick low velocity zone (1.4 km/s) of about 3 m thickness in the first 10 metres of the drift. This exceeded the diameter of the drift (2 metres). Further inside the drift, in less weathered material, the higher velocity material (Vp  2.85 km/s) came closer to the walls of the drift, as shown in Figure 7.9. In the same year, Bonapace, 1983 described rock mechanics testing for the design of an extremely high head (1260 m) inclined pressure shaft. Deformation modulus testing at different scales culminated in a radial

Figure 7.8 Seismic refraction profiles along tunnels in gneiss and granite give a crude indication of EDZ. Berabini and Borelli, 1974.

Excavation disturbed zones and their seismic properties

jacking test chamber (diameter  3 metres) which gave the lowest modulus of 11.5 GPa. In order to extrapolate this result along the shaft alignment, 4 m deep boreholes were drilled at 10 m intervals, in order to measure seismic velocities and correlate these with the measurements at the radial jacking location. These EDZ-style measurements in the 4.8 m diameter shaft wall, shown in Figure 7.10, gave velocities as low as 1 to 1.5 km/s in the outer 1.0 metre of the drill-and-blasted shaft, but velocities no lower than 2 km/s in the outer 0.5 metre of the TBM excavated section. In general, velocities were 1 km/s higher in the case of the TBM excavation, over the depth range of 1 to 4 metres from the shaft wall.

Figure 7.9 EDZ effect accentuated by the initial weathered zone at an investigation adit at a dam site in the Himalayas. Dhawan et al., 1983.

123

Downhole logging by Stead et al., 1990, in a potash mine in Saskatoon, Canada also showed distinct EDZ effects as shown in Figure 7.11a and b. Holes in the roof showed velocity anomalies connected with the opening of clay seams (or the presence of clay seams), while anomalies and reductions in velocity in the walls of mine entries were reportedly associated with stressinduced fracturing of the potash. Freshly mined openings showed only slight reduction in velocity in the future EDZ zone, as fracturing took time to develop. The P-wave velocity clearly appeared to be more sensitive to these anomalies than the S-wave velocity, judging by the two figures. Holcomb, 1988, found that mining of excavations in the bedded salt of the WIPP site in New Mexico had greatest effect on the attenuation of compressional waves. The EDZ could be detected to a depth of some 3 metres (about 1/2 D). The mining induced radial stress relief and increased tangential stress would tend to cause undersaturation due to dilation of the salt. The reduction in compression wave amplitude, which increased with time after excavation, was a stronger indicator of EDZ than the minor reduction in P-wave velocity (0.5 km/s). In softer rocks such as chalk the EDZ effect can be even more marked in terms of percentage change in velocity. At a storage cavern site in Eocene chalk with one predominant set of vertical joints of about 1 m spacing and a second, less well developed set, McDowell et al., 1992, showed mean background velocities of 2.34 km/s reducing to 1.47 to 1.56 km/s in the outer 1 to 2 metres of the wall of the pilot tunnel. Borehole investigations at the same site had shown significant increases with depth; Vp was 1.25 km/s from

Figure 7.10 Contrasting EDZ effects on Vp from drill-and-blast and TBM excavated shaft. Note the travel time-distance-velocity plotting format. Bonapace, 1983.

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RQD variations. This suggests a stress-related increase in Vp, rather than systematically reduced jointing. In this relatively low velocity chalk, the authors experienced the seismic restriction caused by shotcreting of a fault zone. This stiffer, high strength layer caused a thin, high velocity surface layer to be registered.

7.3

EDZ investigations in selected nuclear waste isolation studies

Starting in the late 1970s, but increasingly from the 1980s and since that time, there have been a growing number of nuclear waste disposal studies at potential or generic sites, and at underground laboratory facilities. Some of the facilities have become ‘household’ names in rock mechanics circles, starting with Stripa (in Sweden), Grimsel (in Switzerland), URL – underground research laboratory (in Canada), BWIP – basalt waste isolation plant (in the USA), Äspö (in Sweden) and several other prominent facilities. In this review of selected EDZ data, significant results from four of these facilities will be described here. In Part II, Chapter 16, further results from additional sites in the United States will be described, due to their seismically-relevant jointed-rock-mechanics aspects.

7.3.1

Figure 7.11 EDZ effect and clay seam velocity anomalies in a potash mine roof. Vp is seen to be more sensitive to the EDZ than Vs. Stead et al., 1990.

0–30 m, about 2.2 km/s at 70 m depth, and 2.6 km/s at 90 m depth. (This closely follows the Q c  0.1 velocity–depth curve in Figure 5.37, with a 10% porosity correction, but requires an upward correction to an appropriate rock quality Q-value: e.g. to Q  1 if c was 10 MPa.) A corresponding increase in S-wave velocities was not recorded in the chalk; values were mostly 1.4 km/s, with small variations (0.3 km/s) related to lithology and

BWIP – EDZ studies

King et al., 1984, and King et al., 1986, reported on a series of cross-hole seismic measurements performed in a flow-entablature, columnar-jointed basaltic rock mass. The columns were regular but sinuous, 0.15 to 0.36 m in thickness, dipping 70 to 90°, with frequent low angle, discontinuous cross-jointing. The measurements were made between four horizontal boreholes drilled 12 metres into the wall of a drill-and-blasted underground opening, at 46 m depth, and theoretically above the water table. The objective was to investigate the effect of blast damage and stress redistribution, i.e., two of the assumed chief components of the EDZ or excavation damage and disturbed zone. A vertical separation of boreholes 1 and 2 of 3 m, and a horizontal separation of boreholes 3 and 4, also of 3 m (in the form of a cross) allowed both the vertical, horizontal and diagonal paths to be investigated, thereby crossing different joint sets (predominantly sub-vertical columnar) at different angles. Figure 7.12a and b show the test set-up.

Excavation disturbed zones and their seismic properties

(a)

(b)

(c)

(d)

125

Figure 7.12 Experiment for measuring EDZ effects in a tunnel wall (or ‘face’), at the Basalt Waste Isolation Project (BWIP). a) Test set-up, b) test principle, c) and d) four of the selected ray paths and the effect of the EDZ on the P-wave velocities. King et al., 1984.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 7.13 RQD variation in the boreholes in basalt showed no marked EDZ effect. King et al., 1984.

The large contrasts in Vp values for the vertical path (#1 to #2) and for the horizontal path (#3 to #4) close to the opening (1.5 to 2.0 km/s difference) are indicated in Figure 7.13c. A significant reduction in velocity of 1 to 2 km/s, most in the diagonal directions shown in Figure 7.13d, is seen in the outer 2 to 3 metres. There is also some indication of a tangential stress concentration effect; the background (far-field) velocity of about 5.4 to 5.8 km/s appears to be elevated by about 0.5 m/s from about 4 to 8 m depth in the wall. Signs of loosening effects of the sub-vertical joints are evident in the horizontal velocity reductions. The additional effects of potential stress anisotropy and joint anisotropy are clearly illustrated in King et al., 1984, 1986, results. The authors registered no consistent trend in RQD values with depth. Figure 7.13 does not suggest that increased jointing caused the marked velocity reduction. The velocity reductions are a product of blast-damage, stress relief (and redistribution) and possible reduction in moisture content. The authors noted water flow from some of the horizontal holes during the tests and originally assumed more or less saturated conditions. The horizontal and (to a lesser extent) the diagonal seismic measurement paths crossed the more open columnar joints, and these features clearly opened most as a result of excavation, giving the strongest reductions in velocity (55% to 65%). King et al., 1986, also investigated the effects of stress (7 to 21 MPa) and saturation on Vp, on Vs, on the dynamic modulus, and also on the Poisson’s ratio of ten intact specimens. Comparison of Figure 7.12 and Figure 7.14 indicate a higher velocity in the vertical in situ planes

Figure 7.14 Effects of stress on laboratory samples of the basalt, in the dry and saturated states. King et al., 1984.

than in the intact laboratory samples (6.3 km/s compared to 6.0 km/s). In the dried-out state, the parameters showing most response to stress level were Vp and the dynamic Young’s modulus. The authors also analysed in some detail the seismic quality factor which also has the symbol Q. This seismic quality (which we have termed Q seis to avoid confusion) is inversely proportional to the attenuation coefficient, for a given frequency. Only in the vertical direction was it significantly increased in situ, perhaps in response to the tangential stress increase. King et al., 1986 laboratory test data for the same rock also showed the positive effect of stress on Q seis, with the S-waves showing the strongest reduction in attenuation and the highest increase in Q seis, as clearly shown in Figure 7.15. In a subsequent paper, Zimmerman and King, 1985, used the known effects of saturation on dynamic moduli. Theoretically, shear modulus is unaffected, while bulk modulus increases linearly to equal the uncracked rock when s  100%. They suggested that the degree of saturation and the joint or crack density were each contributing to the measured reductions in cross-hole velocities Vp and Vs, as shown in Figure 7.16a and b. These results are presented in order to emphasise the possibility of drying out of some of the joints, despite water flow from some of the holes. The theoretical analysis of crack density does not appear to be supported by the RQD measurements in general (Figure 7.13) but is perhaps an expression of joint void ratio changes (equation 7.1) with the joints closest to the tunnel wall showing the largest voids and therefore suggesting an apparent (but false) increase in joint density.

Excavation disturbed zones and their seismic properties

7.3.2

Figure 7.15 The effect of stress on the seismic quality Q, the inverse of attenuation, for the basalt samples. Note that the authors’ use of the term ‘rock quality factor’ is left unchanged in this reproduction of their drawing. (As will be discussed in detail in Part II, Chapter 10, there are indeed certain numerical similarities between rock quality Q and seismic quality Q). King et al., 1984.

Figure 7.16 Vp and Vs as a function of depth in the tunnel wall (or ‘face’), saturation level and crack density variations in the EDZ in BWIP basalt. Zimmermann and King, 1985.

127

URL – EDZ studies

The underground research laboratory (URL) in Manitoba, Canada was the subject of numerous and very informative rock mechanics and geophysical studies. Novel instrumentation was used for monitoring responses to test tunnel excavation through the limited areas of natural fracturing. However, the dominance of massive, unjointed, highly stressed granite resulted in particular focus on stress-related EDZ, with down-hole sonic logging and acoustic emission monitoring, together with parallel laboratory tests and numerical modelling studies. Several phases of investigation of EDZ effects, and several scales of investigation were accomplished in this mostly massive, highly stressed granite. (Martin et al., 1995). We can start at the smallest scale, by looking at the effect of the high in situ stresses, and mode of excavation, on the state of micro-cracking in cored samples. The French group, ANDRA (Homand-Etienne and Sebaibi, 1996) selected core samples from radial boreholes drilled in the walls of a drift where excavation was either by normal blasting or by smooth blasting. Micro-cracking, partly induced by the excavation and partly pre-existing, indicated Vp reductions of about 1 to 1.5 km/s in the outer 0.8 m of the normally blasted tunnel, and reductions of about 0.5 km/s in the outer 0.5 m of the smooth blasted excavation, as shown in Figure 7.17. In each case the core samples recovered from various depths into the tunnel wall had been machined into cubic specimens prior to the velocity measurements. The effects of highly anisotropic, sub-horizontal stresses at the URL were studied in a unique test tunnel (ED2Z only), at the 420 m level. (Figure 7.18). Excavation was by line drilling and reaming, followed by mechanical breakout to avoid blast damage. Principal stresses of approximately 60, 45 and 11 to 15 MPa, caused classic ‘break-out’ resembling that in a borehole. The originally intended circular, 3.5 m diameter tunnel, was excavated parallel to 2 in order to maximise the potential for stress-induced fracturing. The isotropicelastic theoretical tangential stresses of 165 MPa (31 – 3) in the ‘rotated’ 11o’clock roof and 5o’clock floor, and 15 MPa (33 – 1) in the side walls, caused prominent V-shaped notches of rock failure. Associated micro-cracking and stress changes were imaged tomographically (Maxwell and Young, 1996) as will be shown shortly. The walls of boreholes drilled in this carefully excavated ED2Z, provided important information about stress-related disturbance. This was measured directly

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Figure 7.17 Core samples recovered from 3 m long radial holes at a drift in the highly stressed URL, where both smoothblasting, and normal blasting were used, show evidence of micro-cracking having originated in the differently configured EDZ. Homand-Étienne and Sebaibi, 1966.

(a)

in 1 m deep boreholes using a micro-velocity probe with 10 cm separation of the transducers. Maxwell and Young, 1996, installed their probe in holes drilled both into the tensile region in the test tunnel wall, and into the compressive region. Since their measurements of velocity were in a radial direction, micro-cracking was registered in the ‘fast’ direction and in the ‘slow’ direction, the latter perpendicular to the micro-cracking. Figure 7.19a shows how both the P-wave and S-wave velocities reduce by some 10% in the outer 1 m of the tunnel wall in the tensile region of tangential stress. The unstressed core from the same hole showed additional damage and lower velocities due to the loss of radial stress (Figure 7.19b). Carlson and Young, 1993, and Maxwell and Young, 1996, also recorded acoustic emission (AE) locations during careful (mine-by) extension of the 420 m deep test tunnel. Calculated compressional wave velocities showed quite strong anisotropy in this massive granite. This was obviously caused by the principal stress anisotropy (60, 45 and 11 to 15 MPa). The lower hemisphere Vp stereonet shown in Figure 7.20 gives a clear indication of the link between stress anisotropy (caused by the very different maximum and minimum tangential stresses), and P-wave velocity. The authors’ velocity data showed a clear EDZ effect in the first 1 metre depth of tunnel wall with velocities reducing from about 5.8 km/s to 5.3 km/s in the case of the vertical direction. The acoustic emission results confirmed that rock failure was initiating just inside the tunnel wall, orthogonal to the 1 direction. The authors

(b)

Figure 7.18 A unique line-drilled and hand-mined test tunnel at URL, showed classic break-out related to the sub-horizontal 1 orientation. Maxwell and Young, 1996. Note location of AE sensors.

Excavation disturbed zones and their seismic properties

(a)

129

considered that the Vp anisotropy (10 to 14%) was due to open-crack porosity in addition to the micro-crack fabric. The location of the microseismic sensors in relation to the drilled-and-hand-mined test tunnel can be seen in Figure 7.18. The AE events shown in Figure 7.21 are seen to cluster both where tangential stresses were highest and where seismic velocity (Vp) gradients were steepest. Relatively decreased velocities were seen in the two regions that were under tensile tangential stress. It is of particular interest to note the ‘broadness’ of the high velocity regions, which presumably reflect an increase in deformation modulus due to the particular alignment of the maximum tangential stresses. The relevant isotropic elastic stress distribution calculated with a boundary element program is also shown in Figure 7.21. In subsequent work at the URL for an experimental tunnel sealing experiment, Young and Collins, 1999 were able to demonstrate AE-interpreted reductions in average P-wave and S-wave velocities in the highly stressed zones caused by post-excavation of larger diameter ‘dog-collars’ (or sealing-bulkheads) for forming separate concrete and bentonite seals. The particular tunnel; Room 425, was elliptical in shape to reduce the previously

(b)

Figure 7.19 EDZ effect registered by downhole sonic probe at URL test tunnel. a) Vp and Vs in situ down a 1 m deep horizontal hole b) P-wave velocity in situ compared with that of unstressed, but micro-cracked core from the same hole. Maxwell and Young, 1996.

Figure 7.21 AE events, and the interpreted regions of increased average velocity, are reasonably consistent with the elastic continuum model of the stress distribution. Maxwell and Young, 1996.

Figure 7.20 Principal stress-orientated velocity anisotropy (lower hemisphere plot) and EDZ effects on Vp at the same URL test tunnel, Canada. Carlson and Young, 1993.

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referred maximum tangential stresses to a tolerable 105 MPa. The microseismic instrumentation available to monitor this tunnel sealing experiment (TSX) was extensive, consisting of 16 grouted-in-borehole triaxial accelerometers, operating in the 0.1–10 kHz band, and providing 3D coverage of an outer 100 m  100 m  50 m volume surrounding the tunnel. Two higher resolution AE arrays for recording in a 10 m  10 m  10 m volume around the collars, consisted of 24 ultrasonic transducers operating in the 50–250 kHz band. Each of these arrays had 16 receivers and 8 transmitters. Young and Collins, 2001 described the way their AEbased monitoring of temporal changes in Vp and Vs was used to estimate the theoretical change in crack density (c) and saturation (s) along any particular ray path. They also refer to Maxwell et al., 1998 who used these techniques to monitor (c) and (s) along radial boreholes at the line-drilled mine-by test tunnel shown in Figure 7.18. The theoretical assumption was that the saturation (s) did not affect the dynamic shear modulus ( ), but that the dynamic bulk modulus (k) increased linearly with (s), even equalling that of uncracked rock when s  1. Concerning the crack density (c), defined as the number of cracks per unit volume multiplied by the cube of the mean crack radius, they assumed that the dynamic Young’s modulus Edyn and the dynamic Poisson’s ratio in the damaged material, when normalized by the undamaged material, decreased exponentially with (c). Young and Collins, 2001 showed a small reduction in (s) from 0.485 to 0.455, and a small increase in crack density (c) from 0.198 to 0.206, during a 16 months monitoring period, for a ray-path from the tunnel perimeter to 3.5 m into the wall of the tunnel. The development of a rock fracture adjacent to the heat-producing curing of the concrete part of the bulkhead, and its effect on AE monitoring of velocities, is also described by Young and Collins, 2001 and Young and Baker, 2001. This fracture caused a temporary loss of AE signal, both for average P-wave velocity and P-wave amplitude monitoring. There was subsequent recovery of both signals caused by remedial grouting. The approximate 90% drop in P-wave amplitude caused by the fracture was about 30% recovered by the effect of grouting. A steady, slow rise in Vp (40 to 50 m/s increase was noted during one of the monitoring periods), was associated with the slow hardening of the concrete. All raypaths through the concrete bulkhead, when averaged, suggested 0.18 m/s and 0.13 m/s per day increases in Vp

and Vs. When constant density was assumed, these increases suggested a theoretical 3.5% per year increase in Edyn for the concrete. The focus on microseismic and acoustic emission monitoring when excavating variously shaped tunnels in these highly stressed, massive granites has naturally aroused curiosity about both the exact location of failure around an opening (how close to the wall is initiation?), and curiosity concerning the type of fracturing responsible for the microseismic events. Cai et al., 1998, together with mining-rock-mechanics colleagues Kaiser, and Martin, who had most responsibility for URL rock mechanics experiments, collectively address the dominance of tensile fracturing in brittle rocks, and the apparently unrealistic source sizes provided by shear-failure based models. Contrary to failure around tunnels or boreholes in weaker, less brittle materials, which seems to be dominated by log-spiral-type single-set or conjugate-set shear failure (e.g. Addis et al., 1991, Barton, 2004), the rock mass fracture process near underground openings in hard brittle rocks appears to be dominated by extension cracking, as extensively reviewed by Cai et al., 1998. The authors therefore argue that the focal mechanism will differ from that of natural earthquakes, where slip on pre-existing faults may dominate. Out of the 3,500 events recorded when excavating the line-drilled test tunnel depicted in Figure 7.18, some 800 events were located within the volume of a subsequently excavated 3.5 m thick slice, that was line-drilled from the floor of the tunnel. These events mostly clustered in the region, shown in Figure 7.22a, where 2D deviatoric stress (actually a shear stress) was larger than the crack initiation threshold, which the authors suggested was about 70 MPa, or (0.4  0.1)c. This was also where the ‘notch’ failures occurred. When the authors estimated the crack sizes using traditional shear models, they appear to have obtained unrealistically large crack radii. They argue that the ratio of the S-wave energy to the P-wave energy is an important indicator of the type of focal mechanism. The S-wave energy usually dominates, as the energy radiated in P-waves is only a small fraction of that of S-waves. It appears from their review that when Es/EP  10, the cracking process involves a dominant tensile failure component, whereas if Es/EP  20 to 30 the cracking process is dominated by shear failure. Reportedly, many mininginduced seismic events of large moment magnitude also have high Es/EP ratios, and can be analysed realistically by shear models.

Excavation disturbed zones and their seismic properties

(a)

shows the recorded ratios of Es/EP and their location in relation to the advancing face of this carefully excavated test tunnel. In the region where X/2R  2, i.e. within two diameters of the advancing face, where the 3D stress distribution is changing to a 2D distribution, there are greatest numbers of likely tensile-dominated events, and a small number with such high S-wave/ P-wave energy ratios (Es/EP), that shearing events may be suspected. Martin et al., 1997 reported that the ‘slabbing’ associated with the notch formation (Figure 7.22a), started at 0.14 to 0.28  1 diameter from the face (X/2R  0.14 to 0.28). Earlier during the URL work, Maxwell and Young, 1996, had reported an interesting case of ‘passive-source’ (i.e. AE) tomography from South Africa. Concurrence of AE events with high stress conditions ahead of the mining face in the South African Blyvoor gold mine were again associated with high velocities (for example 5.8–5.9 km/s) in the P-wave tomogram. Therefore using passive source (AE) tomography, the velocity image could potentially be used to map problem areas. The majority of small magnitude rock bursts in the mine were located in regions of high velocity gradient, between a low-velocity failed zone and a high-velocity, highly-stressed zone. Logic would perhaps indicate that this was a region of high shear stresses.

7.3.3

(b)

Figure 7.22 a) Some 800 microseismic events recorded in the 3.5 m thick slice that was line-drilled in the floor of the URL mine-by tunnel. The notch formation is also shown, together with a 2D calculation of the deviatoric (1–3) stress contours from an isotropic elastic model. b) Microseismic event location relative to the advancing face of the test tunnel, and the relevant ratio of S-wave and P-wave energies (Es/EP). The 78% of ratios 10 suggested dominance of tensile cracking sources. Cai et al., 1998.

Their URL data for the 800 or so events clustered within the line-drilled 3.5 m thick slice, showed that Es/EP ratios were most frequently between about 6 and 12, and 78% of events had ratios 10. Figure 7.22b

131

Äspö – EDZ studies

The Äspö hard rock laboratory (HRL) is the second major location in Sweden for investigating nuclear waste disposal problems such as the excavation disturbance zone. (The first was at the disused Stripa mine, where many international teams cooperated in SKB’s facility.) At the 420 m level in Äspö HRL, extensive seismic and radar investigations were performed, principally in order to compare the depth of excavation damage zones in immediately adjacent drill-and-blast and TBM sections of tunnel. The site of the ZEDEX (zone of excavation disturbance experiment) is illustrated schematically in Figure 7.23. Some of the results of the radial cross-hole tomography performed by Cosma and Enescu, 1996a,b, are shown in Figure 7.23. The borehole radar and seismic cross-hole tomography produced comparable locations for some major joints, which correlated with core logging in the relatively good quality granite and diorite (rock mass quality Q-value mostly 10 to 40, weighted mean  23).

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(a)

(b)

Figure 7.23 The Äspö ZEDEX site for TBM and D  B evaluation of EDZ effects, with cross-hole seismic tomography results. Cosma and Enescu, 1996a,b.

There was a very mild EDZ effect on Vp and Vs due to the high stresses and the partly discontinuous jointing. P-wave velocities measured across horizontal planes were 6.06  0.1 km/s for both the TBM and drill-and-blast tunnels. In the vertical planes, differences in the two cases were observed, 5.96  0.15 km/s around the TBM drift and 6.26  0.1 km/s around the drilland-blast drift. Prior to excavation, the three-dimensional principal P-wave velocities were 6.06 (vertical), 5.99 (horizontal, NW) and 5.90 (horizontal, NE) km/s respectively. Principal stresses at the ZEDEX site were approximately 32, 17 and 10 MPa. Emsley et al., 1996, showed that Vp (fast) was parallel to 3 (vertical), while Vp (slow) was perpendicular to 1 due to anisotropy caused by jointing. In this case Vp (intermediate) was parallel to 1. In fact, both jointing and the stress-anisotropy caused the moderate anisotropy in seismic velocities at Äspö. In the ZEDEX damage zone studies at Äspö, Bauer et al., 1996, also recorded the changes of velocity in 3 m long radial boreholes drilled in the wall and floor of the TBM and drill-and-blasted drifts, using sonic logging. Reductions in Vp from the background value of 5.9 to 6.0 km/s were recorded in the first 0.25 m into the TBM tunnel walls, and up to 1 metre into the walls of the drill-and-blasted tunnels. It is of interest to note the ‘flat’ response seen in Figure 7.24, where tangential stress changes around the tunnel are not ‘seen’ by the seismic velocity, due presumably to the good quality of the rock (Q-value
22–24) and the existing high stresses, which were high enough to have acoustically closed the joints, but not high enough to cause excavation induced micro-cracking, as shown earlier at the URL (Homand-Etienne and Sebaibi, 1996). The rock quality Q c-Vp-M inter-relationships reproduced in Figure 7.25 can be utilised to demonstrate some concurrence with the above data. Some 800 metres of drill core logged by NGI at the ZEDEX site showed a weighted mean rock quality Q-value of 24 (‘good’ quality). If we utilise the c/100 normalisation of Q (Chapter 5) using c
200 MPa as measured, Q c equals approximately 50. Vp is predicted to range from about 5.8 to 6.2 km/s for an equivalent depth range (relevant to the principal stress range) of about 400 to 1200 metres, rather close to the measured values reported above. The intact rock laboratory E-modulus was 69 GPa, and a simple UDEC model showed concurrence with the small measured deformations of 1 to 2 mm when a

Excavation disturbed zones and their seismic properties

133

velocity range of 5.8 to 6.2 km/s. Calculated dynamic moduli around the drill-and-blast drift ranged from 76 to 79 GPa. Presumably the situation M
Edyn has some implied relation to ‘acoustically closed’ jointing.

7.3.4

(a)

(b)

(c)

Figure 7.24 EDZ measurements of Vp in 3 m long radial holes in the TBM section of the Äspö ZEDEX project. Bauer et al., 1996.

deformation modulus of 60 GPa was used. The equation relating mean deformation modulus M with Vp shown in Figure 7.25 (see inset), suggests deformation moduli ranging from 58 to 79 GPa, for the predicted

Stripa – effects of heating in the EDZ of a rock mass

The EDZ studies performed in relation to nuclear waste isolation problems focuses much attention on the disturbed properties in this zone. We have seen many examples of increased disturbance from the frequently measured reductions in seismic velocity and deformation modulus, and these reductions, taken in conjunction with increased joint void ratios, generally lead us to expect enhanced permeability in the EDZ. This does not always occur however. In the Stripa SCV (Site Characterisation and Validation) experiment (Olsson et al., 1993), inflow to the test tunnel was less than almost all the hydraulics modellers had predicted, based on dedicated borehole permeability testing, using holes drilled along the future periphery of the tunnel. Several potential reasons for this discrepancy were described by the researchers involved, including dissolved air coming out of solution at the reduced pressures, blast gas invasion of the joints, and Poisson expansion in the third (axial) dimension causing increased axial (i.e. normal) stress on dominant joints crossing the tunnel. Rock mechanics modelling with two- and three-dimensional distinct element codes (UDEC-BB and 3DEC) had shown insufficient shear (mostly 1 mm) for dilationenhanced permeability changes, due to the small size (2  3 m) of the test tunnel, which had quite discontinuous jointing. This property was modelled with ‘numerically glued’ joint ends. (Barton et al., 1992b). The planned use of the geosphere as a potential disposal volume for nuclear waste has meant that the heating (and cooling) effect in the rock exposed in the floor or walls of test tunnels has been the subject of much research. Large diameter disposal boreholes for high level waste canisters will also be in the EDZ of the excavations, and will create their own smaller EDZ around the large boreholes. What effects can we expect on local rock stresses, on seismic velocities, and on permeability, due to the production of considerable heat over long time-spans in the early disposal period, followed by the cooling period?

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Figure 7.25 Rock quality Q-value observations from 800 m of core logging, corrected to Qc by the high value of c
200 MPa, gives a realistic prediction of Vp and deformation modulus at 450 m depth, when compared with ZEDEX data.

A drift in the Stripa mine in Sweden, used for borehole heater tests, showed some interesting effects of thermally induced strains. These caused increased seismic velocities between drained monitoring holes in the jointed quartz monzonite. A schematic of the experimental set-up shown in Figure 7.26a, indicates the relative locations of the ultrasonic monitoring holes, which were drilled to 10 metres depth, twice as deep as the heater borehole. Paulsson and King, 1980, showed the increases of seismic velocity for cross-hole measurements (M8–M6), as a function of time after heater turn-on and turn-off. Preand post-heater velocities were generally similar, as shown in Figure 7.26b, and a velocity anomaly at about 3 m depth was ‘smoothed-out’ by the heating but ‘returned’ when the rock was cooled. Across the mid-plane of the heater, at 4.2 m depth, the four sets of cross-hole velocities (Figure 7.26c) showed more or less parallel behaviour, except for an extra strong reduction in velocity for M7–M9 after heater turn-off. The authors give interesting similar-trending curves for monitored displacement and stress change about 1 m from the heater (Figure 7.26d). They do not have a confirmed explanation for the anomalous net reduction

in velocity at the end of the test (M7–M9). However, it might be related to the improved closure of joints at elevated temperature, even under constant normal stress, as measured by Hardin et al., 1981, and discussed in more detail by Barton et al., 1985. Upon cooling, the less rough, interlocked joints may ‘spring-open’ more than their closed neighbours, to avoid tensile stress development. This could then cause a marked reduction in seismic velocity if the open joint or joints, happened to cross the path of the seismic array. Related local increases in joint conductivity, and reduced shear strength, of any ‘open’ and more planar joints, could be an added uncertainty in nuclear waste related disposal scenarios, as emphasised by Barton and Makurat, 2006. Further details of this Stripa heater experiment (Paulsson and King, 1980) were subsequently reported in a comprehensive analysis by Paulsson et al., 1985. The full duration of the test was 750 days with 398 days of heating. The long period of cooling generally returned seismic velocities to values lower than before the heating, suggesting permanent changes (such as local excessive joint opening as hypothesised above). A significant quantity of water expelled during the heating signified a

Excavation disturbed zones and their seismic properties

(a)

135

(b)

Figure 7.26 Heater experiments at Stripa, with velocity changes matched by stress and displacement records. Paulsson and King, 1980.

general closing of the joints. Temperatures were over 100°C in a small region around the heater and water was expelled also from distant boreholes where perhaps the low initial permeability was less reduced. The initial increase in velocity with temperature was linear and varied from 2 to 4 m/s/°C. The average joint frequency in the test area, analysed from 224 m of core, was 8.3/m, and an elastic continuum analysis conducted prior to the test had indicated larger stresses and local displacements than were actually measured, presumably due to the compliance of all these joints. This effect was also presumably experienced in a ‘heated-mine-by’ experiment in the Climax Mine, in the USA.

The full record of P-wave and S-wave velocities over the 750 days duration of the test is shown in Figure 7.27a and b. The largest velocity changes caused by the heating, amounting to 0.2–0.3 km/s were interpreted as occurring in the direction of the minimum horizontal stress, which is logical since the calculated thermal stress was as much as 55 MPa in, presumably, the direction of maximum horizontal stress. The effect of the heating in an in situ experiment such as that described by Paulsson and King, 1980, and Paulsson et al., 1985, is to change both the stresses in the rock and the degree of saturation, particularly close to the source of heat. In an effort to understand and

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(a)

(b)

(b) (c)

Figure 7.27 Complete P- and S-wave velocity record for one of the Stripa heater tests. Maximum Vp increase was parallel to minimum stress. Paulsson et al., 1985.

isolate some of these effects, Paulsson, 1984, conducted uniaxial tests (0–52 MPa) on granitic (quartz monzonite) samples from the same Stripa test drift. The samples were intact but because of micro-cracks showed strong effects of saturation levels on P-wave velocities. Figure 7.28a shows the effects of axial stress on axially measured P and S-wave velocities in the dry and saturated states. The standard deviation of results from eleven specimens is shown by the length of the crosses. A clearer indication of the important effect of degree of saturation on Vp at different stress levels is given in Figure 7.28b. Lesser effects are seen on Vs in Figure 7.28c. This particular sample showed stronger effects than the general trend given in Figure 7.28a, and may presumably have been due to increased porosity from low aspectratio micro-cracks, since the initial velocity when dry was only 4.6 km/s (at 5 MPa), and rose to more than 5.8 km/s with full saturation.

Figure 7.28 Uniaxial tests on intact but micro-cracked Stripa granite show the important influence of stress and degree of saturation on Vp, and to a lesser extent, Vs. Paulsson, 1984.

7.4

Acoustic detection of stress effects around boreholes

Plona et al., 1997, utilised the effects of compressive stress concentrations around boreholes to investigate if principal stress orientations could be determined by acoustic measurements from within boreholes, at stress levels lower than needed for break-out. They referred to the triaxial tests on sandstone reported by Sammonds et al., 1989, reproduced in Figure 7.29, to emphasise the possibility of differentiating the high tangential stress from the low tangential stress region around a

Excavation disturbed zones and their seismic properties

Figure 7.29 High pressure triaxial tests on sandstones showing the strong coupling of stress with velocity changes. Sammonds et al., 1989.

137

Figure 7.31 High frequency, axial P-wave monitoring around a 10 cm borehole in a uniaxially loaded cube of sandstone. Plona et al., 1997.

Figure 7.32 Acousto-elastic calculation of Vp anisotropy around a uniaxially loaded borehole in sandstone (H  10 MPa) Plona et al., 1997. Figure 7.30 Theoretical elastic stress distribution around a uniaxially loaded borehole. Jaeger and Cook, 1977.

borehole. An elastic model of the latter is shown in Figure 7.30 for the case of uniaxial loading (Jaeger and Cook, 1977). Plona et al., 1997, used a 50 cm cube of sandstone with a central 10 cm diameter borehole loaded uniaxially to 21 MPa, to investigate the potential of axial acoustic refraction monitoring at numerous azimuth locations around the borehole. Their principal results are shown in Figure 7.31.

Break-out reportedly started at the 15 MPa stress level where velocity maxima were registered across a diameter. The decline of velocity seen at 19 MPa was due to mechanical damage in the same diametrically opposite  max locations. In Figure 7.32, the authors show the results of an acousto-elastic model for a borehole in sandstone, loaded with a boundary stress of 10 MPa. The general similarity of model and experiment is striking. One may wonder whether these effects are taken into account in the general interpretation of sonic logging down boreholes, since several hundred m/s variations in

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velocity are seen in a ‘simple’ unjointed sandstone, with admittedly, an extreme induced tangential stress anisotropy of 30 MPa for  max, and (-) 10 MPa for  min (based on the isotropic elastic tangental stress ‘rule-of-thumb’ 3A-B, 3B-A). Significant azimuthal velocity anisotropy effects would seem to be possible in wells where there was significant horizontal stress

anisotropy, plus structure in the form of vertical or subvertical jointing that would be variously opened or closed by the respective effects of  min and  max. Is it possible that the sonic logging ‘misses’ such effects of velocity anisotropy around the horizontal plane, due to principally vertically and steeply inclined ray paths?

8

Seismic measurements for tunnelling

Tunnel face seismic tomography using a pair of boreholes that was performed by NGI at the Oslo Fjellinjen Tunnel, in the late 1980’s, was used to help the contractor plan for ground freezing in one tube, while careful multiple drift excavation was performed in the other tube. The 2  13 m span motorway tunnel beneath the Oslo downtown harbour district, passed through a wide regional fault zone with 2 to 4 m of crushed alum shale over the arch, underlying 20–30 m of soft, sensitive marine clays. The advantages of the ahead-of-the-event data far outweighed the relatively short stoppages and modest cost involved. There are now several companies around the world who are offering the use of reflection techniques for mapping marked reflectors out to many hundreds of

Figure 8.1 Cross-hole seismic tomography performed by NGI at the face of the Oslo Tunnel in 1987, when approaching a major fault zone. Nord et al., 1991.

meters ahead of an advancing tunnel face. Here, both sources and receivers are placed within the tunnel. By the nature of the reflection result, it is difficult to determine if the quality will be better or worse. Others have proposed, and demonstrated, the advantages of combining this with in-tunnel seismic refraction, with an intunnel source and both internal and external (mountain side) receivers. One can then obtain reliable velocity and rock quality predictions ahead of the face, both in front of, and behind the reflectors, which will thereby correlate better with possible pending tunnelling difficulties.

8.1

Examples of seismic applications in tunnels

Concerning the obvious need to have information ‘ahead-of-the-event’ in a tunnel, Nord et al., 1991, commented that the present ‘lack of information has only been accepted due to the high cost of obtaining it’. The authors went on to analyse the duration and frequency (in metres) of down-time at some hard rock projects. They concluded that probe drilling to 50 metres, and 1/2 to 1 hour for the seismic probing measurements would likely be sufficient. It does not take long to percussiondrill to 50 m with modern hydraulic jumbos, when 1 to 4 m per minute rates of penetration are achieved. We will now go backwards in time to an impressive early example of the use of geophysical surveys in tunnels, as given by Scott et al., 1968, for the Straight Creek pilot bore of 4.0 m diameter, driven under the continental divide in Colorado, USA in 1963 and 1964. (Figure 8.2). Both seismic and resistivity measurements were made at regular and irregular intervals along the bore, in order to sample each class of rock. Five rock classes were defined, based principally on joint spacing (3 cm to 0.9 m), mineral alteration (%) and presence of fault gouge, foliation or schistocity. The rock types themselves (granite, diorite, gneiss, migmatite and schist) did not appear to determine rock class. The seismic velocity of the deep layer beneath the

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 8.2 Cross-section of Straight Creek pilot bore showing geophysical test locations. Scott et al., 1968.

excavation-disturbed low-velocity layer (caused by stress redistribution and gravity induced loosening in the arch) was correlated to a number of key construction parameters by the authors, and good correlation was indicated in many cases. The following deep layer velocities were measured at the five seismic spreads shown on Figure 8.2: #1 5.2 km/s, #2 5.1 km/s, #3 4.8–6.1 km/s, #4 4.2 km/s and #5 6.0 km/s. Later, the much lower shallow layer velocities will be introduced into the discussion. Figure 8.3a and b compare the thickness of the lowvelocity layer and the so-called ‘tension arch’, defined by the authors as the depth where no further measured dilation of the rock in the arch could be detected. The range of seismic velocities shown (14000 ft/s  4.3 km/s, 20,000 ft/s  6.1 km/s) correspond to the range of rock classes 5 to 1, and obviously reflect the confinement effect from the mostly 200–500 m of overburden. The worst quality (class 5) corresponded to seismic spread #4 in Figure 8.2 (Vp  4.2 km/s), which had a local overburden of about 300 metres, and obviously was strongly affected by the depth or stress level. Our earlier hard rock relation Vp  3.5  log10 Q with depth correction, (Figure 5.36), suggests a possible Qc – value of about 0.1 assuming low porosity, hard rock is involved. At the surface a Vp value of 2.5 km/s is implied for this rock mass quality i.e. severely faulted ground which appears to correspond to the authors’ description of class 5 rock. (A disturbed zone of at least one diameter was indicated for such rock.) Scott et al., 1968, showed good correlations between Vp and construction data such as steel set spacing (Figure 8.3b), and rate of construction (Figure 8.3d). They also showed a significant correlation of tunnel support type with electrical resistivity (Figure 8.4a) which

is itself partially correlated with the deep layer velocity (Figure 8.4b). Already at this early date (the mid 1960s), the authors envisaged a time when geophysical probing ahead of tunnels would have enough correlations to conditions in tunnels of different size, and ‘in all environments’, that a full diameter bore could be driven directly, without the need for time-consuming pilot bores. It is of interest to speculate that the great difficulties encountered when driving the full-scale, twin bore Straight Creek tunnel were caused by, among other factors, an unexpectedly large scale effect caused by the 4 m to 12 m tunnel size difference, and perhaps insufficient appreciation of the effect of stress on the seismic velocities at that time. There is also the possibility of adverse interaction between the twin tubes, with ‘plastic zone’ overlap, a problem of relevance when assessing risk in twin-bore TBM tunnelling, where conditions are very unfavourable for any type of tunnelling. (Barton, 2004c). The attempted use of steel sets in fault zones at Straight Creek, probably allowed too much (scale dependent) loosening of the ground, with the low velocity layers even more affected than in the pilot bore of 4 m span. The seismic velocities of the shallow layers at the five seismic spreads listed above (#1 to #5, Figure 8.2) were respectively: 3.0 km/s, 2.3–2.7 km/s, 2.3–3.1 km/s, 1.3–1.6 km/s (worst case, class 5) and 2.3 km/s. Perhaps more attention should have been paid to these extremely low EDZ velocities (and to the thicknesses of such zones in the worst rock) which caused almost insurmountable problems in the main bore, which took several year to complete. The Q-system support pressure database (Barton et al., 1974) includes Straight Creek main bore as almost the highest recorded tunnel support

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Figure 8.3 Disturbed zone thickness and some support and construction rate details based on Vp measurement at the Straight Creek pilot bore. Scott et al., 1968.

capacity of at least 300 tnf/m2, and an estimated rock mass ‘quality’ Q-value as low as 0.001. Multiple perimeter drifts filled with concrete of some 2 to 3 m thickness were needed in some zones. Ikeda, 1970, assembled a comprehensive set of technical data from some 70 rail tunnels in Japan. He first classified rock types into classes A to F, as reproduced in Table 8.1. Examples of Class A rocks were metamorphic rocks such as gneiss, quartzite, etc., while examples of Class E were Pleistocene rocks such as mudstone and volcanic ejecta. He then listed typical ranges of seismic velocities (Vp) under rock conditions (Classes 1 to 7), shown in Table 8.2 for each of the previous rock type classes A to F. The two examples under Class 3 rock condition would be

A/3  4.0 to 4.6 km/s, E/3  2.6 km/s. Based on the classification of rock conditions (Classes 1 to 6), he gave tunnel support loads in the range 0.01 to 0.3 MPa (1 to 30 tons/m2 range for Classes 1 to 6), and spacing of the steel arch support in the range 1.5 to 0.75 m, and concrete thickness in the range 0.3 to 0.9 m, for 30 m2 and 60 m2 tunnel sections from his 70 case records. These data are reproduced in Figure 8.5 a, b, c and d. This is a valuable set of early case records and their technical description, using seismic velocities. A somewhat finer division of rock types than the original Japanese Railways classification of Ikeda, 1970 has been used in more recent years by the Japanese Highway Authority. This is reproduced in Figure 8.6 (from Barton and Itoh, 1995), showing the addition of

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Figure 8.4 Some cross-correlation between support type, resistivity and undisturbed (deep layer) velocity. Straight Creek pilot bore. Scott et al., 1968.

Table 8.1

Rock type classes (A to F) of Ikeda, 1970 based on lithology and geology.

Rock qualities

A

B

C

D E F

Names or rocks

a) Paleozoic rocks Mesozoic rocks

clayslate, sandstone, greywacke, conglomerate, chert, limestone, ‘schalestein’, etc.

b) Plutonic rocks

granite, granodiorite, diorite, gabbro, peridotite, etc.

c) Hypabyssal rocks

granite porphyry, quartz porphyry, porphyrite, diabase, etc.

d) Volcanic rocks (some part)

rhyolite and andesite of Mesozoic era, basalt, etc.

e) Metamorphic rocks

gneiss, hornfels, schist, phyllite, quartzite, etc.

a) Metamorphic rocks having conspicuous schistocity b) Paleozoic and Mesozoic rocks having fine bedding planes a) Mesozoic rocks (some part)

shale, clayslate, sandstone, tuff breccia, ‘schalestein’, etc.

b) Palaeogene rocks (some part)

silicified shale and sandstone, tuff breccia, welded tuff, etc.

c) Volcanic rocks (greater part)

rhyolite, dacite, andesite, basalt, dolerite, etc.

a) Tertiary rocks

mudstone, shale, sandstone, conglomerate, tuff, tuff breccia, welded tuff, agglomerate, etc.

a) Pleistocene rocks Neogene rocks

mudstone, siltstone, sandstone, sand and gravel rock, tuff, terrace, talus, fan, volcanic ejecta, agglomerates, etc.

a) Alluvium rocks Diluvium rocks

clay, silt, sand, sand and gravel, loam, volcanic ejecta, fan, talus, terrace, etc.

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Table 8.2 Rock condition classification using seismic P-wave velocities based on 70 Japanese rail tunnel case records analysed by Ikeda, 1970. (Note writer’s interpretation of some of author’s words under ‘Remarks’ and ‘Notes’).

5.0 5.0–4.4 4.6–4.0 4.2–3.6 3.8–3.2 3.4

B

C

D

4.8–4.2 4.4–3.8 4.0–3.4 3.6

4.8 4.8–4.2 4.4–3.8 4.0–3.4 3.6–3.0 3.2

4.2 4.2–3.6 3.8–3.2 3.4–2.8 3.0–2.4 2.6

E

F

2.6 2.6–2.0 2.2–1.6 1.8 1.4

1.8–1.2 1.4–0.8 1.0

bad

A

medium

1 2 3 4 5 6 7

Rock qualities

good

Classification of rock conditions

Remarks: 1) Always go to a poorer class when ground water will inflow into tunnel. 2) Rocks with expansive nature have no relation to this classification. 3) Raise 1 or 2 classes when the Poisson’s ratio of the weathered rock is better than 0.3. Notes: 1) The numbers 1–7 are the rock condition ratings. 2) The numerals show the velocities of elastic wave in the rock (km/s). 3) See Table 8.1 for the rock qualities A through F.

(a)

(c)

(b)

(d)

Figure 8.5 Relationships between support intervals (steel sets), concrete lining thickness and support pressure, each as a function of rock condition classes 1 to 7, which were defined by Vp ranges. Ikeda, 1970.

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Rock quality, seismic velocity, attenuation and anisotropy

a preliminary rock quality Q-scale at the base of the figure. A comparison of the velocity ranges shown in Figure 8.6, with Table 8.2 shows, of course, broad similarity in view of the common, relatively young geology, that has to be tunnelled by the two state authorities. Note that the appended Q-scale is based on the simple shallow, hard rock equation (Vp  3.5  log Q), with no immediate attempt to correct for uniaxial strength through Qc, nor to adjust for significant matrix porosities. The ‘fit’ of Vp with Q will therefore be increasingly in error in the case of the lower velocity, weaker, and more porous rocks, which require individual interpretation of these (usually) inter-related factors, which collectively have a strong Vp-reducing effect. This means that a low velocity Tertiary sandstone with a shallow-seismic refraction velocity of 2.5 km/s, may have an initially implied Qc value of only 0.1, while the implied Qc value is 1, if n  15%. (Figure 5.36). A significantly higher apparent Q-value (due to c  100 MPa) is implied, concerning the usual factors describing the structure of the rock mass, like RQD, Jn (number of joint sets), Jr and Ja. However if the rock is incompetently weak, RQD is zero (according to the definition of Deere et al., 1967), but a minimum of 10 in the Q-calculation to avoid an impossible Q  0. Furthermore, and most importantly, there may be an unfavourably large ratio of stress-to-strength in the context of tunnelling, giving the need for an elevated SRF (see Appendix A). The differences seen above are due to a fundamental difference between characterization (with no excavation involved), and a classification, which has become known in tunnelling, as a scheme for selecting appropriate rock support and reinforcement, via RMR (Bieniawski, 1989), or Q. An account of pre-investigations and experiences while driving Norway’s first sub-sea road tunnel to the west-coast island of Vardø, was given by Palmström, 1982. Seismic refraction profiles totalling almost 13 km covered a 500 m wide zone across the 1.5 km wide sound and gave depth to bedrock with an accuracy of 0.5 m in relation to 36 soundings in the sea bed. The presumed and actual weakness zones encountered during driving of the 9.4 m span tunnel are shown in Figure 8.7. The rock cover (mean 40 to 50 m) and shallow sea depth (20–40 m) are also shown. Up to 4 joint sets were logged in the quartzitic sandstones, siltstones and shales, which had frequent clay coatings on the generally steeply dipping joints, giving poor stability, especially in the low velocity (e.g. 3.2–3.3 km/s) crushed zones shown

Figure 8.6 The Japanese Highway rock-mass-class and rock-type tabulation, together with the anticipated seismic P-wave velocities from shallow refraction seismic. Approximate rock mass quality Q-scale from Barton and Itoh, 1995.

in Figure 8.7. The overall distribution of Vp is also shown in Figure 8.8, for a rock mass with a mean logged Q-value, outside the weakness zones, of the following: 90 1 1    1.9 12 4 1 Palmström, 1982, recorded a 560 m length of concrete lining (350 m placed at the face), 2500 m3 of shotcrete Q 

Seismic measurements for tunnelling

145

Figure 8.7 Norway’s first sub-sea tunnel to Vardø, showing assumed and encountered weakness zones. Palmström, 1982. % 40 35 Distribution

30 25 20 15 10 5 0.14

(a)

3000

4000 5000 Seismic rock mass velocity

6000

(b) Figure 8.8 P-wave velocity statistics for Vardø sub-sea tunnel. Lower velocity zones and corresponding support methods. Palmström, 1982.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 8.9 Vp-Qc-M correlations with depth and porosity correction. Barton, 1995.

and 168,000 rock bolts giving an average tunnelling progress of 17 metres/week and a cost of USD 8000 per metre. The weighted mean value of Vp outside the weakness zones was close to 5.0 km/s which, according to Figure 8.9 (Barton, 1995) implies a Q-value, perhaps equal to 15 if we assume 50 m of cover and a nominal 1% porosity for these generally hard rocks. This estimate of rock mass quality from Vp compares poorly to the quoted value of about 2, which might of course be in error. Another reason for this discrepancy might be stress-related, or an effect of the hard beds of quartzitic sandstones, masking the lower velocity, weaker beds of siltstones and shales. The low-velocity zones (Vp  3.2–3.3 km/s) also created greater tunnelling difficulties than the values would suggest, implying an artificially elevated velocity in relation to rock quality. This will be discussed further. There is obviously a broad correlation between tunnel support costs (as a percentage of total costs) and seismic velocity, as shown for example by Nilsen, 1998, for the case of half a dozen sub-sea tunnels (Figure 8.10). Support costs may rise from 50% to at least 75% of total costs, when the P-wave velocity reduces from 5.5 to 4.5 km/s. As pointed out by Nilsen, the most important factor is the quality of pre-investigation and follow-up, and an understanding of the need for good investigations by the owner.

Figure 8.10 Support costs (as % of total cost) versus Vp, for some road, pipeline and water tunnels. Nilsen, 1998.

Errors in interpretation of seismic measurements, for example due to horizontally interlayered stiff (meta-sandstones) and softer shales, have on occasion caused unwelcome surprises, i.e., with ‘false’ velocities, apparently as high as 4.5 to 5.0 km/s, nevertheless requiring immediate cast concrete lining up to the tunnel face. In one such case, the depth effect upon Vp shown in Figure 8.9, may have been responsible for some of the ‘false’ velocity increase in

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147

Figure 8.11 Rock cover in relation to seismic velocities at sub-sea tunnel sites. Nilsen, 1998.

a generally extremely dry sub-sea tunnel (Barton and Monsen, NGI contract report concerning North Cape Tunnel, 1997, for Norwegian Road Authority). The logged rock mass quality Q-values of only 0.01 and the need for heavy support right up to the face were ‘inconsistent’ with the general range of Vp  4.5–5.0 km/s. In this case the rock load and the sea depth may each have contributed, due to the undrained situation. Nilsen, 1998, also gave rock cover versus bedrock depth (water  sediment) data for numerous sub-sea tunnels together with associated P-wave velocities. As expected, the highest velocities were usually associated with the lowest rock covers, while the zones with lowest velocities (as low as 2 km/s) tended to have higher designed rock cover, as shown in Figure 8.11. Sjøgren et al., 1979, performed shallow refraction seismic investigations at sites where subsequent subsurface excavations were planned or actually carried out. They were therefore able to show several cases where seismic velocity showed a broad correlation with tunnel support measures such as shotcrete and concrete lining. Although excavation span is listed in Figure 8.12, the authors did not give depth, for the caverns or tunnels listed. Significant depth is probably the reason why velocities between 3.8 and 4.7 km/s (which might correspond to hard rock Q-values of about 2 to 15 at 25 m depth) apparently were associated with such major stability problems at Rendalen (cases 5 to 8), where different sections of the headrace tunnel required from

Figure 8.12 Mean P-wave velocities at some tunnel and cavern sites in Norway, with shotcrete and concrete lining frequencies. Sjøgren et al., 1979.

15 to 55% concrete lining and from 20 to 50% shotcrete lining (with rock bolts). The mean velocities given in Figure 8.12 are of course a bit misleading, as it is the lower values in any given distribution of velocities that require the rock support. For example the few shotcrete lined sections of the Mongstad oil storage caverns (case 1, Figure 8.12) would certainly have had a lower, local velocity than the mean value of 6.0 km/s for these massive, foliated metaanorthosites. As the authors point out using an illustrative statistic from the Vardeåsen site in Norway, the high velocities (4.8 to 6.2 km/s) completely dominate the usual range of velocities from these relatively unweathered Scandinavian sites, and it is the much smaller number of tectonic zones (shear zones, faults), dykes and joint swarms with velocities from about 2.5 to 3.5 km/s that cause the construction problems, especially when high inflows of water occur. If we utilise the shallow-depth, hard rock, low porosity Q-Vp conversion given below: Q
10( Vp 3.5)

(8.1)

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 8.13 Geological profile and rock classification details for Tunnel A. Mitani et al., 1987.

the above velocity ranges for good rock and fault or fracture zones can be approximately converted as follows: 1) Vp  4.8 to 6.2 km/s (Q  20–500) 2) Vp  2.5 to 3.5 km/s (Q  0.1–1) As can be seen from Figure 8.9, a velocity as high as 6.2 km/s may for reasons of depth of measurement (or unusually high rock strength) only imply a Q-value of say 25, so conversions using this equation must always be related to the more comprehensive Q–Vp–depth–porosity model reproduced in Figure 8.9. At the Veas sewage treatment plant near Oslo, Norway, where seismic surveys were performed by Geoteam (Sjøgren, 1984), and logging of excavations in the nodular limestone were performed by NGI colleagues, the reported correlations between Vp and rock quality Q were as follows: Vp (km/s) 3.0 4.4

Rock quality Q 1 to 5 (with support) 20 (no support needed)

For hard rock at shallow depth, with negligible porosity (central trend, Figure 8.9), the above velocities would have suggested somewhat lower Q-values than the above (0.3 and 8 respectively). However, the nodular limestone, consisting of inter-bedded and well cemented shale and limestone layers, has some porosity (5 to 10% could be estimated) and its uniaxial compressive strength (c) is

less than the nominal 100 MPa for hard rocks. We can therefore use the porosity (n%) and Qc  Q  c/100 corrections in the Qc–Vp chart, which then help to explain the somewhat higher Q-values. Cecil, 1971, warned of another source for the possible lack of correlation between seismic velocity and rock quality, when considering the presence of thin clay coatings in otherwise widely spaced jointing. The latter cause potential stability problems but may hardly change RQD or Vp values. On the other hand, the Jr/Ja terms in the Q-system may capture the correct stability problems by reducing the Q-value, but Q will then not correlate so well with the velocities. These potential pitfalls in the general, near-surface correlation for hard rocks (equation 8.1) need to be carefully evaluated from case to case.

8.2

Examples of the use of seismic data in TBM excavations

A good example of the application of seismic velocity measurement to interpret TBM penetration rates is given by Mitani et al., 1987. They investigated the rate of advance of two small diameter TBM tunnels (  2.6 m) by measuring Vp and Schmidt hammer rebound values for the wide variety of rocks encountered. Tunnel A (shown in Figure 8.13) was mostly driven in sandstones, slates, porphyry and weathered conglomerates, with generally strongly developed jointing and poor stability.

Seismic measurements for tunnelling

149

(a)

(a)

(b)

Figure 8.14 a) Vp (solid bars), and Schmidt hammer rebound %, in two Japanese TBM tunnels of 2.6 m diameter, b) correlation of Vp to steel rib support spacing. Mitani et al., 1987.

Tunnel B was driven in more homogeneous but variously weathered granites. Figure 8.14a shows Vp in relation to Schmidt hammer rebound %, while Figure 8.14b shows the degree of rock support in relation to the Vp values. (Rock support consisted of unsupported sections, or various grades of steel rib, steel channel or I-beam, with successively reducing spacing, i.e., 1.5, 1.2, 1.0, 0.8 m as Vp reduced. Penetration rates, ranging from 0.6 to 5 metres per hour are shown correlated with seismic velocities in Figure 8.15. Utilisation of geomechanics and seismic testing to correlate with TBM penetration rates (PR  net-instantaneous, and AR  effective advance rate), was described by Sampaola et al., 1978. Figure 8.16 shows a quite sensitive correlation between progress in m/hr and rock mass class A, B or C (which represented statistically homogeneous zones). The tunnel was only 6.4 m in diameter, and was bored in granites of variable quality caused by alteration and variations in jointing frequency. The depth range for the tunnel was not given by the authors. The TBM appears to have been a little under-powered in relation to the strongest, least jointed rock mass class. The set of data given by Sampaolo et al., 1978, can be reproduced approximately as shown in Table 8.3.

(b)

Figure 8.15 Net penetration rates as a function of Schmidt hammer rebound and seismic velocity for 2.6 m diameter TBM tunnels in Japan. Mitani et al., 1987.

As can be noted by the above, the range of assumed rock qualities (approx. Q  0.1 to 15) do not penalise advance rates by any time-consuming support needs, so effective rates of advance for this hydropower tunnel were inversely ‘correlated’ to two of the geomechanics measures given above, and were therefore effectively inversely correlated with Q-values. This is consistent with the QTBM model of Barton, 2000. 8.3

Implications of inverse correlation between TBM advance rate and Vp

In view of the intended aim of correlating, where possible, the seismic velocity and the rock quality, it is

150

Rock quality, seismic velocity, attenuation and anisotropy

appropriate to consider in more detail the inverse correlations seen in the two previous case records. We have seen from Figure 8.15 the strong correlation between support needs and seismic velocities, which follow the normal trend of increased support with lower Vp-values, and with lower assumed Q-values. However, it will be noted that net penetration rates (PR), correlate inversely with Vp values, in other words, the increased degrees of jointing and reduced strength (also seen in the Schmidt hammer results) help to increase the penetration rate. The same trend is seen in Table 8.3 for a larger TBM (  6.4 m) boring in granites. The documented trends of degree of jointing and rock strength on drilling or boring rate seen in the above examples are summarised in diagrammatic form in Figure 8.17. The same type of inverse correlation with Vp values can be envisaged by converting the rock mass quality Q-class to a Vp-class in the upper portion

Figure 8.16 Correlations between rock mass class A, B, C and excavation speed for a TBM driven hydropower tunnel. Respective classes had Vp  5 km/s, 3.5–4.5 km/s, 3.5 km/s, and c 150 MPa, 50 MPa and 8 MPa. Sampaolo et al., 1978.

of the figure. Faster boring will correlate with lower Vp values up until some limit, as suggested by the two descending portions of the drilling rate trends. Until the above support/stability limit is reached, the net penetration rates (PR) seen in the comprehensive data of Mitani et al., 1987, may be considered to have the approximate upper and lower bound values given in Table 8.4, in relation to Vp and assumed, shallow depth (nominal 25 m), hard rock Q-values.

Figure 8.17 Conceptual inverse correlation of boring or drilling rate with Q-value or Vp-value. Modified from Barton, 1996b.

Table 8.3 Correlations between advance rates and seismic velocities (Sampaola et al., 1978), with last column added by writer, using central trend for 100 m depth, or 50 m depth, from Figure 8.9. Zone

Alteration

Vp (km/s)

c (MPa)

Effective advance rate (m/hr) (AR)

Net rates m/hr (PR)

F m1

Qest. (Barton, 1995)

A. Sound granite B. Jointed granite C. ‘Cataclastic rock’

little or no alteration medium degree of alteration high or very high alteration

5.0 3.5–4.5 3.5

150 50 8

0.4–0.6 1.8–2.0 2.5–3.0

1.0 2.5–5 4–5

2 2, 5 5

8 or 15 0.07–2, 0.2–4 0.07, 0.2

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Table 8.4 Upper and lower-bound PR–Vp–Q trends from Mitani et al., 1987 with additional interpretation. Net penetration rate (PR) Upper-bound PR (m/hr) Vp (km/s) Q

8.4

1.0 6.0 300

2.0 5.0 30

3.0 4.0 3

Lower-bound 4.0 3.0 0.3

1.0 4.5 10

2.0 3.0 0.3

3.0 2.0 0.03

5.0 1.5 0.01

Use of probe drilling and seismic or sonic logging ahead of TBM tunnels

The last decade of developments with double-shield TBM’s that use the PC-element liner for thrust when resetting the grippers, have made it possible to tunnel through a range of geological conditions, generally with less delays. However, the complexity of the machines has drawbacks in commissioning and learning-curve time, and a simpler design could in principle be used, if prior information of ground conditions were available through probe drilling and geophysical measurements. The concrete element liner, while convenient from many points of view, may be an expensive solution if most of the rock is actually of very good quality, requiring only light support. Nord et al., 1991, indicated that TBM advance rate could be optimised in mixed ground conditions, by always selecting the right tunnelling mode in response to advance information. The other needs for advance information relate of course to support needs and to the possibilities of water inrush or caving ahead of the face. There are numerous TBM around the world that are stopped for long periods (some few, even permanently), due to inadequate information about pending adverse rock conditions. (Barton, 2000) In Figure 8.18, the concept of advance seismic velocity information for subsequent rock quality class and tunnel support class estimation is presented. Ideally this should be made a routine operation, made by fast percussion drilling, such that support components such as steel arches, rock bolts or shotcrete can be immediately available, and applied with appropriate timing , at and behind the tunnel face. A more complete concept is illustrated in Figure 8.19. Here, displacement monitoring is also performed in an effort to roughly confirm the Vp–Q correlation. Since special depth or anisotropic stress effects make the Q-Vp

Figure 8.18 Conceptual drawing of sonic probe and conversion of data to rock mass Q-values and rock support classes. Barton, 1996b.

linkage complex in many cases, the approximate expectation that final displacement (, millimetres) is approximately given by:




SPAN(m ) Q

(8.2)

may be an invaluable correction to the Vp-Q correlation, which may have a ‘stress problem’, concealing the actual poor quality. (See Barton, 2000, for detailed correlations between , tunnel dimension, Q-value and other stressrelated factors). Unfortunately, the fact that the rock mass Q-value logged in a TBM tunnel may be higher than that logged in a drill-and-blasted tunnel will affect the measured deformation as described above. (Q will appear to be higher and  will be smaller). Likewise, if refraction seismic measurements were performed along the wall of the TBM tunnel, the values of Vp obtained would also tend to be higher than in the equivalent drill-andblasted tunnel for at least two reasons: 1) Reduced level and depth of damage in wall of TBM tunnel 2) Higher tangential stresses closer to the tunnel wall. Such aspects will influence other details of the behaviour of the rock mass, due to coupled behaviour. For example there will be a tendency for lower permeability and less drainage around the TBM tunnel, which, for reasons of more complete saturation might also increase the seismic velocity. However, a seismic velocity probe ahead of the tunnel will not see the difference between the TBM

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 8.19 Conceptual use of sonic probe for rock mass Q-value estimation, with displacement monitoring for confirmation of support needs. Barton, 1996b.

tunnel and the drill-and-blast tunnel, unless the measurement was made too close to the face of the tunnel. 8.5

In-tunnel seismic measurements for looking ahead of the face

The Japanese, with an extremely active tunnelling industry, in combination with far from ideal geological

conditions, appear to have taken a lead in the use of seismic for ‘probing ahead’ of their tunnels, in particular TBM tunnels, where the consequences of delays are more critical, due to both the investment level and the normal expectation of fast tunnelling. Following on from Mitani et al., 1987 analyses of the relation between TBM progress and seismic velocity, reviewed earlier, we will briefly refer to some

Seismic measurements for tunnelling

Figure 8.20 Seismic reflection for identifying a change of conditions, combined with the results of sonic logging in a probe hole. From Kajima Corp. Nishioka and Aoki, 1998.

more recent advances concerning seismic ‘probing ahead’. The advantage of being fore-warned of changed conditions by means of in-tunnel reflection methods is nicely illustrated in Figure 8.20. Also shown is the use of a probe hole, and a sonic logging of this hole, with a low velocity fractured zone correlating with an interval of reduced ‘breaking energy’, possibly actually referring to compressive strength, in view of the units used. Clearly, the reflector further ahead, presents the possibility of either reduced or increased rock mass quality. A radically reduced Vp and Q-value and a decision for pre-injection, pre-reinforcement and perhaps overboring may save weeks or months of delay and cost only one or two days in ‘lost’ production. Such an investment appears worthwhile. Hayashi and Saito, 2001 described an interesting approach to seismic surveys for tunnelling that is a logical extension of conventional high-resolution surface refraction seismic, namely the use of sources and receivers also at, and close behind, the tunnel face. The concept is shown schematically in Figure 8.21. GPS clocks are needed to synchronise the sources within the tunnel and the receivers at the surface. The authors pointed out that the already developed reflection method of HSP or TSP (horizontal or tunnel seismic profiling, e.g. Sattel et al., 1992), with both source and receiver in the tunnel, locates seismic reflectors ahead of the tunnel face, as desired, but that the reflector distributions are not related to rock quality directly. It is also difficult to determine if the rock quality will get better or worse at a given reflector, and they suggest that there may be inaccuracies of location in view of the unknown actual velocity field.

153

Figure 8.21 Seismic refraction principle, for both in-tunnel and surface sources, with both in-tunnel and surface receivers. Hayashi and Saito, 2001.

The authors suggested that this situation could be rectified by using the in-tunnel refraction estimates of velocity distributions ahead of the face, so that the accuracy of reflector positions could be increased. With the necessary velocity distribution ahead of the face, the rock mass could be characterized both up to and beyond the better-located reflectors. The authors justified their method by demonstrating the steadily improving match to a hypothetical mountain velocity model, as numbers of in-tunnel sources were increased. The model, and two stages of improvement, are reproduced in Figure 8.22.Theoretical travel times were calculated by ray-tracing, and were considered like observed data. The authors applied their proposed method to a tunnel under construction, in Mesozoic slates, sandstones and chert, with an overburden varying from 100 to 300 m. Figure 8.23 shows the detailed surface refraction seismic model of the mountain terrain, which was produced before tunnel construction. A general velocity along the tunnel route of about 4.0 to 4.2 km/c was indicated at this stage. The subsequently installed in-tunnel sources and receiver are also indicated, together with the string of surface receivers down the ‘opposite’ mountain face. An in-tunnel reflector method that was being used in this tunnel, had imaged a clear reflector some distance ahead of the face when the face was at 439 m. The intunnel source refraction method subsequently utilised with only one in-tunnel source, predicted a sharply declining velocity ahead of the face. In fact a face collapse occurred at chainage 544 m, 105 m ahead of the measurement location, and a 300 m wide zone of weak rock, with velocity as low as 3.7–3.8 km/s was indicated by the second method.

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c) Figure 8.22 a) A velocity model with ideal number of in-tunnel sources and limited surface sources. b) Two sources within the tunnel portals, and limited surface sources, improves the reconstructed velocity model, with improved definition and location of the low velocity zones. c) A series of mostly systematic tunnel sources, but with a central gap, gives greatly improved match to the ‘actual’ case. Hayashi and Saito, 2001.

8.6

The possible consequences of insufficient seismic investigation due to depth limitations

In the final section of this chapter a TBM case record will be briefly referred, in which the depth of tunnel (mostly 700 to 900 m), and mountain-side screes and loose deposits, had hindered the correct interpretation of the actually very adverse structural conditions. The case also illustrates the problem with stress effects, or virtual ‘seismic closure’, on this occasion due to compaction and near-invisibility of actually very troublesome faults. Figure 8.24 indicates the initial geometric difficulties of this valley-parallel, TBM-driven headrace tunnel, for the Pont Ventoux hydroelectric project in north-west Italy. This drawing of a valley-parallel fault swarm was developed several years after the original investigation, and shows the limited surface seismic that was attempted at the time, together with some insufficiently deep boreholes. The case was summarized in Barton, 2004c as follows: ‘Unpredicted fault swarm parallel to valleyside, together with very high (and fault-eroding) water

pressures, at depths of 700–900 m. TBM tunnel (diameter 5 m) eventually ran sub-parallel to individual faults, causing delays of at least half a year for each 1 m wide fault (AR  0.005 m/hr). TBM finally abandoned; new contractor for D  B from other end of tunnel.’ The tunnel was plagued by these sub-parallel valleyside faults for at least 2 years, with up to 6 months faultrelated delays on several occasions, until TBM tunnelling was abandoned. An attempt to detect the continued presence of a particular fault (see sketches from daily geological log in Figure 8.25) using seismic tomography between two divergent pilot boreholes, proved to be unsuccessful, due to the presumed confining and densifying effect of the high stresses (from 800 m of overburden) on the fault-zone materials. In Figure 8.26, the rock quality Qc-based velocitydepth model is shown again, this time with some appended comments concerning the possibly elevated velocities of highly confined fault zones. Such zones, despite their Qc values as low as 0.01 or even 0.001, can nevertheless exhibit a stiffness and compactness at

Seismic measurements for tunnelling

155

(a)

(b) Figure 8.23 a) Pre-construction surface seismic result, showing the in-tunnel sources for in-tunnel and surface receivers. b) An in-tunnel reflector method had indicated a reflector ahead of the face and a small reduction in velocity was assumed. The in-tunnel source refraction method subsequently predicted a sharply declining velocity ahead of the face, and a face collapse occurred about 105 m ahead of this location. Hayashi and Saito, 2001.

Figure 8.24 Original seismic refraction profiles and inadequate borehole depths, are compared with the geologist’s later re-assessment of the actual valley-parallel fault swarm, that had a dramatic effect on the fate of the TBM, and the final decision ‘to drill-and-blast’ from the other end of the tunnel. Pont Ventoux, Italy.

156

Rock quality, seismic velocity, attenuation and anisotropy

Figure 8.25 Plan and elevation views of the ‘2750’ fault at Pont Ventoux, based on a super-position of the site geologists sketches of the developing situation. This was a case of an unexpected combination of high stress, high permeability, and high fault frequency, and the eroding power of high pressure water. Barton, 2004c. Attempts to ‘probe ahead’ using seismic tomography between two diverging boreholes, proved not to be as successful as expected, due to the relative ‘invisibility’ of the assumed extension of the fault.

depth, that makes them nearly ‘invisible’. But in fact there is hope that they will still show a recognisable contrast to the even higher velocities of surrounding rock, as suggested in the labels in this figure. There is an interesting support for the above logic from the first case record referred to in this chapter, namely the continental divide Straight Creek pilot tunnel in Colorado, described by Scott et al., 1964. It may be recalled that the in-tunnel seismic refraction had been differentiated into ‘deep layer’ and ‘shallow layer’ velocities. The following deep layer velocities were measured at the five seismic spreads shown on Figure 8.2: #1 5.2 km/s, #2 5.1 km/s, #3 4.8–6.1 km/s, #4 4.2 km/s and #5 6.0 km/s. The seismic velocities of the shallow layers (i.e. the loosened, near-surface-of-the-tunnel layers) at the five seismic spreads listed above, were respectively: 3.0 km/s,

2.3–2.7 km/s, 2.3–3.1 km/s, 1.3–1.6 km/s (worst case, class 5) and 2.3 km/s. The worst quality (class 5) corresponded to seismic spread #4 in Figure 8.2 (deep layer Vp  4.2 km/s), which had a local overburden of about 300 metres, and obviously was strongly affected by the depth or stress level. At the surface a Vp value of 2.5 km/s is implied for this rock mass quality i.e. severely faulted ground which appears to correspond to the authors’ description of class 5 rock. (A disturbed zone of at least one diameter was indicated for such rock.). So in fact one may conclude that the deep layer velocities bore no resemblance to the eventual major tunnelling difficulties experienced when excavating the 12 m span twin tunnels. The deep layer velocities were either undisturbed (but highly stressed), or were perhaps subject to additional tangential stress compaction effects.

Seismic measurements for tunnelling

157

Figure 8.26 Rock mass quality Qc – Vp – depth model, showing the potentially elevated P-wave velocities of nevertheless seriously-delaying fault zones, if encountered at great depth, as at the Pont Ventoux head-race tunnel. Contrast to the even more elevated velocity of the surrounding ‘country rock’ can nevertheless be expected. Barton, 2004c.

The more relevant, extremely low EDZ velocities from the pilot bore investigations, truly representing the poorer rock classes, , were actually what caused the almost insurmountable problems in the main bore, which took several year to complete. Multiple perimeter drifts filled with concrete, making some 2 to 3 m effective wall thickness were needed in some zones. One may also note from the Hayashi and Saito, 2001 case record, reproduced in Figure 8.23, that the face collapse at 544 m chainage, actually occurred in a Vp  4.1 km/s rock mass. This is ‘illogical’, without the

depth or stress effect that masks, in velocity terms, the true low quality. The 300 m overburden at this collapse location, would from Figure 8.26, suggest a near-surface Vp of about 2.5 km/s – i.e. relevant to a serious fault zone, or extremely poor rock. Finally, one may note the adverse effects of low Q-values on TBM progress, shown in Figure 8.27, specifically because of fault-zones. Velocity measurements at depth may not suggest such low values of Q. The TBM may nevertheless be delayed.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 8.27 The typical performance trends derived from analysis of 140 TBM tunnels, with ‘unexpected events’ strongly tied to low rock mass quality Q-values. Barton, 2000. It is probable that extremely low actual Q-values might show a deceivingly ‘high’ range of P-wave velocities, in the case of imaging ahead of deep tunnels.

9

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

Since matrix porosity, and in particular joint porosity, each affect the permeability of a rock mass it is perhaps logical that the seismic P-wave velocity should show some degrees of correlation with the permeability. When the joint void space is artificially increased by a particular type of ‘permeability’ testing (i.e., high pressure Lugeon injection tests), stronger correlation with velocity can be expected, due to the lowering of effective stress. This may apply most strongly in the case of rock masses of poor quality that are easily deformed around the injection boreholes, during the Lugeon tests, but the possible presence of clay is a complicating factor. The unit Lugeon is defined as the number of litres per minute flowing from each metre of a doublepackered section of borehole, under an excess injection pressure, above the groundwater pressure, of 1 MPa. Since a rock mass generally contains joints and microcracks, which are both a source of water and compliant, the application or existence of an anisotropic (effective) stress distribution may preferentially have closed those oriented at an obtuse angle to the major stress, while keeping those at acute angles or sub-parallel to the major stress, ‘open’. There are then grounds for expecting both anisotropic permeability tensors, and a corresponding anisotropic velocity, with both maxima tending to be parallel or sub-parallel to the major stress. Since subvertical jointing may dominate in the same way that horizontal stress anisotropy may dominate, the anisotropy will tend to be related to azimuth. However, there is a potential source of error here. The permeability test holes must intersect the ‘open’ structure to register their higher permeability. The test holes needs to be drilled in the ‘slow’ direction, parallel to the minimum stress. The lower Q-value given by crossing all the ‘open’ joints, should correspond to the higher permeability. 9.1

Correlation between Vp and Lugeon value

In Chapter 2, the strong effect of saturation on P-wave velocity was convincingly demonstrated by the extensive

data of Saito, 1981 (Figure 2.17) and by the use of the time average equation for dry and saturated chalk (Grainger et al., 1973). The approximate ‘porosity’ which appears in the time average equation may contain air or water, and this porosity obviously affects the overall velocity, i.e., whether Vair  0.33 km/s or Vwater  1.44 km/s is involved. So we have a theoretical starting point for a saturated velocity. The key question is whether this helps in predicting possible permeabilities. Does the saturated velocity give any indication of actual flow resistance? Extensive sets of in situ measurements of rock foundation moduli, permeability and seismic velocity were assembled by the Comité National Français, 1964, from numerous dam site investigations. For the special case of two sites in jointed granite (from France’s Massif Central), a strong correlation was evident between Vp and the Lugeon test results. Figure 9.1 shows an approximately linear distribution of data on a semi-log plot of Vp versus the Lugeon value.

Figure 9.1 Evidence for a correlation between Vp and Lugeon value at two granitic dam foundations (Comité National Français, 1964) (Q-value scales have been added by the writer.)

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Rock quality, seismic velocity, attenuation and anisotropy

If we make the assumption that shallow refraction seismic, or relatively shallow cross-hole measurements of velocity were used, then we can tentatively investigate the relation Vp
3.5  log10 Qc (the diagonal line in Figure 9.1) as a means of relating Q-value and Lugeon value. In very approximate terms we can see from the data that not only proportionality, (i.e., L  1/Q) but equality L
1/Q is evident in the approximate range 100 to 1.0 Lugeon. The scatter of velocities and Q-values is seen to be about one order of magnitude, in other words neither velocity measurement, not Q-logging must be substituted for the testing. However, L
1/Q (Lugeon) might be utilised in extrapolation exercises, or to identify non-conforming behaviour. We may therefore tentatively write: L(Lugeons)


1 Q

(9.1)

as a useful approximate for fitting to data in some rock masses, and for explaining deviation (i.e. channelling, in other cases). There is an upper-bound Vp-L trend in the French data that exactly parallels the Q
1/L envelope; as can be clearly seen in Figure 9.1. Two campaigns of core drilling at a shallow tunnel site in Wales; first with vertical holes, then with 45° inclined holes to intersect more of the steep structure, gave mean Lugeon results of 12 and 28. If we assume Q
1/L, then Q values of 0.08 and 0.036 are derived. Completely independent Q-logging of the relevant boreholes (8 from phase 1 vertical holes, and 13 from phase 2 inclined holes) by the writer, gave weighted mean Q-values from many hundreds of observations of the six Q-parameters that were as follows: Q (BH 1 to 8)  0.11 (‘higher’ Q, lower permeability: L  12) Q (BH 13 to 21)  0.08 (‘lower’ Q, higher permeability: L  28) The tunnel itself showed an overall weighted mean Qvalue of 0.05, i.e. it was rather unstable rock. Downhole Vp logging in BH 1 to 8 gave a mean Vp  2.6 km/s for the same depth range that was core logged. This converts to a predicted Q-value of 0.12, almost the same as logged. By using the following ‘hard rock’ method of conversion, based on Vp
3.5  log10 Q and L
1/Q, and eliminating Q we obtain: L
10(3.5 Vp )

(9.2)

Figure 9.2 Correlation between Vp and Lugeon values at four hard rock sites in Norway. After Sjøgren et al., 1979. (Q-values scale added by the writer. Stippled curve given by equation 9.1).

which suggests a Lugeon value of 8 when Vp is 2.6 km/s. The measured value in the relevant holes was 12. The above logging data from clay-bearing metasediments shows remarkable similarities to the L
1/Q model, and also shows the potential anisotropy of the Q-value due to different joint sampling frequency with hole orientation. Lower Q-values, higher Lugeon values, and lower seismic velocities will tend to be measured when perpendicular to major structure. The opposite occurs when paralleling major structure. Of course there can be exceptions to this basic concept caused primarily by an eventual rotated stress-anisotropy, that no longer matches the joint patterns: a less likely scenario. Sjøgren et al., 1979, gave correlations between Lugeon tests and seismic velocities for several locations from four of their investigated hard rock sites in Norway. A total of 29 data points are given in Figure 9.2. They defined 1 Lugeon in the usual way, and mentioned the constant pressure of 1 MPa. It is not known if this standard excess pressure was reduced closer to the surface, but if not, this could be the reason for some of the

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

161

Table 9.1 Approximate correlations between measured transmissivities and seismic parameters based on measurements in five boreholes in marl. Albert, 2000. Transmissivity

[m2/s]

1014

1012

1010

108

106

104

102

Vp Vs Vp/Vs Dynamic shear modulus Dynamic E-modulus Poisson’s ratio

[m/s] [m/s]

5500 3000 1.72 24 60 0.28

5117 2700 1.84 20 50 0.30

4733 2400 1.96 16 40 0.32

4350 2100 2.09 12 30 0.35

3967 1800 2.21 7 20 0.37

3583 1500 2.33 3 10 0.39

3200 1200 2.45 0.1 0 0.41

[GPa] [GPa]

unexpectedly high values (e.g., 10 to 20 Lugeons) seen in rock with velocities from 3.5 to 4.5 km/s. However, in general their results showed the expected lower Lugeon results at higher velocities, as in the French data. The rule of thumb 1/Q
number of Lugeons was tested against the Sjøgren et al., 1979, data using the assumed, near-surface, hard rock relationship Vp
3.5  log10 Q (Barton, 1995). It appears from Figure 9.2 that the ‘1/Q’ curve is a suitable lower bound to some of the velocity-Lugeon data. Accuracy could potentially be improved if Lugeon values were correlated with depth zones, and if these depth zones had been given, a more correct Vp–Q relationship could have been selected from Figure 8.9 (see Chapter 8). Curiously, some of the points plotted by Sjøgren et al., 1979, exactly fit the dotted line (Q
1/L) relationship, as also experienced in Figure 9.1, possibly indicating conforming or non-conforming data, as the case may be. In poorer quality rock masses, a Lugeon test is a form of rock mass deformability test, with unusually sensitive (‘aperture cubed’) registration of joint deformation, due to the tendency, under laminar flow conditions, for flow rates to be proportional to e3, where e is the hydraulic aperture. However, in very stiff rock masses this may not apply, especially if channel flow dominates due to outwash channels in filled joints, or if joint jacking (slight opening) occurs due to low Ko (v/h) values, or if jacking occurs due to over-dimensioned water pressures close to the surface. From extensive work in marl formations in Switzerland, Albert, 2000, indicated quite strong relations between selected seismic parameters and transmissivity measurements in five deep boreholes at Wellenberg, a potential nuclear waste repository site. Good correlations with transmissivity were obtained with Vs, dynamic shear ( ) and E-moduli, Vp, Vp/Vs and dynamic Poisson’s ratio. Table 9.1 shows the author’s approximate correlations between the seismic parameters (using linear

scales) with the logarithmic transmissivity scale. (The transmissivity is the product of the permeability and the thickness of the measured aquifer or ‘aquiclude’.) Most of the measurements reported by Albert, 2000, were in the transmissivity range 105 to 1012 m2/s. A 1 m long test section assumption would convert these to the more familiar engineer’s m/s units.The borehole depths ranged from about 400 m to 1800 m, and included faulted and brecciated rock. One must assume that the ‘hydraulic tests and fluid logging’ were of the non-deforming type, unlike the civil engineering Lugeon testing (often for evaluating groutablity), discussed elsewhere in this chapter. Compaction effects on this relatively weak rock at borehole depths up to 1800 m presumably have affected permeabilities more than the seismic velocities. The smaller steps in velocity at the lower transmissivities resemble the effect of depth in the Qc-M-Vp engineering model (Figure 8.9). The successive reductions in dynamic E-modulus with increased transmissivities (and Qcvalues?) have a certain similarity to this rock engineering model, bearing in mind the Edyn  M inequality. Examples of correlations between seismic refraction surveys and drilling and tunnelling results are given by Sjøgren, 1984. This example is given in this chapter due to permeability links. Figure 9.3 shows successive stages of an investigation, and confirmation during construction, for a water supply tunnel beneath the Skien river in Norway. Four seismic refraction profiles are shown in the top figure. Three low velocity zones were indicated beneath the river, the largest of which (Vp  2.5 km/s) was proved by an inclined borehole to be a partly consolidated breccia and loose alum shale (core loss averaged 75% in this zone). The Lugeon value in this zone was 14, which might correspond to a Q c value of about 1/14 (0.07). This is close to the value of Q that could be predicted from Figure 8.9, using a nominal porosity for the zone of 5%, and the 50 m depth shown in Figure 9.3c. At this

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 9.3 Correlations between refraction seismic velocities and borehole and tunnelling experiences through the same zones. Sjøgren, 1984.

depth (and with n  5%) Q  0.07 corresponds to Vp  2.5 km/s, as measured by chance or good physics. The tunnel was driven through the same zone, in the direction of profile 1 (Figure 9.3c). Grouting was necessary for the Vp  3.0 km/s zone (perhaps Q
0.3 and L
3 from equations 9.1 and 9.2). Probe drilling and heavy reinforcement was used through the 12 m wide fractured alum shale zone, which had Vp  2.5 km/s (and L  14, and Q
0.07?). 9.2

Rock mass deformability and the Vp-L-Q correlation

Dam sites throughout the world are investigated by means of borehole water injection tests, typically using double packers, and injection-pressures related to depth below the surface, but usually limited to about 0.25 or 0.5 or 1.0 km/cm2 per metre depth. (The choice

is related to national or regional practice.) The number of Lugeons is expressed by the well-known relation L  litres/min/m/1 MPa excess pressure. Most of the flow losses (and joint deformation) occur close to the borehole in such a test, which differs greatly from the careful, low pressure pumping (or extraction) tests favoured in permeability testing (Quadros, 1995). By good fortune or correct physics, the modulus of deformation (M) that was shown in Figure 8.9 is proportional to Q1/3 or to Q 1/3 c in the case of rocks weaker or stronger than our nominal c  100 MPa. Similarly, it is well known that flow rate is more or less proportional to e3 in jointed rock masses (where e  equivalent hydraulic aperture of the joints, and intrinsic permeability can be expressed as e2/12). The smaller value of (e) approaches the physical aperture (E) when e
1.0 mm, and this inequality (E/e  1) is related to joint roughness JRC (Barton et al., 1985, Barton and Quadros, 1997). Around the injection borehole we may assume that the natural joint apertures are deformed significantly, especially when maximum injection pressures of 0.025 up to 0.1 MPa per metre depth are used. The latter European injection pressure limit at dam sites is about two times the assumed vertical total stress. When ko ( h/v) is 1.0 and causes lower minimum stress than these figures, some slight hydraulic jacking of some of the joints is an obvious consequence in the initial radii around the boreholes. The following basic assumptions will be made concerning this all-important joint deformation region around the injection holes: 1. The Lugeon value (L) which is recorded as volumetric flow rate (litres/min) will tend to be proportional to the cube of the new apertures that have been created, i.e., ( E3). There is some evidence from grouting results (over-coring or excavation) that the most permeable and well-connected joints open most at the expense of others in the same set. The resulting Lugeon value will often be dominated by the Emax value and we can roughly approximate here 3 that L  Emax , since the smallest micron-size apertures will contribute only minutely. 2. The locally gapped joint will have an aperture Emax that is approximately inversely proportional to deformation modulus M. 3. The calculation of a ‘double’ Boussinesque elastic foundation calculation for the radially distributed deformation of each side of the joint, with realistic input for dimensions, supports this.

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

Therefore we have the following possible inter-relationships between maximum apertures, Lugeon values, deformation moduli and Q-values, which in turn are linked to seismic velocities: L Emax M Therefore L

   

E3max M1 Q1/3 c Q1 c

(Note ‘’ implies ‘approximately proportional to’ in the above proportionalities). These simple proportionalities therefore suggest that the number of Lugeons may indeed be proportional to 1/Q c, unless other mechanisms than local joint deformation are responsible for the flows, for example outwashed chlorite fillings, severely canalised flow due to basalt flow-top weathering, uncontrolled hydraulic joint jacking, and so on. The data that follow the lower-bound trend L
1/Q in Figures 9.1 and 9.2 are therefore consistent with this theoretical model, and explain why Vp and L (Lugeon) can show a degree of correlation. In Figure 9.4, the above inter-relationships have been expressed in the form of a nomogram, using the basic structure derived in Chapter 5 (Figure 5.36). Five illustrative ‘type curves’ have also been added, to show what might be typical Vp-Q-M-L data for fault zones, weak porous rock, hard jointed rock and hard massive rock. For simplicity (and continuity of the curves), it has been assumed that porosity only develops in the shallow, near-surface weathered zone in each case (H  25 m). In the case of a hard porous rock, there will be a velocity correction caused by porosity at all depths, and this will mean that the central curve shown in Figure 9.5 will give the correct velocity, roughly midway between the ‘hard rock’ reference curve (top) and the porosity correction curve (bottom). The steepening gradient of the type curve is in this case affected by the assumed Q-value increase at greater depth. If, for some reason, this does not occur, then the ‘type curve’ could be a straight vertical line, as for the ‘hard massive’ rock shown in Figure 9.4. Any porosity correction would merely reduce the ‘height’ (i.e., reduce the maximum velocity) of such a line. The Qc correction factor is the same as that developed in Chapter 5 (Figure 5.36). The nomogram can be illustrated by the following ‘coupled’ example. At the Chinnor Tunnel in chalk marl, Hudson et al., 1980, (‘seismic’ Hudson) referred to very low velocities (0.6 to 1.0 km/s) for badly fractured/jointed areas of

163

the chalk marl and quoted permeabilities from Lugeon type tests of 104 to 106 m/s in these areas. If we assume for simplicity that 1 Lugeon
107 m/s then the very high Lugeon values obtained of 1000 to 10 imply Q c values of 0.001 to 0.1 according to equation 9.1 (where Q has been replaced by Q c). These low Q c values can be converted to ‘tunnel support’ Q values of 0.02 to 2 if we assume a mean c value of 5 MPa for the chalk marl. This range is in line with expectations for the heavily jointed rock mass at Chinnor. (The term ‘tunnel support Q-value’ is used to remind of the original development of the Q-system for selecting tunnel support: Barton et al., 1974.) Although one should in general resist the temptation to convert 1 Lugeon to 107 m/s (approx.) as if ‘rock mass permeability’, because deformability of the medium is very likely in the case of Lugeon testing in weaker rocks, it is nevertheless of interest to note that the 1000 to 0.001 Lugeon scale shown in Figures 9.4 and 9.5, would convert to 104 m/s to 1010 m/s. This resembles the wide range of permeability often encountered where thousands of well tests are assembled in one plot. However, channelled flows in weathered basalt flow tops may exceed 102 m/s, and some massive igneous rock may have permeabilities as low as 1012 m/s, due to lack of joint connectivity and lack of micro-cracks. (The latter may appear only after sampling from strongly anisotropic virgin stress states, as discussed in Chapter 3). A further example of Q-Vp-L correlation can be developed from the columnar basalt foundations of the Segunda Angostura dam site in Argentina. Classification of the site together with preliminary testing were reported by Di Salvo, 1982. mean RMR mean Q

 63  8.5

(These are close to the Barton, 1995 suggested interrelationship RMR
15 log10 Q  50) Vp (downhole)  4.5 km/s below ‘decompressed zone’ Vp (downhole)  2.0 km/s in the ‘decompressed zone’ The higher velocity suggests Q c
10, based on the relation Vp
3.5  log10 Q for hard rock. A uniaxial strength for the basalt of e.g. 125 MPa, would mean Q
8. L (Lugeon) in decompressed zone  16, suggesting Q c
0.06 based on L
1/Q c. A Q c-value of 0.06 suggests a Vp value of 2.3 km/s, i.e., very close to the measured velocity.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 9.4 Potential inter-relationships between Vp, Q, M and L, with corrections for depth, porosity and compression strength. Barton, 1999.

Figure 9.5 Hard porous rock of 10–20% porosity. Example type curve for estimating Vp-Q-M-L data.

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

9.3

Velocity and permeability measurements at in situ block tests

During the 1970s and 1980s, a series of large scale, in situ block tests were performed by Pratt and co-workers in the USA, in order to evaluate test methods and instrumentation suitable for nuclear waste disposal projects which were being planned at that time. The block tests were designed to give large-scale properties (1 to 3 metres scale) under controlled loading conditions (using flatjacks), and some were at elevated temperatures (using borehole heaters). The effects of stress application on velocity and permeability in jointed granite were first investigated on a large scale by Pratt et al., 1977, who used a flat-jack loaded block measuring 3  3  3 m, which contained three sub-parallel, vertical joints. The rock was an anisotropic, but quite massive granite, and the site was in Wyoming, USA. The authors investigated velocity changes as a function of applied stress (0 to 9 MPa) applied either parallel or perpendicular to the jointing (so-called E-W or N-S velocities, respectively). Results for different measurement lengths, including 0.15 m long laboratory samples, are shown in Figure 9.6. The lab samples, which may have experienced microcracking on release by drilling, show the strongest Vp response to stress increase. Although the 3 m cubed block was released on all four vertical sides, the ‘contact’ with ‘virgin’ rock stresses along its intact base may presumably be the reason for less response of Vp to stress along these in situ measurement lengths of 1.0 and 2.85 metres. The block also remained nearly saturated, compared to the lab sample ‘0.15 m, D’ (D  dry, S  saturated). More details of the in situ response of rock mass velocity to increasing stress are given in Figure 9.6c. Increased wetting of the surface of the block caused the small (0.1 km/s) increases in velocity seen between the pairs of curves 4 and 9, 1 and 8 respectively. The authors finally presented a composite plot (fully coupled behaviour) of joint displacement (mm), flow rate along joint J1 (cm3/s) and velocity, each as a function of stress. Figure 9.6d shows that increased closure of the joint after about 2 to 3 MPa normal loading, caused a plateau on the permeability-stress curve, and a sharp reduction in the sensitivity of Vp to further stress increase, especially beyond 5 MPa loading. This is consistent with stress-Vp data reviewed in Chapter 5, and broadly in line with the non-linear effect of depth on velocity shown in Figures 5.36, 9.4 and 9.5.

165

Another in situ block test, this time in jointed sandstone in Colorado, USA was reported by Swolfs et al., 1981. The block was 2 m3 in volume and contained a near-vertical joint. The joint was calcite filled, and appeared to be about 1.5 mm wide at the surface. The P-wave velocity of the surrounding jointed rock of about 1.5 km/s appeared to be independent of joint frequency and orientation. This is surprising in view of the presumably drained state of the test site (Figure 9.7a). However, ‘moist’ laboratory samples had about the same value of Vp. In situ stresses of about 1 MPa were relieved by line drilling of three sides of the block. The long side of 2.3 metres and 1.2 m depth was parallel to the joint. This resulted in Vp and Vs changing from 1.5 and 0.8 km/s to 0.9 and 0.5 km/s respectively. Calculated values of Edynamic thereby changed from 3.3 to 1.2 GPa, assuming a rock density of 1.97 gm/cm3 , because the sandstone has a high porosity of 25%. The uniaxial strength was about 11 MPa, and static Young’s modulus was 2.3 GPa, based on laboratory samples. The block was loaded uniaxially (normal to the joint) and biaxially, using multiple flatjacks in each of the three slots. The effect on P-wave and S-wave velocities is shown in Figures 9.7c and d. Pre-excavation velocities (shaded lines) were reached at about 1 MPa. This is exactly the stress acting when undisturbed velocities were measured. An anomalous increase in joint deformation was also recorded above this same stress level of about 1 MPa. The authors also applied shear stresses to the joint by activating the flatjacks at the end of the block, while holding a constant normal stress across the joint (0.7 or 1.4 MPa). Since the block was attached at its base, joint shearing was limited (even at the top surface of the block) to about 0.7 mm, which represents pre-peak strength. Dilation was negligible (10 m), and is perhaps the reason why Vp and Vs slightly increased during application of shear stress to 3.0 MPa, probably mostly in response to the simultaneous application of normal stress of 0.7 or 1.4 MPa (Figure 9.7a). If significant dilation had occurred during increased shearing, a reduced velocity would presumably have resulted. The small velocity response to moderate stress change seems to be a feature of relatively unjointed, porous rock. The authors also performed a permeability test using injection in a central hole that intersected the joint. They calculated a permeability of 3.7  107 m/s. There are several interesting coincidental values of the reported tests that we can compare with the Qc -VpM-L model (Figure 9.4). If we follow the ambient

Figure 9.6 Vp changes caused by loading a 3  3  3 m block of granite containing vertical joints, and laboratory tests of the same rock. a,b) Velocity-stress behaviour for three types of loading conditions, and for three measurement sizes. c) Nomogram linking effects of uniaxial joint closure stresses with joint J1 deformation D4, velocity across jointed block, and flow rate along part of joint J1. Pratt et al., 1977. Note tendency for acoustic closure beyond 5 MPa.

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

167

P-wave velocity of 1.5 km/s at the ambient stress of about 1 MPa (equivalent to about 20–25 metres of overburden) in the lower left-hand corner of the Q-Vp-M-L chart, we find a Q c value of about 0.4 at 25% porosity. Independent of this, the 1/Q c model for Lugeon estimation suggests a back-calculated Q c-value of 0.27. This is very close to the velocity-based estimate. The low uniaxial strength of 11 MPa means that the Q-value can be estimated as about (0.4 or 0.27) 100/11  3.6 or 2.5. These are close on a six-order of magnitude Q-scale. The estimation of deformation modulus (M) can be based directly on Vp according to Figure 9.4. Thus we see that 2 GPa is estimated, which is close to the laboratory value of 2.3 GPa, and to the Edynamic estimates of 1.2 GPa (unloaded) and 3.3 GPa (undisturbed, loaded to approximately 1 MPa). In this case this deformation modulus estimate is based on Vp (Figure 9.4, righthand column of M values derived from): M
10

( Vp 0.5 )/ 3

(9.3)

and this gives a more accurate estimate of 2.1 GPa when Vp  1.5 km/s. The relevant modulus value is also obtained using the direct equation between M and Q: M
10 Q 1/3 c

(9.4)

which again gives an estimated 2.1 GPa, when using Q
 0.01. We refer to Q
as ‘Q-prime’ since it has not been corrected for porosity. The real Qc value needs the porosity correction, and final correction for the ratio c/100, to reach the assumed rock mass quality Q, which we estimated from both velocity measurement and independent Lugeon testing as ranging from about 2.7 to 3.6. Further checks on rock mass quality can be made the direct way by using the authors’ descriptions of the jointing; three sets, spaced at 0.6, 0.9 and 0.3 metres, with the most prominent set filled with about 3 mm of calcite. Via the volumetric joint count of Palmström, 1983, we can calculate Jv  6.1, and RQD
95%.

Figure 9.7 a,b) Loaded block test in (drained) unit of in situ sandstone containing a vertical joint, loaded on three sides by flat-jacks. c,d) Vp – and Vs – stress trends for uniaxial and biaxial loading, compared with pre-slot velocities – shaded. e) Effect of joint shearing on Vp at two different normal stress levels. Swolfs et al., 1981.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 9.8 Permeability – stress coupling for three bituminous coals, due to the detailed cleating or jointing: an extreme analogue for jointed rock masses. Somerton et al., 1975.

The independently estimated Q-value is therefore approximately as follows: J J RQD Q   r  w Jn Ja SRF 

95  100 1  1.5 1    1.7  2.8 8 9 6 1

All of the above estimates are very close, considering the logarithmic (six orders of magnitude) Q-value rock quality scale. We have thus demonstrated that Q, Vp, M and L are inter-related, and that we may be able to include the Lugeon value in this inter-relation, if care is taken to eliminate irrelevant non-deforming, channel flow cases. The implication is that depth or stress level, also an axis in Figure 9.4, also plays an important role in these mutual inter-relationships. Using an analogue material for heavily jointed rock, namely coal, one can also see how there is great potential sensitivity between velocity, stress level and permeability,

Figure 9.9 a) Permeability-Vp coupling for two of the bituminous, cleated coals. b) Velocity-mean stress coupling for one of the cleated coals. Somerton et al., 1975.

which will also be present in jointed rock masses at large scale, when in situ effective stress states are altered by large scale pumping or injection experiments. Three bituminous coals having large differences in hardness and degree of jointing (cleats, etc.) showed almost equally great sensitivity to applied stress level, despite their five order of magnitude range of permeabilities (0.1 to 100 millidarcys). Somerton et al., 1975, applied mean stresses over the range 1 to 14 MPa and noted between two and three orders of magnitude reduction in permeability (Figure 9.8). Simultaneous monitoring of ultrasonic velocity showed increases of velocity of about 0.3 to 0.6 km/s (from 1.8 km/s when stress-free) for each order of magnitude reduction in permeability. This is shown in Figure 9.9a together with the Vp-stress behaviour of one of the coals in Figure 9.9b. Both these figures indicate greatest changes in Vp and permeability at the lowest

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

stress levels (and lowest velocities), just as found in rock masses, due to improved acoustic coupling across joints.

9.4

Detection of permeable zones using other geophysical methods

Since the mid-eighties, researchers working at nuclear waste related rock laboratories such as Stripa, Äspö, and Grimsel have utilised both seismic and radar tomography to characterize major fault zones. Their studies have generally helped to explain why these relatively small volumes of fractured (or heavily jointed) rock are responsible for such large percentages of the total flow of water. At the Grimsel site, Martel and Peterson, 1991, found that seismic velocity tomography delineated major geologic structures better than radar attenuation or radar slowness tomography. However, they point out that anomalies on tomograms can reflect a wide range of features (rock types, alteration, changed porosity) besides different degrees of jointing or fracturing. Knowledge of geological background data is therefore helpful in making better interpretations. Injection of brine for tracing flow paths has been successful in many projects. Martel and Peterson, 1991, found that radar attenuation difference tomograms were more reliable in locating brine than slowness tomograms, at the Grimsel US/BK site. Radar and seismic signals are sensitive to different physical parameters (mechanical stiffness and electro-magnetic wave conductivity, respectively). For this reason, the respective tomograms highlight different features of the rock mass. Radar may delineate permeable zones (porosity caused by pore space or by joint apertures) in slightly different locations to the low seismic velocity zones associated with clay filled discontinuities. The one will usually lie parallel to the other, since higher permeability may be associated with the heavily jointed zones that are often found adjacent to faults. This was a phenomenon that at first made geophysics teams question each other’s coordinates at the Stripa SCV (Site Characterisation and Validation) site (Olsson., 1992). Green et al., 1989, described the use of vertical seismic profiles and cross-hole seismic surveys at the Camborne School of mines 2 km deep hot dry rock geothermal project. The objective was to show that the microseismicity generated during stimulation experiments corresponded to regions of enhanced permeability. The majority of micro-seismic events were interpreted as

169

minute (10 to 50 microns) shear displacements on a set of near-vertical joints that were not aligned to H(max). The joint roughness was assumed to create some increase in permeability despite the assumed small shear displacements. During a stimulation experiment in which the reservoir was kept ‘inflated’ by a well-head pressure of 6 MPa and a flow rate of 9 litres/s, the velocity showed small reductions in the depth zone between 2100 to 2500 metres. The seismic data suggested that the permanently stimulated cracks and joints were dilating as the pore pressure increased, even though the pore pressure was only 20% of that required for jacking (30 MPa). A certain degree of joint aperture increase can be expected from the elevated pore pressure, whether or not significant shearing was occurring. Aoki et al., 1991, describe the use of cross-hole seismic measurements to compare with (and verify) the directional distributions of hydraulic diffusivity. In the case of tests in a heavily jointed rhyolite, the lower velocity zones (3–4 km/s) between two of the boreholes corresponded quite closely to the location of highly permeable zones between these boreholes at 6 and 13 metres depth, as seen in tomographic plots of cross-hole test data. It is well known that low resistivity measurements correlate with zones of increased water content and frequently with higher permeability. At a site in South Korea, where the writer logged a series of boreholes in weathered granites, the opportunity arose to compare these independently derived Q-parameter statistics with resistivity tomograms that were given to the writer after his draft report was delivered. It was found that sections of the boreholes with increased joint frequency (low RQD, high Jn) did not always correlate with low resistivity and vice versa, as was reasonably to have been expected. The parameters that did show a consistent correlation with low resistivity were the low values of Jw (estimated, for example, from iron staining or apparent aperture) and the high values of Ja (for example from sand or silt fillings and due to clay fillings). The latter gives low resistivity due to the ionic effects of the clay, since water content (and permeability) are clearly lower in such discontinuities than in those that are sand or silt filled. There is therefore in fact a potential source of error in judging the meaning of low resistivity zones. This end of the rock mass quality spectrum is also unfortunately the region where the usual link of low Vp, low rock mass quality Q-value and high permeability

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Rock quality, seismic velocity, attenuation and anisotropy

also may break down, due to the ‘adverse’ effect of clay on permeability. We will see in Chapter 16 that a partial solution has been found for this clay-based phenomenon, by rearrangement of the function of two Q-parameters, namely the reversal of Jr with Ja in a simple term called ‘QH2O’. This depth-dependent model appears to provide a realistic, preliminary estimate of permeability to many kilometres depth.

9.5

Monitoring the effects of grouting with seismic velocity

A simple illustration of the benefits of seismic velocity monitoring at grout injection jobs was given by By, 1988, using cross-hole (average velocity) measurements at a dam abutment in Norway. Blast damage from reflected waves caused by a nearby quarry for rockfill was suspected to have caused shearing and dilation along adversely dipping foliation planes, giving Vp measurements as low as 0.5 km/s in the drained, 5 to 10 metres depth zone. Following extensive surface injection (Figure 9.10) Vp locally increased to between 2 and 6 km/s. However, the depth interval of 7 to 15 metres did not show acceptable velocities (only 2 to 3 km/s) and this was confirmed by additional water leakage tests. A strong depth-velocity effect was observed at the site (velocities rising from 2 to 5 km/s from about 10 to 25 m depth) presumably related both to apparent rock quality improvement at depth, and to a post-stressing effect from the increasingly confined grout at greater depth. Rodrigues et al., 1983, also refer to the correlation between seismic velocity and reduced permeability achieved by grouting at the Cabril dam site founded on granite, in Portugal. The dam had been grouted 30 years previously and had already quite a high P-wave velocity (range 4.2 to 5.5 km/s), partly as a result of this earlier foundation treatment. The new round of grouting increased Vp by 2 to 20% and reduced the permeability, as registered by Lugeon testing, by anything from 40 to 100%. A larger grout take (where there was presumably a larger rock mass ‘porosity’), also corresponded to the locations where the largest increases in Vp were registered, following the grouting. It was noted by Grujíc, 1974, at the 220 m high Mratinje dam (shown in Figures 4.1 and 4.2) that effective consolidation grouting could be performed when Vp was in the range 2.5 to 3.5 km/s (i.e., approximately Q
0.1 to 1.0 or 10 to 1.0 Lugeon according to the

Figure 9.10 Superficial and deeper-layer grouting at a dam site abutment, where nearby (and too close) quarry blasting had caused suspected shearing along the dipping foliation planes, resulting in a (drained) P-wave velocity of only 0.5 km/s. Note the dramatic improvements in the (assumed) foundation properties as a result of grouting. By, 1988.

relation L
1/Q Lugeon. Velocities above 4.0 km/s (Q
3? or K
0.3 Lugeon?) could not be improved upon by the grouting. Such results emphasise the reasons for combined use of high injection pressures and micro or ultrafine cements, if e.g. 0.3 Lugeons (or rather 4.0 km/s), should be improved upon. Barton, 2004a. At the 270 m high Inguri arch dam in Georgia, Savitch et al., 1983, used the seismic velocity criteria shown in Figure 9.11 for judging the success of grouting. One can first interpret that very high pressures must have been used here, since it is implied that velocities as high as 4.5 km/s could be improved by grouting. However, the depth effect on Vp (e.g., Figure 9.4) is probably playing a role here. A Vp value of 4.5 km/s implies Qc  10 in near-surface, hard un-weathered rocks. However at the 270 m high dam, deep injection grouting and deep Vp monitoring (say at 100 to 200 m depth) might have caused a depth (or stress) related enhancement that was equivalent to a much lower rock

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

Figure 9.11 Grouting efficiency (I  excellent, II  good, III  Satisfactory, IV  unsatisfactory) based on velocity monitoring at the Inguri arch dam. Savich et al., 1983.

quality of Qc  1, or even less, which was likely to be injectable. Savich et al., 1983, results are therefore readily understandable when the Vp-Q-depth effect is taken into account. Grouting at the Zavoj hydro electric project in Yugoslavia was monitored by cross-hole velocity measurements and by cross-hole seismic tomography performed between two galleries. Slimak et al., 1991, showed three-dimensional contour plots of velocity distributions before and after grouting, and a difference tomogram showing the net gain in velocity, as a result of the grouting. The authors emphasised the efficiency of such measurements in checking the effectiveness of a large-scale injection programme. Unfortunately, the authors did not give the results of Lugeon testing before and after the grouting. The velocity increase of only 0.25–0.75 km/s and the relatively high velocity (mostly 4.0–5.5 km/s) before grouting suggest only a moderate result. One may speculate that these velocities are also affected by stress level, since ‘nearsurface’ Q-values of 3 to 100 derived from the above velocities (if measured in the upper 25 metres) would imply low Lugeon values (0.33 to 0.01 Lugeon) if one accepts L
1/Q as a useful lower bound estimate, as discussed

171

Figure 9.12 Before, and after grouting Vp measurements in sandstones and marls, showing increased velocity, and increased anisotropy. Capozza, 1977.

earlier. These are hardly values that would justify grouting. Presumably some of the velocity increase caused by grouting is due to the increased stress, and some due to reduced volume of joint apertures and better seismic coupling. Velocity monitoring alone may therefore not guarantee a good (i.e., low leakage) grouting result. Bernabini and Borelli, 1974, describe a variety of early seismic tests performed at hydro electric projects in Italy in the 1950s, 60s and early 70s. In ‘stratified rocks’ they show about 35% increase in seismic velocity caused by successful grouting with cement. However, they observed that the scatter of data did not change; the stratified rock maintained its anisotropic character, just the mean velocity was increased (1.96 to 2.65 km/s). The before-and-after grouting measurements of Vp referred to by Bernabini and Borelli, 1974, are reproduced in more detail by Capozza, 1977. The inter-bedded sandstones and marls experienced an average velocity increase of 0.7 km/s (2.0 to 2.7 km/s) as a result of the grouting. Since the cross-hole measurements performed before and after grouting gave a range of ray-path angles () in relation to the gently dipping bedding, it was possible to show the influence of angle ° on the results. Figure 9.12 from Capozza, 1977, shows not only the higher velocity after grouting but also the increased anisotropy, which was closer to that of the unweathered

172

Rock quality, seismic velocity, attenuation and anisotropy

formation at depth. Presumably, the weathered and jointed sandstone layers between the marl were more easily injected, giving this increased anisotropy. Wenhua, 1991, described the use of seismic velocity measurements to monitor the effects of grouting on the deformation modulus of jointed and faulted powerhouse foundations, at the 1750 MW Gezhouba hydroelectric project on the Yangtze River in China. The fracture zone of concern originally had a modulus of deformation as low as 0.1 GPa and a permeability greater than 10 Lugeons, and was affected by small, karstic voids and cracks. Velocity measurements in the faulted and permeable zone, showed values of 2.5–3.2 km/s after grouting, compared to 1.5–2.0 km/s before the treatment. The average values for the whole foundation were 3.18 km/s before grouting and 4.74 km/s after grouting which imply an effective Q-value increase from (very approximately) 0.5 to 17 or a Lugeon value reduction from perhaps 2 to 0.06 (using equations 9.1 and 9.2). This implied low Lugeon value is so low that a stress related effect on the 4.74 km/s velocity achieved after grouting is suspected. As suggested earlier, the stress related effect may be a combination of depth (greater than the reference 25 m, Figure 9.4) and post-stressing by high pressure grouting, which could give a ‘locked-in’ stress after curing at least in vertical or sub-vertical planes. In horizontal planes any potential ‘locked-in’ stress caused by local ‘lenses’ of grouting, would need to be over a limited volume, if arching were to give a local stress greater than v. ‘Artificially’ high Vp values could then be registered, which might exaggerate the true effect of the grouting, which is primarily designed to reduce permeability, but has several other positive effects (i.e., increased modulus, shear strength, etc.).

9.6

Interpreting grouting effects in relation to improved rock mass Q-parameters

Since we have indicated a general potential relationship between Lugeon value, Q-value, and measured velocity, and have also obviously noted an apparent change in Lugeon value and velocity as a result of grouting, it is of interest to investigate the potential physical effects of grouting on Q-parameters. The tunnelling situation can be used in this exercise, as pre-injection is a commonly needed measure to reduce problems ahead of a tunnel face, either in permeable, leaking rock masses, or

Figure 9.13 Top left: a depiction of a Lugeon or water injection test in a rock mass with three joint sets, and the Snow, 1968 idealized cubic network, consisting of a Poissondistributed, and limited number, of conducting ‘smooth parallel plates’ with equal permeability. The lower diagrams emphasise the joint-roughness-related, inequality of the physical joint apertures (E), and the theoretical hydraulic apertures (e). Barton, 2004a.

beneath environmentally sensitive areas, where groundwater draw-down cannot be tolerated. Most tunnel engineers experience that correctly carried out pre-grouting reduces leakage, and that it apparently increases deformation modulus and probably shear strength, since tunnels that are pre-injected show each of these implied characteristics, meaning improved stability, less deformation, and lessened support needs. The same is probably true in dam foundations, minus the support needs. A helpful, if very idealized figure, concerning the ‘available’ joint porosity for potential grout penetration, is given in Figure 9.13. The top right-hand diagram is based on Snow, 1968 with the addition of nonconducting joints between Snow’s idealized cubic

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

173

Since 1 Lugeon
107 m/s, and 107 m/s
1014 m2, a laminar flow 3D interpretation of Lugeon tests can be expressed as follows: e
(6LS  108 )

1/ 3

(9.8)

where (e) and (S) in millimeters, L is the average Lugeon value, and each apply to the local domain, rock type, or borehole depth. Although average physical apertures (E) are significantly larger than (e), they are hardly of different orders of magnitude. It is therefore clear that there will be difficulties of grouting a Vp  4.5 km/s rock mass (measured at nominal 25 m, shallow refraction seismic depth), if we assume the approximate validity of equation 9.2: L
10(3.5V ), suggesting a Lugeon value of only about 0.1 in this case. It is simple to understand from grouting case records that the higher the Lugeon value, or the lower the velocity before grouting, the better the potential improvement (e.g. Figure 9.11). A useful demonstration of this is the practical case of trial grouting of a dam abutment in Figure 9.15, from Quadros and Correa Filho, 1995. Three boreholes permeability-tested before grouting, were re-drilled in roughly the same location following the grouting, so that the before-and-after permeabilities could be compared. The lower-left diagram, treating just the individual borehole results, suggested that the following before-and-after results could be expected. (Only industrial cement was used in these tests). p

Figure 9.14 The evaluation of equation 9.8 in graphic and tabulated format, for typical Lugeon values between 0.01 and 100, equivalent to assumed isotropic rock mass permeabilities of approx. 109 to 105 m/s, and average spacings for the water-conducting joints of 0.5 m to 3.0 m.

network. The physical (aperture E), compared to the theoretical (apertures e), available for grouting are depicted in the lower diagrams. A further visualization of the size of the theoretical hydraulic apertures available for grouting, if the rock mass had three equal joint sets, is given in Figure 9.14, which was derived in Barton, 2004a, from equations in American units from Snow, 1968. Based also on the hydraulic theory of Louis 1967: 1. Permeability of one smooth parallel plate: k

e2 12

(9.5)

2. Permeability of 1 set of parallel plates: K1 

e2 e  S 12

(9.6)

3. Permeability of ‘the conducting rock mass’ ( 3 sets): ! mass


2e 3 12S

(9.7)

Before k  103 m/s k  105 m/s

After k  107–108 m/s k  106–107 m/s

In the tunnel situation, the need for reduced tunnel support following pre-grouting, can be documented, if prognoses of required support using an ‘ungrouted Q’ are accepted as realistic. This claim has been supported by recent rail tunnels for the Norwegian Jernbaneverket in the Oslo area. Tunnels were driven under built-up areas founded on clays, using over-lapping preinjection ‘umbrellas’ established every 3 to 4 rounds, by performing a regular, high pressure (5 to 10 MPa), single-stage, 24 hours-duration pre-grouting routine, over many kilometres if tunnel. (Moen, 2004). Since tunnel deformation is closely linked to SPAN/Q (Barton et al., 1994, Barton, 2002) and support needs are linked directly to Q, the inescapable conclusion (which would also be arrived at by velocity monitoring

174

Rock quality, seismic velocity, attenuation and anisotropy

Figure 9.15 Permeability testing at a dam abutment in Brazil, using before-and-after testing of the effect of grouting, and both single-hole and 3D measurements. Note the rotation of permeability tensors, and their reduced magnitude, suggesting progressive sealing of joint sets. This suggests a possible scenario for individual Q-parameter improvements. Quadros and Correa Filho, 1995.

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

and deformability testing) is that the effective Q-value has itself been increased by the pre-injection. The Q-value (Barton et al., 1974, Barton and Grimstad, 1994) is determined from the modified core recovery RQD (i.e., counting competent pieces of core  100 mm in length as recovery). In addition to RQD, Q is calculated from the number of joints sets (Jn), the roughness (Jr) and the degree of alteration (Ja) of the least favourable set, and from the water inflow (Jw) and stress/strength condition (SRF). From Figure 9.4, a velocity increase of 1 km/s from say 3.5 to 4.5 km/s at a dam site, or in a wet, jointed zone ahead of a large tunnel, will imply that the Q-value has increased from 1 to 10 as a result of grouting. Following equation 9.1, a drop in Lugeon value from 1.0 to 0.1 is also implied, and using equation 9.3: M
10Q1/3 c , the modulus of deformation may be predicted to have increased from 10 GPa to at least 20 GPa. Are these changes possible to explain via changes in the six component Q-parameters? The answer is definitely yes, but the exact answer will always be unknown. We can speculate that the following orders of magnitude of effective rock mass quality improvement (each very modest), may occur in practice during grouting ahead of a tunnel or at a dam foundation: 1. RQD of say 30%, increases to say 60%, due to grouting of the most prominent set of joints that were most permeable. This occurs largely as a result of hydraulic joint jacking. 2. Jn of say 15 (four sets) is effectively reduced to 9 (three sets) for the same potential reasons as above. (This is a very conservative argument). 3. Jr of 1.5 (rough, planar) changes to 2 (another set) or to 4 (discontinuous), also for the same reasons. 4. Ja of 2 (weathered) changes to 1 (another set) or to 0.75 (cemented), also for the same reasons. 5. Jw of 0.5 (high pressure inflow) changes to 0.66 (small inflow) due to preferential sealing of the most permeable set. (This is also conservative). 6. SRF of 1 (unchanged). (In the case of a minor fault, even SRF might change). We therefore have the following potential ‘before’ and ‘after’ scenarios: From: Q 

J J RQD  r  w Jn Ja SRF

(9.9)

175

Q1 

30 1.5 0.5    0.8 15 2 1

(9.10)

Q2 

60 24 0.66  
9  23 9 1  0.75 1

(9.11)

The effective Q-value has increased in terms of round figures, by a factor of 10 to 30, which is broadly consistent with the increased Vp and M values, and with the reduced Lugeon value and rock support needs. It should be noted in particular, that when the seldom reported or measured 3D permeability is analysed in before-and-after-grouting scenarios, a rotation of the permeability tensors (and reduction of their magnitude) is seen (Figure 9.15, from Quadros and Correa Filho, 1995). This is the tentative justification for suggesting, as above, that the least favourable joints – and those causing the lower before-grouting velocities – are those that are (first) sealed by the grout. In this particular example we can estimate the following ‘hard rock, shallow near-surface’ results for before and after grouting, based on Vp
3.5  log10 Q, L
1/Q, M
10Q1/3:

Table 9.2 Potential effects of grouting according to empirical predictions.

Q Vp L M

Before grouting

After grouting

0.8 3.4 (km/s) 1.3 (Lugeon) 9.3 (GPa)

9 → 23 4.5 → 4.9 (km/s) 0.1 → 0.04 (Lugeon) 21 → 28 (GPa)

As with some of the cases reviewed earlier, this apparently good grouting result would need to be attributed to hydraulic joint jacking and perhaps to the use of micro-cements. In relation to the Inguri arch dam (Figure 9.11), Savich et al., 1983, would allocate the result (Vp  3.4 → 4.5 → 4.9 km/s) to class II (good grouting result). The interaction of rock mechanics, rock hydraulics and rock dynamics through application of seismic monitoring and rock quality description has many applications for rock engineers. The ‘core’ interactions (Vp, Q, L and M) illustrated above and in Figure 9.4 can also be expressed in alternative ways. By ‘extracting’ the uniaxial strength (c) of a rock from Q c( Q  c/100) we

176

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c)

Figure 9.16 Alternative nomograms for estimating typical interactions between c, Q, M, Vp and L. Note that porosity and depth (or stress) effects have been ignored for simplicity of presentation. (All predictions for nominal n  1% porosity, and typical refraction seismic depth
25 m.)

Relationships between Vp, Lugeon value, permeability and grouting in jointed rock

can make c one of the principal variables as shown in the nomograms for M, L and Vp shown in Figure 9.16. The numbers distributed within Figure 9.16a are estimates of the static deformation modulus (M), while the numbers distributed within Figure 9.16b and c, are the estimates for P-wave velocity. The units of M are

177

GPa and Vp are km/s respectively. The common x-axis in each diagram is the Q-value of the rock mass, i.e., the rock mass quality and not the seismic quality, although as discussed in more detail in the next chapter, these numbers, each having the same Q symbol, are inevitably related quite closely.

II

Introduction to Part II

The subduction zone diagram showing ‘extremely low Q’, ‘low Q’ and ‘high Q’ reproduced on the back cover of this book, the ‘familiar’ Vp-depth trends of midocean ridge seismic investigations, and the continentwide seismic velocities also showing ‘familiar’ increase with depth were each strong reasons for delving deeper into the subject of ‘seismic velocity and rock quality’, which was the original title planned for this book. Possible parallels with engineering scale phenomena were evident, in something resembling a ‘fractal’ earth. Of course the subduction zone ‘Q’ values proved to be attenuation related. However the possibility that a commonly used rock mass quality parameter, also

Fig. PART II Schematic section, after Barazangi and Isacks 1971 and Kearey and Vine 1996, of the Tonga arc, with inferred seismic Q variations. A possible relationship between seismic Q and rock mass quality Q is one of the first objectives of Part II.

called ‘Q’ (range 0.001 to 1000) and seismic quality Q (range 1 to 5,000), where attenuation  Q1, could in some way be related, proved to be one of the incentives for deeper research into seismic phenomena, and are the reasons for developing Part II material. Part II contains a wide sampling of interesting large scale continental and sub-ocean seismic behaviour, also high pressure laboratory rock physics tests designed to improve understanding of both crustal and reservoir variation-with-depth phenomena. A broad sampling of in situ reservoir related topics is given in later chapters, such as borehole stability and their seismic effects, and fractured reservoir investigations, involving P-wave anisotropy, S-wave splitting and polarization, and poroelastic modelling of the dispersive and anisotropic nature of fractured reservoir simulations. An attempt has been made to bridge between engineering, geological and geophysical scales of depth and time, in this continued investigation of ‘seismic velocity and rock quality’. The last chapter addresses geomechanics understanding of joint and fracture behaviour, in particular permeability-stress performance, with a view to suggesting alternative interpretations of aligned fracture orientations that actually involves multiple sets. Deep well behaviour in which impermeable and permeable fracture sets are separated by the determination of either dominance of normal stress or dominance of shear stress, represents a more correct understanding for maintenance of permeability in the face of high effective reservoir stresses. The ‘parallel to H max’ assumption for aligned single sets of conducting fractures from shear-wave anisotropy may be an over-simplification, and is often in conflict with geomechanics test data and theory.

10

Seismic quality Q and attenuation at many scales

In this chapter the term ‘Q’ used in the title in the classic paper of Knopoff, 1964 will be distinguished from the engineering rock mass quality Q-value of Barton et al., 1974, by reference to the seismic quality as ‘seismic Q’, Qseis, or Qp or Qs if the compressional wave or shear wave components have been distinguished. In fact, as we shall see, there are obvious connections between Qseis and the rock quality Q-value; a heavily jointed clay-bearing rock mass with low Q-value (probably less than 0.1) will inevitably cause great attenuation and have a correspondingly low Qseis (perhaps less than 5), while an almost unjointed massive rock mass with very high Q-value (e.g. 100–500) will inevitably cause little attenuation and have correspondingly high Qseis, depending on whether shallow or at great depth. Knopoff, 1964, introduced his review of seismic Q (or Qseis) by stating ‘Were it not for the intrinsic attenuation of sound in the earth’s interior, the energy of earthquakes of the past would still reverberate through the interior of the earth today. The chaos resulting from this awesome prospect is a speculation which lies outside the scope of this paper.’ We can conclude that Qseis and any of the physical reasons for Qseis that are captured in the Q-value rating (Appendix A) are fundamental to our well-being, even though low values of both may cause problems when tunnelling or when preparing a large dam foundation.

in the same volume. Common sense would suggest that Qseis can never be less than 2; however values below this magnitude are quite frequently recorded near the surface, including negative values which presumably may reflect interpretation difficulties of some sort. At the time of Knopoff’s review it was customary to assume that Qseis was substantially independent of frequency. His assumptions of ‘a homogeneous sample’ and ‘at low frequencies’ are clearly important in view of what is now understood about potential dissipation mechanisms in microcracked rock samples or in rock masses with sets of bedding planes and/or joints. Laboratory experiments on many homogeneous solids had shown that up to moderately high frequencies, the dimensionless quantity Qseis was virtually independent of frequency. This preliminary conclusion indicated that the mechanism by which energy was removed from elastic waves in solids was not the same as the mechanism for attenuation in liquids, where attenuation is frequency dependent. Some typical values of Qseis for longitudinal excitation of various solids, selected from Knopoff, 1964, are reproduced below. In this very selective list, the attempt is made to link Qseis to the relative stiffnesses of these materials. In reality the satisfactory-looking ‘order’ seen here is more scattered. One may comment already that the sandstone,

10.1

Table 10.1 Some examples of Qseis for longitudinal or bending excitation of various solids, selected from Knopoff, 1964, sorted by magnitude.

Some basic aspects concerning attenuation and Qseismic

Using the definition of Qseis given by Knopoff, 1964, as a starting point, we may refer to the familiar electrical circuit theory for energy loss:

2 E  Q seis E

(10.1)

In this definition, E is the amount of energy dissipated per cycle of a harmonic excitation in a certain volume, and E is the peak elastic energy in the system

Material

Qseis

Steel Copper Silica Glass Diorite Limestone Lead Sandstone Shale Celluloid

5000 2140 1250 490 125 110 36 21 10 7

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Rock quality, seismic velocity, attenuation and anisotropy

since presumably not jointed, was likely to have been very weak and porous, in view of later values for sandstones that we will review. Interestingly, and as a less serious aside, the 2003 Paramont film ‘The Core’, about an improbable voyage towards the centre of the earth to ‘fix’ an electromagnetic hazard, contains an opening sequence where the soon-to-be-seconded professor (Dr. Joshua Keys, played by Aaron Eckhart) has written the following Q-quality factors on the blackboard of the University of Chicago lecture room: Shale 20 to 70 Limestone 45 to 90 Granite 40 to 230 Also: Q : ": no attenuation The writer was informed about this sequence by a lawyer who wondered if it was ‘my’ Q. These Qseis magnitudes are of course entirely feasible extensions of the above list of Qseis magnitudes selected from Knopoff. As we will see, the numbers for any rock will change with degree of microcracking, with pressure, with the dry or saturated state, with weathering, and with the degree of jointing and faulting when at larger scale. Due to each of the above, the frequency band of the dynamic loading will also affect the result, due to factors to be explored in this chapter. It is now known that higher frequencies are attenuated at a higher rate than lower frequencies. Thus in a constant seismic Q (or rock quality Q) region of the rock mass, the amplitude of high frequency waves will decrease faster than that of the low frequency waves. Although most of the early evidence suggested that the seismic quality factor Q was frequency-independent over a wide range of frequencies (e.g. 102 to 107 Hz for the case of shales, MacDonal et al., 1958), this is now generally rejected, as a result of laboratory tests conducted under different frequencies, under smaller more realistic strain levels and over wider ranges of confining pressures. More recent data from in situ well tests conducted over wide ranges of frequency show the fundamental frequency dependence of seismic Q, due to the range of scales of the various attenuation mechanisms. Some of these newer sets of data will be reviewed in this chapter. Although Knopoff, 1964 assumed that the attenuation of elastic waves in dry (intact) rock was independent of frequency, it is a different matter when microcracks and joints and water saturation (or partial saturation) are added. Attenuation increases and becomes

frequency dependent, due to the inertial forces of the fluid in the microcracks and joints, and due to scattering. Walsh, 1966, proposed a frictional-dissipation-atcrack-surfaces model to explain the simpler attenuation in dry rock. There were parallels with his observation of hysteresis when loading and unloading rock in uniaxial compression. Concerning attenuation in intact rock, Walsh envisaged the following. Among the large number of cracks of all orientations and lengths, some are open and some are closed at any given pressure. As a compressional wave traverses the rock, (micro-scale) sliding on one crack-face past the other will occur on cracks which are barely closed and which have favourable orientation with respect to the wave propagation. This crack-face motion is opposed by friction, and some of the elastic energy of the wave is dissipated. As the wave traverses the material, the normal stress between the crack-faces increases, and thus the frictional shear stress also increases. As the wave passes, the direction of the frictional shear stress is reversed, and again work must be done against friction as the crack returns to its equilibrium position. Clearly, micro-scale deformations are implied here. Numerous mechanisms have been proposed to explain attenuation of seismic waves in rock and in rock masses. Johnston et al., 1979 listed the following in their landmark paper: ● ●

●

●

●

● ●

Matrix anelasticity Frictional dissipation due to relative motions at grain boundaries and across crack surfaces (cf. Walsh, 1966) Fluid flow causing relaxation due to shear motions at pore-fluid boundaries Relative motion of the matrix frame with respect to the fluid inclusions in the case of fully saturated rock (cf. Biot, 1956a) Squirt phenomena (cf. Mavko and Nur, 1975 and O’Connel and Budianski, 1977) Gas pockets squeezing when only partial saturation Geometrical effects due to small pores, larger irregularities, thin beds (this category obviously extends to major discontinuities, faults, rock boundaries, dykes etc.)

Attempts to illustrate some of the smaller scale mechanisms of intrinsic attenuation are reproduced from Johnston et al., 1979, in Figure 10.1. The fluid flow attenuation mechanisms really fall into two

Seismic quality Q and attenuation at many scales

183

Figure 10.2 A generalized chart concerning strain magnitudes and frequencies, for various deformation processes. After Batzle et al., 2005.

Figure 10.1 Schematic illustrations of several of the proposed intrinsic attenuation mechanisms. Johnston et al., 1979.

frequency-dependent categories: the inertial resistance which is important at ultrasonic frequencies, and squirt flow which is more prominent at lower frequencies. It appears that friction across thin cracks and grain boundaries may be the dominant attenuation mechanism (at small scale), if strain levels are sufficient. Increasing pressure decreases the aperture and effective number of cracks, and thereby reduces attenuation. Water wetting and saturation reduces the friction coefficient, thereby increasing attenuation. We will see much more detail of these aspects in the next section, and a detailed treatment of the effect of strain levels and pressure on attenuation mechanisms. 10.1.1

A preliminary discussion of the importance of strain levels

A useful summary of key concepts concerning elastic (contra plastic) strain as a function of frequency, and relaxation mechanisms as a function of frequency, was given by Batzle et al., 2005. Two diagrams presented in their EAGE Madrid poster are reproduced here, in

Figure 10.3 Conceptual diagram of elastic constants for different relaxation mechanisms, with a frequency scale, and an indication of whether the fluid involved is of low or high mobility. After Batzle et al., 2005.

Figures 10.2 and 10.3. These supplemented their extended abstract. They give a useful perspective on the orders of magnitudes involved in these fundamental earth-science topics. The authors emphasised that moduli or velocities measured in one amplitude or frequency domain were usually not valid in other domains, since different deformation mechanisms would likely be operating. Concerning the ‘elastic 4 plastic’ ‘static 4 dynamic’ cross-plot in Figure 10.2, one may put forward a ‘jointed-rock-mechanics’ viewpoint that in the presence of the usual heterogeneities of jointed, stressed rock masses, there will be a tendency for the four ellipses below the horizontal ‘static-dynamic’ axis to stretch their long axes upwards, into larger strain territory. The

184

Rock quality, seismic velocity, attenuation and anisotropy

reason for this opinion is that dynamic joint compliances derived from the registration of seismic anisotropy, reviewed in later chapters, have inverted magnitudes that are, perhaps surprisingly, partly within experimental ranges of pseudo-static joint stiffness data, from rock mechanics ‘macro-deformation’ testing. It is difficult to believe, on this basis, that joint microdisplacements involved in developing the characteristic deformation-load units of compliance (m.Pa1) from in situ seismic inversion, could be as small as ‘subatomic’, as a prominent physicist has suggested. Such an opinion probably stems from consideration of the effect of microstrain on microcracks (in intact samples), giving ‘too small’ influence to mobilize conventional concepts of friction, as we shall see shortly. In the in situ reality, a rock mass consists of joints and discontinuities with both length dimensions, and spacings, many, many orders of magnitude larger than the rock physicists microcracked ‘intact’ samples. The nanostrains to sub-microstrains presumably experienced in a rock mass during the passage of seismic waves (depending on distance from source and its magnitude) may then, through discrete micro-displacement in the rock mass, experience attenuation due to the larger scale features as well. Possibly the response of the joint to the dynamic pulse, is to initiate response from the current operating normal and shear stress-deformation gradients. Dynamic microexcursions above and below these gradients would then occur, with an increased (or nearly equal) slope presumably depending on the quality of the joint walls and surrounding rock. A useful geophysics concept, in this context, is that ‘rock quality is defined as whether Edynamic is more than or equal to Estatic’. Clearly, as shown in Chapter 6, when rock is hard and joints are fresh, the inequality of these two moduli is small – in which case the inverse of ‘dynamic’ joint or fracture compliance is also likely to be similar to the ‘static’ joint or fracture stiffness. When on the other hand rock (and joint) quality is poor, which in the rock mechanics world would be when rock quality Qc was low ( and joint wall compression strength JCS also low, perhaps even with clay-smear-or-filling), there will then be a big inequality, with Edynamic  or  Estatic, and a presumably corresponding inequality of 1/dynamic compliance  or  ‘static’ stiffness, or as we shall see in Chapter 16, 1/ZN # Kn, (and 1/ZT  or  Ks). In both the above scenarios: high or low rock quality, and the existing stress-deformation gradients, be they steep or shallow, will likely determine the ‘static’ starting

point for the similarly steep, or much increased gradients of 1/Z. It is surely logical to assume that the four ellipses depicted in Figure 10.2 stretch more into higher strain territory, the lower the rock quality, with the likelihood of some slight, irreversible deformation in the case of seismic, low frequency motion, especially near the rock surface, where stresses and deformation resistance are low. According to the dispersion relation of Kjartansson, 1977, cited by Mavko and Nur, 1979, the attenuation Q1, or inverse seismic quality Q can actually be used to explain the difference between the static and dynamic moduli of intact rock (See Chapter 6 for general results for rock masses). It is well known that the dynamic modulus can be at least double that of the static modulus even in intact rock, if flat pores or microcracks are present. Part of the difference in moduli may be due to fluid stiffening, in addition to the above dynamic-compliance/static-stiffness differences required when going up to in situ scale. According to Kjartansson, 1977, the ratio of moduli (M) at different frequencies (f ) can be expressed as: f  M1
 1   f 2  M2

2

pQ

(10.2)

It is assumed here that Qseis remains roughly constant over the frequency band of interest. Taking a ‘static’ value of f2  0.01 Hz and a dynamic f1  105 Hz and Qseis  1000, 100, 50 and 20, we find predicted ratios of M1/M2 of 1.01, 1.1, 1.2 and 1.7 respectively. Obviously, the more flaws (pores, microcracks) that are present in a rock sample, the lower will be the seismic quality Q, and the higher the predicted ratio of M1/M2 (the dynamic/static ratio of moduli). The above is consistent with the idea of a broadly related Qseis and rock quality Q, since dynamic moduli diverge more from the static moduli, as rock (mass) quality reduces. The above ‘intact rock’ difference is accentuated when larger scale is considered, since the rock joints will usually have lower values of the ‘static’ normal and shear stiffnesses, than the inverse of the dynamic compliances of the same joints.

10.1.2

A preliminary look at the attenuating effect of cracks of larger scale

A useful insight into the effect of changes in crack porosity (and number of cracks) on the seismic quality

Seismic quality Q and attenuation at many scales

factor Qseis, was given by Remy et al., 1994. We will utilise this in this introductory section, before reviewing intact laboratory data concerning seismic Q. The authors’ laboratory investigations involved sixteen freeze-thaw cycles (20°C to 20°C) over a period of sixteen days, in order to simulate part of the first appearance of weathering effects. The rock investigated was a thin-bedded (1 cm), Jurassic limestone from Lorraine in France. Cylinders (5 cm diameter, 10 cm length) and cubes (5 cm sides) were used, having a bulk density of 2.1 gm/cm3 and porosity of 22%. The bedding planes were perpendicular to the axes of the cylinders, and parallel to the top surface of the cubes. The repeated cycles of freezing (5 hrs), frozen (6 hrs), thawing (5 hrs), thawed (8 hrs) and corresponding changes of P-wave velocity are shown in Figure 10.4. P-wave velocities were higher when frozen (e.g. 4.7 km/s) than when thawed (e.g. 3.4 km/s) due to the higher wave velocity in ice (3.8 km/s). Maximum velocities were reached at the end of the freezing. As shown in Figure 10.5a and b, Vp (frozen state) fell with each cycle, while Vp (thawed) fell most rapidly on the first two cycles. It is important to note that the creation of new cracks caused under-saturation of the initially water-saturated samples, which were jacketed, and immersed in a solution of methanol. The two marked drops in Qseis values signify cracking episodes, the second of which was perpendicular to the

185

bedding planes (during the 8th cycle). Physical evidence for the cracking was seen from hydrostatic loading tests on the cubic samples, where definition of the total volumetric crack porosity (the sum of the components of each axis) was recorded. This parameter increased successively, and uniformly, during sixteen cycles of freezing and thawing, and clearly intimately affected the reduction in Qseis. The reduced values of Vp and Qseis with successive accumulation of crack-related damage have direct parallels in rock mass quality changes (i.e. reduced rock mass Q-value due to the fact that RQD reduces, Jn may increase, Jw reduces and, subsequently Ja increases as a result of weathering. See Appendix A for descriptions of the Q-parameters of rock quality (Barton et al., 1974).

Figure 10.4 A unit freeze-thaw-time cycle of 24 hours applied to thin-bedded limestones, and its basic effect on Vp. Remy et al., 1994.

Figure 10.5 a) Velocity Vp versus number of freezing and thawing cycles. b) Seismic Q versus number of freezing and thawing cycles. (Remy et al., 1994).

186

Rock quality, seismic velocity, attenuation and anisotropy

In the literature there are numerous references to the relatively low values of Qp (and Qs), in near-surface jointed or altered rock (e.g. 50 or less) and the higher values for intact samples of rock (e.g. 10 to 250) and the higher still values for deep igneous and metamorphic basement rocks (e.g. 100 to several 1000s), sills (e.g. 2000) and salt (e.g. 1000).

10.2

when considering both the P-wave and S-wave related attenuations, the ratio of Qs/Qp proves to be an even better indicator of the degree of saturation. In each case, pressure, with its microcrack-closing ability, causes a rise in velocity and a reduction in attenuation. Qseis therefore rises. According to the model of attenuation developed by Johnston et al., 1979, the relative contributions of friction and fluid flow on the overall attenuation are as shown in Figure 10.8.

Attenuation and seismic Q from laboratory measurement

A compilation of Qseis values for specific groups of rocks, without distinction between different frequencies or degrees of saturation shows, inevitably, a wide scatter as shown in Figure 10.6, from Bradley and Fort 1966. This shows only porosity as the plotted variable, and consequently a range of Qseis from less than 10 (for porous sandstones) to nearly 900 (for low porosity igneous and metamorphic rocks). There is a general trend of Qseis inversely proportional to porosity, but this is compromised by too many hidden mechanisms of attenuation. Early investigations of the effect of the degree of water saturation in reducing Qseis for porous rocks, and its strong pressure sensitivity as the rock reverts from dry to different degrees of saturation, are shown in Figure 10.7, from Gardner et al., 1964 data, reproduced by Johnston et al., 1979. As we shall see later,

Figure 10.6 Qseis as a function of porosity for igneous and metamorphic rocks (triangles), limestones (squares), and sandstones (circles). A wide range of frequencies and degrees of saturation contribute to the scatter of data. From Bradley and Fort 1966, reproduced by Johnston et al., 1979.

Figure 10.7 Saturation and pressure dependence of Qseis. From Gardner et al., 1964 data.

Figure 10.8 Relative contribution of friction-based and fluid flowbased attenuation for a brine saturated Berea sandstone, according to the model of Johnston et al., 1979.

Seismic quality Q and attenuation at many scales

As pointed out by Johnston et al., 1979, since the porosity and permeability (of these intact specimens) is relatively unchanged by the range of pressures applied, there is limited effect on the fluid-flow contribution to attenuation. Such would presumably not be the case if a jointed specimen or a jointed rock mass was involved, where pressure sensitivity of the permeability and secondary porosity would be marked, and non-linear, thereby giving a strong rise in Qseis with the reduced attenuation and velocity increase. 10.2.1

A more detailed discussion of friction as an attenuation mechanism

According to the models of Johnston et al., 1979, the relative effects of frequency and pressure can be combined to elevate the total Qseis (specifically Qp) of the Berea sandstone. At low pressures, the friction mechanism dominates and is almost independent of frequency. With increasing pressure and low frequencies Qp climbs beyond 100, but as frequency increases there is a reduction of Qp due to the contribution of squirt flow and so-called shear relaxation. Eventually, at very high frequencies, Qp declines sharply again due to scattering. This general scheme of predicted behaviour is illustrated in Figure 10.9.

Figure 10.9 Total Qp predicted for brine-saturated Berea sandstone, from Johnston et al., 1979.

187

The question of whether friction is a viable source of seismic attenuation; along microcracks, across cracktips, (and also along joints and filled discontinuities, and within the multiple surfaces of faults), will now be addressed again, with the benefit of more understanding of the effects of strain levels, provided by Winkler and Nur, 1982. With its title: ‘Seismic attenuation: effects of pore fluids and frictional sliding’, one would certainly expect that both mechanisms were still to be emphasised as potential sources of attenuation. In their conclusions the authors however, state the following: ‘Since the conditions required for sliding friction to be observed (large strains and small confining pressures) generally do not apply to seismic wave propagation in the earth, we conclude that simple frictional sliding is not a significant attenuation mechanism in situ.’ Their conclusion was drawn, at least partly, on the basis of extensional resonance tests, conducted on long, thin (intact) bars of homogeneous rock, such as sandstone, which were contained inside a long pressure vessel, and made to oscillate with an electro-magnet, while supported rigidly at their mid-point. Figure 10.10 shows the results of resonance decay measurements, giving both

Figure 10.10 Variation of attenuation (1000/QE) and velocity with strain amplitude, based on extensional resonance decay measurements on long (intact) bars of sandstone, suspended at their mid-point in a pressure vessel, and excited by an electro-magnet at one end, with a phonograph pick-up at the other end. (Note Q⫺1 sensitivity of 19%, and velocity sensitivity of only 0.7% to the 2-order of magnitude strain amplitude variation). Winkler and Nur, 1982.

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Rock quality, seismic velocity, attenuation and anisotropy

Table 10.2 Effect of strain amplitudes on extensional seismic quality, showing negligible effect on velocity. Selected data from Winkler and Nur, 1982. Material

Strain amplitude

QE

Velocity

Sierra white granite

1.44  106 4.15  108

185 204

3,629 m/s 3,637 m/s

Berea sandstone

2.10  106 2.30  108

103 140

1,937 m/s 1,955 m/s

Lucite

1.43  106

23.4

2,108 m/s

8

23.2

2,108 m/s

3.04  10

velocity and Q1 as a function of strain amplitude. The authors used frequencies from 500 to 9000 Hz, and studied the effects of confining pressure, degree of saturation, strain amplitude, and frequency. The changes in attenuation and velocity they observed with increasing strain amplitude (Figure 10.10) were interpreted as evidence of frictional sliding at grain contacts. But since this amplitude dependence supposedly disappeared at strains and confining pressures that they considered were typical of seismic wave propagation in the earth, they consequently inferred that frictional sliding was not a significant source of seismic attenuation in situ. They referred to other problems with the frictional attenuation mechanism. Savage, 1969 had pointed out that for typical strain amplitudes of seismic waves, and for reasonable microcrack dimensions, the computed slip across crack faces would be less than the interatomic spacing. They assumed, probably correctly, that this extremely small interaction would not be described by conventional models of macroscopic friction. In addition, they referred to the widely held assumption that frictional attenuation caused nonlinear wave propagation, which had not apparently been observed at the low strain amplitudes typical of seismic waves. Winkler and Nur provided a useful summary of the strain amplitude dependence of extensional attenuation QE for intact samples of several rock types, and some man-made materials. (The Massilon sandstone result is shown in Figure 10.10). Only the materials (i.e. rocks) that contained potential (micro) sliding surfaces, indicated strain amplitude dependence, and the author’s tests showed that (intact) rock samples almost lost this dependence with moderate increases of pressure, as shown in Figure 10.11. Noting the effect of confining pressure on extending the strain amplitude ‘limit’ for QE sensitivity, to about

Figure 10.11 Effect of confining pressure in reducing the strain amplitude-dependence of extensional attenuation QE, for dry Berea sandstone. Curve A  1 MPa, B  2 MPa, C  3 MPa, D  5 MPa, E  5 – 3  2 MPa (helium pore pressure of 3 MPa). Note therefore the closeness of curves B and E. Winkler and Nur, 1982.

106, as shown when comparing Figures 10.10 and 10.11, the authors suggested that it was significant that this strain level was in the same range as that needed for cusped stress-strain loops to become elliptical (Brennan and Stacey, 1977). They then posed the question: why is a strain of 106 or larger needed to cause frictional attenuation? (At least for the case of intact rock specimens, excited in the extensional mode?). They explored the answer to this question by suggesting that displacements across crack surfaces should at least be comparable to inter-atomic spacings of about 1010 m. They then equated a shear strain (␧) to a maximum displacement (d ) across a crack of length (L), suggesting d
␧.L. With (d )
101 0 m, (␧)
106, a crack length (L) of 104 , or 0.1 mm is implied. The authors considered this to be a realistic upper-bound for microcrack sizes in rock, so concluded that at strains below 106, sliding displacements would generally be too small for friction to describe the (sub-micron) interaction. The obvious corollary to this is to pose the question: what about all the larger cracks, i.e. intra-bedding joints, tectonic joint sets, major clay-filled discontinuities, and multiple internal interfaces in fault zones, all of which have large, or extremely large (L). With potential length dimensions of 0.1 m 1.0 m and 10 m for the ‘smallest’ three of the above five categories of discontinuity, and assumed spacings of the same order of magnitude (for convenience of estimation), an unchanged

Seismic quality Q and attenuation at many scales

189

5

Vp (km/s)

4

3

2

Dry Partially (~90%) saturated Fully saturated

1

(a)

1.5

2.0

Vp / Vs

2.5

Dry

continuum-based shear strain of 106 generated close to a given seismic source, might well imply maximum (close to the source) displacement discontinuity events of the order of 0.1, 1.0 and 10 m for these three joint/discontinuity types, if the continuum strain was converted to intermittent discontinuous shearing events with the same frequency as their length scale. Can such events be the source of dynamic joint compliances in geophysics, that have recognisable (nearly same order) magnitudes and units, as the MPa/mm pseudo-static stiffnesses of rock joints that are familiar to rock mechanics engineers? Shear strains decaying to one or two orders of magnitude less than 106, further from seismic sources, are surely still capable of providing displacement discontinuities of sufficient magnitude for frictional attenuation to be a valid mechanism in rock masses, as opposed to intact bars of homogeneous rock. While on the subject of the importance of strain level and frequency on Qseis, it is of interest to look at soils, nicely illustrated by the results of Marmureanu et al., 2000, using resonant column equipment. They tested cylindrical samples from surface soil layers, applying torsional and longitudinal vibrations, in studies connected with seismic risk mitigation. Figure 10.12 shows seismic Q as a function of shear strain level (%) and frequency, almost showing independence from frequency over a typical engineering seismology range of interest, i.e. about 5 to 100 Hz. The angular and shear strain dependence of soil, giving non-linear behaviour, was emphasised in their focus on earthquake hazard estimation.

2.0

Partially (~90%) saturated Fully saturated

1.5 Qs /Qp

Figure 10.12 Seismic Q as a function of angular frequency and shear strain level, measured on cylinders of near-surface clay, in a resonant column apparatus. Marmureanu et al., 2000.

1.0

0.5

(b)

1.5

2.0

Vp / Vs

2.5

3.0

Figure 10.13 Cross-plots of Vp versus Vp/Vs, and Qs/Qp versus Vp/Vs, showing the distinctive effects of the dry, partly saturated, or fully saturated states, when using these parameter ratios. Winkler and Nur, 1982.

10.2.2

Effects of partial saturation on seismic Q

Figures 10.13 a and b, show a useful summary of some of Winkler and Nur, 1982 work on the effects of the dry, partly saturated, or fully saturated state on the P-wave velocity and its variation with Vp /Vs. A ‘companion’ set of data for the moisture-detecting ratio Qs/Qp versus Vp/Vs is also shown. The S-wave attenuation increases with saturation (Qs reduces), thus making the ratio Qs/Qp a particularly sensitive indicator of the degree of saturation, since P-wave attenuation, though increasing with initial saturation levels, eventually reduces to less than the S-wave attenuation: thus the ratio Qs/Qp reduces to low levels, since Qp has increased. The separation of data into ‘environmental compartments’ is very interesting, and also useful for in situ interpretation.

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Rock quality, seismic velocity, attenuation and anisotropy

As we have seen above, seismic attenuation in partly saturated rock with pore space and microcracks provides interesting insights into the frequency dependence of seismic Q and Q1 for this small-scale element of rock mass. The early work of Knopoff, 1964, showed that attenuation in dry rock was independent of frequency even over a wide range, because of the assumed velocity-independence of sliding against friction across crack faces. When a sample is fully saturated, attenuation becomes frequency-dependent because of energy losses from viscous dissipation, which depends on shearing velocity. As discussed by Walsh, 1995, when attenuation is plotted against saturation for the same rock, there are peaks of attenuation at low saturation (e.g. 1%) and at high saturation (e.g. above 60 to 90%), depending on whether loading is in pure compression or in shear, where the peak attenuation comes only at greater saturation. It is believed that the attenuation peak at very low saturations is the result of viscous losses in fluid trapped in microcracks, which are filled first due to stronger capillary forces where apertures are very small. Over a wide range of saturation from a few percent to some 50%, no change of attenuation occurs, but as continuous saturated regions arise, fluid pressures rise in response to the pore volume reduction caused by the harmonic compressive wave, and energy loss becomes frequency dependent due to viscous dissipation. However, at very high frequencies, no fluid transfer occurs and the saturated region responds elastically. At very low frequencies, flow occurs, but if viscous stresses are low, dissipation of energy may be negligible. The bell-shaped frequency dependence of seismic 1 Q occurs at the intermediate frequencies, when viscous dissipation is not negligible. This is illustrated in Figure 10.14. The narrow peaks of attenuation in both shear and hydrostatic compression were suggested by Walsh, 1995, to be the result of the ‘squirt’ phenomenon (Mavko and Nur, 1975). At low frequency, pore fluids influence the attenuation due to their lack of rigidity, compressibility and density, while at higher frequencies, attenuation occurs due to viscous and inertial forces. Nur, 1973, interpreted temporal velocity anomalies as evidence of dilatant strain and varying pore water saturation in the crust prior to certain earthquakes. Mavko and Nur, 1979, showed that even a small amount of water can dramatically enhance the attenuation, when very flat pores (or joints) are present. This is because high pressure gradients cause (micro) flow at the contact between wet and dry pore space.

Figure 10.14 Attenuation as a function of frequency in dry rock (open squares) and rock fully saturated with water. The bell-shaped curve is characteristic of viscous damping. After Paffenholz and Burkhardt, 1989; and Walsh, 1995.

P and S waves passing through a medium exert oscillatory stresses which can be resolved into normal and shear components in the plane of each pore space. Attenuation can be demonstrated both for the normal component and for the shear component. The ratio Qp/Qs is 1 for dry rocks and is 1 when almost fully saturated, as we have seen earlier. It appears from the model of Mavko and Nur, 1979, that the state of saturation of the flat cracks (or rock joints) rather than the overall saturation of the rock is the most important factor for the attenuation. 10.3

Effect of confining pressure on seismic Q

Resonant bar techniques for the sonic frequency range, and pulse transmission techniques for the ultrasonic frequency range were used by Lucet and Zinszner, 1992, to demonstrate that not only frequency range, but also confinement can affect the seismic quality Qseis. Their 3 to 7 kHz and 500 kHz testing with some 30 rocks that included limestones and sandstones, included confinement to 45 MPa and water saturation. Pore pressure was fixed at 1 atmosphere. Care was taken to select core from adjacent samples in the same homogeneous quarried block, so that the effect of different frequencies could be truly compared. Figure 10.15a shows a set of results for a sandstone, in which sonic and ultrasonic attenuation as a function of increasing confining pressure are (in this case) similar. The vertical scale of 1000  Q1 shows that Qp (or QE), increased from about 6 to nearly 100 as a result of confinement. This can be seen by ‘inserting’ seismic Q

Seismic quality Q and attenuation at many scales

(a)

(b)

Figure 10.15 Sonic (resonant bar extensional mode), and ultrasonic measurements, a) on a saturated sandstone, and b) on a saturated crinoidal limestone, as a function of confinement. Lucet and Zinszner, 1992.

values down the right-hand axes at convenient arithmetic intervals, giving Qseis values of 5, 10, 20, 50 and 100. To one with a rock mechanics background, a resemblance to E-modulus increases with confinement is seen in both sets of sonic data, with units of GPa. More of this will be seen later. In the case of a crinoidal limestone shown in Figure 10.15 b, there is clear separation of the attenuation

191

according to frequency. The ultrasonic Qp1 (attenuation) is significantly higher, or Qp numerically much smaller (6 to 10) than for the sonic tests, where QE ranges from 7 to 100 or more, as confinement is increased. The authors interpreted these differences as being due to scattering of waves due to ‘density’ heterogeneities in the case of the limestone. Another limestone which was fine-grained showed less dramatic separation of behaviour as a result of frequency differences, and almost negligible effect of confining pressure. Seismic Q values were in this case a more or less constant 50 (ultrasonic) and a more or less constant 100 (sonic), over the full confining pressure range. In an important series of tests on two sandstones, Prasad and Manghnani, 1997, investigated not only the effects of effective stress change, but also pore pressure changes on the P-wave velocity and attenuation Qp1 Their experimental set-up, which is simply and clearly illustrated, has been reproduced in Figure 10.16. This figure defines Pc and Pp, and the difference Pd  Pc Pp is found in subsequent figures showing their results. The two sandstones investigated, Berea and Michigan, had bulk densities of 2.28 and 2.36 gm/cm3, and corresponding porosities of 21.2% and 16.9%, respectively, causing the higher velocities in the Michigan sandstone. The Berea sandstone had visible bedding planes and weakly cemented angular grains with microcracks. We can therefore select this sandstone for reproducing some of the author’s important results. These results, and equivalent ones for the roundedgrained and less porous Michigan sandstone, enabled the authors to differentiate the pore pressure dependence of the two sandstones. Referring to the classic effective stress equation: Pe  Pc  nPp

(10.3)

where n is the effective stress coefficient (Biot, 1962, Todd and Simmons, 1972), the authors found that both the Berea sandstone and the Michigan sandstone had values of n that reduced from about 0.78 and 0.62 respectively, when the confining pressure was high. These results applied to experiences in interpreting Vp. In the case of Qp, equivalent results were 1.10 and 0.86, reducing to 0.81 and 0.71, respectively. In other words, Vp and Qp measured at elevated pore pressures and elevated confining pressures are governed by effective stress coefficients significantly less than the classic n  1 obtained for more permeable media. The authors Prasad and Manghnani cited differences in the type of

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(a)

(b)

(b)

Figure 10.16 Schematic diagram of the ultrasonic pulse transmission experiments of Prasad and Manghnani, 1997.

Figure 10.17 Vp and Qp as a function of effective confining pressure for two sandstones, in this case at a pore pressure of 1 atmosphere. Prasad and Manghnani, 1997.

contact areas between the grains in the two sandstones as the reason for the differences in the pore pressure dependencies of the two sandstones. Before leaving the above results of confining pressure on Qp (there will be more data in some other chapters), it may be of interest to mention a finding, now a conviction, first noted when writing the chapter dedicated to rock physics results (Chapter 13). It was finally recognised that the variation of Qp with confining pressure resembled the well known rock mechanics effect of triaxial confinement on the E-modulus of rock samples. When the latter is expressed in GPa, quite remarkable

likeness to seismic Qp was noticed. This can be seen in broad terms in Figures 10.15, 10.17, 10.18 and 10.19. The likeness of Emass in GPa and in situ Qp has continued to be seen in field data reviewed. Almost all rock mechanics modulus data, from laboratory testing representing near-surface to kilometre depths, and from in situ testing at dam sites and deep tunnel deformation back-analysis, show moduli within the extreme range of 1 to 150 GPa, most commonly 5 to 75 GPa. In exceptionally weathered, weak, or clay-bearing conditions, moduli can reduce to 0.1 GPa, where ‘total’ attenuation in less than a wave length no doubt occurs.

Seismic quality Q and attenuation at many scales

193

(a)

(a)

(b) (b)

Figure 10.18 Changes in Vp and Qp in Berea sandstone: in both cases with pore pressure PP constant. Prasad and Manghnani, 1997.

10.3.1

The four components of elastic attenuation

Before looking at the (non-linear) effects on attenuation of samples loaded towards fracturing, at the end of this section on laboratory tests with confining pressure, it is appropriate to refer to Batzle et al., 2005 laboratory testing of intact, porous samples in a so-called forceddeformation apparatus. These authors’ tests neatly demonstrated the relative magnitudes of the elastic attenuation components. According to Nur and Winkler, 1979, the different modes of elastic attenuation (1/Qk  bulk, 1/Qp  compressional, 1/Qe  Young’s and 1/Qs  shear) are related to each other through inequalities.

Figure 10.19 Changes in Vp and Qp in Berea sandstone: in both cases with differential (or effective) pressure Pd constant. Prasad and Manghnani, 1997.

1. 1/Qs  1/Qe  1/Qp  1/Qk (for low Vp/Vs with partial saturation) 2. 1/Qs  1/Qe  1/Qp  1/Qk 3. 1/Qs  1/Qe  1/Qp  1/Qk (for high Vp/Vs with full saturation) The Batzle et al., 2005 forced-deformation apparatus was capable of applying frequencies from 0.3 Hz to 2,000 Hz, with strain amplitudes below 107. Note that the latter is very low. Micro-valves were used to control fluid movement into or out of the samples, in response to the dynamic loading. Both brine-saturated and partly brine-saturated states were investigated. Batzle et al., 2005 found that opening or closing their sample boundaries to fluid, using special microvalves, caused a significant change in the velocity and dispersion values, when at full saturation. Two sets of

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Rock quality, seismic velocity, attenuation and anisotropy

their experimental results are reproduced in Figure 10.20. The authors noted with the open boundary, that low frequencies caused the rock-fluid conjunct to behave as if partially saturated. The fluid movement

(a)

(b)

Figure 10.20 The relation between the four different modes of elastic attenuation with a) partial brine saturation, where attenuation due to the bulk modulus dominates, and b) 100% brine saturation and an open boundary, where at low frequencies 1/QK and 1/Qp dominate, as fluid can flow in and out of the samples. Batzle et al., 2005.

across the boundary was absent at high frequencies, due to the lack of time to reach (pressure) equilibrium. Beyond 100 Hz, saturated samples (with open boundaries) showed a low cumulative elastic attenuation. Batzle et al., 2005 cited the fundamental coupling of attenuation, velocity and frequency, from the illustrative Cole and Cole, 1941 developments in dielectrics, which were applied to attenuation measurements by Spencer, 1981. The authors added the effect of fluid mobility and partial saturation, and indicated the typical measurement window, in Figure 10.21 The authors also addressed the more complex question of attenuation and frequency dependence, or dispersion, in samples of shale, finding that dispersion had strong directional dependence. Because of the low permeability and inhibited fluid motion, yet observed dispersive results because of strong attenuation, they suggested that interactions among clay particles and between the clays and bound water may be responsible. They also showed that viscous fluids like heavy oil had their own internal viscous losses, which could contribute to overall rock attenuations. The conclusion from their studies of the multiple components of (elastic) attenuation was that attenuation-related attributes extracted from seismic data have to take such controlling parameters into account. Problematic here is that the fracturing or joint set developments in a rock mass will often be concentrated in the higher modulus layers, whose internal attenuation

Figure 10.21 The Cole-Cole relation coupling velocity, attenuation and frequency from the field of dielectrics. Cole and Cole, 1941. This was applied to attenuation in rock by Spencer, 1981. Batzle et al., 2005 also indicated the approximate dispersive effect of low or high fluid mobility, and of partial saturation.

Seismic quality Q and attenuation at many scales

components have thereby changed, or are different, from surrounding rock. Fluids of different viscosity in the differently fractured layers will add to the challenge of inverting data. 10.3.2

Effect on QP and QS of loading rock samples towards failure

An important contribution was made to our understanding of the influence of fracturing on attenuation, with simultaneous velocity effects, by Wulff et al., 1999. The authors made a careful study of the seismic effects of microfracturing during constant, low strain rate uniaxial compression testing, up to and beyond the point of microfracturing. They tested tuffaceous sandstone and granite samples, both related with Hot Dry Rock projects in Japan. As the authors pointed out, attenuation was not directly related to the strength and elastic moduli, but to mechanisms such as fluid flow, friction and scattering due to microcrack and crack density effects. Testing only dry specimens, they concentrated on interpreting the relative roles of scattering and friction. They reviewed several studies of attenuation in dry rock, (slate, sandstone, gabbro), that indicated good

195

agreement of observations with the intrinsic attenuation mechanism of frictional sliding, developed by Walsh, 1966, and good agreement with the semi-empirical pressure-dependent theory of Johnston et al., 1979, that is also based on Walsh, 1966. They also cited studies of scattering attenuation in micro-fractured marble where the scattering attenuation theories of Hudson, 1981 and 1990 (the first-order scattering model), did not predict sufficient attenuation in relation to test results. Wulff et al., 1999 found that crack density squared was needed in the Hudson, 1981 model, rather than a linear relation to crack density, to explain their own results. The authors’ tests on blocks of tuffaceous sandstone and granite, measuring 100  100  250 mm, were conducted under ‘room-dry’ conditions, following four weeks of drying at room temperature. New cracks were assumed to be dry ‘or at least not to have absorbed enough water molecules to permit fluid flow during the time of the experiment’. Several of their very interesting results are reproduced here. Figure 10.22 shows the separate effects of axial strain (with associated development of microcracking) on P- and S-wave velocities, and on Qp and Qs, for two samples of tuffaceous sandstone (t2-l, and t1-f ). The wave propagation was perpendicular to the

(a)

(b)

Figure 10.22 Effects of uniaxial stress-strain: symbol (o), and the associated microcracking, on Vp, Vs, Qp and Qs for two tuffaceous sandstone samples (100  100  250 mm, n  18.6%,   2.05 gm/cm3) from Japan. Note sample failures at 25 and 39 MPa. a) The upper pair of results (sample t2-l), have wave propagation (400 kHz) perpendicular to the loading direction, and therefore perpendicular to dominant microcracking. b) The lower pair (sample t1-f), have wave propagation (also 400 kHz), parallel to the loading direction, causing increased velocity and less attenuation with increased load. (solid symbols: Vp and Qp). Wulff et al., 1999.

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

Figure 10.23 Effects of uniaxial stress-strain: symbol (o), and the associated microcracking, on Vp, Vs, Qp and Qs for a granite sample (100  100  250 mm, e.g., average grain size 1.3 mm, n  1.4%,   2.62 gm/cm3) from Japan. Note failure at about 150 MPa. Wave propagation (400 kHz), is perpendicular to the loading direction, and therefore perpendicular to dominant microcracking, causing the reduced velocities and increased attenuation (reaching a minimum Qp  5). (solid symbols: Vp and Qp). Wulff et al., 1999.

loading direction in Figure 10.22a, and parallel to the loading direction in Figure 10.22 b. In each case the axial load – axial strain curves are given by (o) symbols. Equivalent results for a granite specimen, with wave propagation perpendicular to the loading direction, are shown in Figure 10.23. The increase of seismic Qp from about 18 to 30 (and Qs from about 30 to 50) in the case of the measurement parallel to the loading direction, are both potentially recognisable as ‘deformation modulus’ results, if the latter were expressed in GPa. On the other hand, the measurements of seismic Q made perpendicular to the loading direction, showing both Qp and Qs reducing from about 18 to 7 or 10 were actually registering a

‘Poisson expansion’ effect. In the case of the tests on granite shown in Figure 10.23, seismic Q was also measured perpendicular to loading, so registered similar reductions to Qp and Qs, following a slight increase in Qs during the first half of the loading. The authors investigated theoretical crack densities (crack number density  crack radius cubed), based on the theories of Hudson, 1981 and 1990. They interpreted a non-linear increase in attenuation with crack density as being due to pressure-increased crack sizes in addition to crack density increase. The frequency dependence of the P-waves, proportional to approx. f 2 or 3, suggested attenuation by scattering and possibly by friction. They therefore investigated the (Rayleigh) scattering attenuation predicted by the Hudson 1981 model, and found that only when using the largest plausible crack dimensions could they explain the total attenuation, if scattering alone was responsible. The attenuation mechanism caused by frictional sliding along the tapered tips of microcracks, according to Mavko, 1979, was also investigated, giving a good fit to the total attenuation of two of the four samples, based on their assumptions. The mechanism is independent of frequency, which the authors found consistent with the fact that the measured total attenuation was less frequency dependent than expected if scattering was the only mechanism. Figure 10.24a compares the scattering attenuation calculated with the Hudson, 1981, model, based on maximum plausible crack sizes, with measured data, and Figure 10.24b shows the calculated attenuation due to crack-tip friction, following Mavko, 1979. The authors concluded that attenuation in the rocks investigated was probably by a combination of frictional attenuation and scattering. A laboratory study involving ‘flaws’, this time naturally existing, concerning the cavities in carbonate rock, such as vugs or karsts, was described by Hackert and Parra, 2003. These cavities cause scattering attenuation like the fracturing seen above, but quantification is difficult due to the unknown scale and structure of the cavities. The authors described the use of X-ray computerized tomography scans to obtain the exact vug structure of two cores. They then used 3D finitedifference modelling to determine the P-wave scattering attenuation at ultrasonic frequencies. Qseis in the saturated states were as low as 8 and 15 near the source frequency of 250 kHz. The two cores had respective total porosities of 32.1% and 16.6%, with CT-computed vuggy porosities of 13.4% and 4.5%. The respective dry-state P-wave velocities were 3.97 and

Seismic quality Q and attenuation at many scales

Figure 10.25 Basic test set-up, for conducting normal loading and dynamic testing of joint samples, with add-on facilities for hydraulic testing and contact area estimation using Woods Metal. Pyrak-Nolte et al., 1990.

(a)

(b)

Figure 10.24 a) Calculated scattering attenuation for sandstone sample t2-l, using the Hudson, 1981 method, assuming crack sizes of 600 m. Solid lines represent the model with randomly oriented cracks, and dashed lines represent cracks oriented in the loading direction. b) Calculated attenuation due to friction, using the Mavko, 1979 model, based on estimated crack densities for randomly oriented cracks. Wulff et al., 1999.

4.25 km/s, and dry densities 1.85 and 2.20 gm/cm3. The authors observed that if the vugs had been karsts 1000 times larger (about 5 m), then the attenuation would have been seen at seismic frequencies in the range 100 to 500 Hz.

10.4

197

The effects of single rock joints on seismic Q

We will end this section on laboratory tests concerning seismic Q, with an appropriate transitional stage, namely the seismic Q behaviour of laboratory samples that are

‘divided’ by single natural joints or fractures. Landmark work was done in this area by Laura Pyrak-Nolte and colleagues Neville Cooke and Larry Myer, with important links to the hydraulics of joints or fractures via Paul Witherspoon. This pioneering research, originating from the University of Berkeley and from Lawrence Berkeley Laboratory, followed on from the rock mechanics developments of Goodman twenty years previously, and the theoretical geophysics of Schoenberg, and represents one of the few and important links between rock mechanics, hydraulics and geophysics. Most of Pyrak-Nolte’s and colleagues’ better known work was focussed on the behaviour of just three samples of joints in quartz monzonite from Stripa Mine ‘granite’ in Sweden. Even the much described sample numbers E30, E32 and E35 are sometimes referred to by geophysicists. These robust samples were subject to numerous tests, on numerous occasions, and have given the profession important insight into ‘fully-coupled’ earth science behaviour. We will review different aspects of this work in this and later chapters. An understanding of the basic principles for their tests is given in Figure 10.25. Besides the dynamic testing under normal load, as indicated, there was the possibility to measure permeability by linear (sector-to-sector) flow across the circular joint specimens, which had a diameter of 52 mm. There was also a facility to inject non-wetting molten Woods Metal into heated joint samples, which upon cooling, gave a measure of the area of the joint available for flow, at the given normal stress level. Joint roughness, such as JRC was not described, but a test result was referred to by Pyrak-Nolte et al., 1987a, where negligible effect of temperature (95°C) on aperture was indicated. (This differs from some other

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Rock quality, seismic velocity, attenuation and anisotropy

experiences of temperature effects on joint apertures where there is appreciable roughness, e.g. Barton et al., 1985, Barton, 1999, Barton and Makurat, 2006). The hydraulic apertures of the three joints E 32, E 30 and E 35 can be interpreted as reducing from approximately 3, 5 and 26 m to approximately 1, 1 and 6 m, as the joints were closed by measured amounts of approximately 4, 9 and 22 m (Pyrak-Nolte et al., 1987a). Thus E/e was in the low range of 1.1–2.25, suggesting quite planar joints, in relation to the Barton et al., 1985 model for the JRC-controlled measured inequality E  e, or E  e usually seen. A preliminary estimate suggests that JRC may have been in the range of only 2 (two cases?) to 4, which would readily explain the relatively high stiffness and small closures under stress, exhibited especially by two of the three Pyrak-Nolte et al., joint samples (E30 and E32). Figure 10.26a shows joint (or fracture) deformation versus normal stress for one of a series of load-unload cycles. The equivalent ‘specific stiffness’ (the inverse of tangent slopes) for these three load-deformation events, is shown in Figure 10.26b. These roughly 1,000 to 30,000 MPa/mm normal stiffnesses are of the same order of magnitude as the results for fresher, i.e. stiffer joint samples in various hard rock types, tested by Bandis, 1980. (See Bandis et al., 1983 and joint stiffness data reproduced in Chapter 16). Pyrak-Nolte et al., 1990 performed dynamic tests both across the three joint samples and across intact samples taken from adjacent core. (Stripa ‘granite’/quartz monzonite, ␥  2.65 gm/cm3, Young’s modulus E  60 GPa). The three pairs of samples had equal length and diameter (77  52 mm). Figure 10.27 shows three sets of ultrasonic (‘0’ to 1.5 MHz) P-wave amplitude spectra, conducted in the dry state in this case, for the three pairs of ‘companion’ samples (jointed, and adjacent intact). The comparison of ‘intact’ and jointed response gives a very instructive image of the effect of the more open and deformable E 35 joint (top), on P-wave transmission, showing selective filtering of highest frequency. (Note the lower normal stiffness of E 35 in Figure 10.26b, compared to the very stiff and presumably well interlocked E 32 sample). Sample E 30, with intermediate stiffness, gives intermediate response. This fairly long, but necessary introduction to these important tests, brings us to the subject of seismic Q. Pyrak-Nolte et al., 1990 calculated seismic Q by taking the ratio of the spectral amplitudes of the intact and jointed ‘companion’ samples, in comparison to the

(a)

(b)

Figure 10.26 a) One set of load-deformation results for the three quartz monzonite (Stripa granite) joint samples. b) Specific stiffness (inverse tangent slopes) as a function of normal stress, for the three joint samples tested dry. Pyrak-Nolte et al., 1987a.

spectral amplitudes obtained from a non-attenuating cylinder of aluminium of identical dimensions, and loaded in an identical manner to the same loads. The authors, following Johnston et al., 1979, compared the spectral amplitudes of the different samples, starting with the dispersive wave equation: A  A0 e where

&x

2Qc

(10.4)

%  frequency X  travel path length Q  inverse of attenuation c  phase velocity of wave A0  amplitude at x  0 The ratios of the spectral amplitudes of the seismic pulses transmitted through the companion rock samples

Seismic quality Q and attenuation at many scales

199

Table 10.3 Seismic Qp and Qs calculated by Pyrak-Nolte et al., 1990, using equation 10.4, for both jointed and intact, and dry and saturated states, at two levels of normal (axial) stress. The results for the most deformable E 35 joint sample are selected, as the 25 m joint closure with 85 MPa stress increase is considered realistic for non-planar joints. Qp

Qs

Specimen type and test condition

2.9 MPa

20 MPa

2.9 MPa

20 MPa

Sample No. Jointed-dry Intact-dry Jointed-wet Intact-wet

E 35 7 12 9 15

E 35 14 39 30 51

E 35 12 32 28 41

E35 23 71 39 56

compared to the aluminium (A/A1), were then calculated (by Johnston et al., 1979) as: ln

Figure 10.27 Comparison of intact and jointed sample response to ultrasonic P-waves up to 1.5 MHz frequency. The magnitude spectra show the positive, magnitudeincreasing, effect of higher normal stress. Sample E 35 has least normal stiffness, due to its 25 m of closure under normal stress to 85 MPa. It demonstrates the maximum filtering of higher frequencies, compared to the high stiffness sample E 32, which only closed some 5 m under 85 MPa stress. PyrakNolte et al., 1990.

A A fx   ln 0 A1 Qc A 01

(10.5)

where f  %/2 The authors gave a comparison of seismic Q calculated from this equation, for both the dry and saturated states. A selection of their interesting results is reproduced in Table 10.3. The marked reduction in attenuation when loading the jointed specimen at 20 MPa instead of 2.9 MPa is typical of in situ response. Qp increases by a factor of 2 when dry, and by a factor of 3 when wet. It is interesting to note however, that the less attenuating intact specimen shows Qp increasing by a factor of at least 3, both when dry and when wet. The seismic waves are of course transmitted perpendicular to the microcracks most likely to be closed by the axial stress. Pyrak-Nolte et al., 1990 made an alternative seismic Q calculation, because of the non-linearity of the spectral ratio data. By assuming that A0/A01  1 in equation 10.5, they were able to re-arrange the equation and express seismic Q as a function of frequency. Figure 10.28a shows the result of applying equation 10.6 to the data from the dynamic tests on jointed sample E 30. This joint had an intermediate level of normal stiffness in relation to E 35, and to the least deformable, stiffest joint E 32 (Figure 10.26). Q 

fx clnA/A1

(10.6)

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 10.28 a) The frequency-dependent attenuation calculated for the medium-stiff sample E 30 (dry), with comparison to the lesser attenuation of the intact (dry) companion sample. Normal stress levels were 2.9, 10 and 70 MPa. Small circles were the result of calculation using equation 10.5, at a specific frequency of 0.5 MHz. b) Analytical solutions assuming increasing values of dynamic normal stiffness, as described in the text. Pyrak-Nolte et al., 1990.

Figure 10.28a shows the dispersive results of the seismic Q calculation, using this equation for the tests conducted on E 30, when in the dry state. The small circles in the figure were calculated using equation 10.5, at a specific frequency of 0.5 MHz. The similar shape of the curves for the jointed and intact samples was interpreted by the authors as evidence for similar (closure-understress) behaviour of both the joint and the microcracks most likely to be (partly) closed by the axial stress. The theoretical curves shown in Figure 10.28b were developed by the authors, by assuming a joint or fracture density of 1 per 77 mm, as tested, in an otherwise nonattenuating medium (clearly a simplification). The single fracture was represented by a displacement discontinuity

(based on the theory of Schoenberg, 1980), with dynamic normal stiffness varying from 6.4  1012 to 1.6  1013 Pa/m. In rock mechanics units, this is more easily understood as 6,400–16,000 MPa/mm, in fact typical for the pseudo-static normal stiffness of fresh rock joints at high stress levels. (See Chapter 16.) The theoretical curves show good correspondence to the interpreted data using the spectral amplitude ratio method described above. Before leaving these interesting studies for the time being, the earlier referred suspicion that deformation modulus (in GPa) is similar to seismic Q, will be addressed again. If we ‘insert’ a virtual Qseis scale down the right-hand axes in Figure 10.28, we obtain ‘simple’ magnitudes for seismic Q of 5, 10, 20, and 100 for 1/Qseis values of 0.2, 0.1, 0.05 and 0.01. The jointed sample shows the lowest Qseis values when measured at the ‘lower’ frequencies of 0.2 MHz, and values varying from 5 to about 20 as normal stress increases from 2.9 to 70 MPa while the solid control sample, at 0.5 MHz shows Qseis of 8, 15, 20 and 90 as stress was raised from 2.9 to 10, 20 and 70 MPa. These results remain in the typical range of moduli (when expressed as GPa), but the low stress value of Qseis seems to be lower than expected. In-seam seismic measurements in coal have been used for a number of years to indicate the state of stress and fluid drainage in this fine-structured, deformable, low velocity material, which in some ways resembles a miniature (and property-scaled) roughly cubicallyjointed rock mass. A set of laboratory test data, including effects of the dry to fully saturated state, with confining pressures from near-surface, up to minerelevant levels (2 to 40 MPa) was given by Yu et al., 1993, using a transversely isotropic Permian coal from Tower Colliery, Wollongong, Australia. Some of the key results of these comprehensive studies are reproduced in Figures 10.29 and 10.30. The strong effect of water saturation, which tends to fill the flat (low aspect ratio) cracks and cleats in the coal, is evident in all the data. This miniature ‘rock mass’ also displayed the classic anisotropic effects of lower Vp perpendicular to bedding, and higher Vp parallel to bedding, with 45° wave transmission giving intermediate values. S-waves were little affected by saturation, which is also a traditional result, when S-wave splitting is not involved. In Chapter 15 we shall see that polarized split shear-waves are affected by degree of saturation and even fluid type, due to changed joint or fracture compliances. At higher confining pressures, the water content (one of the contributing causes of attenuations) was reduced

Seismic quality Q and attenuation at many scales

Figure 10.29 Vp as a function of confining pressure (pore pressure  atmospheric), for dry and saturated macrobedded coal specimens. The specimens were loaded and dynamically tested in three orientations relative to bedding. Yu et al., 1993.

by partial closure of the fine cubic structure of cracks and cleats. Vp (dry) and Qp (dry) approached the values of Vp (saturated) and Qp (saturated) as confining pressure was increased. The seismic Q values were lowest for the four dry specimens, while there was much less attenuation for the four saturated samples. The authors emphasised the fact that the decrease in attenuation for fully-saturated specimens of coal, with its low aspect ratio cracks, differed diametrically from the usual result for sandstones. This could be questioned based on earlier results, but the point is made that cracks close easier than equant pore space. Yu et al., 1993, also emphasised the relatively low values of dynamic E-moduli for the coal (e.g. about 8 GPa: at low stress?) and the relatively high values of

201

Figure 10.30 a) The spectral amplitude behaviour across and parallel to the coal’s bedding, showing the strong effect of saturation on wave transmission. b) Qp for dry and saturated coal specimens, as a function of confining pressure (pore pressure  atmospheric). Yu et al., 1993.

the dynamic Poisson’s ratio (e.g. about 0.4) in relation to typical intact rocks. The effect of higher stress in the coal reducing the difference in seismic Q between dry and saturated conditions was assumed to be because of both increased frictional resistance along the cracks, and due to the reduced water content caused by the closing cracks. Again we see the general trend of seismic Q increasing with stress in a similar manner to deformation modulus. Thanks to these excellent laboratory Q-studies, the scene is now set for going into the field, to see fractures and rock joints (not forgetting the ‘ever-present’ microcracks), in their in situ seismic Q environment. First we will look at some near-surface seismic Q, including some quite shallow studies in reservoir-type sediments.

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This will be followed by seismic Q at great depth connected with earthquakes and continental-scale studies. Finally we will return to ‘medium’ petroleum reservoir depths at the end of this chapter on seismic Q, where the potential economic rewards of understanding Qseis are pressing further developments. Understanding petroleum reservoir behaviour, first from more rock physics (laboratory) contributions, then from in situ anisotropy effects, (i.e. shear wave splitting), forms much of the material in Chapters 13 to 15.

10.5

Attenuation and seismic Q from near-surface measurements

Seismic reflection and refraction techniques used to illuminate major features beneath the earth’s surface obviously depend on the existence of seismic wavelets. There may not always exist sufficient seismic impedance contrasts between rock boundaries to cause reflection or refraction. But absorption is continuous, and significant information can accumulate on the progressing wavelets. Ecevitoglu and Bingol, 1999 pointed out that the absorption information may be crucial as far as the rock’s consolidation, porosity, fractures, and fluid contents are concerned. Near surface measurements of seismic Q are however complicated by the presence of near-surface weathering layers, and of course by faulting. The seismic energy will be strongly attenuated, and waveforms may also be distorted.

10.5.1

Potential links to rock mass quality parameters in jointed rock

With our progression from laboratory to field scale, implicit links between Qseis and rock mass quality Q (Barton et al., 1974, see Appendix A), can apparently be seen, due to the logical results of near-surface, seismic Q that rapidly increase with depth. This also mirrors the way that rock mass deformation modulus, calculated from the rock mass Q-value, also increases with depth, to match in situ measurements of this fundamental rock mass parameter. This seems to be because the features of a rock mass that are described by a rock mass characterization method, such as rock mass quality Q, contains elements of the in situ medium deemed potentially important for both the intrinsic and scattering attenuation mechanisms.

When moving to in situ scale, joint spacing (captured in RQD) and the number of joint sets (Jn) are clearly going to have an influence on scattering losses, just as microcracks and induced rock sample cracking and individual joints are seen to influence scattering and intrinsic losses in laboratory samples, as shown by Wulff et al., 1999, and Pyrak-Nolte et al., 1990. It is also intuitively reasonable to suspect that the condition of joints – their degree of interlock as determined both by stress level and by roughness (Jr), and the presence or absence of mineral coatings or clay fillings (Ja) – will have potential influence on (micro) permeability and therefore on potential squirt losses, when there is a variable degree of saturation, as is frequently the case in the near-surface. Joint characteristics are also expected to influence eventual frictional losses, if magnitudes of continuumbased shear strain (actually discrete micro-displacement discontinuities), are of sufficient magnitude. The fact that seismically determined in situ dynamic rock joint compliances, the inverse of stiffnesses, have immediately recognisable (i.e. expected) magnitudes, and are expressed in the same (but inverted) units as in the rock mechanics of discontinua (e.g. Bandis et al., 1981, 1983, Pyrak Nolte et al., 1990), is further justification for looking also beyond microcrack-scale, for the contributions of the jointing of the rock mass, to both scattering and intrinsic losses. In the last section on laboratory testing of the dynamic response of joints under load, the results of Pyrak-Nolte et al., 1987a and 1990, showed ‘static’ normal stiffnesses for the most deformable joint (E35, Figure 10.26b) that varied from 5,000 MPa/mm at 5 MPa normal stress, to about 30,000 MPa/mm at 70 MPa normal stress, each in the dry state. These authors’ ultrasonic joint measurements, showed for the same sample E35, a dynamic normal stiffness varying from ‘only’ 4,000 to 7,600 MPa/mm (dry), and from 9,500 to 15,000 MPa/mm (saturated), at comparable low normal stresses of 2.9 and 6.0 MPa respectively. At normal stress levels of 70 MPa, the authors showed dynamic normal stiffnesses of 32,000 MPa/mm when dry, and 59,000 MPa/mm when saturated. Only the latter is higher than the ‘static’ stiffness, showing similar relative increases as the Edynamic to Estatic inequality that reduces strongly with high quality rock joints and rock masses. Of importance for in situ uses of seismic Q, the authors Pyrak-Nolte et al., 1987b noted that velocities soon reached the level of the intact rock, when using

Seismic quality Q and attenuation at many scales

high frequencies. They showed that this ‘seismic closure’ could occur at lower stress levels when the joints were less stiff (as for their sample E 35, Figure 10.26b), and at higher stress when the joints were stiffer. Most importantly, even when the effect of a joint on velocity was almost ‘erased’ by stress and high frequencies, the change of amplitude of the transmitted wave, i.e. the spectral amplitude basis for seismic Q-estimation, remained very strong. Kang and McMechan, 1994 showed near surface data from N. Texas where the smallest Qp value of 36, and the smallest Qs of 23, were relevant to the highly variable surface weathered zone. According to these authors, very few in situ measurements of scattering in the upper few metres to tens of metres were available at that time. ‘The near surface velocity/density structure may be more variable than previously thought: some of this variability may have been hidden in previous measurement that did not explicitly separate intrinsic and scattering effects.’ This of course is supported, implicitly, by engineering experiences: see for example Chapter 1 and the rapidly changing (laterally and with shallow depth) refraction seismic velocities of Sjøgren et al., 1979. Such would also imply rapidly changing rock mass qualities, deformation moduli, and by implication, seismic Q, since in the near-surface, Vp
3.5  log Q km/s, where Q is in this case the rock mass quality of Barton et al. 1974. (See Chapter 5 for rock quality and velocity variation at shallow depth). A hydraulically conductive, gently dipping fracture zone at SKB’s study site at Finnsjön, north of Stockholm, was imaged using the seismic reflection method. Amplitude decay curves as a function of distance, given by Juhlin, 1995, showed that a seismic quality Qseis of 10 fitted the data, assuming an average frequency content of 150 Hz and a P-wave velocity of 5.5 km/s. The value of Qseis  10 was assumed to be relevant to the upper 100 metres of this granodioritic rock. Juhlin, 1995, considered the result to be consistent with higher Qseis values of 30 and 50 at depths of between 200–1100 m in crystalline rocks of comparable character. Again note the similarity to rock mass deformation modulus expectations, when the latter is expressed in GPa. In relation to the Q-value of rock quality, a P-wave velocity of 5.5 km/s at 100 m depth in a crystalline, hard, low porosity rock (Figure 5.36, Part I) suggests a Qc value of about 40, and when compression strength of say 200 MPa are allowed for, the rock mass quality Q-value would be about 20. This is a very typical rock

203

quality value for a good quality but jointed crystalline bedrock with two to three joint sets. It might have Q-parameters as follows (see Appendix A). Q


100 2 0.66  
20 6 1 1

Greater frequency of jointing in a fracture zone would probably reduce this value to 1 or less. This is consistent with independent Q-logging results at SKB’s Swedish nuclear waste investigation sites, performed on 4,000 m of core by the writer in 2003. Shaw et al., 2004, reported near-zero offset VSP investigation of Qseis in a 50 to 600 m deep section of a well through a Faroe Islands Upper and Middle basalt series, typical of other North Atlantic basalt formations. The source used was a 150 cubic inch air gun fired in a pit under 2 m of water. The receiver was a clamped, three-component geophone, with spatial intervals of 10 m. The authors were able to assess the errors in the Qseis assessment, by testing with slightly different receiver separations of 280, 290, 300, 310 and 320 m. Their results, expressed as Qseis versus midpoint depths from 200 to 450 m, showed Qseis increasing rapidly from about 10 to 50 in the upper third of the well, and levelling off at about 60 at greater depths. The effect on seismic Q of lower stress in the upper levels of the basalts is implied in these and other studies. The results are also typical of rock mass deformation modulus variation with depth, where rock quality Q might typically vary from about 2 to 20, based on Q-logging of numerous basalts. Payne et al., 2005 described a seismic (sparker P-wave) experiment at a shallow borehole test site in N.E. England in variously jointed Cretaceous chalk. Cross-well seismic was performed between three wells, at a frequency band width of 500 to 3,000 Hz. Spectral modelling was performed to provide Qseis estimates for a shallow 30–36 m deep highly jointed zone, with permeability of about 1 darcy (
105m/s), and for a deeper (36–50 m), less jointed interval, which had an implied permeability close to that of the matrix of about 1 millidarcy, or 108m/s. The respective Qp values were 20 and 60. To help assess whether the higher attenuation in the highly jointed zone was mostly caused by scattering rather than by intrinsic mechanisms, the authors used a discrete particle numerical model, as described by Toomey and Bean, 2000. (Although several numerical

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

Figure 10.31 a) Numerical simulation, based on Toomey and Bean, 2000 model, of a random, vertically fractured section, with source and receiver at opposite sides, representing part of the cross-hole experiment in jointed chalk. b) Amplitude of received waves, as affected by fractures with two different compliance assumptions. Reference case without fractures is the solid line. Payne et al., 2005.

models will be described in Chapter 15, we may examine this model here, in the context of seismic Q). A horizontal compressional wave was applied from one side of a random generation of vertical fractures having compliant bonds, with the receiver at the other side. The compressional wave amplitude at the receiver is shown in Figure 10.31, and indicates three amplitudetime curves. When the (dynamic) compliance ZN was as large as 4  101 2 m/Pa (or dynamic Kn as small as 250 MPa/mm), there was merely a small time shift of the signal in relation to the homogeneous unfractured case (see dotted, parallel curve). The authors indicated that this implied that the apparent seismic Q of this numerical assembly of particles-containing fractures was then ‘close to infinite’.

(This was perhaps surprising, as dynamic stiffnesses as low as 250 MPa/mm do not imply either high stress or non-attenuating conditions. Perhaps the discontinuous nature of the modelled ‘fracturing’ had something to do with this ‘close to infinity’ seismic Q). When on the other hand, the fracture compliance was increased by an order of magnitude to 4  101 1 m/Pa (or when the dynamic Kn was as small as 25 MPa/mm), a marked reduction in wave amplitude was registered (see third, attenuated curve in Figure 10.31b). An apparent seismic Q of 15 was calculated for this attenuating case. Scattering within the highly jointed zone was therefore considered a plausible mechanism, presumably because a dynamic Kn as low as 25 MPa/mm (and its inverted compliance value) were thought to be reasonably representative of the shallow joints or fractures in the chalk. As will be shown in Chapter 16, such low values of normal stiffness indeed imply very low normal stress, quite consistent with the ‘macro-deformation’ and comparatively ‘static’ normal closure testing results for natural, fresh or partly weathered joints reported by Bandis, 1980 and Bandis et al., 1983. ‘Static’ (extreme low frequency) testing, perhaps at a rate of only 103 Hz, displays strong non-linearity in relation to normal stress level, when loading is from zero to about 60% of the joint wall strength JCS – usually represented by many tens of MPa of normal stress. The so-called ‘initial normal stiffness’ described by Bandis, has values of the same low magnitude as assumed above for the dynamic modelling. An interesting example of low, near-surface seismic Q structure, with comparison to refraction seismic structure, was given by Ecevitoglu and Bingol, 1999. They introduced a new methodology to rapidly compute and graphically map seismic Q, arguing that absorption measurements are tedious, subject to noise, and not common in everyday geophysics in the near-surface. It appears from a necessarily brief (extended abstract) description that the direct wave and all the refracted waves were each considered as the first breaks. Figure 10.32 shows an example of their tomographylike seismic Q distribution from the near-surface to 50 m depth. The high Q anomaly of 20, at 45 m depth, was found independently in a conventional seismic refraction interpretation with an upper layer of Vp of 1.97 km/s, and a second layer of 4.26 km/s, resulting in a 45 m depth for the refractor. ‘The exact location we have found independently from seismic Q imaging’.

Seismic quality Q and attenuation at many scales

205

Figure 10.32 Seismic Q imaging of an anomaly at 45 m depth with correspondence to a Vp of 4.26 km/s from independent refraction seismic imaging of this second layer of higher velocity. Ecevitoglu and Bingol, 1999.

10.5.2

Effects of unconsolidated sediments on seismic Q

Extremely low values of Qp in unconsolidated sediments such as a value of 4 between 60 and 100 m depth in sands and gravels (Gibbs and Roth, 1989), and values between 2 and 6 for the case of artificial, glycerolsaturated, random packs of glass beads and coarse sands (Molyneux and Schmitt, 2000), emphasise the character of these unconsolidated and unlithified low Qseis media. If energy dissipation is small, the seismic quality Qseis (also called the internal friction or dissipation factor) was previously defined as: 2 E  Q seis E

(10.7)

where E is the elastic energy stored at maximum stress and strain and E is the energy loss per harmonic excitation cycle. Qseis can however apparently be smaller than 2 (i.e. E  E), but alternative definitions of Qseis seem to be needed if larger dissipation (i.e. exceptionally low Qseis) is measured or assumed. In the case of shallow seismic investigations in sediments, it is likely that Qseis has a frequency-dependent component because near-surface layers of sediment tend to be unconsolidated and may contain fluid. This was verified by Jeng et al., 1999, who measured Qs values as low as 2 to 5 using different sources of energy, and found these lowest values corresponded to the lowest frequencies used of about 50 Hz. A roughly 5 times higher frequency (250 Hz) resulted in about 6 to 8 times higher Qs-values (16 to 30 approx.). Less attenuation (higher Qseis) is observed at higher frequencies because it

is less easy to accelerate the pore fluid along the pores (due to inertial forces) than to compress the pore fluid, as in the flat-pores model of Mavko and Nur, 1979. Jeng et al., 1999 used artificial source and receiver pairs, and a frequency-dependent Q estimation, in contrast to the conventional spectral ratios with constant Q assumption. When examining the triaxial-geophone data with varied (2 m interval) offsets, the frequencydependent and frequency-independent assumptions reportedly gave ‘dramatic variation’ of Q. The authors carried out experiments at three different sites in Taiwan, but concentrated their attention at the Yuan-Lin site in the foothills of central Taiwan, where two different sources were available. The surface of the site had a 2 to 3 m thick layer of alluvium and unconsolidated sediments, overlying a 200 m thick gravel formation. Their data showed Qp values linearly increasing from between 1 and 3, to between 10 and 16, as frequency was increased from 50 to 300 Hz. There was marked instability, and therefore lack of linearity, at frequencies beyond 300 Hz. The frequency components for the power law Q  kf n were 1.11 and 0.93 for the P and S waves, respectively. Their investigation using the conventional frequencyindependent assumption for Q, and geophone intervals of 5, 7.5, 10, 12.5, 15 and 17.5 m gave average Q tending to increase from about 10 to 13 over this range of geophone intervals. The modified frequency-dependent approach at the same location, gave Q values varying approximately linearly from about 2 to about 18, as frequency was increased from 57.5 to 575 Hz. The authors conclude that for weathered loose layers Qseis smaller than 2 is obviously possible, despite the classic formulation of energy loss per harmonic cycle,

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 10.33 Downhole logs of Vp, density and Qp for ooze and transition to increasing layers of chalk, in sub-ocean studies made during the Ocean Drilling Program, at the Ontong Java Platform, in the western Pacific. Frazer et al., 1997.

compared to the elastic energy stored at maximum stress and strain. The authors Frazer et al., 1997, working in the Ocean Drilling Program at the sub-ocean Ontong-Java Platform carbonate sections in the western Pacific, emphasised that attenuation measurements made at ultrasonic frequencies in the laboratory, often on disturbed sediment samples, or estimated from seismic experiments over long wave lengths, may reveal little about the geologic/depth evolution of sediment attenuation. Compaction of loose grains, through diagenesis, to sedimentary rocks at depth, can be a fragile environment to sample, especially when the shear-wave velocity is lower than the borehole fluid velocity. The authors used the Schlumberger long-spaced sonic (LSS) tool which has two sources and two receivers in a special arrangement. Every 6 inches (0.15 m), four microseismograms were recorded, with three sourcereceiver spacings. The frequencies involved were about 5 to 25 kHz, lying between laboratory and seismic measurements. The actual Vp-density log for one of the holes investigated is shown in Figure 10.33. The velocity increased

almost linearly from 1.8 km/s at 200 m below sea level, to 2.6 km/s at 700 mbsl. The reduced density appeared to be at the base of the ooze-to-chalk transition, where more chalk was present. In the transition zone the chalk first appeared in distinct, several centimetre thick layers, separated by ooze layers. The thickness and proportion of the chalk increased towards the base, where there was more calcium carbonate cement. The seismic quality Qp for the same hole is also shown in Figure 10.33. In the loose, high-porosity sediments the attenuation was assumed to be mostly due to fluid motion relative to the framework of loosely packed grains. With greater depth of burial, the number of points of contacts and their load increases, and friction was assumed to become a more important mechanism of attenuation. The authors showed porosities as high as 60 to 70% in the ooze, from 60 to 75% in the transition, and thereafter reducing in the chalk from 60 to 45%. Presumably the effects of layering/bedding and perhaps jointing through the thin chalk beds (?), and related fluid flows, contributed to the higher attenuation at the base of the transition, where Qp was as low as 20. An increase in Qp was seen where harder chert occurred at greater depth.

Seismic quality Q and attenuation at many scales

207

Figure 10.34 Laboratory tests, shown by stars, and sonic borehole logs of Vp and Qp showing the marked effect of frequency on Qp. Sams et al., 1997. The sonic logging gave the lowest estimates of seismic Q of all the methods investigated.

10.5.3

Influence of frequency variations on attenuation in jointed and bedded rock

When a dynamic load is applied to a rock at low frequencies, the fluid in compliant large aspect ratio cracks will tend to be squeezed into the pores and cracks that are less compliant. As we have seen, the geophysics profession has termed this mechanism ‘squirt flow’ (e.g. Mavko and Nur, 1975; Palmer and Traviolia, 1980; Jones, 1986; Dvorkin et al., 1995). At higher frequencies inertial effects cause the fluid in the compliant cracks to be less mobile, and there is lower attenuation, making seismic Q higher. Laboratory tests which offer the flexibility of using different saturating fluids having different viscosities, in fact show that there is a peak attenuation when the product of frequency and viscosity is between 1 and 10 (units of Hz.Pa.s) (e.g. O’Connel and Budiansky, 1977). It appears that cracks or joints with aspect ratios of about 103 to 104 cause most of the attenuation (Jones, 1986). The assumption of frequency-independent intrinsic Q and frequency-dependent scattering Q implies that when the total Q for S-waves (Qs) is smaller than for P-waves (Qp), the intrinsic Q is dominant; when it is larger (Qs  Qp), scattering Q is dominant over intrinsic Q (Kang and McMechan, 1994). In fact, scattering

and intrinsic Q contributions are separable by assuming that they have different frequency dependencies, as we shall see in particular from Chapter 13. A local (micro) fluid flow mechanism is found to be the only mechanism that can account for widely observed variations of compressional and shear wave attenuation with frequency, both in partially saturated and fully saturated rocks. However, evidence for frequency-dependent attenuation from field experiments is apparently less conclusive: a few cases were reviewed by Sams et al., 1997. Sams et al., 1997, made a very important contribution in this area of frequency effects, by investigating a sequence of saturated sedimentary rocks (a finely layered sequence of limestones, sandstones, siltstones and mudstones) using four boreholes drilled to 250–280 m depth at the Imperial College test site in NE England. They acquired many data sets at widely different frequencies: ● ● ● ●

VSP experiments (30–280 Hz) Cross-hole experiments (200–2300 Hz) Sonic logging (8–24 kHz) Laboratory measurements (0.3–0.9 MHz)

P-wave velocities for core samples at equivalent depths, and ultrasonic Qp estimates measured on core samples (each shown by stars) are compared with the sonic log results in Figure 10.34. The good correspondence in the

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Table 10.4 Frequency dependence of Vp and Qp (Sams et al., 1997). Type

Freq. range

Median Vp

1000/Qp

i.e. Qp

Core Sonic VSP Cross-hole

500–900 kHz 8–24 kHz 30–280 Hz 200–2300 Hz

3.95 3.48 3.20 –

37.0 96.5 32.0 63.6

27.0 10.4 31.3 15.7

case of Vp, and the poor correspondence in the case of Qp at these two different frequencies, is readily seen. The dependence of median Vp and median Qp measurements on frequency is shown in Table 10.4. These contrasting results for the frequency dependence of Vp and attenuation (expressed as 1000/Q), are plotted in Figure 10.35 with curve fitting based on the authors’ modelling, assuming squirt flow, following Jones, 1986. This modelling suggests that different sizes of ‘soft pore space’, i.e. bedding and intra-bedding joints are sensed by the different frequencies, as a single aspect ratio fits lower frequency VSP and cross-hole data, but not necessarily the sonic data. Sams et al., 1997 estimates of the amount of stiff porosity (i.e. conventional matrix pores) apparently confirmed the results of Mavko and Jizba, 1991, and showed that the soft porosity responsible for squirt-flow attenuation occupied only a fraction of the total pore space. Sams et al., 1997, found that the dominant aspect ratios causing most attenuation were 8.1 to 8.8  104, even though a much wider distribution of crack (and joint) geometries is obviously present in this and other rock masses. We can estimate as an example that if the mean intra-bed joint apertures were 0.05 mm, the implied lengths of these would be only about 6 cm. Perhaps bed-limited jointing, specifically that under least effective normal stress, could be responsible for most of the attenuation, in view of these relatively ‘large’ aspect ratios. Sams et al., concluded that the marked frequency dependence demonstrated by their measurements ‘points to the amount of information about the rocks that we should be able to obtain from broad-band seismology once we have fully understood the processes that are operating’. It is unfortunate that readily obtainable rock quality descriptions such as RQD and the Q-value are not presented together with these important geophysics results. If the physical components of these rock masses were logged in the conventional manner of engineering geologists, possibly it would be easier to understand the potential roles of scattering and intrinsic attenuation in these results.

Figure 10.35 The dependence of P-wave attenuation, Vp and Vs on the frequency of measurement in a finely layered sequence of limestones, sandstones, siltstones and mudstones. Sams et al., 1997. The curves relate to the author’s modelling of squirt flow losses, using the model of Jones, 1986. A range of aspect ratios was used to represent the ‘soft pores’, or assumed cracks, intra-bed jointing, and bedding planes.

Concerning the four sets of Sams et al., 1997, field data, presenting 1/Q versus frequency for VSP, cross-well, sonic and ultrasonic (shown in Figure 10.35), Vogelaar and Smeulders, 2005 recently showed that the levels of attenuation measured in these field experiments in the relatively shallow experimental borehole site, exceeded

Seismic quality Q and attenuation at many scales

by far, the theoretical prediction of Biot, 1956a,b, comparing just the viscosity-based damping of the Biot theory. This comparison is shown in Figure 10.36. In efforts to improve the fit of theoretical approaches to the four sets of attenuation-frequency data presented by Sams et al., 1997, Vogelaar and Smeulders, 2005 modelled a periodically layered porous medium, where the repeating layers 1 and 2 had pore fluids with different properties. They applied Biot’s poroelasticity equations, together with elements of White et al., 1975, who separated strain due to the fast compressional wave and strain due to the slow compressional wave, the former obeying the wave equation, and the latter the diffusion equation. They showed that the resulting numerical model solution based on White’s local flow model, demonstrated an attenuation rising to 0.05 (Q  20), more than an order of magnitude higher than the Biot theory, at a frequency of between 20 and 100 Hz. They stated that an extension of the White model to higher frequency, made it capable of predicting the levels of attenuation seen in the field data. The three factors they investigated showed firstly a maximum attenuation at a specific frequency, secondly the maximum attenuation occurred at some specific percentage of gas, and thirdly that increasing the gas fraction caused the attenuation peak to shift towards higher frequencies.

10.6

Attenuation in the crust as interpreted from earthquake coda

Since the 1960s, the seismic quality of the crust as interpreted from attenuation of earthquake waves has been the focus of much attention. This research was guided by attempts to find reliable ways of interpreting the precursors of earthquakes. The source, in place of surface-explosives or borehole piezoelectric devices, was the earthquakes themselves, and their after-shocks. We will trace some of the earlier measurements, and progress from surface recordings to some of today’s down-hole recording of earthquake sources.

10.6.1

Coda QC from earthquake sources and its relation to rock quality QC

Coda waves are the tail of a seismogram (after the arrival of major wave types such as P, S and surface waves)

209

Figure 10.36 Comparison of Sams et al., 1997 field data of attenuation versus frequency, with modelled data from the viscosity-based damping of the Biot theory. Vogelaar and Smeulders, 2005.

recorded at a certain distance from an earthquake epicentre. (Aki and Chouet, 1975). Seismic coda waves of local earthquakes appear to be produced by backscattering of waves from numerous randomly distributed heterogeneities. The longer the waves travel, the greater the variety of heterogeneities they encounter. The later portions of a seismogram may therefore be the result of some kind of averaging of many samples of the heterogeneities of the intervening crust (Aki, 1969). The spectral contents of the early part of a local earthquake seismogram depend strongly on the travel distance and on the nature of the wave path to the recording station. The coda excitation also depends on the local geology of the station site, and can be 5 to 8 times larger on sediment than on granite (Aki, 1969). Most coda measurements are made in the 20 to 200 seconds time window. As we shall see later, there are obvious advantages of in-borehole seismometer location, at kilometre depths, to help minimize ‘site effects’. The attenuation related to the rate of decay of the coda is termed Qc1 in the geophysics literature, so seismic Qc has by chance, an identical symbol to rock quality Qc (Barton, 1995), that is used to describe rock mass quality Q (from Barton et al., 1974). This original, widely used term for rock mass quality, was at this time also normalized by uniaxial compressive strengths greater or lesser than 100 MPa, to the form Qc  Q  c/100. This was done to improve fit to velocity and modulus of deformation data. As we have noticed, there appear to be some

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numeric similarities between seismic Qp at shallow depth (i.e. 1 km), and the estimated deformation modulus (Emass, or symbol M), when expressed in GPa. It may be of interest to observe that the inverse of rock mass quality (Qc1) is roughly proportional to the rock mass permeability or Lugeon value for central ranges of rock quality, when without the complication of clay-sealing of joints that is common near the surface. (The Lugeon value L
1/Qc, where 1 Lugeon
107 m/s, Barton, 1999, 2002). By implication, less attenuation (high coda Qc) would correspond not only to high rock qualities Qc, but also to lower permeability, and higher deformation modulus.

10.6.2

Frequency dependence of coda QC due to depth effects

The coda Qc was found to increase with frequency, though according to Aki and Chouet, 1975, this did not necessarily mean that the coda Qc of crustal material was frequency dependent. The above frequency effect was thought to be due to the dependence of coda Qc on depth, since waves were scattered from different parts of the earth’s crust. As the primary waves from an earthquake spread out, they leave behind a pool of scattered energy which quickly becomes homogeneous inside the pool because of high diffusivity. Since a large volume surrounding the earthquake source is ‘sampled’, the seismic coda Qc has been considered as a potential measure of the assumed changing rock properties, due to accumulation of stress and strain in the hypocentral zone (e.g. Chen and Long, 2000). Temporal variations of coda Qc before or following earthquakes have been reported in some cases, while unfortunately in other cases, no changes have been noted. Several of these case records will be reviewed in this section of Chapter 10. The apparent frequency dependence of coda Qc waves can be explained if the coda waves at 1 Hz are primarily composed of surface waves scattered from shallow heterogeneities, while coda waves at 20 Hz are primarily back scattering body waves from deeper heterogeneities in the high Qseis lithosphere. At the two sites investigated by Aki and Chouet (western California and Japan), the coda Qc ranged from 50 to 200 at 1 Hz in the shallowest crust (resembling possible deformation moduli in GPa), to about 1000 to 2000 at 20 Hz in the deeper crust. The latter, by chance, resembles the rock mass Qc value itself, assuming that jointing is effectively closed

or almost absent. On the other hand there is no possibility of ever acquiring a reliable measure of deformation modulus at extreme depth, without compressing ultra-small, unjointed laboratory samples, as done by tectonophysicists in the past. Perhaps, unknown to the writer, the E moduli at 20 km depth or 300 (to 500) MPa effective (to total) confining stress, could reach much higher values than the most typical 50 to 75 GPa seen at an order of magnitude smaller depths, for the case of hard crystalline rocks. As we shall see in Chapter 16, the differential stress (1  3) tolerated by small rock samples can be increased by a factor of 5 to 10, by similar magnitudes of confining stress to the above. (See Figures 16.57a and b). Aki’s and Chouet’s observations were interpreted as showing the combined effect of variation of coda Qc with depth and the frequency-dependent composition of coda waves. The average coda Qc over the depth range 0 to 12 km was 300 in the case of the Stone Canyon site, some 15 km to the north of the San Andreas Fault, where average magnitude 1 earthquakes were analysed by these authors. Figure 10.37 shows the regional variations of the coda attenuation Qc1 in the range of frequencies from 1 to 20 Hz derived from the California Stone Canyon earthquake events, and from the Japanese Tsukuba Oishiyama earthquake events. Attenuation Qc1 reduces and coda Qc increases with increasing frequency. At Tsukuba, where earthquakes are deeper, attenuation Qc1 was lower and coda Qc therefore higher, especially at the highest frequency of 24 Hz. (Qc1
0.001, Qc
1000). Carpenter and Sanford, 1985, used spectra from 130 digitally recorded micro-earthquakes (M  0.9 to 0.3) to compute the apparent seismic Q for upper crustal rocks near Socorro, in the Rio Grande Rift, New Mexico. Most of the seismic wave attenuation due to intrinsic absorption and scattering was computed over the frequency range of 3 to 30 Hz. Their apparent seismic Q values were found to increase with event distance, for the eight recording stations used in the study. This increase was modelled with a varying thickness, low seismic Q, low-velocity layer, lying above a relatively high seismic Q, high-velocity half space. As illustrated in Figure 10.38, the waves from the more distant earthquakes would have a greater fraction of their total ray path in the deeper rocks, therefore indicating that seismic Q was greater at depth. The seismic Qp and Qs values were found to be less than 50 directly beneath the sites at 0.3 to 2 km. This again

Seismic quality Q and attenuation at many scales

Figure 10.37 Regional variations of Qc1 for the frequency range 1 to 20 Hz, derived from analysis of earthquake coda waves. Aki and Chouet, 1975. (A potential seismic Qc scale on the right side of the figure would range from a minimum of 67 at about 1 Hz, through 100, 200 and 1000 at 25 Hz).

Figure 10.38 The two-layer model used to interpret event-distance effects on seismic Q. Carpenter and Sandford, 1985.

211

resembles rock mass deformation moduli magnitudes, expressed in GPa. A stronger seismic Q gradient near the surface was accounted for by lumping all of the low seismic Q material into this one layer. Significantly, the near-surface Swave Qs values for stations resting on apparently competent Pre-Cambrian and Paleozoic rock were quite low (25) and generally less than for stations resting on Tertiary tuffs. The authors interpreted this as being due to a greater incidence of open and water-filled fractures in the otherwise more competent rock. Such would also be consistent with lower rock quality Q-values, due in particular to higher, near-surface values of SRF, causing lower Q-values and lower rock mass deformation moduli. (See Appendix A for Q-parameter ratings for describing different rock mass conditions). Qp/Qs ratios ranged from 0.34 to 1.39, and a decrease of this ratio was generally measured with increasing distance. Carpenter and Sanford took this to imply varying degrees of saturation in the upper crustal rocks. Near the surface, fully saturated rocks have Qp  Qs, while at depth, partially saturated or dry rocks may have Qs  Qp. (Winkler and Nur, 1982). In a gas-producing region of Uzbekistan in 1.4 km thick Tertiary sediments, Clouser and Langston, 1991, determined values of Qp (10 to 70) and Qs (10 to 25) based on a spectral ratio method of analysing aftershocks from the 1984 Gazil earthquake. There was conjecture that these 10 to 20 km deep thrust-faulting events could have been induced by gas extraction. Clouser and Langston, 1991, investigated various QpQs relations, comparing some theoretical straight line relations with some in situ measurements. Figure 10.39 shows the stratigraphic section through this 1.4 km of sediments, and increasing P and S wave velocities down to the basement. The Qp and Qs relations are shown in Figure 10.40, together with black dots representing other authors’ data for comparable sedimentary rock and rock sequences. The various initials against the Qp-Qs curves are from their six monitoring stations SP-1, GSN, OFT, GAZ, TSV and K31. Intuition would now suggest that these lower Qp and Qs magnitudes, varying as they do from about 5 to 70, may represent the lower frequency, nearer-surface sampling of the jointed crust. Clouser and Langston, 1991, evaluated the following two equations: 4 Qs  3

 V 2  s Q p V   p 

(10.8)

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Rock quality, seismic velocity, attenuation and anisotropy

10.6.3

Figure 10.39 Stratigraphic section through the 1.4 km Tertiary basin investigated by Clouser and Langston, 1991.

Figure 10.40 Qp-Qs relations determined for each station, from spectral ratio slopes and travel times. Black circles are laboratory and in situ data from other authors. Clouser and Langston, 1991.

Qs 

Vp Vs

 Qp

(10.9)

Using their average Vs/Vp and Vp/Vs ratios of 0.534 and 1.87 respectively, the above equations gave the lower and upper limit curves shown in Figure 10.40, namely Qs  0.38 Qp and Qs  1.87 Qp. Their measurements using spectral ratios, and accounting for differences in basin thickness between each station, showed Qs varying from 10 to 70.

Temporal changes of coda QC prior to earthquakes

Initially encouraging indications of a temporal change in coda Qc before two large Chinese earthquakes were reported by Jin and Aki, 1986. This was based on measurements of coda decay rate for small local earthquakes in the general area that is ‘preparing’ for a major earthquake. The authors referred to the significant difference of duration of coda Qc from local earthquakes, which may last several minutes in a stable area like Norway, but which die out quickly in seismically active places like California. (Presumably, significant differences in attenuation, seismic Q and the rock quality Q-value would also be registered in such contrasting regions). During the three-year period preceding the Tangsham earthquake in China (M  7.8, 1976), the coda Qc was about 3 times lower than it was before or after this period, i.e. attenuation was greater in the three years before the event. Apparently a comparable change occurred at the time of the Haicheng earthquake, also in China. The authors emphasised that first appearances suggested a change of focal depth. Tsujiura, 1978, reportedly found that coda Qc for Japanese earthquakes were higher when focal depths were at 100–160 km, than when at 40–80 km. Roecker et al., 1982, found coda Qc to be four times higher when sampling 400 km depth than when sampling less than 100 km depth. The authors concluded that a coda Qc change by a factor of 2 to 3 would imply a change in focal depth of about 100 km. They also discussed the possibility of changes in predominant frequency affecting the coda Qc: Qc  Qof m

(10.10)

where 0  m  1. For the coda Qc to change by a factor of 2 to 3 the frequency must change significantly also. However, their analyses showed mean variations of frequency of only 20%. They therefore concluded that the observed coda Qc change was due to a ‘change in the property of the earth medium’, namely the opening of cracks or dilation. For the case of the referenced Tangsham earthquake, the actual low coda Qc value was 71 (in the period 1973 to 1976) and 200 (in the period 1969 to 1972). The P-wave velocity was reportedly also anomalously low in the period 1973–1975 just preceding the earthquake. However, Jin and Aki, 1986, preferred using coda Qc, since it covered an entire ellipsoidal region determined by the lapse time, whereas monitoring of the Vp/Vs anomaly requires that locations

Seismic quality Q and attenuation at many scales

of source and receiver make the wave path go directly through the anomalous source region. Peng et al., 1987, used several thousand seismograms of small earthquakes in the Mammouth Lakes area in the USA to measure values of Qc from the decay of the earthquake coda. They added a certain degree of sophistication to the interpretation, by observing two opposite trends at different distances from the source: a) in the region near the main epicentre, measurements of coda attenuation (Qc1) were higher for earthquakes that occurred after the main shock, than coda attenuation Qc1 of those that occurred prior to the main shock (i.e. Qc was lower after the main shock, due to greater attenuation). b) further away from the main epicentre, measurements of coda attenuation Qc1 were lower after the main shock than before it (i.e. Qc was higher after the main shock, due to reduced attenuation. Could this perhaps be due to the reduced shear stress at distance, and more ‘damage’ closer to the source? Such would also give lower rock qualities: quite logically closer to the source following the main shock. Peng et al., 1987, reviewed numerous cases of temporal changes of coda attenuation (Qc1) before and after large earthquakes. For brevity we will make a list without individual references, and refer the reader to the above authors. To aid interpretation with respect to coda quality Qc as opposed to attenuation Qc1, we will list changes to coda Qc in the list that follows. The changes are therefore inverted compared to the Peng et al., 1987 list: 1. 30% reduction in coda Qc before Hawaii earthquake, 1975 (M  7.2) 2. 20% reduction in coda Qc before 3 large KurilKamchatka earthquakes, (M  8.0) 3. 30% reduction in coda Qc (at 6 Hz) before Petatlan earthquake (M  7.6) 4. anomalous, low coda Qc before E. Vamanashi earthquake, 1983 (M  6.0) 5. 300% reduction in coda Qc for 3 years before Tangsham earthquake, 1976 (M  7.8) 6. 200% reduction in coda Qc for period before Haicheng earthquake, 1975 (M  7.3) Following this list an increase in coda Qc is mentioned for a 2 to 3 year period before the Misasa earthquake in Japan, 1983 (M  6.2), and the authors also record the possibility that coda Qc changes without an obvious relation to a major earthquake.

10.6.4

213

Possible separation of attenuation into scattering and intrinsic mechanisms

Based on their own Mammouth Lakes data and on other case records, Peng et al., 1987 proposed that coda Qc reduced within the aftershock zone but increased outside this zone, when the main shock occurred. The observed temporal changes to coda Qc suggested that heterogeneities were responsible for the scattering component. Presumably such features as lithological boundaries, clay-filled discontinuities and branch faults, could cause scattering while the intrinsic component of attenuation might be microcrack and joint related (i.e. thin cracks that were bearing high fluid pressures, that were therefore sensitive to small stress changes. Peng et al., 1987 emphasised that separation of the intrinsic and scattering components of coda Qc introduced a severe nonuniqueness in determining these parameters. However, they suggest that probably a small number of strong scatterers dominated the coda in a seismically active zone. Concerns about the relative magnitudes of intrinsic attenuation (Q1 intrinsic) and scattering (Q1 scattering) has led to methods for separating these effects by integrating the S-wave energy for successive time windows, as a function of earthquake hypocentral distance. The method is described by Hoshiba et al., 1991. Figure 10.23 shows how it was applied to Central California, Long Valley and Hawaiian earthquakes, giving a separation of Qs1 scattering and Qs1 intrinsic, whose sum is equal to Qs1 total. Interestingly, when adding two larger Qs intrinsic and Qs scattering components, the sum Qs total is less than either of the above, since attenuation is being accumulated, not Qseis. In general, for frequencies 6.0 Hz, scattering Qs1 was greater than intrinsic Qs1, whereas above 6.0 Hz the opposite applied. In all three regions, scattering Qs1 was strongly frequency dependent, decreasing proportionally to frequency increase, or even faster. Intrinsic Qs1 was considerably less frequency dependent. A concurrent suggestion of a depth-dependent intrinsic Qs1, which increases with depth, apparently can reduce the discrepancy between theoretical predictions and observations (Zeng et al., 1991). Sato and Fehler, 1998, (Seismic wave propagation and scattering in the Heterogeneous Earth, Springer Verlag & AIP Press), who collected regional seismic data from around the world, also showed the separation of the scattering and intrinsic attenuation. Clearly, and in almost all cases, the lower frequencies give the greatest attenuation

214

Rock quality, seismic velocity, attenuation and anisotropy

Figure 10.42 Regional seismic data assembled by Sato and Fehler, 1998, showing the relative magnitudes of the intrinsic and scattering attenuation and its frequency dependence, even between 1 and 10 Hz. KTJ  KantoTokai, Japan; KJ  Kanto, Japan; LV  Long Valley, California; H  Hawaii; SC  Southern California; SP  Southern Spain; and CC  Central California.

Figure 10.41 Plots showing total Qs1, together with scattering Qs1 and intrinsic Qs1, for earthquakes that occurred between 1987 and 1990. Focal depths are between 5 and 20 km and magnitudes are between 1.5 and 3.6. Mayeda et al., 1992.

both from scattering and from intrinsic mechanisms. This seems to suggest the extreme importance of the structural geology (joint sets, faulting), and of the conducting properties of these larger scale, nearer the surface features. Figure 10.42 shows the relative magnitudes of

these total, scattering and intrinsic attenuations. (The socalled ‘Albedo’ (Bo) is defined as the ratio Qsc1/Qtotal1). Mayeda et al., 1991, had suggested that the more complex regions of Hawaii and Long Valley required models which incorporated heterogeneously distributed, non-isotropic scatterers in a layered medium with depth-dependent intrinsic Qs1. They suggested that their results for scattering Qs1 indicated a length scale of heterogeneity at least comparable to the wavelength for the lowest frequencies studied, of the order of a few kilometres, presumably implying fault-size features, or perhaps lithological contacts.

10.6.5

Changed coda Q during seismic events

As we have seen, and perhaps confusingly for earthquake precursor analysis, some investigators have recorded

Seismic quality Q and attenuation at many scales

decreases in the seismic coda Qc value prior to major earthquakes, while others have recorded decreases following the occurrence of a major earthquake. Beroza et al., 1995, using nearly identical (doublet) earthquakes in a pre-seismic, co-seismic and post-seismic search for temporal changes in coda Qc, found a nearly stable attenuation throughout the Loma Prieta, California sequence. The main shock in October 1989 (M  6.9) nevertheless reportedly resulted in an almost total stress drop, and effects on coda Q had clearly been expected. In earlier studies, increases in coda Qc by as much as 50% had been cited as precursors to large earthquakes. Unfortunately, changes in coda Qc by as much as 50% had also been reported even in the absence of a large seismic event. To address possible effects of source size, geometric spreading and earthquake mechanisms and location, most researchers estimate coda Qc from late coda, the part of the seismic wave arriving after twice the S-wave arrival time. The relatively long paths taken by waves in the late coda are assumed to sample a large volume of the crust with a variety of takeoff angles from the source. Using earthquake doublets, Beroza et al., 1995, employed a technique for measuring coda Qc that was assumed to be insensitive to geometric spreading, location and source mechanism, because these factors are common to the two (doublet) events. Furthermore, both the early and late coda can be used; but the former is usually sensitive to the focal mechanism. The stability of coda Qc throughout the Loma Prieta sequence was in sharp contrast to other studies (e.g. Peng et al., 1987), who reported larger pre-cursory changes in coda Qc for many (but not all) of the earthquakes that were analysed, as we saw earlier. Previously it had been assumed that the coda samples a large volume. However, Chen and Long (2000) showed that temporal variations in the seismic coda Qc could in fact be explained by hypocentre migration over small distances compared to the radius assumed to be sampled by the coda. These authors used data from an earthquake swarm in Georgia, USA (Norris Lake Community). They first noted the apparent temporal variation in coda Qc during a five month period. Figure 10.43 shows that reductions occurred in the three orthogonal directions (vertical, NS, EW) during the period of maximum seismic activity. Over 4000 shallow (1.2 km) earthquakes were recorded altogether. However for this analysis, 108 earthquakes of similar size were chosen that were uniformly distributed during the period of the swarm activity. About 2 weeks before the peak of seismic activity, the coda Qc began to reduce.

215

Figure 10.43 Temporal variation of coda Qc for a swarm of earthquakes with peak activity in August and September. Chen and Long, 2000.

Chen and Long, 2000, found that their coda Qc values were related to the locations of the earthquakes. Early events were mainly located in high coda Qc areas, while later earthquakes occurred preferentially in low coda Qc regions, in other words there was a shifting of hypocentres. (Rock quality or attenuation levels could presumably change also in a given location, due to fracturing events, but hypocenter migration was considered the main effect). The coda attenuation Qc1 increased from about 0.005 (Qc  200) to 0.010 (Qc  100) from the early period to after the peak activity, due to this assumed shift of hypocentres. A short distance (1 km) migration of hypocentres generated this halving of magnitude of Qc, possibly related to migration from ‘geologically uniform’ gneiss to an area with ‘mafic dikes and more complicated topographic relief ’. These dikes were interpreted as strong, and inhomogeneously distributed scatterers. The authors concluded that the normal assumption that coda scatterers (i.e. large discontinuities) are uniformly distributed may be one reason for earlier misinterpretations of temporal variations in coda Qc. An assumed homogeneity of velocity structure would be another. The strong spatial variation of coda Qc (and by implication of the rock quality Qc-value also) does not eliminate the possibility that intrinsic attenuation and scattering may also be affected by more subtle changes in rock mass properties and the effects of stress change. However, in rock engineering, we would certainly expect that spatial variations of rock mass quality Qc would tend to be greater than those caused by stress change, especially in view of the moderate stress drops

216

Rock quality, seismic velocity, attenuation and anisotropy

that occur as a result of earthquakes (i.e. often just fractions of, or a few MPa). Following rock quality Qc values a little further, one can see from Figure 5.36 (Part I, Chapter 5), that higher rock quality Qc values imply higher P-wave velocities and higher deformation moduli. Such areas would likely be under highest stress, and have least permeability, so a spatial migration of hypocentres to lower seismic coda Qc areas, with lower rock mass quality Qc and lower moduli and higher permeabilities, is entirely logical. Perhaps the ‘complicating’ factor of frequency dependence of seismic Q reviewed earlier, is another way of recognising a scale effect. Certainly the evaluation of rock mass quality Qc could also be considered scaledependent, since the inclusion of larger volumes of the rock mass (including faults) will inevitably adversely affect all the six Q parameters, resulting in lower overall rock mass quality and the strong likelihood of greater attenuation. Hellweg et al., 1995, also used the Parkfield Dense Seismograph Array (of the US Geological Survey) to estimate coda Qc from up to 42 recordings for each earthquake that occurred. Coda Qc was determined in two frequency bands (4 to 8 Hz, and 8 to 16 Hz), from a tight cluster of 26 seismic events between December 1989 and

January 1994. Despite magnitude (M 4.7 and M 4.6) events in 1992 and 1993, they found that Qc had not systematically changed. Figure 10.44 however, shows various interesting trends of the data, including a certain anisotropy regarding azimuth (graph c), and a clear distance dependence (graph d) which may be related, as observed earlier, with deeper sampling of the earth’s crust as distance increases, and therefore higher coda Qc values. Concerning the coda Qc magnitude and time period, Hellweg et al., 1995, suggest that there had been no systematic change in the coda Qc. One may however observe that if allowed to plot a least-squares (or other) best fit to the time/date data in graph (e), a certain reduction of Qc with time would be observed. However this would apparently be invalid as the events cannot actually be compared with each other directly, as they are determined from different length windows regarding each seismogram. The authors proposed that Qc should always be measured from the same length window starting at the same lapse time regardless of the source location. As a contrast to the coda Qc obtained from seismically active areas, Kvamme and Havskov, 1989, determined the coda Qc in Southern Norway, finding values at 10 Hz frequency to vary from 780 to 1530, for source-to-station distances varying from 15 to 300 km.

Figure 10.44 Coda Qc from the 4–8 Hz band: a) coda Qc dependence on depth, b) coda Qc dependence of earthquake magnitude, c) coda Qc dependence on azimuth, d) coda Qc dependence on epicentral distance (km assumed), and e) coda Qc as a function of time. Dotted lines show the average of all coda Qc values, f ) coda Qc calculated for selected events with epicentres less than 30 km. Filled diamonds are measured from a 30 s window which starts at 2ts. Hollow diamonds are measured from a 30 s window which starts at a lapse time of 20 s. Hellweg et al., 1995.

Seismic quality Q and attenuation at many scales

A certain increase in coda Qc with window length was interpreted as increased Qc with depth, as in other studies reviewed here. They considered the Norwegian measurements of coda Qc to be similar to values found in another shield area (Canada), but observed stronger frequency dependence as possible evidence of stronger scatterers in Southern Norway. Some of the paths shown in Figure 10.45, certainly cross some major regional zones of weakness (i.e. the Oslo fjord), and regional faulting. They used window lengths of 5, 20, 30 and 40 s and observed variations of coda Qc with frequency: Qc  Qof m

(10.11)

and found (m) to be 1.15 for most of the Norwegian data. Comparison of their own and other frequency dependent coda Qc are reproduced in Figure 10.46. Hiramatsu et al., 2000, reported temporal changes in coda Qc1 in the Tamba region of Japan, to the northeast of the main rupture zone of the 1995 M 7.2 Hyogoken Nanbu earthquake. This region has the densest distribution of Quarternary active faults in Japan, with very high seismic activity for several decades.

Figure 10.45 Location of Southern Norway profiles for Kvamme and Havskov, 1989, spectral ratio analyses. The dotted line direction gave seismic Qp  575 from measurements by Kanestrøm and Haugland, 1971.

217

The authors used local earthquakes recorded from 1987 through 1996, and concentrated their analyses on highquality data from the depth range 45 to 15 km. Values of coda Qc1 were averaged over three recording stations for each earthquake. They divided the data into two periods: 8 years before and 2 years after the major (M  7.2) 1995 earthquake. The average value of coda Qc1 increased after the major earthquake, especially for the lower frequency bands between 1.5 and 4 Hz, as illustrated in Figure 10.47, and in Table 10.5. The authors emphasised that no change in focal mechanism was reported, citing the fact that changes in epicentres, focal depths, or focal mechanism can cause false temporal changes in coda Qc1. Even in a small 1  1  1 km volume, the value of Qc1 increased after the main shock at frequencies below 5 Hz, suggesting that changed epicentres were not the cause of the increased attenuation (and reduced seismic quality). The average depth remained in the 9 to 10 km range. The authors considered that a numerically estimated change of shear stress at 10 km depth of only 0.02 MPa due to the Hyogo-ken Nanbu earthquake, was the cause of the increased attenuation. The sensitivity of Qc1 to shear stress change was estimated to be
10 (MPa)1 at around 3 and 4 Hz frequency, which the

Figure 10.46 Coda Qc as a function of frequency for different regions. A–Aleutian Islands, m  1.05, B–Carolina, USA, m  0.94, C–New England, m  0.40, D–Southern Norway, m  1.15, E–Canadian shield, m  0.20, F–former Montenegro region, Yugoslavia, m  1.00. (See Kvamme and Havskov, 1989 for references).

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 10.47 Distinct increases in attenuation (coda Qc1) following the January 1995 Hyogo-ken Nanbu (M  7.2) earthquake. Hiramatsu et al., 2000. Table 10.5 Increase of average Qc1 and decrease of average Qc following the 1995 Hyogo-ken Nanbu earthquake. (Hiramatsu et al., 2000). Frequency (Hz) Qc1 before

Qc1 after

Qc before

Qc after

1.5 2.0 3.0 4.0

0.015 0.013 0.0093 0.0062

81.3 91.2 131.8 186.2

67.6 77.6 107.2 162.2

0.012 0.011 0.0076 0.0054

authors suggested was much larger than the stress sensitivity of seismic velocity. However they also referred to the fault or fracture dimensions of micro-earthquakes (M  3) as about 400 m, consistent with the characteristic length of scatterers of 300–600 m estimated from the wavelengths of 3 to 4 Hz which had the greatest influence on Qc1 increases. They found in addition, that the frequency dependence of coda Q1 varied with time. Using the proportional to power of frequency expression: 1 1 n Q c  Qo f

(10.12)

where Qo1 is the Qc1 value at 1 Hz and n is a constant, they used the least squares method to determine values of

(n) for the activity periods I to V (shown in Figure 10.48). All ten frequency bands (from 1.5 to 24 Hz) were analysed. As clearly shown in this figure, there was a clear reduction in the n-value in the years leading up to the event, followed by a marked increase in the n-value, especially after the major event. As suggested by Kvamme and Havskov, 1989, (and others), a greater density of scatterers could be the logical cause of this greater sensitivity to frequency, following the major earthquake.

10.6.6

Attenuation of damage due to acceleration

Mandal et al., 2001 interpreted 110 aftershocks following the Mw 6.4 Chamoli earthquake in the Garhwal Himalaya as propagating up-dip along a thrust plane from 20 to 2 km depth, the main shock having occurred at 15 km depth. The region had five earthquakes exceeding magnitude 6, and twelve exceeding magnitude 5 in just the 20th century, which was presumed to have caused a high level of shallow crustal heterogeneity. They analysed 48 of the local earthquakes with magnitudes varying from 2.5 to 4.8, with recordings at nine digital stations, with three-component seismometers, covering an area with a 150 km radius. Sub-surface recording is not mentioned.

Seismic quality Q and attenuation at many scales

219

a zone V (potential M8 earthquake zone), despite the intraplate location of this Kutch area, is evidenced by the two 7.7 magnitude quakes of the last 200 years. The authors suggested, as at Garhwal, that these were the reasons for a high level of shallow crustal heterogeneity. The coda Qc interpreted from 200 local earthquakes of magnitudes varying from 3.0 to 4.6, in an area of 140 km radius, suggested Qo  102 f 0.98. On this occasion, based on the attenuation curve estimated for Qo  102, they estimated a ground acceleration at 240 km distance (from an assumed 1 g source) of 0.13 g, almost agreeing with a 0.11 g accelerograph recording at similar distance. To be read in conjunction with this locally attenuating, seismically active crust, is the very variable velocity-depth model for the uppermost 6 km of the region given by Mandal et al.: Figure 10.48 Frequency dependence of Qc1 increases over the same 10-year period. Hiramatsu et al., 2000. The sharp rise after the event in period IV was referred to in their figure.

The estimated Qo value (Qc at a frequency of 1 Hz) at the various stations was on average only 30 at 1 to 3 Hz, indicating a strongly attenuating crust. Higher Qc at higher frequencies were interpreted as propagation of back-scattered body waves through deeper parts of the lithosphere where less heterogeneities were expected. South of the main central thrust belt is a less rigid, slightly metamorphosed sedimentary wedge, while north of the thrust are more rigid highly metamorphosed crystalline rocks. The frequency dependence of the Garhwal Himalaya coda Qc also gave a quite ‘steep’ curve in relation to Figure 10.46 data from other seismically active regions. Qc  30 f 1.2 was typical. The author compared the Garhwal Himalaya Qo of 30, and its frequency component (n) of 1.21, with the Indian Peninsula Qo of 550 and n  0.84. From the above high attenuation, the authors, in 2001, infer that the acceleration (from a hypothesised 7.4 magnitude earthquake at Chamoli, with 1 g at the source), would decay to 50% at 20 km distance, and to 7% at 100 km, suggesting less significant damage beyond 100 km if such should occur. In a later paper, Mandal et al., 2004 report on the low coda Qc interpreted from the devastating, intraplate Mw 7.7 earthquake that occurred in Gujarat in 2001, named the Ghuj earthquake. On this occasion the distribution of aftershocks defined a 45° dipping zone of some 40  60 km in area. The presence of high seismicity, in

0.9 km 2.2 km/s 0.2 km 4.8 km/s (basalt) 2.6 km 3.5 km/s (Jurassic sediments) 0.1 km 4.8 km/s 2.2 km 5.9 km/s 10.6.7

Do microcracks or tectonic structure cause attenuation

When considering the mechanisms of attenuation of the crust from a great earthquake, the decay of wave amplitude with distance can clearly take many forms: conversion of elastic energy into heat, scattering caused by heterogeneities such as changes of rock types, changes of velocities, sub-surface topography, and cracks and faults. The authors Mandal et al., 2004 also cite ‘sliding along grain boundaries’, but in the opinion of the writer this seems insignificant in relation to the, admittedly surface-magnified, ground deformation, with widespread uplift, deep cracks, liquefaction, ejection of water and sand, even at 275 km distance, and collapse of 50 high-rise buildings in a city (Ahmedabad) 240 km distant from the epicentre. There was damage even at 1,600 km distance on the SE coast of India – probably due to the high seismic Q of the intervening crustal plate. It seems intuitively impossible that micro-friction along microcracks, joints and faults, as an attenuation mechanism does not exist in the crust. An earlier opinion from the 1980s, based mostly on the basis of high frequency, sub-micro-strain oscillation tests on intact rods of sandstone, and continuum concepts of strain, deduced that friction was not a source of attenuation in the earth. Some geophysicists hold this viewpoint even today.

220

Rock quality, seismic velocity, attenuation and anisotropy

Due to the higher stiffness of grain boundaries and microcracks – they have ‘high’ aspect ratios – it would also seem that the ubiquitous rock joint, and its probable several sets, could be a likely candidate for microfriction attenuation combined with squirt flow losses. Attenuation caused by friction is certainly easy to envisage in the case of an earthquake induced, 8.5 m rupture at 23 km depth, reducing to about 1 m near the surface, where there was uplift of the southern side of a major fault. Neighbouring rock masses resisting such motion are clearly absorbing frictional energy, suffering microdisplacement discontinuities in the process. If joint and fault compliances that fit attenuation data somehow ‘acquire’ realistic magnitudes and units of Pa1 m (or the more familiar MPa/mm of stiffness) during even minor man-made seismic or sonic exploration, how can friction-caused attenuation, of however small magnitude, actually be avoided in the case of natural seismic events? Such ‘displacement-discontinuity’ events in a jointed rock mass are surely a part of the intrinsic attenuation. That scattering occurs from these features as well, seems hardly justification for excluding compliance effects from intrinsic mechanisms, as implied in some interesting analyses of fault-related attenuation. From another seismically active region, the authors Akinci et al., 2004, present highly attenuated data from the North Anatolian Fault Zone in Turkey, and compare this with a sediment influenced region of Southern Germany. The NAFZ is an intra-continental transform fault boundary between the Eurasian Plate in the north, and the Anatolian block in the south. This major strikeslip fault extends through many segments, for about 1400 km, from a triple plate junction in eastern Turkey to the Aegean in the west. Figure 10.49 and 10.50 show the results of the authors P-wave Qp analyses for the western and eastern portions of the NAFZ, with Qp versus distance data, and Qp versus seismic event magnitude. Since there is little sediment beneath the stations in either region, the low Qp results possibly apply to crystalline basement, a lot of it of Triassic age, although ‘site effects’ from a more attenuating near-surface rock mass beneath the recording stations, should perhaps not be neglected here. Most of the seismic Q results lie between about 4 and 40, suggesting, on the basis of an intuitive Qseis – Qrock quality relation, that fracturing/jointing and faulting must be extensive in this tectonically disturbed region. The range of data for Qp shown in Figure 10.49, fortuitously or for scientific reasons, exactly matches the

(a)

(b)

Figure 10.49 Qp interpreted from seismic events, in terms of a) distance and b) magnitude, in the western and eastern portions of the North Anatolian Fault Zone. The NAFZ stretches 1400 km from eastern Turkey to the Aegean. Lack of sediments at all the receiver stations suggested to the authors that the low Qp applied to crystalline basement rocks of Triassic age. Akinci et al., 2004. Sub-site attenuation also seems a possible source of the lowest values. Significant levels of jointing/fracturing/faulting must be assumed in view of the low values of Qp.

range of expected rock mass deformation moduli for the following conditions: 1. Near-surface (e.g. immediately below station): rock with a compression strength more than 10 MPa and a rock mass Q-value in excess of 1 (heavily jointed), giving rock mass Qc  0.1. Figure 10.54, and 13.60 in Chapter 13 show Emass  5 GPa (as per minimum seismic Qp in Figure 10.49a). 2. At 1 km depth, rock with a compressive strength of 100 to 300 MPa, and a rock mass Q-value of 100 (jointed but massive) to 1000 (almost without joints – or completely closed joints) giving Qc from

Seismic quality Q and attenuation at many scales

221

depth than ever directly measured. Linked Qp-Emass values in a range of 100–400 (also GPa) would appear reasonable, but this is pure speculation of course.

10.6.8

(a)

(b)

Figure 10.50 a) Separation of sediment and basement Qp values by proportioning of the respective velocities and distances, following Hough et al., 1988. b) Effect of correction on the corrected Qp values for the Southern German seismic data. Akinci et al., 2004.

100 to 3000. Figure 10.54, and 13.60 in Chapter 13 show Emass from approx. 50 to 140 GPa (according to empirical equations: specifically 46 to 144 GPa). 3. Note the great body of seismic Qp data between 10 and 40, suggesting domination of near-surface, substation, heavily jointed and sometimes faulted rock mass. Refer to ‘minor fault’ curve in Figure 10.54, at depth from 50 to 1000 m: Qp data is matched by moduli of 10 to 40 GPa. By way of comparison of a seismically active region with one that was less so, the authors also presented their Qp results for a region of southern Germany. As indicated in Figure 10.50, they made a correction for the low Q sedimentary cover of some 2 km thickness, which had a low range of Qp from 6 to 10, thereby revealing the corrected Qp for the 8 to 10 km of basement of between 100 and 500. The fact that the uncorrected 2 km deep data match the above, while the 8 to 10 km of basement exceeds the above Qp – Emass (potential) link, can perhaps be ascribed to the need for an extreme extrapolation of deformation moduli to an order of magnitude greater

Down-the-well seismometers to minimise site effects

Knowledge of attenuation magnitudes in the upper few kilometres of the earth’s crust is clearly an essential ingredient in modern seismic hazard analysis. Earlier studies using only surface seismometers were limited by relatively high noise levels and by the strong attenuation at shallow depth, preventing high frequency signals from being recorded. The installation of borehole seismometers in more recent years has greatly improved knowledge of the nearsurface attenuation of some individual sites. Abercrombie, 1998 pointed out that seismograms recorded at the earth’s surface are contaminated by both seismic and man-made noise. The frequency range of observed signals tends to be limited to below a few tens of Hertz at most surface sites. This makes it difficult to link observations of attenuation in the real earth with the much smaller scale and much higher frequency laboratory studies. The ideal situation for recovering uncontaminated measurements is installation of wide-bandwidth seismograms down deep boreholes, where there is low background noise. The problem of strong attenuation in the near-surface is thereby avoided. As part of the Californian earthquake prediction programme, a region of the San Andreas fault near Parkfield, California was equipped with an array of seismic instrumentation in boreholes averaging about 250 m depth, with a more extensive downhole array both at 1.5 km and almost 3 km in the Cajon Pass deep well, some 1.5 km NE of the fault. Deep instruments reportedly failed soon after installation in the 5150 ft. deep Varian well (Malin et al., 1987). In this area, quite different basement rocks are juxtaposed by the fault, with higher velocities to the SW than to the NE. Deployment of closely spaced seismometers has reportedly shown extensive variation in recorded amplitude, frequency content, and coda duration over short distances, meaning that the ‘site effect’ (the near-surface, nearreceiver rock), can have a strong effect on earthquake recordings. Amplification in the low velocity, low density near surface, scattering, and resonance within shallow layers, plus attenuation of high frequency energy, also play a role in earthquake damage.

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Rock quality, seismic velocity, attenuation and anisotropy

Seismic Q (i.e. Qp unless Qs is specified) is now known to be as low as 10 in the upper 100 m of many sites, in varying rock types. Attenuation at shallow depths in fact appears to exhibit little dependence on rock type. This, to a degree, is also basically true for the rock mass quality Q. According to reviews by Abercrombie, 1998, and Abercrombie (2000), the instrumented deeper boreholes show seismic Q increasing with depth to about 100 between 1 and 2 km, and reaching about 1000 at greater depths. Adams and Abercrombie, 1998, found seismic Q
1000 below 2.5 km depth at Cajon Pass. Studies using both direct and coda waves down-hole-recorded at over 2 km depth, have shown seismic Q to be high (
1000) at seismogenic depths in California. Hough et al., 1998, found seismic Q  1000 at 5 km depth at Anza, in California. A useful comparison of the relative magnitudes of attenuation in the Varion and Cajon Pass wells given by Abercrombie, 1998, is reproduced in Figure 10.51. Despite the difference in rock types, the seismic Q profiles are essentially similar. However at greater depths, the thicker and lower velocity Franciscan rocks to the NE of the San Andreas fault at Parkfield, appear to give lower Qp and Qs than the higher velocity Mesozoic crystalline basement rocks at Cajon Pass. Abercrombie’s analyses of the spectral ratios at different recording depths, having linear slopes on a log-linear plot, suggested that the near-surface seismic Q was almost independent of frequency, in the frequency range of about 2 to 100 Hz. A velocity model crossing the fault at right angles is shown in Table 10.6, based on Abercrombie, 2000. Qp and Qs estimates down the Varion well on the NE side of the fault are given in Table 10.7. Earthquake sources reportedly lie within the steep velocity gradient separating the higher velocity SW side of the fault from the lower velocity NE side. This is consistent with micro-seismic and rock burst observations reported in mining and deep tunnelling projects referred to in Chapter 7. Greatest AE activity occurs where velocity gradients are highest, as in such parts of deep gold mines, according to interpretation of seismic AE arrays. Abercrombie, 1997 calculated that an earthquake recorded at the Cajon Pass wellhead, with a hypocentral distance of 15 km, would suffer 90% attenuation in the upper 3 km, 80% in the upper 1.5 km, and 50% in the upper 300 m, at frequencies of a few Hertz and above. Equivalent calculations using the data in Figure 10.51, for the same earthquake hypocentral distance at the Varian well, suggested that less than 50% of the attenuation

Figure 10.51 A comparison of attenuation-depth profiles for Qp and Qs in the Varian well, Parkfield, and in the Cajon Pass well, S. California. Both sites show very low Qseis near the surface, increasing with depth. As observed elsewhere in this chapter, similarity to depth-modulus trends for jointed rock masses is striking. Abercrombie, 1998. Table 10.6 A velocity and attenuation model for either side of the San Andreas Fault (SAF), with average seismic Q inversion results for the upper 5 km, assuming a Qp value of 1000 below 5 km (Ambercrombie, 2000). Depth

Vp (SW)

SAF

Vp (NE)

0–2 km 2–5 km 5–10 km 10 km

4.7 5.9 6.1 6.5

SAF SAF SAF SAF

4.0 5.15 5.35 6.0

Qp (SW) 0–5 km 5–12 km

199 1000

Qp (NE) 49 –

Qs (SW) –5 km 5–12 km

236 1000

99 1000 Qs (NE)

78 –

84 1000

[SAF  San Andreas Fault: Qp
50, Qs
80 (top 5 km)].

would occur in the upper 1 km: the relatively lower and deeper seismic Q magnitudes at this well constituting a form of ‘site effect’, with most attenuation occurring at greater depth than 1 km.

Seismic quality Q and attenuation at many scales

223

Table 10.7 Qp and Qs estimates at various depth intervals in the Varian (VAR) well from Ambercrombie (2000) and Jongmans and Malin, 1995. Depth interval (m)

Qs

Qp

0–298 298–938 572–938 0–938

7–10 31 53–94 18, 33–45

20 30 55 33

Analysis of seven earthquakes recorded at 2.5 km depth in the Cajon Pass well, reported by Learey and Abercrombie, 1994, found a weak increase in Qs with frequency (
500 at 10 Hz, increasing to
1200 at 100 Hz). They found that intrinsic attenuation was the dominant mechanism, because of the ratio Qscatter  10 Qintrinsic, at all observed frequencies. (Relevant here, perhaps, is a contribution to the question of frequency-dependence by Van Der Baan, 2002. He used wave localization theory to show that ‘constant’ Q might be due to apparent attenuation due to scattering losses, if the earth displayed fractal characteristics over a certain range of scales, thereby creating an absorption band. The author drew attention to the usual constant Q at low frequencies, and some form of positive power law dependence at higher frequencies. Constant Q for example between periods of 1 hour and 10 seconds (0.3  104 to 0.1 Hz), is followed by an increase for f 1 Hz. The author suggested that it may be very difficult to distinguish between intrinsic and scattering attenuation using only frequency-dependent Q measurements. He also claimed that, in most cases, the common assumption that the scattering and intrinsic effects could be separated, by allowing only for frequency-dependent scattering, could be invalid. His numerical modelling indicated that in the case of non-perfect fractals, a constant Q only occurred within a given frequency band, and that Q became proportional to f  for higher frequencies, as in fact observed in most cases.) Adams and Abercrombie, 1998, analysed more than 100 earthquakes recorded at a range of depths in the Cajon Pass borehole. They employed a multiple time lapse method to determine the relative contributions of intrinsic and scattering attenuation concerning Qs and its frequency dependence. They confirmed only a weak frequency dependence (Qs
800 at 10 Hz, increasing to
1500 at 100 Hz, similar to the above). These authors also found intrinsic attenuation to be the dominant mechanism, compared with scattering, at seismogenic depths.

Figure 10.52 A compilation of Qs estimates and their frequency dependence between 1 and 10 Hz. Abercrombie, 1998, from Adams and Abercrombie, 1998, Leary and Abercrombie, 1994, and Kinoshita, 1994.

Abercrombie, 1998 cited several studies from other tectonic areas in the Western USA and from Japan, which showed frequency dependence of Qs between frequencies of 1 to 10 Hz, with a levelling off of frequency dependence above 5 or 10 Hz. The lesser frequency dependence above 5 to 10 Hz (see compilation in Figure 10.52), is suggested as a possible reflection of changes in the nature of the crust at scale lengths of a few hundred metres (an REV effect?), or that it could be due to an artefact of the models, which at the outset, assume body or surface waves that are isotropically attenuated (no lateral or depth variation) – reasonable with at-depth recordings, but not with many surface recordings. The level of current tectonic activity, a thinner warmer crust, the presence of large crustal faults characterized by low velocity zones, were each referred to, as possible reasons for the marked frequency-dependence between 1 and 10 Hz. There has been much made of the strong and continued frequency dependence indicated by earlier recordings of Qp and Qs from seismic coda, but most likely such records were not recorded at various depths below the surface, and therefore had numerous potential ‘site effects’. Abercrombie, 2000, compared recordings of nine local earthquakes at seven different depths down the Varian A1 well (0, 24, 298, 572, 877, 907 and 938 m) and at the other borehole network in the Parkfield area (the high resolution seismic network – HRSN). The layout of these measurement locations in relation to the various branches of the San Andreas fault is shown in Figure 10.53. In the

224

Rock quality, seismic velocity, attenuation and anisotropy

listed from Abercrombie, 1998 discussion of this topic, as follows:

Figure 10.53 Parkfield, California high resolution seismic network (triangles) and Varian array (VAR). Earthquake epicentres used in the Abercrombie, 2000 analysis of depth dependent and spatially variable attenuation, across the San Andreas fault are shown as circles. The station depths follow the station initials.

analyses performed, Abercrombie, 2000, assumed that attenuation was exponential and frequency-independent The San Andreas fault zone was confirmed as being a strongly attenuating zone with Qp averaging 50 over the depth range 0 to 5 km. Seismic Q appears to increase most rapidly at shallow depths, as is also the case for Vp, for the rock quality Q or Qc, and therefore for the rock mass deformation modulus. The attenuation to the deepest instrument (0.9 km) on the lower velocity NE side of the fault was comparable to the attenuation to the instrument at only 200 m depth on the higher velocity SW side of the fault. Abercrombie emphasised the value of multiple-depth monitoring and lateral arrays, in improving the level of characterization. If Qp or Qs were linked to rock quality terms, such as the rock mass deformation modulus, even better understanding might perhaps be achieved of the physical nature of the rock masses close to and within the fault. The range of Qp from the top 300 m to 2 km depth, seen in Figure 10.51 (10 to 180) is a near match to entirely feasible deformation moduli (expressed in GPa), as we saw for the Turkish data. 10.6.9

Rock mass quality parallels

The potential reasons behind the strong attenuation in near-surface rock masses are numerous, and can be

1. Fracture densities at outcrops and in cores suggest perhaps an order of magnitude decrease at 500 m or more depth (this of course is variable). 2. The presence of fractures (or joints) in the upper kilometres, and the moderate pressures, suggest that friction may be a dominant mechanism of intrinsic attenuation. 3. Analysis of seven earthquakes recorded at 2.5 km depth in the Cajon Pass well, had reported Qscatter  10 Qintrinsic, at all observed frequencies. 4. Joints and fractures are also major scatterers of seismic energy, and reduction of scattering losses with depth would be expected due to their reduced frequency and greater closure with higher stress. 5. Mining induced seismic events (Spottiswood, 1993) at 2 to 3 km in South Africa show Qseis of about 1000 through ‘solid rock’ (i.e. probably more massive quartzites), while close to stopes through highly fractured ground (see the velocity EDZ of Chapter 7) could be as low as 20. The above mechanisms of attenuation, and the depth-dependent seismic Q data, continue to support the idea that seismic Q gives a strong reflection of rock mass characteristics, with low values of seismic Q corresponding to the poorer, more jointed, more open structure that is typical of shallower rock, and perhaps present beneath recording stations that are supposedly without ‘site effects’, i.e. those founded at the surface, on crystalline basement rocks. It seems increasingly reasonable to assume that the typical features of rock masses that make them variable media for engineering construction (foundations for large buildings and dams, tunnels and rock caverns), make them also ‘variable media’ and variably attenuating, in terms of seismic Q. Rock mass quality is important, perhaps at all depths where jointing is present or slightly open, because of implicit deformation moduli links to Qp variation with depth in the upper 2–3 km. Up to this ‘mining depth’, empirical rock mass data is still acquirable, or already existing. One may speculate about what the rock mass Qvalue distribution would be at the various depths in the Varian well, if Q-logging had been performed on recovered core, as done regularly in (usually shallower) nuclear waste related projects, such as the 9 km of Qhistogram core logging, sometimes to 1.6 km depth, performed at UK Nirex’s Sellafield site (Barton et al.,

Seismic quality Q and attenuation at many scales

225

Table 10.8 Three progressively worsening rock mass qualities and their predicted (near-surface, hypothetical recording station) properties. Consult tables in Appendix A for explanation of the selected ratings. RQD

Jn

Jr

Ja

Jw

SRF

Q

c (MPa)

Qc

Vp (km/s)

M GPa

K (m/s)

30 60 90

15 12 6

1 1.5 2

4 2 1

1 0.66 0.66

5 2.5 1

0.1 1 20

50 100 150

0.05 1 30

2.2 3.5 5.0

3.7 10 31

2  106 107 3.3  109

Note: Near-surface: Vp
3.5  log Q km/s, M(Emass)
10 Q1/3 GPa, K
1/Qc  107 km/s (Barton, 2002). A significant degree of anisotropy can be provided if desirable or relevant, by using oriented RQDo and values of Jr and Ja perpendicular to the loading or (dynamic) testing direction. The effects of anisotropic stresses or the effects of increased depth, and the effects of matrix porosity on Vp and M can be handled using the equivalent depth and porosity corrections in Figure 10.54.

1992), and the Q-histogram logging performed at four 1000 m deep SKB wells in Sweden at Forsmark and Simpevarp in 2003. One cannot help but wonder whether the low seismic Q, also recorded elsewhere at crystalline sites, such as the hundreds of Qp values lying between 4 and 40, recorded at the NAFZ (Figure 10.49a) from 5 to 30 km distant events, are also a typical reflection of a strongly jointed, tectonically disturbed rock mass, also present beneath the recording sites, and sampled by the lower frequency wave lengths. It is very easy to imagine a potential range of rock quality Q, composed of the following typical Qparameter ratings, in such site locations (see Appendix A for description of the ratings used to quantify the six parameters): J J RQD  r  w Jn Ja SRF 45  90 0.5  2 0.66  1    9  15 24 1  2.5

Q 

(10.13)

(i.e. three or four sets of joints, spacing typically 15–50 cm, one or more sets possibly slickensided or smooth-undulating, with weathered or clay-smeared joint walls, dry or partly saturated with water, with typical shallow (25 m, or 100 m) near-surface, lowstress characteristics.) From the above example, we obtain Q  0.1  10 (quality described as ‘very poor’ – ‘poor’ – ‘fair’). This calculated range shows, obviously, that Q rock quality  Q seismic, but when Q rock quality is used to estimate the rock mass deformation modulus Emass, values of from about 2 to 30 GPa would be obtained with an appropriate 10 to 100 MPa range of UCS, and the specified 25 to 100 m depth.

Further insight into the meaning of these Q-parameters and their link to engineering parameters may be given by recording the fact that the first two terms RQD/Jn, describing joint structure (the potential scattering component), has a maximum range from 100/ 0.5  200 (massive rock without joints), through 45/9  5 (closely spaced joints in three sets), to 10/20  0.5 (‘earth-like’, crushed rock). This pair of parameters alone, has by chance, a certain ‘familiarity’ in relation to relevant seismic Q magnitudes reviewed earlier. Sophistication, related to shear strength, is added by the next two Q-value terms Jr/Ja, describing, with some level of accuracy, the friction coefficient (a potential intrinsic attenuation component). (see Appendix A for rating descriptions, and for a graphic presentation of Jr/Ja
). Table 10.8 shows some hypothetical constructions of typical near-surface Q-parameter ratings for potential recording-site qualities. Such Q-parameter ratings have been applied on thousands of engineering sites worldwide, and the rock engineering profession is as familiar with ‘Q  1’ as the geophysics profession is familiar with ‘Qp  10’. Interestingly, and frustratingly, both numbers can remain constant when actually composed of different contributions from the various components. In rock engineering it is therefore good practice to quote all six assumed parameter values. In geophysics it would be excellent if at least the near-surface scattering (caused by RQD/Jn) and intrinsic components (caused by Jr/Ja and Jw) could be separated, as increasingly seen with more deeply-acquired data. The hidden ubiquitous microcracks have a ‘multiple role’ in increasing both the attenuation components to varying degrees, but this is possibly masked by significant near-surface jointing, since of potentially stronger effect. Microcracks also have a role in increasing the effect of weathering, thereby reducing RQD and Jw, and increasing Ja, and possibly SRF – due to loosening, all of which , it is suggested, cause a reduction in both of these Q values (Qseis and Qrock).

226

Rock quality, seismic velocity, attenuation and anisotropy

Figure 10.54 Rock engineering parallels to seismic Q. (See Chapters 5 and 9). The rock mass quality Q, with normalization to Qc to account for weak or strong rock, appears to follow the trends of seismic Q values (with rock quality Qc  Qseis), Deformation modulus M (Emass) expressed in GPa appears to match seismic Qp quite closely. Strongly attenuating fault zones, almost ‘invisible’ to seismic velocity, are seen to ‘maintain’ an apparently attenuating level of rock quality Qc at 1 km depth. It has been observed that shallow Californian earthquakes are never found in regions with Vp  6.3 km/s. With appropriate stress correction, this implies some degree of jointing in the neighbourhood of causative faults.

While microcracks are vitally important for attenuation in laboratory samples, they should be less so in the near-surface rock mass, where jointing and weatheringinduced porosity may readily dominate attenuation. Some microcracks have also become macro-cracks in this zone. Joint sets in petroleum reservoirs at 2 to 5 kilometres depth remain a major source of attenuation (also polarizing shear waves), but microcracks presumably still contribute to the local attenuation caused by the fluids. Any remaining pressure-resistant pore space and higher aspect-ratio microcracks at 5 to 10 km depth, may contribute to the strongly declined attenuation, but there will still be scattering from major faults and eventual rock boundaries. Jointing, usually assumed to have ceased to exist at great depth, may in fact be present in the form of minor faulting, thereby explaining the maintained (but low) permeability. See the last sections of Chapter 16 for discussion of these aspects.

10.7

Attenuation across continents

As introduction to this section, concerning attenuation across continents, it is appropriate to reproduce a wellknown diagram of plate tectonics. That reproduced in Figure 10.55 is from Isacks et al., 1968, as presented in Kearey and Vine, 1996. It shows the classic subduction of the lithosphere into the asthenosphere at opposite edges of plates.

10.7.1

Plate tectonics, sub-duction zones and seismic Q

The two-dimensional cross-section of the main features of an oceanic subduction zone, shown in Figure 10.56, is reproduced from Kearey and Vine, 1996. The Benioff zone shown in this figure is the source of deep

Seismic quality Q and attenuation at many scales

Figure 10.55 Block diagram summarising the main features of plate tectonics motions. The arrows shown in the asthenosphere represent possible complimentary flow in the mantle, in relation to the lithosphere. From Isacks et al., 1968, reproduced in Kearey and Vine, 1996.

earthquakes, with the maximum stress direction following the dip of this zone, as indicated in more detail in Figure 10.57. The ‘extremely low Q’ region shown in the figure (Qp of 50 or less) lying in the mantle above the deep earthquake zone appears to be a common feature above such seismic activity. From a rock mechanics point of view, it is reasonable to suppose that this is a zone of high shear and tensile stress, with tectonic disturbance of the strata as a result. Within the original theory of plate tectonics, plates were considered to be internally rigid and to act as extremely efficient stress guides. Supposedly a stress applied to one margin of a plate was transmitted to its opposite margin with no deformation of the plate’s interior (Kearey and Vine, 1996). The plates may be 80 to 150 km thick and thousands of kilometres in width. In fact there are obviously some locations where intraplate deformation does occur, such as the thrust faulting in intraplate mountain belts. In view of the friction to be overcome, from an engineering viewpoint it would seem clear that the thrust at one side of the plate must be more than at the opposite margin, and the variable modulus of deformation, albeit high, would then seem to have relevance in the overall behaviour. It has long been suspected, e.g. Molnar and Oliver, 1969, that high values of Qseis correspond to regions of high strength and high velocity, while low values correspond to low strength and low velocity, possibly associated with high temperature and adjacent volcanic activity. A long time ago, Daly, 1940, had correctly defined crustal strength as ‘enduring resistance to shear stress with a limiting value’. The Benioff zone, which is the source of numerous earthquakes even down to a depth of as much as 700 km, often dips at about 45°. The structure of such

227

Figure 10.56 Cross-section showing main features of an oceanic subduction zone. From Kearey and Vine, 1996.

Figure 10.57 Schematic section crossing the Tonga trench showing the high and low seismic attenuation regions, and the high seismic Q tongue of sinking (and thrusting) lithosphere, which is the source of deep earthquakes. Bott, 1982. The continued application of seismic Q, to hundreds of kilometres depth, is evident, and there is clearly structural/tectonic logic in the location of many of the adjectives: extremely low, high etc.

zones is known from analysis of the different seismic arrivals. High seismic Q travel paths suffer little attenuation and represent stronger (and stiffer) rock. In the case of the Tonga trench which has ocean depths of some 8 km, seismic waves passing up the length of the Benioff zone appear to pass through a region of high seismic Q (about 1000) while those travelling to lateral recorders pass through a more normal region of low seismic Q (about 150). The zone of very high attenuation (or extremely low seismic Q of about 50) identified in the uppermost mantle above the down-going slab, is a region about 300 km wide (Barazangi and Isacks, 1971). It is implied that this is much weaker (and less stiff ) than elsewhere. In the Basin and Range province of the Western USA where there is also anomalously low Qseis in the upper

228

Rock quality, seismic velocity, attenuation and anisotropy

mantle, extensive normal faulting has occurred in a tensional stress regime. In the foregoing summary of estimates of Qseis in the region of subduction zones, we have seen values of Qseis ranging from high values in deep Benioff zones (
1000), low value in more normal (shallower) regions (
150), and extremely low values in the uppermost mantle above the down-going slab (
50); presumably in the region of the pull-apart-basin.

10.7.2

Young and old oceanic lithosphere

Noting that the coda Qc decay rate was supposedly independent of the source-receiver path, yet reduced by an order of magnitude from stable continental upper crust to active tectonic areas, Jin et al., 1985, investigated coda Qc from 22 local earthquakes recorded on islands located in young and old oceanic lithosphere. The authors found that coda Qc values increased with frequency proportional to f n, where n ranged from 0.46 to 0.61, the higher values being for younger oceanic lithosphere. This was similar to continental regions where the active, tectonic, western side of the USA also show higher n values. Crustal coda Qc values at a frequency of 1 Hz reportedly increase from about 140–200 in the western US to around 1300 in the stable central US, as we shall review shortly. Figure 10.58 shows a large collection of data for coda Q1 c (attenuation) versus frequency of measurement, which includes the island data of Jin et al., 1985 (termed ‘this study’) and numerous other authors’ data assembled by R.S. Wu). See Jin et al., 1985 for a complete listing of the sources of data. Most of the geographic areas are marked on the figure. The AKU and GUA data are from Akureyri (Iceland) and the Mariana Islands of Guam. The coda Qc data shown in Figure 10.58 demonstrate largest differences at low frequencies, while all the trends converge at higher frequencies. Coda Qc tended to increase beyond 1000 when frequency was greater than about 20 Hz. Jin et al., 1985 proposed the equation: Q  Qo

( ) f

n

fo

(10.14)

where fo is 1 Hz, and Qo is coda Qc at 1 Hz. They found a good linear relation between log Q (i.e. coda Qc) and log f. Gradient n was 0.346 for the older GUA (Guam)

Figure 10.58 Coda Qc1 from coda analyses cited by Jin et al., 1985, spanning several sites in the USA, Alaska, Japan, Guam, China, Afghanistan, Iceland and Italy. See Jin et al., 1985 for individual references. Note low-frequency, low seismic Qc trend, from suspected shallow crust sampling.

data and n was 0.61 for the younger AKU Iceland data, as indicated graphically in Figure 10.58 Their conclusions from a careful analysis of the data trends were that: 1. At frequencies from about 0.5–1 Hz, the average coda Qc values increased from the youngest oceanic lithosphere to the oldest by a factor or 2. 2. The regional change on the continents follows the same trend, but the difference could be as much as a factor of 10. 3. The coda Qc values from the old oceanic lithosphere were therefore low in comparison to those obtained from stable parts of the continents. 10.7.3

Lateral and depth variation of seismic Q and seismic velocity

Solomon and Toksöz, 1970, were among the early researchers who noted the significant lateral variations in attenuation. They referred to Oliver and Isacks, 1967 experiences of Qseis changing by an order of magnitude over lateral distances of a few 10s of kilometres. Demonstrable regional differences in crust and upper mantle Qseis are also found in the continental USA, for example 200 in the Western seismic belt and 1000 in the east-central US, as will be reviewed shortly. Variation of Vp and Vs with depth and lateral location in the crust, and corresponding Qp and Qs increases

Seismic quality Q and attenuation at many scales

229

Figure 10.59 Deep seismic refraction results showing depth variation of a) Vp and seismic Qp, b) Vs (and Vp/Vs) and seismic Qs. Iwasaki et al., 1994.

with depth, are shown in Figure 10.59a and b, from Iwasaki et al., 1994, from an extensive seismic refraction experiment conducted on a 194 km N-S line across the Kitakami massif of E. Northern Honshu in Japan. A Jurassic accretionary complex lies to the north, and pre-Silurian and Silurian-lower Cretaceous marine sediments lie to the south. In these studies, the uppermost crust was covered with a thin (0.5 to 1.0 km) ‘surface layer’ with Vp ranging

from 3.1 to 5.4 km/s. The velocity structure below this showed lateral variation (as must surely be expected over a 190 km profile), with successive increases in Vp and seismic Qp as depth increased to 35 km. The Moho occurs at about 32 to 34 km depth at the base of the selected profile. Inspection of the variation of Vp and seismic Qp as depth increases was typically as in the simplified table shown on the next page.

230

Rock quality, seismic velocity, attenuation and anisotropy

Note the possibility of tentative extrapolation to 2 (and 5) km depth at the top of Figure 10.54. The implication of the data from Iwasaki et al., 1994, is of a significantly jointed upper 1 km, with low rock quality Q-values. Beyond 2 km depth we move outside the area of empirically derivable deformation moduli, so the seismic Qp-Emass (GPa) similarity breaks down because of lack of empirical data for Emass. Qp beneath two of the world’s four major continental rifts (the Rio Grande, SW USA, and the East African rift) were estimated from 1000 km and 600 km linear arrays during the 1980s. With Qp for the crust taken as 480 to 650, Qp values for the Rio Grande rift were 95 and 100 respectively. The value of Qp for the more strongly upwarped asthenosphere beneath the East African rift was only 27 by comparison. In general terms the asthenosphere is believed to have lower velocity, higher attenuation and the possible presence of partial melt, which significantly reduces the shear modulus. This reportedly causes a larger perturbation in Pwave velocity than density, which in turn signifies partial melt (Halderman and Davis, 1991).

Table 10.9 Typical Vp-Qp inter-relation, with depth as the important variable. (Derived from Iwasaki et al., 1994 data, reproduced in Figure 10.59) Vp (km/s) Qp Depth (km)

3 to 4 100 1

5.9 150 2

6.2 200 5

6.3 300 8

6.4 400 12

6.5 500 15–20

10.7.4

Cross-continent Lg coda Q variations and their explanation

We will conclude this section on seismic quality and attenuation, with continental broad-scale coda Qc variation first across Eurasia, then South America and the United States. Mitchell et al., 1997 showed that at a frequency of 1 Hz, the coda Q (from the so-called Lg coda) varied between 200 and about 1000, with lowest values in the orogenic belt formed by the collision of African/Arabian and Indian plates with the Eurasian plate (Figure 10.60). Low values are also found in the Arabian Peninsula (Qc  350–500), which is a region of recent uplift, extension and volcanism. High coda Qc (800) were found, as expected from earlier results, beneath three shield areas (East European, Siberian and Indian) and beneath the oldest portion of the Altaid belt. Mitchell et al., 1997, suggested that the different coda Qc magnitudes across Eurasia were proportional to the length of time elapsed since the most recent episode of large scale compressional tectonic activity. They interpreted low coda Qc as resulting largely from hydrothermal fluids generated by tectonic activity or heating, residing in permeable portions of the Eurasian crust. Crustal Qc appears to increase with time, as fluids are lost to the surface or absorbed by metamorphism. Companion papers that appeared in the same number of Pure and Applied Geophysics, described recently interpreted continental structures of Qo (the Lg coda

Figure 10.60 Simplified tectonic map of Eurasia. A tomographic plot of Qc at 1 Hz was given for each 3° by 3° cell. Mitchell et al., 1997.

Seismic quality Q and attenuation at many scales

at 1 Hz) for South America (DeSouza and Mitchell, 1998), and North America (Baquer and Mitchell, 1998). These authors used 389 seismic recordings in the case of S. America, and 218 in the case of N. America, to produce back-projection tomography, by inversion, giving regionalized maps of Qo and of its frequency dependence (') at 1 Hz. The Lg phase was explained by Mitchell and Hwang, 1987, as being prominent on regional short-period seismograms, where in stable (high Q) continental regions, it can be observed to distances as great as 4000 km, and forms the basis of magnitude scales for small earthquakes, as recorded over regional (i.e. large) distances. The main Lg phase is followed by a coda, the main duration of which can also be used to determine the magnitude of regional events. However, the later part of the coda may reportedly not be coherent across arrays of seismograph stations, indicating that part of the coda is due to scattering. According to these most recent 1998 studies, the seismically active South American Andean Belt was typified by low Qo (250–450), in a similar manner to the low Qo (250–300) region west of the Rocky Mountains (the Basin and Range province and active Californian coastal regions). In South America there were broad regions of very high Qo (700–1100) spanning the central Brazilian shield, and the Amazonian and Paraná Basins, whereas in North America the highest Qo region was the Northern Appalachians and some of the central lowlands (650–750). The Gulf Coastal Plain and the southern portion of the Atlantic Coastal Plain had intermediate values (400–500), while the Atlantic Shield in South America also had intermediate values (450–700), these last possibly related to the tectonic and igneous activity that occurred during the break-up of Gondwanaland. The authors of these continental studies suggested that the low Qo in the Andes, particularly in two belts across the southern and northern Andes, was probably related with higher upper mantle temperatures, or that there were more, deep hydrothermal fluids in these belts. Fluids in the upper crust, and the energy loss they represent, were also cited as the likely reason for low Qo in the region west of the Rocky Mountains, with variations in that region caused by variable amounts of fluids in faults, joints and rocks of variable permeability. They cited recent studies that showed that a shear velocity transition from high to low velocity, lay further west at ‘intermediate’ depths between 25 and 100 km, than at greater depths than this.

231

Several of the above (1998) Qo ranges for regions of the United States showed some differences to the earlier study of Singh and Herrmann, 1983, where a broad belt in the eastern region below the Great Lakes, had values varying from 1000 to a maximum of 1300. The lowest belt of Lg coda Q along the western coast (Oregon, Washington, California) was given as 200 in these earlier studies.

10.7.5

Effect of thick sediments on continental Lg coda

Baquer and Mitchell, 1998 emphasised the role of thick deposits of Mesozoic and younger e.g. Cretaceous sediments, typically sandstones and shales, in significantly reducing Qo in various regions of North America, while older sedimentary rocks did not. They also cited the ‘positive’ effect of dolomites and limestones in maintaining high Qo, and of fluids that had been lost with time. Earlier work by Mitchell, 1995, had suggested that seismic Q was influenced in a ‘positive’ (less attenuating) direction by the time elapsed since the most recent major episode of tectonic activity. This seemed to be supported by these most recent measurements, and by the Eurasian studies. In earlier studies, Mitchell and Hwang, 1987 had investigated in some detail, whether the lateral variations in Lg attenuation across the United States, could be explained by known variations in the thicknesses of shallow sedimentary layers. They stated that many of the features of the coda at frequencies near 1 Hz could be approximately duplicated in synthetic seismograms produced by plane-layer models, which included layers of low-velocity surface sediments. As they pointed out, soft and unconsolidated sediments could be characterized by very low velocity and low Q values. However, deep sedimentary basins bounded by sharp discontinuities could influence Lg by scattering (or even wave blockage, as described by Baumgardt, 1985), and thick sediments of low Q could cause rapid attenuation due to intrinsic absorption. Their assumption, based on earlier studies, was that Lg Q and coda Q were approximately equal, and could show regional variations of greater than 1:6 across the United States. Two aspects to be investigated were how far regional variations could be explained by sediment of different age (as we have seen in the latest studies), and why there could be low and laterally varying values of Q in the

232

Rock quality, seismic velocity, attenuation and anisotropy

(a)

depth, reproduced in Figure 10.62. The implicit ‘geometric’ similarity to the velocity  depth structure of the jointed rock mass Q-Vp-M model (Barton, 1995), is striking. Possibly the rock mass quality Qc value is about 1/10 of the coda Q, which would then give an equivalent velocity scale along the top of Figure 10.61b, stretching from about  3.5 km/s (due to porosity effects) to about 5.8 km/s (porosity ‘compensation’ by 2 km depth). A rock quality Qc  1 suggests Vp  3.5 km/s (less, with significant porosity), while a rock quality Qc  200 suggests Vp  5.8 km/s (less, with significant porosity, but partly compensated by the depth effects of 2 km of sediment). Conversion of rock quality Qc to modulus of deformation again indicates the potential match of seismic Qp and Emass, when given in units of GPa. As Mitchell and Huang noted, there was clear evidence for lower seismic Q at depths of less than 400 m. For the modelling of sediment-layer effects, the authors used the stepped trend in Figure 10.61a, where the following was suggested: ● ● ● ●

(b)

Figure 10.61 a) An assembly of Q ⫺1 data for sandstone and shale sediments as a function of depth. (See Mitchell and Huang, 1983 for complete references). 1: Pierre shale, 2: Gulf Coast sediments, 3: various VSP data sets, 4: unknown, 5: unconsolidated sediments, 6: San Francisco Bay sediments, 7: El Centro area sediments. b) Reversal and rotation of data by the writer to match Figure 10.62 Vp – Qc format. (See Chapter 5 for derivation).

crystalline crust, where deep accumulations of sediment were absent, as in the western USA. Mitchell and Hwang assembled Q seis values for sandstones and shales, excluding limestones due to their high Q seis values. Figure 10.61a shows this sedimentary Q⫺1 data, with reversal and rotation by the writer (Figure 10.61b) to match the plotting format of rock mass quality Qc versus

0–100 m Q
30 100–300 m Q
50 300–600 m Q
75 600 m Q
100

In their synthetic modelling the authors assumed frequency independence of seismic Q below 1 Hz. The authors found that their low seismic Q thick-sediment models, while applicable and explanatory of Lg coda Q in those regions with seismic Q ranging from 400 to 1300, were not applicable to the lower Q of the western United States. Surprisingly, the authors, at that time, did not mention jointing and faulting in (the seismically more active) western United States, as a likely cause for lateral and depth variation of the generally low Q in this region of mostly crystalline basement.

10.8

Some recent attenuation measurements in petroleum reservoir environments

As will also be observed in many of the Vp, Vs, Qp, and Qs sets of data to be presented in Chapter 13, the attenuation is a relatively more sensitive indicator of the degree of saturation than velocity. In particular, the Qs/Qp ratio in sedimentary rocks is much more sensitive to the degree of saturation than the Vp/Vs velocity ratio. Seismic Q has therefore become increasingly important in hydrocarbon exploration. For similar reasons, Winkler and Nur, 1979, suggested using these relatively

Seismic quality Q and attenuation at many scales

233

Figure 10.62 Rock quality Qc-Vp depth model for comparison to previous data set. Making a gross approximation of rock quality Qc
1/10th of Q, an approximate velocity scale of 3.5 km/s to 5.8 km/s (less, due to sediment porosities) is suggested in Figure 10.61b.

large changes in seismic Q with saturation as an earthquake predictor, since pre-earthquake dilatancy could affect the degree of saturation in fault zone rocks. These saturation/partial saturation effects were reviewed in section 10.2, but derived only from intact bars of dynamically excited sandstone, Anomalously low seismic Q values at depth, adjacent to a 5 km deep well where VSP was performed, were reported by Keehn and Kanasewich, 1987. The spectral ratio method was used to obtain values of seismic Q of 10 in a Lower Triassic sandstone, and a second low seismic Q of 12 at about 4,000 m depth. (Figure 10.63). The authors considered that they were observing the effects of scattering caused by intrabed multiples, together with intrinsic attenuation associated with the sandstone lithology. The strongly attenuating zone between 1,930 and 2,320 m depth was associated with an almost uninterrupted Lower Triassic sandstone layer. The authors referred to studies showing that increased content of sand, rather than shale, were responsible for high attenuation. For some reason, the possibility of a fractured reservoir in this location was not directly referred to, possibly due to confidentiality. The likelihood that oil bearing rock in a jointed reservoir was being described, is however evident from their conclusions. ‘The existence of the two low-Q zones may be attributed to one or more of the following factors which contribute to high attenuation: the presence of fluids of higher viscosity than those in the

Figure 10.63 Depth plot of 1/Qseis and Q, smoothed with a 200 m running average, together with the interval P-wave velocities. The well is on Melville Island, in the Canadian Arctic. Keehn and Kanasewich, 1987.

remainder of the hole, pores with smaller aspect ratios, more pore space, and a higher degree of saturation’. Cross-well tomography data of Quan and Harris, 1997 shown in Figure 10.64, emphasises the generally high level of attenuation in transversely isotropic (‘layer cake’) sedimentary series. Seismic Q values were between about 20 and 90. The attenuation coefficient () in the

234

Rock quality, seismic velocity, attenuation and anisotropy

central log, is given by the relation Qseis  f/  V, where V is the wave speed, and f is the frequency. It is apparent from the figure that there were certain similarities, in this case, between the cross-well velocity structure and the seismic quality Q. The 8 to 17 K ft/sec velocity scale converts to 2410 m/s – 5120 m/s. Each of these values (Vp and Qseis) showed a clear differentiation between shale, limestone and clay, and there was a certain indication of a less jointed (or less porous) area in the overlying chalk. The cross-well Q seismic data shown in Figure 10.64 are unfortunately specific only to the frequency range

Figure 10.64 Sonic log, cross-well Vp, and cross-well attenuation and seismic Q from roughly 600–900 m depth, in the BP Devine Test Site (Quan and Harris, 1997), reviewed by Pride et al., 2003. Centre frequency was 1750 Hz.

employed, as emphasised by the important set of attenuation data from the Imperial College test site in NE England, reproduced earlier, in Figures 10.34 and 10.35, from Sams et al., 1997. The differences in attenuation between sonic, cross-well, VSP and ultrasonic measurements in the same formation were significant The four boreholes utilised by Sams et al., 1997, were drilled to about half the depth of the above, to just a few hundred metres depth in a layered sequence of limestones, sandstones, siltstones and mudstones. The variability of 1/Q for each type of seismic survey was due both to rock heterogeneity (i.e. implicit rock quality Q-value variations) and frequency variations. The authors Hustedt and Clark, 1999, drew attention to the fact that the seismic attenuation factor Q is an important parameter in the processing and interpretation of seismic data, both because of the detrimental effect it has on the data, and because it can itself be an indicator of rock properties. Hustedt and Clark referred to the QVO (Q versus offset) technique that had recently been introduced by Dasgupta and Clark, 1998. This could be used for extracting Q from routine marine surface seismic reflection data. As they explained, in exploration analyst jargon: ‘The QVO method applies the well-known spectralratio method to a true-relative-spectrum-processed, NMO-corrected, CMP gather.’ They compiled QVO-derived seismic Q-values in relation to interval velocities, from a variety of hydrocarbon exploration settings, as shown in Figure 10.65. Q-values ranged from 50 to 700–800, suggesting that some of

Figure 10.65 A compilation of QVO (Q versus offset) data for seismic quality Q versus interval velocity. Hustedt and Clark, 1999.

Seismic quality Q and attenuation at many scales

235

the ‘rules-of-thumb’ attempting to relate an approximate Q to the interval velocity, may be inappropriate. The potential ‘central trend’ of the data – a steepening curve – was unfortunately defeated by a dense ‘clump’ of low seismic Q (40 to 50), yet displaying medium high velocity, of about 3.9 to 4.1 km/s. In the context of jointed rock (possibly inapplicable at the undefined, but presumed several kilometres depths), a certain Vp – Q coupling, as in Figure 10.64, would be understandable. In relation to the ‘curving trend’ of much of the data in Figure 10.65, a slightly better fit than the straight lines could be Qp
(Vp500)0.6, implying the ‘disappearance’ of a measurable Qp at Vp as low as 0.5 km/s. 10.8.1 Anomalous values of seismic Q in reservoirs due to major structures Dasgupta and Clark, 1998, reported seismic Q values of 46 and 130 for top chalk and base chalk, from some North Sea data. In Figure 10.66 Qp is shown falling from 100 to a minimum value of about 50 in the anticlinal crest. The implied reservoir values (13 to 33) caused by gas effects agreed with trends shown in laboratory studies (See Chapter 13). A low value of seismic Q for a fault zone (or possibly several faults) encountered in a well in the North Sea (Qseis averaging 45), was described by Worthington and Hudson, 2000. Figure 10.67 shows the roughly 1000 m to 2000 m depth trace of the fault in the seismic migrated time section, reproduced from Harris et al., 1997, and its approximate intersection with the well. The

(a)

(b)

Figure 10.66 Qp values interpreted in a North Sea UK sector anticlinal crest, with further reduced values in a gas bearing pay zone. (Dasgupta and Clark, 1998).

Figure 10.67 Anomalously low seismic Q related with fault zones in a North Sea reservoir. Worthington and Hudson, 2000, from Harris et al., 1997 data.

236

Rock quality, seismic velocity, attenuation and anisotropy

fault zone caused an abrupt increase in attenuation, relative to the Triassic and Lower Jurassic age sandstones, siltstones and claystones that were predominantly encountered in the well. Worthington and Hudson described their modelling of the effects of a down-going P-wave between 1000 and 2000 m depth, by assuming that a fault or several faults, intersected the transmission path. By using a compliance model of a major discontinuity with not completely conforming opposite faces, they showed the need for a remarkable, but actually very realistic, inequality of the normal and shear compliances. We will examine these important parameters (whose inverse is dynamic stiffness), in detail in Chapters 15 and 16, seeing the similarity of their inverted magnitudes, to the normal stiffnesses of joints, clay-filled discontinuities, or faults that are more familiar in the macro-displacement world of rock mechanics. This subject was also addressed earlier in this chapter, concerning the important work of Pyrak-Nolte et al., 1990 related to dynamic and static loading tests on joints.

10.8.2

Evidence for fracturing effects in reservoirs on seismic Q

Evidence for the subtle effects on seismic Q, of fracturing in petroleum reservoirs, was given by Parra et al., 2002, who described field characterization at the Buena Vista Hills reservoir, in California. They described the use of seismic Q derived from high-resolution crosswell seismic data, to detect vertical, joint-like tectonic fracturing dominating in the Antelope Shale and en echelon, sigmoidal, vein fracturing that was restricted to the Brown Shale, where the joint-like fractures also occurred, but with less frequency. The Brown Shale displayed both low Qseis, and low P-wave velocity. The sand-shale sequences were too finely layered to be detected by sonic logging, with layer thicknesses and bed thicknesses ranging from fractions of centimetres to tens of centimetres to meters. The Antelope Shale formation, containing the highest densities of jointing, consisted of thin, siliceous, clay-free shale beds, with intercalated thin laminae of clayey sand and carbonates. A 290 m core interval contained nearly 750 sand laminæ. The cores averaged 28% porosity, but had only 70 micro-darcies permeability due to the dominance of siliceous shale. Since only 5% of the rock consisted of the sands, hydrocarbon production was assumed to be

due to the fracturing, which indicated permeabilities of 2.5 to 5 milli-darcies. The en echelon vertical fractures were very short 0.4 to 8 cm, frequently occurring features, perpendicular to the bedding in the Brown Shale. The joint-like features that were more dominating in the Antelope Shale, were nearly vertical, and also had modest heights averaging only 13 cm, due to the bedding thickness limits. Joint densities were from 0 to 2 per meter. There were also less frequent larger fractures and micro-faults, also perpendicular to the bedding. The cross-well tomography, with sources and receivers at 1.5 m (5 feet) intervals over 457 m (1500 feet) of the reservoir formation, showed expected, distinctly layered velocity trends in the range of about 2.4 to 3.4 km/s over a selected depth range of 3,900 ft (1,190 m) to 4,600 ft (1,400 m). Figure 10.68 indicates the P-wave velocity and computed Qseis for an interval in the Antelope Shale. Also shown is the core-plug permeability. It is particularly interesting to note the good ‘geometric correlation’ of Vp and Qseis in the fractured part of the formation with lower core-plug permeability. This was the Brown Shale, which contained both styles of fracturing. In the lower parts of the formation with more sand, there was a marked increase in core-plug permeability, but Qseis remained low, even below 20, probably due to intrinsic squirt-flow attenuation in the sand and carbonate beds, where the P-wave velocity was markedly higher. The Q seismic data is reproduced at more exaggerated scale in Figure 10.69. This shows the strong influence of the two styles of jointing that were described. The authors also conducted poro-elastic numerical modelling, based on a Biot squirt flow attenuation mechanism. They demonstrate in Figure 10.70 the effect of frequency and azimuth angles on computed attenuations, referring to the actual vertical fracture azimuths of 0° to 30°. It is interesting to note from their modelling of the Brown Shale, that there was little attenuation of seismic waves propagating from sources at the surface, where Qseis was a surprising 1000. In contrast, they found that the en echelon and joint-like features in this shale were strongly attenuating to seismic waves propagating parallel to stratification, and perpendicular to the fractures (Qseis of 20), in the frequency range of sonic and cross-well seismic. The lower Antelope Shale with its frequent sand beds, indicated a higher attenuation of seismic waves propagating from the surface, with Qseis typically 100, while waves propagating parallel to stratification and

Seismic quality Q and attenuation at many scales

237

(a)

Figure 10.68 Vp and Qseis results computed from velocity dispersion data (1 to 10 kHz), for a selected 1,220 to 1,330 m deep section of the en echelon fractured and infrequently jointed Brown Shale, and the lower, well jointed, sand-laminae bearing Antelope Shale, Buena Vista Hills field, California. Also shown is the core-plug permeability, which is highest where sand is more frequent in the Antelope Shale. The uppermost low Qseis zone corresponds to the Brown Shale. Parra et al., 2002.

perpendicular to ‘open’ fractures, indicated seismic Q values of 18 to 20. For their modelling, they had selected permeabilities perpendicular to the fracture systems of 50 d, similar to the matrix, while parallel to the fractures they selected 5 md. (Note: 1 darcy  108 cm2, or 101 2 m2, which is roughly equivalent to an engineering unit of 105 m/s for water). The uses of seismic Q appear to be expanding rapidly, as time goes by, due to its greater sensitivity to some physical properties than seismic velocity. Rossi

(b)

Figure 10.69 Low seismic Q in jointed Antelope shale, and in en echelon fractured Brown shale, plotted at exaggerated scale. Buena Vista Hills studies described by Parra et al., 2002.

et al., 2005 described the use of attenuation and velocity tomography, using an array of ocean bottom seismometers (OBS), crossed by a dense pattern of shot lines, on the western continental margin of Svalbard, on the lower part of the continental slope, close to an active mid-ocean ridge. Data was acquired within the EU Hydratech Project. An important boundary condition was a reflector, marking the boundary between gas-hydrate and free-gas

238

Rock quality, seismic velocity, attenuation and anisotropy

10.8.3

Figure 10.70 They computed Qseis values of 15, 19 and 28 in the frequency range of 120 to 1000 Hz using an assumed squirt flow length of 3 cm for the modelled fractures. (Parra et al., 2002).

bearing sediment zones below the reflector. Qp showed a strong decrease from around 200 to values declining below 50 and even below 25, below this reflector, corresponding to the sediments containing free-gas. The high values of Qp corresponded to the expected gas-hydrate zone, and its probable ‘strengthening of the solid frame’ of the rock. The authors generally found good spatial agreement between the Qp and Vp variations, both vertically and laterally. The corresponding Vp values were about 1.75 to 1.8 km/s above the reflector in the gashydrate zone, declining rapidly to 1.5–1.6 km/s in the free-gas zones below. The authors also noted that the small graben-causing faults in the area, correlated with the Qp and Vp reductions. Interestingly, the Qp values began to decline just above the reflecting boundary, where Vp was still high. The authors considered that this might have been due to interference in the frequency-shift calculations, caused by the liquid to gas phase change. One other anomalous result when comparing the two parameters was the almost full recovery of Vp at greater depth, while Qp increased only to about 75. At greatest depth there was a further unexplained Qp of about 20, while the velocity attained its highest value of 1.9 km/s. The consistent rise in velocity in the deeper levels resembled typical velocity-depth (stress-closing-structure) trends seen in particular in Chapter 11. Possibly a strongly developed structure, under significant effective stress, would be capable of showing an ‘increased Vp, reduced Qp’ reaction.

Different methods of analysis give different seismic Q

On several occasions, different methods of estimating seismic Q have been compared by the same authors. We will briefly review two such cases, in order to emphasise both the difficulties that can sometimes arise, and the potential errors involved. As an observer of geophysical results, rather than a practitioner, it is not possible to judge whether the levels of error reported here, are a serious threat to the use that the geophysics community is currently making of seismic Q, in all its various forms. Badri and Mooney, 1987 used several processing methods, in both time and frequency domains, to compute the seismic quality factor Q for water-saturated, unconsolidated sediments. The methods used included measurements of the spectral amplitude ratio, peak-topeak and first-peak amplitude ratio, rise time, pulse broadening, and the Futterman causal attenuation operator for attenuating signals. The authors used compressional seismic waves generated from explosive sources ranging in size from 1 to 64 mg of silver azide, at a depth of 7.6 m below the 70% saturated, silty sandy clays, near Wendover, Utah. The hydrophone receivers were spirally distributed at distances ranging from 25 to 200 m from the source. The computed seismic Q values showed a remarkable variation, as indicated below. The authors suggested that the spectral amplitude ratio method was probably the most reliable, as it is applicable independent of the source. 1. Spectral amplitude ratio method, with five explosive source sizes, over frequencies of 450–725 Hz. Average Q  23. 2. Peak amplitude ratio method. Average Q  123. 3. Rise-time method. Range of Q  50–207. 4. Pulse broadening technique. a) Quarter-cycle measurement: range of Q  25–158. b) Half-cycle measurement: range of Q  26–114. 5. Futterman causal attenuation operator. Range of Q  200–300. Intuitively, in view of the unconsolidated material and shallow depth involved, one could be permitted to assume that the three lowest seismic Q values listed above (23, 25 and 26), were likely to be the most realistic, and the author’s preference for the spectral amplitude ratio method, seen in much of the literature, seems likely to be the most reliable. Toverud and Ursin, 2005 went further than the above, and compared eight methods of determining

Seismic quality Q and attenuation at many scales

seismic Q, using (almost) zero-offset VSP for three separate zones, obtained from a well off the Norwegian coast. The source was deployed at 4 m depth at 40 m of horizontal offset from the well. Depths analysed ranged from 2907–3907 m, using 10 m intervals. A minimum frequency close to zero up to 90 Hz was indicated. The authors evaluated eight different attenuation models, using a least squares model-fitting approach. They used the geometric ray approximation approach of Ursin and Arntsen, 1985, for point source, vertical wave propagation in a 1D viscoelastic medium, with planewave reflection coefficients. A formula for the complex velocity was assumed, with inversion of the attenuation parameters at three different depth intervals, to obtain the parameters in three homogeneous layers: (2907–3335 m Table 10.10 Comparison of eight methods for estimating seismic Q. Toverud and Ursin, 2005. Minimum normalized misfits are shown. (For brevity, results for two of the three layers are selected here. Velocities have been rounded to the nearest 10 m/s. Variations were less than 5 m/s). Model

Layer

Qp

Vp m/s

Kolsky-Futterman

1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3

32 36 35 39 31 37 34 40 36 44 34 40 22 25.5 27.5 32

3.14 2.98 3.14 2.98 3.14 2.98 3.15 2.98 3.15 2.98 3.14 2.98 3.14 2.99 3.14 2.99

Power law Kjartansson Müller Azimi’s second law Azimi’s third law Cole-Cole Standard linear solid (SLS)

239

was 427 m of mainly shales, with some limestone and marls; 3335–3650 m was 315 m of marl/limestone, with some shale; 3650–3907 m was 257 m of sandstone, siltstone and shale). The results for the second layer (marl/limestone with some shale) gave considerably higher Q and more variation. This zone had the highest content of limestone and marl, which perhaps explains both the higher values (Q  90–160), and the large range. The apparent good correspondence of the models for layers 1 and 3 was a function of the use of the minimum (normalized) misfit in Table 10.10. An example of their normalized misfit analysis, for the Kolsky-Futterman model, is shown in Figure 10.71. They considered that this performed slightly better than the other models, except in the middle layer. In reality, and in Figure 10.72, the authors show that there is actually a lot of difference between the models concerning their frequency-dependence. As may be noted, the Kolsky-Futterman and Kjartansson models assume almost negligible frequency dependence.

Figure 10.72 A comparison of the eight models for interpreting seismic Q, for the case of layer 1. Large differences between models are indicated concerning frequency dependence. Toverud and Ursin, 2005.

Figure 10.71 An example of Toverud and Ursin, 2005, normalized misfit analysis, using the Kolsky-Futterman model, for the three layers of VSP data analysed for seismic Q.

11

Velocity structure of the earth’s crust

This chapter summarises the velocity structure of the continental crust, the continental margins, and the subocean spreading ridges, where zero-age crust is forming. The velocity-depth models of large scale (100 m to 1 km to 50 km) naturally represent an extension of near-surface experiences from Part I. However there are some important parallels and points of basic similarity, especially beneath 3 km of ocean. Although mainly concerned with velocity-depth trends and their reasons, there are also some parallel seismic Q results, where separation into Chapter 10 would have been undesirable.

11.1

An introduction to crustal velocity structures

The text of Part I of this book was dominated by civil engineering scale velocity-depth and rock quality trends. In Part II, Chapter 11 we will now concentrate on the velocity-depth trends of the continental and oceanic crusts. However, when contemplating assembling a review of the velocity structure of the crust, a complete section to the inner core of the earth, as summarised in Figure 11.1, is clearly an important starting point for delineating the outer boundaries of behaviour.

Figure 11.1 A simplified velocity structure through the crust and mantle down to the inner core. Kearey and Vine, 1996, from Hart et al., 1977.

Figure 11.1, reproduced from Kearey and Vine, 1996, shows a ‘familiar’ increase in Vp and Vs through the crust and upper and lower mantle. However, due to the great pressure and much higher densities of the rocks involved, the magnitude scale for Vs (4 to 7 km/s) now looks more ‘familiar’ than the exceptional 8 to 13 km/s range of the P-wave velocities. The depths of nearly 3000 km of course exceed by up to five orders of magnitude, the near-surface phenomena reviewed in Part I. When reaching the outer core and assumed fluid conditions beyond 3000 km, the S-wave is shown as falling to zero due to the loss of shear strength, and the P-wave also shows a dramatic fall of some 5 km/s to ‘only’ 8 km/s, increasing thereafter to about 10 km/s, before reaching the inner core with its increased density, where the S-wave makes a return, albeit to less than 4 km/s. In 1909, Mohorovic
ic
interpreted a first arrival P-wave of magnitude 5.7 km/s within 200 km of an earthquake epicentre, and another first arrival P-wave of 7.9 km/s at greater distance from the epicentre, as evidence for a velocity discontinuity. This is now termed the Moho. Figures 11.2a, b show travel time-distance gradients consistent with the Moho velocity discontinuity both for the case of the thicker sub-continental crust (shown here as 54 km) and for the case of the much thinner sub-ocean crust (shown here as about 12 km). The direct wave (Pg) and the refracted wave (Pn) show different gradients. At first, there was suspicion of another velocity discontinuity at intermediate (sub-ocean) depth, based on Conrad, 1925. A velocity increase from 5.6 to 6.3 km/s is shown in Figure 11.2b. It is now known that the Conrad discontinuity is not always present and a gradational increase with depth is generally seen. We shall see much evidence of these gradational increases in velocity in this chapter. Information about the uppermost parts of the earth’s crust is now available from direct sampling in ultradeep boreholes, and indirectly from experimental data on velocities measured over ranges of temperature and pressure consistent with crustal conditions. Pressure (total stress) increases at a rate of about 30 MPa per

242

Rock quality, seismic velocity, attenuation and anisotropy Table 11.1 A simplified, classic model for the seismic structure of oceanic crust (from Bott, 1982, reproduced by Kearey and Vine, 1996).

Water Layer 1 (sediment) Layer 2 Layer 3

P-wave velocity (km/s)

Average thickness (km)

1.5 1.6–2.5

4.5 0.4

3.4–6.2 6.4–7.0

1.4 5.0

Moho discontinuity Upper mantle

Figure 11.2 a, b Diagrams of time-distance gradients that demonstrate the sub-continental and sub-ocean evidence for the Moho. From Kearey and Vine, 1996.

kilometre due to the high average density, but there is an initial pore pressure increase to perhaps 20 km or more. At shallower depth, it is common to assume about 16 or 17 MPa/km increase of the effective stress (i.e. 26 minus 10  16 MPa/km) in crystalline rock, and closer to 10 or 12 MPa/km in less dense hydrocarbon reservoir sediments, neglecting over-pressured zones. Temperature increases at a rate of about 25°C per kilometre up to the Moho, which usually varies from 20 to 80 km depth beneath continents. The uppermost 5 km of the crust shows a rapid increase in deformation modulus and density, as pore space and joints are closed. However, the thermal expansion partly balances the increase in seismic velocity, and P-wave velocities above about 6.5 km/s do not appear to be common. The P-wave velocity range in the lower crust, from about 6.5 to 7.6 km/s is explained by chemical transformation to more dense phases, e.g. basalt to garnet granulite to ecologite, or by the presence of higher density

7.4–8.6

gabbroic anorthositic rocks which therefore give a higher range of velocity (Kearey and Vine, 1996). The oceanic crust of the earth is much thinner than the continental crust, and is usually about 6 to 7 km thick, beneath an average water depth of 4.5 km. Table 11.1 reproduced from Kearey and Vine, 1996, and based on Bott, 1982, gives velocities for a simplified layered model, while Figure 11.3 shows more detail and a more gradual velocity increase (dash line) based on inversion techniques. The type of measurements traditionally required to obtain such information, so-called reversed deep-sea refraction, are illustrated in Figure 11.4. Here we can see the typical layer 1, 2, 3 and Moho separations of velocity, that were state-of the-art prior to more extensive investigations (and investments), from the end of the 1970s. Measurements of the type illustrated were extended from continental shelf to deep sea, giving as in Figure 11.5, a good illustration of the relative thickness of continental and ocean crust, which are due to great differences in age, as we shall see later in this chapter. Of course there are also anomalies to complicate the simple picture of increasing velocity (and seismic Q) with depth, as implied so far. A seismic low-velocity zone at depth in the crust is widely accepted as evidence of a region of partially molten rock. It can explain the occurrence of low seismic Q and large negative gradients of both velocity and seismic Q with depth. It was also considered by Mavko and Nur, 1975 as a likely zone of relaxation that could be responsible for transient deformation following large earthquakes on plate boundaries. Their ‘melt squirt’ mechanism – possibly involving flow of molten rock between cracks of different orientation to the changed stress field, apparently gives a relaxation time of the right magnitude (a few years) to explain transient deformations that may follow the ‘elastic rebound’ phase of deformation, following

Velocity structure of the earth’s crust

243

Figure 11.3 Simplified models, dating from 1965 and 1978, of supposed layering in the oceanic crust. On the left, with the benefit of improved inversion techniques, is a Spudich and Orcutt, 1980, and Harrison and Bonatti, 1981, interpretation of a more gradational increase in velocity with depth.

Figure 11.4 Reversed deep-sea refraction, using two ships and explosive charges. From Bott, 1982, based on Talwani, 1964.

the accumulation of surface deformations that may be approximately ‘cancelled’ during a large earthquake. A multidisciplinary investigation of the tectonostratigraphic terrain that compose the Alaskan lithosphere by Beaudoin et al., 1992a, revealed low-velocity (6.4 km/s) rocks extending to a depth of approximately 27 km. In this case, little complexity was suggested, with seismic layering typically as shown in Figure 11.6 The bedrock composition was metasediments, metagranitic rocks and granitic plutons. Principal mineralogical compositions were quartz, plagioclase and mica, which reportedly have similar average compressional wave velocities. Therefore although the geology

was complex, the seismic structure was simple. The average velocity-depth gradients for the investigated terrain were as shown in Figure 11.7. Here the field data is compared with relevant laboratory data. To conclude this introduction to crustal velocities we will return to greater depth, by first considering the velocity and seismic Q structure within and above descending crustal material, followed by a glimse of the deeper velocity and seismic Q trends. One of the most typical subduction zones in the world is the north-eastern Japan arc. The oceanic Pacific plate subducts downwards into the mantle at a convergence rate of about 10 cm/yr and at an angle of 30° and steeper at greater depth. Many shallow earthquakes occur beneath the Pacific ocean along the upper boundary of the Pacific plate. Intermediate-depth and deep earthquakes are generated within the subducted Pacific plate. Beneath Japan, shallow earthquakes also occur in the upper crust of the continental plate. Active volcanoes are distributed on the land area, parallel to the trench axis. A modern interpretation of this north-eastern Japan convergent margin is shown in Figure 11.8 from Hasagawa et al., 1994. In the base of the mantle wedge, low-velocity, low seismic Q zones are distributed in parallel to the dip of the high seismic velocity, high seismic Q subducting plate. Decompression melting within the ascending flow of hot mantle material from depth produces low seismic velocities and high seismic attenuations. The lower portion of the crust and mantle wedge are governed by creep or flow, and are weak and incapable of supporting high stress. According to the review by

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Figure 11.5 Refraction lines from Argentina and 1000 km eastwards into the Atlantic Ocean. From Ewing, 1965, reproduced in Bott, 1982.

Figure 11.6 Typical ray diagram (for shotpoint 52) for the East Central Alaska crust (Beaudoin et al., 1992a).

Hasagawa et al., 1994, horizontal compressive stress caused by the convergence between the subduction plate and the overlying continental plate is supported mostly by the upper 15 km of the crust. This is a strong seismic zone, resulting in shallow, thrust-fault earthquakes. Stress concentration will also arise beneath the volcanic regions where the seismogenic zone is locally thin. P-wave velocities plotted on a depth scale of 0 to 1200 km for the western USA, determined from spectral amplitudes of seismic body waves, given by Archambeau et al., 1969, appear to ‘start’ at about 6 km/s rapidly reaching about 8 km/s through the crust with intermittent increases to almost 12 km/s at 1200 km depth. Their studies also suggested a frequency-dependent value of seismic Q, with magnitude increasing with frequency. Seismic Q values inferred from the ‘anelastic dissipation’ of compressional body waves and surface waves are shown to increase from about 150 to 8000 between

the depths of 100 km and 1200 km. These extreme depth trends for Vp and Q p are shown in Figure 11.9. Strong variations in the upper 20 km of solid crust are suggested in this large-scale data, within the Q p range of about 130 to 1000. There is an inferred fall of Q p from about 1000 to 150 through the Moho, between depths of about 40 and 80 km, followed by a rapid increase of Q p to 200 km depth, and a slower increase of Q p values to about 8000 at 1200 km depth. 11.2

The continental velocity structures

A definitive, updated summary of the seismic velocity structure and composition of the earth’s continental crust has been provided by Christensen and Mooney, 1995, who gave a global review based on 560 determinations by

Velocity structure of the earth’s crust

245

Figure 11.7 Average Vp-depth data (stepped line) compared with temperature corrected laboratory data (curved lines). Beaudoin et al., 1992a.

Figure 11.8 Schematic cross-section of crust and upper mantle in the NE Japan convergent margin. Numerous open circles show focal mechanisms. Solid circles show low frequency micro-earthquakes in low velocity (and low seismic Q) zones beneath volcanoes. Hasagawa et al., 1994.

more than 100 investigators. The geographic locations are illustrated in Figure 11.10. The data reviewed and selected by these authors covers the years 1950 to 1993. In the refraction seismic methods applied, the apparent seismic velocities are directly measured, while the depths of the refracting horizons are calculated from the uppermost layer down to the deepest layer. The depth determinations generally have larger percent errors than the velocities.

Figure 11.9 a, b Ultra-deep Vp and Q p structure interpreted for western USA, by Archambeau et al., 1969.

The average crustal thickness, weighted to correctly represent the total global areas of each major crustal type is 41.1 km, while the thinnest is in Ethiopia (Afar Triangle: 16 km), and the thickest is in China (Tibetan Plateau: 72 km). The average compressional wave velocity is 6.45 km/s. By chance, this is close to the ‘focal point’ in Figure 5.36, satisfying the intact, massive rock quality Q-value  1000 ‘limit’ of 6.5 km/s, for an undefined, average mineralogy.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.10 Locations of 560 seismic velocity-depth measurements. Christensen and Mooney, 1995.

Average compressional wave velocities of common crustal rocks show excellent correlations with density. Based on tests of 3000 cores of igneous and metamorphic rocks, taken to 1 GPa confining pressure (similar to 35 km depth), Christensen and Mooney estimated a mean 2830 kg/m3 density for the continental crust. The seismic velocity data was considered to be accurate to 3%, or about 0.2 km/s, while the depths were considered to be accurate to 10%. Figures 11.11a, b and c show the very clear trends of crustal depth, average crustal velocity and upper mantle velocity (the normal P-wave termed Pn by tectonophysicists). These three worldwide compilations suggest a 10 to 20% thicker continental crust than previous estimates (due to under-representation of shields, platforms and orogens while the average velocities lie within previous Eurasian, North American and global estimates of 6.30 to 6.55 km/s (for Vp, continental crust) and 7.7 to 8.6 km/s (for Pn of uppermost mantle). Histograms of average velocities for 5, 10, 15, 20 and 25 km depths are reproduced from Christensen and Mooney, 1995, in Figure 11.12. Shallow crustal velocities of less than 5.0 km/s, corresponding to sedimentary rocks have not been included. (This applies to the upper 10 km.) The histograms at 5 and 10 km are sharply peaked at 6.0 to 6.2 km/s, typical of crystalline upper crust. Possibly a minimum of ‘effective’ jointing is found at these high pressures of 140 to 280 MPa. In other words in engineering terminology, we would be talking of a very massive

tight structure, probably with Q-values of rock mass quality (Barton et al., 1974; Barton, 2002) of 250–500, combined with the effect of exceptionally high confining stress. If sedimentary rocks were included, we would likely be operating with a rock mass quality Q c value (Q c  Q  c/100 plus porosity adjustment) less than the above, depending on the effects of c 100 MPa and porosity  5% on the seismic velocity (see Figures 5.36 and 5.37 in Chapter 5). In Table 11.2, mean velocities for five principal tectonic provinces as a function of depths of 5, 10, 15, 20 and 25 km are given. The uppermost (lowest Vp values) reflect a great range of lithologies, and presumably some residual (i.e. tightly closed) jointing. The velocity-depth gradients for these five tectonic provinces, and for an average continental crustal model, are compared in Figures 11.13a and b. The almost linear gradient between 5 and 25 km for the average crust displays a gradient of about 0.6/20  0.03 s1, while the gradient between 5 and 10 km for the five tectonic regions is approximately 0.5/5  0.1 s1. The reduced gradient at greater depth is due to the expansion effect caused by increased temperature. Based on a very extensive (3000 cores) laboratory study, stretching over some ten years, Christensen and Mooney, 1995, were able to distinguish anisotropic (mineral/fabric orientation related) velocities for a wide range of crustal rock types. The results for a confining pressure of 1 GPa (
35 km depth) are reproduced in Figure 11.14. However the authors pointed out that it

Velocity structure of the earth’s crust

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Figure 11.11 a) Histogram of crustal thickness, from 560 measurements. b) Histogram of average continental crust velocity (Vp). c) Histogram of uppermost mantle velocity beneath the continental crust (Pn). Christensen and Mooney, 1995.

was not possible to take into account the effects of larger scale anisotropy in their crustal averages, since the presence of crustal anisotropy had only recently been documented. They expected maximum anisotropy in upper crustal metamorphic rock with abundant phyllite and higher

Figure 11.12 Histograms of crustal velocity at 5 km depth intervals. Christensen and Mooney, 1995.

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Table 11.2

Velocities for five principal tectonic provinces. Christensen and Mooney, 1995.

Crustal property

Orogens

Shields and platforms

Continental Arcs

Rifts

Extended crust

Average crust

Vp at 5 km Vp at 10 km Vp at 15 km Vp at 20 km Vp at 25 km

5.69  0.67 6.06  0.39 6.22  0.32 6.38  0.34 5.53  0.39

5.68  0.81 6.10  0.40 6.32  0.26 6.38  0.26 6.53  0.27

5.80  0.34 6.17  0.34 6.38  0.33 6.55  0.28 6.65  0.28

5.64  0.64 6.05  0.18 6.29  0.19 6.51  0.23 6.72  0.35

5.59  0.88 6.02  0.45 6.31  0.32 6.53  0.34 6.69  0.30

5.95  0.73 6.21  0.27 6.31  0.27 6.47  0.28 6.64  0.29

Figure 11.13 a) Average velocity depth trends for five tectonic provinces, compared to b) the average crust. Christensen and Mooney, 1995.

Figure 11.14 Average anisotropies for laboratory samples at 1 GPa confinement. Christensen and Mooney, 1995. Phyllite, slate and schist dominate as expected, even at these high pressures.

grade slate, and in deeper crustal sections of amphibolite and mica schist. To this one could perhaps add the possibility of azimuthal velocity anisotropy, even at depth, resulting from regions of strong horizontal stress anisotropy, in e.g. thrust belts. In general, these results are based on rock cores taken in three mutually perpendicular directions. The authors’ reported that the change in anisotropy with depth was minimal for most of the rock types. Anisotropies reach 9.5%, 13.0% and 17.2% on average for the mica quartz schist, phyllite and slate respectively. Even at upper mantle depths, azimuthal-dependent Pn velocities are consistently shown, particularly along (and across) the axes of continental rift structures. When one considers the added effect of near-surface (upper 5 km) jointing that may be parallel or sub-parallel to dominant fabric, anisotropy will presumably tend to increase on average as the surface is approached. Average velocities at 20 km depth equivalent and at 309°C (using average heat flow assumptions) for each rock type are shown in Figure 11.15. The majority of rocks lie between velocities of 6.0 and 7.0 km/s. As has been noted, the effect on velocity of increased heating in a given laboratory test sample tends to counteract the effect of increased pressure due to thermal expansion effects. However a single rock type ‘taken from 5 km to 50 km’ does not show the average continental crust velocity-depth gradient, which is brought about by a combination of lithological changes, mineralogical changes and temperature-induced expansion. Within the mid-crustal depths of 10 to 25 km, where amphibolite facies rocks are likely to comprise the bulk of the crust, there is a gradual change in composition from granitic gneiss and tonalitic gneiss to mafic mineral assemblages rich in amphibolite. At greater depth, the garnet content increases. These gradual changes give the crust its composite average velocity-depth gradient, in relation to the single rock type, laboratory trends shown in Figure 11.16. The contrasting trends shown in Figure 11.16 are again from Christensen and Mooney, 1995, who must

Velocity structure of the earth’s crust

Figure 11.15 Average laboratory velocities for each rock type, at 20 km equivalent depth, and at a temperature of 309°C. Christensen and Mooney, 1995.

be commended for their extraordinarily far-reaching review, from which we have borrowed many figures in this chapter on crustal velocities. A new global model for the earth’s crust, based on seismic refraction data published in the period 1948–1995 was provided by Mooney et al., 1998. The model was based on 5°  5° tiles (that measure 550  550 km at the equator). In each tile, crustal properties were described by seven layers: 1) ice, 2) crater, 3) soft sediments, 4) hard sediments, 5) crystalline upper crust, 6) middle crust, 7) lower crust. The source location (mid-profile) of the numerous seismic refraction profiles for this monumental (2000 cases) study by Mooney et al., 1998 and others, are given in the world map in Figure 11.17. The triangles refer to the locations within continents, and on margins, where a velocity-depth function could be extracted from a published interpretation. The mid-point of a major profile corresponds to the triangle location. In about 10% of the cases the shear velocity-depth profile was also reported.

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There were 2592 tiles of 5°  5°, and more than 2000 available sets of field measurements of oceanic and continental crust. Primary continental and oceanic crustal types and mean Vp as a function of depth are shown in Figures 11.18a and b. Note the predominance of average velocities 6.0, 6.1 and 6.2 km/s for the upper crust (range 5.7 to 6.3 km/s) and mostly 6.6 km/s for middle crust (range 6.4 to 6.7 km/s). On continents, the P-wave velocity averages 2.0 to 3.0 km/s in unconsolidated soft sediments, and 4.0– 5.3 km/s in the consolidated (hard) layer. A comparison with a ‘site-specific’ (continental USA) vertical-section, from Kearey and Vine, 1996 is also shown in Figure 11.18c, for comparison with the continental ‘crustal types’ model in Figure 11.18a. One-dimensional crustal models of Vp, Vs and density to 40 km depth for the whole globe, continental crust and shelf, and the oceanic crust are given in Figure 11.19. Interesting insights into the local nature of crustal reflections, and of course excellent velocity-depth data from sonic logging and VSP have been obtained from the KTB deep drilling project in Germany, where results of 9.1 km of borehole logging and core analysis were available in Harjes et al., 1997. The thirteen authors of this paper related some interesting experiences about the nature of the strongest reflectors, which tended not to be lithological boundaries alone, but fluid-filled fractures and cataclastic fracture zones, sometimes associated with such boundaries. The most pronounced and discrete reflections were reportedly found in the compositionally homogeneous amphibolite unit, and originated from hydraulic fracture zones at 4.0 and 4.8 km. Other reflections correlated with fluid-filled fracture zones in gneiss-amphibolite contrasts, so uniqueness could not be determined. One may speculate that the hydraulic fracture zones had become propped in some way, perhaps due to sheared-dilated sections (non-parallel to maximum stress), as discussed by Barton, 1986, and extensively reviewed in Chapter 16. The predominantly gneiss and amphibolite sequences shown in Figure 11.20 showed lower Vp/Vs ratios in the gneiss than in the amphibolite (due mainly to quartz content differences). In general, decreases of the Vp/Vs ratios were caused by decrease of Vp rather than by an increase of Vs, which the authors liken to typical behaviour in fractured, or jointed, and porous rocks. The mean trends and individual results of sonic and VSP measurements down this unusually deep borehole, are shown to at least 8.5 km depth in Figure 11.20. The strong Vp (and Vs) velocity-depth gradient shows the

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.16 Average continental crustal velocities (shaded) compared to average laboratory velocities at simulated depths and temperatures. Christensen and Mooney, 1995.

classic knee-shape, with average Vp increasing from about 3 km/s close to the surface to about 5.3 km/s at 500 m depth and to about 5.7 km/s at 1000 m (based on mean VSP data). Comparison with the velocitydepth-Q (rock mass quality Q or Q c) curves shown in Figures 5.36 and 5.37, suggests that this upper 1 km of paragneisses (with some amphibolite) may have Q-values

(or Q c values) as low as 1, which signifies a good deal of jointing. The calliper log measurements also shown in Figure 11.20a indeed support the idea of borehole walls with a good deal of joint-related ‘overbreak’, which normally occurs when there are 2 or more joint sets (i.e. Jn probably in excess of 4 or 6 in the Q-system of rock mass quality description, combined with unfavourable

Velocity structure of the earth’s crust

251

Figure 11.17 Location map for the Mooney et al., 1998 global crustal model seismic refraction profiles. The triangles refer to the locations within continents, and on margins, where a velocity-depth function was extracted from a published interpretation. In about 10% of the cases the shear velocity-depth profile was also reported.

(a)

(b)

(c)

Figure 11.18 Vp-depth structures for primary crustal types. a) Continental. b) Oceanic. Mooney et al., 1998. c) Continental USA velocity-depth section. Kearey and Vine, 1996.

anisotropic stress and presumably water pressure see: Appendix A for Q-parameter ratings). Moving to an entirely different geology and location, and into an artificial ‘seismic’ environment, namely the

Nevada Test Site in the western USA, one may note that nuclear ‘events’ of 155 to 1300 kilotons equivalent yield were used for forward modelling of surface velocity data that was recorded within 15 km of the underground

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Rock quality, seismic velocity, attenuation and anisotropy

nuclear test explosions. Barker et al., 1991, used a plane-layered structural model of the porous, low-density volcanic sequences beneath the Pahute Mesa to derive the velocity-depth structures shown in Figure 11.21. These velocity structure models were needed to determine the effective source functions of the underground explosions. The upper part of these velocity-depth trends show broad similarity to the Vp-depth-Q c (normalised rock mass quality) trends shown in Figure 5.37. Clearly the porous, jointed volcanics are at the lower end of the Q c range, or alternatively represent a ‘porous version’ of the trends shown by Q c  1 to 10 in Figure 5.37. Before leaving continental velocity structure, we may look at two near-surface extremes, namely sea ice, or

Figure 11.19 Depth-velocity-density profiles from a crustal model CRUST 5.1. Mooney et al., 1998. The predominance of oceans causes the average and oceanic crust velocities to be low in the upper 3 km.

Figure 11.20 Borehole measurements and geological profile of the KTB super-deep well. Note (a) shows calliper log measurements and hole diameter. Note the ubiquitous nature of faulting at all depths. Harjes et al., 1997.

Velocity structure of the earth’s crust

glacial ice and beach sand. These occur just above sea level and they have two aspects in common. They each display high gradients of velocity, but from different starting points.

Figure 11.21 Velocity-density-depth trends for the Nevada Test Site Pahute Mesa. Barker et al., 1991.

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While thin, floating sea ice, typically 10 m thick constitutes an approximately constant velocity layer, an ice accumulation such as the Ross Ice Shelf, Antarctica of many hundreds of metres thickness, displays a sharply declining velocity gradient with depth. A multi-layered upper 50 to 100 m called firn is responsible for the steep velocity gradient. This includes snow cover which becomes firn after one melt season, and eventually becomes glacial ice when permeability to liquid water drops to zero with subsequent burial. Investigations using seismic reflection and seismic refraction profiles, reported by Beaudoin et al., 1992, were located on the 200 to 850 m thick Ross Ice Shelf as shown in Figure 11.22. The principal results of Vp versus depth are reproduced in Figure 11.23. Compressional wave velocities in the near-surface ranged from 500 m/s at the surface to 2000 m/s at 10 m depth, a gradient of 150 s1. From 10 m to 70 m depth, the velocity increased from approximately 2.0 to 3.8 km/s, which represents a gradient of 30 s1. In this region, metamorphism of the firn is governed by recrystallisation. Below about 70 m, any further compaction of the ice is by deformation of existing air pockets, with little effect on velocity (though possibly giving an orthotropic distribution). Of the four compression wave

Figure 11.22 Location of Ross Ice Shelf seismic reflection and refraction profiles. Beaudoin et al., 1992b.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.23 a) Cross-section of ice and water. b) Near-surface Vp-depth gradient caused by firn c) Overall Vp-depth profile, and chosen models 1 to 4. Beaudoin et al., 1992b.

velocity models shown in Figure 11.23c, No. 1 was consistent with the observed data. Below the ice, 570 m of water with a velocity of 1.44 km/s reached down to subsea sediments with a velocity of 2.7 km/s. Conducting the shallowest possible high-resolution seismic reflection and refraction experiment in the upper 2 m of a sea-beach sand, Bachrach and Nur, 1998, measured a minimum P-wave velocity of 0.04 km/s. They used only a 0.1 m distance between the shot and receiver. They calculated a theoretical minimum possible value of 0.013 km/s, considering the top few centimetres of dry sand as a suspension of sand in air. The effective elastic modulus (Meff) and the velocity of the air-quartz mixture were calculated from the following equations:  1 1    Meff Mair Mquartz

(11.1)

4 M  K    G  3 

(11.2)

eff  (1  )q    air

(11.3)

Vp 

Meff eff

(11.4)

The following parameters were used: bulk modulus Kquartz  36.6 GPa, shear modulus Gquartz  45 GPa,

q  quartz density, air  air density,  is the porosity of the mixture, assumed at the critical value of 40%. Their estimates of theoretical velocity, and their low measured values give velocities that are actually much lower than the velocity of sound in air. 11.3

The continental margin velocity structures

Velocities at continental margins, such as that obtained in the Atlantic margin seismic experiment described by Holbrook et al., 1994, naturally show some of the highest lateral variations of velocity, plus the familiar Vp  6.5 km/s to 10 or even 20 km depth beneath the continental material. Figures 11.24 a and b show velocities and geological interpretation side by side, for a 240 km section off the East coast of the US. Short black and white lines are reflectors. The multi-channel data was acquired using a 177 litre airgun array and 6 km long streamer, and coincident wideangle data from ten ocean bottom seismic instruments. These seismic results along the US East Coast continental margin show the presence of a huge, high velocity (7.2–7.3 km/s) igneous body of as much as 2.7  106 km3 in volume. This East Coast Margin Igneous Province (ECMIP) probably extends seaward, making it one of the worlds really large igneous provinces. The high velocity (in relation to thickness) is nicely demonstrated in the two further versions of the velocity-depth-distance sections, from Kelemen and Holbrook, 1995, shown in Figure 11.25.

Velocity structure of the earth’s crust

255

Figure 11.24 US East Coast continental margin velocities (a), densities in kg/m3 (b), and geology (c). Holbrook et al., 1994. Note that black and white lines are reflectors.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.25 Location and velocity-depth trends of two sections (BA-6, and EDGE-801) through the US East Coast margin, showing the velocity-thickness anomaly. Kelemen and Holbrook, 1995.

11.3.1

Explaining a velocity anomaly

In an effort to understand the likely composition of the rock in this huge magnetic and seismic velocity anomaly, Kelemen and Holbrook, 1995, assembled numerous high pressure laboratory Vp data to try to differentiate the 25 km thick high velocity crust from the general 8 km thick (Vp  6.9 km/s) sub-ocean crust. Figure 11.26a shows a multiple linear regression fit to 188 garnet-free, igneous and metamorphic rocks. Measured Vp at 25°C and confining pressures from 0.6 to 1.0 GPa, are compared with the bulk composition by weight of SiO2 or MgO in the samples. The empirical relation obtained was: Vp  8.054  0.024 (%SiO2)  0.029 (%MgO) (11.5) (where Vp is km/s).

This equation was subsequently corrected to lowercrustal temperatures (
400°C) using an assumed dVp/dT gradient of () 0.0005 km/s/°C, by subtracting 0.2 km/s. Figure 11.26b shows calculated Vp for rocks crystallised from mantle melts as a function of the pressure of partial melting in the mantle. This was estimated by Kelemen and Holbrook, 1995, using their relation: Vp  6.712  0.16 Pmelting(GPa)  0.661 Fmelting (11.6) where Vp  km/s and Fmelting is the melt fraction of the parental melt, using reported SiO2 and MgO contents, and the temperature corrected (0.2 km/s) version of equation (11.5). According to Kelemen and Holbrook, 1995, the goodness of fit of equation 11.6 did not substantially improve when other oxides like FeO, CaO, Al2O3, Na2O etc. were entered, because these compositional

Velocity structure of the earth’s crust

Figure 11.26 a) Vp and mineral composition for 188 igneous and metamorphic rocks at confining pressures of 0.6 to 1.0 GPa. b) Empirical calculation of Vp versus pressure of partial melting. Kelemen and Holbrook, 1995.

variables were closely correlated with SiO2 and MgO in the experimental set of data shown in Figure 11.26a. According to their analyses, the high velocity body could have been produced from partial melting of mantle peridotite, using lower estimates of melt fractions (10%) but higher average pressures (2.0 GPa) than that producing normal mid-ocean ridge basalt. They surmised active upwelling of the asthenosphere at faster

257

rates than lithospheric spreading rates, to produce the necessary high pressure conditions. Gravity anomalies at the surface may be an expression of non-hydrostatic stresses at depth, implying that significant deviatoric stresses may exist. In the case of the Hawaiian Islands, gravity anomalies associated with flexure of the crust on either side of the Hawaiian ridge are associated with average velocity reductions in Layer 2 of some 0.8 to 0.9 km/s within the flexural arch, some 155 km from the ridge (Brocher and ten Brink, 1987). Elastic and elasto-plastic flexural models for the region give predicted stress drops of 80 MPa in the upper lithosphere. These authors compare this with a similar confining pressure drop necessary to reduce velocities in porous basalts by 0.5 km/s in the laboratory. The lateral velocity variations to the north and south of the Hawaiian ridge, produced partly as a result of this flexure, are shown in Figure 11.27. The models go from ocean floor to the bottom of Layer 2. We shall see many more models of oceanic velocities in the next section of this chapter. Tomography was used by Hole et al., 2000, to invert earthquake and air gun travel time data in the San Francisco Bay area, to obtain 3D seismic velocity and earthquake hypocentres. Most hypocentres were relocated up to 2 km from their catalogue locations, and the 3D approach was also important for mapping lateral velocity contrasts (subvertically through most of the crust) where major strike-slip faults were present. These lateral velocity variations correlated well with known surface geology differences. Strong velocity contrasts of 0.3 to 0.6 km/s were observed in the middle crust when crossing the San Andreas fault. Weaker contrast (0.1 to 0.3 km/s) existed at other depths, and across two other faults. The relocated seismicity hypocentres on the active strike-slip faults defined steeply dipping planes beneath the surface expression of each fault. Figure 11.28 compares a Hole et al., 2000, 3D based velocity tomogram with a 2D refraction model of Holbrook et al., 1996. Throughout the Hole et al., 2000, San Francisco Bay study area, no earthquake was found to occur in regions with Vp  6.3 km/s, and usually the various inversion tests produced a maximum velocity of 6.2 km/s. They surmised that the base of seismicity may be thermally controlled by a deeper brittle-ductile transition in the relevant Franciscan rocks. A simpler, shallow depth Q-M-Vp model argument (Barton, 1995, 2002) might be that fracturing, that has to be present, has kept Vp

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.27 Velocity-depth solutions from N and S of the Hawaiian ridge. Brocher and ten Brink, 1987.

below the 6.5 km/s ‘limit’ for intact, strong, highly stressed rock masses. However there is of course a need to extrapolate the Q-M-Vp model to greater depths to be related even to shallow earthquakes. The amount of detail in depth-velocity structures for onshore and offshore southern California (adjacent to the Pacific and North America plate boundary) was recently increased with new 3D Vp and Vp/Vs models using P and S-P travel times from local earthquakes and from controlled sources (Hauksson, 2000). A 15 km horizontal grid-spacing, and an average vertical grid spacing of 4 km, down to 22 km gave new insight into the heterogeneity of crustal structure in this earthquakeprone region. The near-surface increase in P-wave velocity, from the surface to 8 km depth was found to be rapid and had a logarithmic shape for stable blocks, but was slower and had a more linear slope for sedimentary basins (Figures 11.29a, b, c). Ratios of Vp/Vs varied widely in the upper 5 km and often fell outside the typical ratio of 1.7 to 1.8 generally seen at lesser depths. Values as high as 1.9 to 2.0 were seen in sedimentary basins and in locations below an offshore channel (Santa Barbara). High Vp/Vs ratios may be related to the high fluid content of near-surface

cracks and joints, in other words, the joint sets that still remain partly open. The author was able to recalculate the hypocentres of recent earthquakes using the improved three-dimensional velocity models, which clearly differentiated the sedimentary basins from the nearby mountains. Hauksson also compared his 3D Vp-depth profiles (using double standard deviations) with laboratory Vp measurements of triaxially loaded samples from McCaffree et al., 1998. It is of interest to note the ‘reluctance’ of the in situ data in Figure 11.31 to exceed Vp  6.5 km/s – which in the Vp-Q-M model of Barton, 1995, is the supposed limit for completely unjointed rock masses, or rock masses with neither primary or secondary porosity and ‘normal’ composition (i.e. granites, gneisses etc.). Presumably the stress levels at 5 or more kilometres depth are sufficient to completely close (in a joint-normal direction) the apertures of any joints, since stresses of the order of 130 MPa and more are close to the expected JCS values of joint walls in the schists, intrusives and gneisses. (JCS  joint wall compressive strength, Barton and Choubey, 1977.) On the other hand with shearing deformation along the joints, apertures and permeability

Velocity structure of the earth’s crust

259

Figure 11.28 Comparison of a) 2D and b) 3D velocity tomograms for San Francisco Bay area crust. c) Range of velocity-depth models providing solutions to the inverted travel times. Hole et al., 2000.

could remain of finite magnitude at these (and greater) depths, as suggested by the work of Zoback and colleagues, reviewed in Chapter 16. The 3D velocity data shows mean values of 5.4 and 5.7 km/s at one kilometre depth. In the Q-M-Vp model, (see Figures 5.36 and 5.37), a significant amount of jointing and/or alteration along the joints would be suggested, with a Qc (rock quality) value on either side

of 1, if we make no allowance for porosity n  1% or c  100 MPa, or  100 MPa. The relatively low velocities of some of the laboratory samples of schist and intrusives (as low as 4.5 to 5.0 km/s at 1 km depth equivalent) does suggest that n% and c adjustments would be needed to fine-tune Qc rock quality estimates. There are other important details regarding the velocity model for the San Gabriel ranges discussed above

260

Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.29 Velocity-depth data for a) stable blocks, b) sedimentary basins and c) offshore regions off southern California. Hauksson, 2000.

Figure 11.30 Vp/Vs ratio trends for a) stable blocks, b) sedimentary basins, and c) offshore regions of southern California. Hauksson, 2000.

Velocity structure of the earth’s crust

11.4

Figure 11.31 Comparison of velocity-depth trends for two onshore regions of southern California (solid lines: ‘3D’) with laboratory tests (all dotted lines). Hauksson, 2000 and McCaffree et al., 1998.

(Figure 11.31b). Hauksson, 2000, warns that for shallow earthquakes, the seismic waves from the hypocentres to the recording stations are travelling through the schist with subhorizontal ray paths, while rays from deep earthquakes may have steep angles of incidence. Thus in both the Mojave (Figure 11.31a) and San Gabriel (Figure 11.31b) terrains, the rays from the hypocentres will sample the average velocity of the schist, because, in relation to the foliation dip angles (45° to 90° for the Pelona schist) the rays have all possible azimuths and a large range of take-off angles.

261

The mid-Atlantic ridge velocity structures

The object of systematic geophysical inversion techniques is to derive structures which fit a given set of observations. For many years, sub-oceanic marine seismic refraction profiles were interpreted as a small number of layers separated by planar interfaces, with a constant velocity assumption for each layer. A major advantage of layer solutions was that they could be developed using a desk calculator. As equipment (e.g. sonobuoys and repetitive sources such as airguns) and computing capacity improved, homogeneous layering assumptions from the 1960s, e.g. Ewing, 1963, were first replaced by much finer layering and then in the mid-1970s by continuous gradients in velocity (e.g. Kennett and Orcutt, 1976). These authors showed that the seismic data do not require uniform layering as a solution, but they did not exclude the possibility of homogeneous layering. A typical set of their solutions, with bounds compared with the layered solution is shown in Figures 11.32a, b. The first geophysical downhole logging data for oceanic crustal material is reportedly that of Kilpatrick, 1979. He found that the predictions of low velocities from refraction seismic were borne out by downhole sonic logging. In situ sonic velocities were typically from 1.5 to 4.8 km/s in the upper 200 m of oceanic Layer 2A. Calculated porosities of 13 to 41% were unexpectedly high. Formation damage away from the drilled holes was considered to be minor, as electrical resistivity away from the hole showed a lack of radial variation. The measurements were made in hole 396B (leg 46) of the Deep Sea Drilling Project, near the mid-Atlantic ridge. The reasons for the high porosities were interpreted as being due to a combination of sediments, rubble, and solid basalt in contrast to the compact nature of basalt samples used in laboratory tests, which often has Vp between 5.5 and 6 km/s and porosities from only about 2 to 8%. Open fractures and voids were assumed to exist on a scale larger than the laboratory samples, giving high permeability throughout the drilled section. A decade of Lamont-Doherty Geological Observatory sonobuoy data led Houtz and Ewing, 1976, to conclude that the P-wave velocity of the sub-ocean crust at and near ridge crests actually exhibited an increase in velocity with age. Numerous results from the Atlantic and Pacific shown in Figure 11.33 showed an obvious link between Vp and age, up to some 40 million years. Deeper and older layers did not show systematic increase in velocity.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.33 Measured velocities as a function of age for Atlantic and Pacific sites. Houtz and Ewing, 1976.

Figure 11.32 a) Velocity-depth bounds from inverted marine refraction profiles, compared to Layer 2 and 3 constant Vp models. b) Mean value and error bars for same profile CH-10A. c) Resolving kernels for CH10A. Kennett and Orcutt, 1976.

The rocks concerned were generally pillow basalts or vesicular, and could be weathered or massive and fresh. The authors argued that it was difficult to envisage any diagenetic change with the relatively low (effective) overburden pressures, so filling of voids and cracks (and presumably joint sets) with products of hydrothermal mineralization must presumably be one of the mechanisms involved in the increasing velocity with age. Different calculated porosities for 4 m.y. and 62 m.y. crust as a function of depth, given by Whitmarsh, 1978, and reproduced in Figure 11.34, suggested zero porosity beneath 1.5 km of Layer 2A oceanic crust. The two rectangles, the asterisk and the three dots were from limited borehole data available at that time. Filling of cracks by hydrothermal minerals with increasing age was cited as the likely mechanism. The early (and continued) difficulty of obtaining samples of oceanic crust to several kilometres depth, led Salisbury and Christensen, 1978, to ‘reconstruct’ the intact rock Vp, Vs and dynamic Poisson’s ratio structure, along a traverse through an on-land (Bay of Islands, Newfoundland) ophiolite complex. The Vp and Vs data shown in Figures 11.35 and 11.36 were derived from hydrostatically confined and water saturated intact samples. They suggested that the velocity structure should be indistinguishable from normal oceanic crust, but with the notable difference that the structure (voids, joints, fractures etc.) were not of course sampled. The velocities, especially in the upper 1 km, therefore represented maxima. The authors showed from earlier studies (Christensen and Salisbury, 1972), the strong link between velocity and density for oceanic crust basalts. At high porosity, with a density of only 2.5 g/cm3, Vp tended to be only about 4.5 km/s, and from then on showed a linear increase to about 6.5 km/s by the time the density had reached 3.0 gm/cm3. Clearly, seismic velocity and density are mutually dependent properties of a rock, and each are strongly

Velocity structure of the earth’s crust

263

While density is a bulk property independent of direction, seismic velocities can be anisotropic due to the effects of microcrack alignment (e.g. in recovered, stress relieved samples) or due to fabric anisotropy. We may consider that density is related to the ‘hard porosity’ of the rock, while ‘soft porosity’ in the form of jointing (i.e. the rock quality Q-value) gives higher or lower velocities depending on great depth or shallow depth respectively.

11.4.1

Figure 11.34 Estimates of porosity-depth relations for different ages of oceanic crust (basalt) given by Whitmarsh, 1978.

linked to porosity, uniaxial compressive strength and Young’s modulus. A major collection of density-Vp measurements for a wide range of sedimentary, metamorphic and igneous rocks is shown in Figure 11.37, from Ludwig et al., 1970, and P.J. Barton, 1986. The studies with oceanic crust basalts cited above (Vp  4.5 km/s with   2.5 gm/cm3, Vp  6.5 km/s with   3.0 gm/cm3) clearly fit this huge data set. The thin line in the centre of the scatter in Figure 11.37 is the mean velocity-density relationship, while the heavy boundaries contain the great majority of data. At any given value, a density variation of about 0.2 to 0.3 gm/cm3 and a velocity variation of 0.5 to 1.0 km/s are seen. The thick vertical bar, corresponding to a density of 2.8 gm/cm3 is typical for crystalline continental crust, with Vp
5.7 to 7.0 km/s. Closed circles represent sedimentary rocks and open circles represent metamorphic and igneous rocks, relevant in these oceanic crust studies.

A possible effective stress discrepancy in early testing

Extensive laboratory testing of oceanic basement rocks from deep drilling in the mid-Atlantic ridge by Hyndman and Drury, 1976, highlighted the discrepancy between laboratory seismic properties and in situ, bulk velocities obtained from seismic refraction. One of the problems was obviously sampling bias, and the other may have been the early tendency to test at much too high effective stresses. The ‘intact’ basalt cores contain only disconnected vesicules and were earlier assumed to be under a high effective stress due to both sea load and crustal load. The actual effective stress acting on deep-ocean shallow crust, is most likely to be relatively low, due to a highly permeable assemblage of basalt, sediment layers and joints/fractures and larger voids. The typical samples for laboratory tests were minicores of 2.5 cm diameter drilled transversely to the recovered pieces of 6 cm diameter vertical core. The drillers operating onboard the Glomar Challenger drilling ship generally recovered only 20% of the sections drilled in mid-ocean upper-crustal rocks, so there was a further source of sampling bias. Due to the controversial opinion of appropriate stress levels for testing laboratory samples, discussed above, confining pressures of 17 MPa and even up to 207 MPa were used by Hyndman and Drury, 1976, for on-board velocity measurements. A thin metal sheet jacketed the sample so the confining pressure was ‘close to the external pressure, and the internal pore pressure was small.’ Results of these high pressure velocity-density studies are reproduced in Figure 11.38. Hyndman and Drury, 1976, found that the vesicular porosity of their relatively fresh, young basalts, caused Poisson’s ratio to increase with increased velocity (i.e. from 0.28 at Vp  5.8 km/s, to about 0.3 at Vp  6.4 km/s, due to the vesicules affecting Vp more than

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Figure 11.35 Vp and Vs data from hydrostatically confined laboratory samples, plotted as a function of depth in the Blow-Me-Down massif of the Bay of Islands ophiolite complex Newfoundland. Salisbury and Christensen, 1978.

Figure 11.36 Smoothed envelopes of the same Vp and Vs test data, plus density and dynamic Poisson’s ratio, for the ophiolite Blow-Me-Down massif samples. Salisbury and Christensen, 1978.

Vs. In contrast, Christensen and Salisbury, 1972, testing older and shallower depth basalts found Poison’s ratio reducing with increased velocity, due to the greater effect of grain boundary weathering on Vs than Vp. The large scale joints, fractures and voids in situ are also likely to

cause increased Poisson’s ratio with reducing velocities, in contrast to the decrease caused by equi-dimensional (vesicular) pore spaces. Even in 100-m.y.-old sea floor the reduction in velocity caused by weathering appeared to only extend to

Velocity structure of the earth’s crust

265

Figure 11.38 Vp-Vs-density data from high pressure triaxial tests of three rock types. Hyndman and Drury, 1976.

Figure 11.37 An extensive set of laboratory P-wave and density data for sedimentary (closed circles), metamorphic and igneous rocks (open circles). Ludwig et al., 1970, and P.J. Barton, 1986.

about 50 m depth. The mean laboratory velocity for basalts younger than 20 m.y. and generally from deeper than 50 m, appeared to be frequently in the range 5.9 to 6.0 km/s. Hyndman and Drury, 1976 showed laboratory velocities (of about 5.5 to 6.5 km/s) obtained with 50 MPa confining pressure, next to the refraction-seismic inferred velocity depth profiles. However, laboratory data for samples recovered from about 3 m to 60 m depth, given by Hyndman, 1979, gave velocities from as low as 4 km/s to 5.2 km/s just below the ocean floor, up to 5.4–6.5 km/s at 60 m depth. These were also presumably tested at excessively high confining stress levels. The 2.5 to 3.5 km/s in situ velocities were showing an apparent discrepancy of about 3 km/s relative to the intact rock, but in fact some of this difference was presumably due to the excessively high confining pressures applied to the intact samples. It is clear that most of the velocity discrepancy was due to the dominance of larger voids and fractures, and the effect these had on the effective stresses. In a bulk sense,

the effective stresses are much lower than those assumed or actually acting on the intact, but vesicular basalt. Presumably the vesicules may originally be gas-filled at a pressure at least as high as the surrounding water pressure into which they were injected. Whether the matrix porosity is too low to allow either inward saturation with water (while under the ocean) or escape of some of the excess gas pressure (when brought to atmospheric pressure) is perhaps still a point of controversy.

11.4.2

Smoother depth velocity models

A new picture of the seismic structure of the oceanic crust began to emerge at the beginning of the 1980s, with the work of Spudich and Orcutt, 1980a. It was found that velocity models in which velocity varied smoothly with depth generally explained wave amplitude variations better than the earlier ‘thick, homogeneously layered’ models. Some indications of this were apparent some 10 years earlier, but in this compilation, Spudich and Orcutt, 1980a included many sites to confirm the new trends. The three homogeneous layers 2A, 2B and 2C suggested by Houtz and Ewing, 1976, were now considered too simplified, as finer structure, with significant lateral variations, showed a mix of velocity gradients, but generally within the range 1 to 2 s1.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.39a shows selections of the velocity depth models assembled by Spudich and Orcutt, 1980a. The upper diagram is for ten ridge or near-ridge sites, which contrast significantly (at shallow depth) with the higher velocities of the six older than 20 m.y. sites shown in Figure 11.39b. Spudich and Orcutt discussed possible reasons for the quite steep velocity gradients (approximately 1 to 2 s1) of oceanic ‘layer 2’ as being caused by finer structure, which was highly variable laterally (i.e. it varied with increased or decreased age). However the finer structure was difficult to resolve with the currently existing resolution of explosion seismology. Drilling of the shallow crust from submersibles, that had begun in the 1970s, had shown that the shallow crust was permeated with numerous sediment and/or water filled fissures, i.e. voids larger than laboratory sampling scale. Spudich and Orcutt, 1980a argued that if ‘layer 2’ were, on average, composed of the Mid-Atlantic Ridge basalt identified by Hyndman and Drury, 1976: Vp  5.94 km/s Vs  3.26 km/s   2,80 Mg/m3 n  7.8% then the addition of another 10% of porosity in the form of larger water-filled cracks or fissures, could give a Vp range from 5.5 to 2.6 km/s using current crack and spherical pore models. This range could encompass nearly the entire range of layer 2A and 2B velocities observed by Houtz and Ewing, 1976. The aspect ratio of cracks and fissures, whether they were water filled or sediment filled, and whether they could close in response to increased effective stress was, naturally, the subject of much discussion. It was also assumed by now that alteration of the older basalt could have resulted in progressive infilling and cementation of the cracks, thus explaining the increased velocities with age. 11.4.3 Figure 11.39 a) Mid-ocean ridge and near-ridge (i.e. younger) Vp-depth profiles derived by synthetic seismogram modelling. b) Vp-depth profiles derived from sites older than 20 m.y. Spudich and Orcutt, 1980a. For references to each profile, see their paper.

Recognition of lower effective stress levels beneath the oceans

On the subject of effective stresses in the uppermost permeable sub-ocean crust, Todd and Simmons, 1972,

Velocity structure of the earth’s crust

267

Table 11.3 Interpretation of upper ocean crust P-wave velocities east of Guadalupe Island. Profile FFZ of Spudich and Orcutt, 1980b. See Figure 11.40. Layer

Depth of crust (km)

Vp km/s

 (Mg/m3)

3 4 5 6 7 8 9 10 11 12 13 14

0.40 0.43 0.60 0.63 0.79 0.85 1.14 1.22 1.40 1.47 1.72 1.90

4.6 5.0 5.0 5.75 5.75 6.20 6.20 6.20 6.30 6.30 6.42 6.90

1.99 2.15 2.15 2.43 2.43 2.60 2.60 2.60 2.64 2.64 2.68 2.86

and Spudich and Orcutt, 1980b, seem to have been among the first to argue that it must have been the rapidly increasing effective stresses that were acting on the shallow sub-ocean crust that was causing the velocity increase. In other words, with Po as the water pressure at the ocean floor (often 3 or 4 km depth of water), the pore pressure Pp acting at depth z into the ocean crust will be: Pp  Po  w g z

(11.7)

while Pe the external stress at the same depth in the crust will be: Pe  Po  r  g z

(11.8)

Therefore the effective stress Pp  Pe will be given by: Pe  Pp  (r  w)g z

(11.9)

This obvious cause of an effective stress gradient in the crust was cited by these authors as a reason for measuring velocities in laboratory tests down to zero effective stress, rather than the practice (at that time) of measuring velocity at elevated triaxial stress states with zero pore pressure. Based on an interpretation of the sharp velocity gradients shown in Table 11.3, (where a water depth of 3.4 km has been subtracted) and based on Figure 11.40, Spudich and Orcutt, 1980b, argued that a vesicular (‘spherical’) porosity of 18% would match velocities in the top 200 m of the basalt crust (i.e. 4.6 km/s) and that reductions of porosity to 2% could explain the increased velocity down

Figure 11.40 Best fitting Vp and Vs for profile FF2, described by Spudich and Orcutt, 1980b.

to 0.6 km/depth (i.e. 5.75 km/s). While discussing the likelihood of fractures and voids as well as matrix porosity, they focused more on matrix-type porosity changes than on effective stress-induced closure of joints or fractures. 11.4.4

Direct observation of subocean floor velocities

Three new experiments carried out on the Mid-Atlantic Ridge (MAR), near latitude 23°N, were described by Purdy, 1987. The uppermost few hundred metres of the oceanic crust were tested using a fixed ocean floor hydrophone receiver, and a controllable explosive source that was towed within a few tens of metres of the rugged bottom topography. These 1 to 2 km refraction lines produced direct observation of the Vp structure of the upper 200 to 300 m of the young igneous crust. One of the experiments was carried out over the site of Hole 648B of the Ocean Drilling Programme on a small volcano within the median valley of the MAR. This was close to a ‘zero age’ location, the two others were 14 km apart, above 7 m.y. old crust. The latter gave higher layer 2A velocities than the ‘zero age’ location. The sea floor velocity at ‘zero age’ was observed to be 2.1 km/s, overlying an initial 4 s1, roughly 200 m deep, linear velocity-depth gradient. The crust at this location consisted of fresh basalt lavas, with laboratory measured velocities in excess of 5.8 km/s (However these tests, carried out as early as 1978, were conducted at a confining

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pressure as high as 50 MPa. Later tests in 1984 were also at high 40 MPa confining pressures, suggesting about 6.0 km/s for the intact basalt, if ‘artificially’ confined at too high pressure). On the basis of the above in situ/laboratory comparison, Purdy, 1987, suggested that the 3.7 to 3.9 km/s difference in velocities must be due to the presence of large-scale porosity, and various models were discussed. It was inferred that from 30 to 50% porosity might be needed using conventional arguments about pore shape of that period. However, Purdy also referred to the Todd and Simmons, 1972, and Spudich and Orcutt, 1980b emphasis of the actual importance of effective stress (subtraction of pore pressure from total stress), which had been used for a long time in soil mechanics, following Terzaghi’s theory of effective stress developed earlier in the 20th century. Naturally, with exceptional water pressures of around 30 to 40 MPa, it is understandable that the theory of effective stress was apparently late in being adopted in this hostile sub-ocean environment. Purdy considered the possibility (‘an elegant solution’) that increasing differential [sic] (effective) stress could be responsible for the 4 s1 velocity-depth gradient, and presumed a 4 to 5% per 100 m porosity reduction, as seen in the first 200 to 300 m of sub-sea layer 2A. In fact experience from engineering (e.g. tunnelling) projects close to the surface, does suggest very high velocity gradients when rock quality Q and Q c values (Barton, 1995; 2002) are a) low and b) are rapidly increasing with depth, such as Q  0.1 followed by Q  1 and very quickly Q  10 etc. i.e. nominal near-surface ‘jumps’ in Vp from 2.5 to 3.5 to 4.5 km/s with a superimposed stress increase effect on Vp as well. (See later comments on the question of gradients of velocity, and ‘curve jumping’, i.e. increases of rock quality Q-values with depth.) The reality below the near-surface zone is that both effective stress increases and clay gets compacted, and there is less clay as depth increases. Therefore one progresses rapidly from low rock quality Q or Q c to higher Q or Q c values quite quickly, with obvious consequences for increased Vp. The differences between in situ velocity measurement in the shallow oceanic crust and the higher matrix velocities measured at suitable (low) effective stress levels, is obviously caused not only by moderate changes to the matrix porosity but by stress-sensitive (low aspect ratio) jointing and fracturing. White and Whitmarsh, 1984, found that sub-vertical, water-saturated conjugate joint

sets at 30° to 60° to the ridge axis of mid-Atlantic Ridge oceanic crust could explain their observed horizontal (azimuthal) velocity anisotropy of up to 0.4 km/s. There was apparently a negligible seismic influence of pervasive ridge-parallel fractures on this anisotropy, which the authors explained by their infilling by sediment, or hydrothermal precipitation, or by their closure under the high ridge-normal principal horizontal stresses. In the case of this mid-Atlantic crust of 1.1 to 3.4 m.y., White and Whitmarsh reported that the top of the basement had a velocity of approximately 3.7 km/s which increased on average at 1.0 to 1.2 s1 in the uppermost 2.5 km, giving 6.0 km/s at about 2 km depth. The uppermost 200–300 m showed higher gradients than this. In relation to the Vp-Q-porosity-depth model (Figure 5.36 in Part I), such velocities would suggest Q-values of about 4 to 6 if the matrix porosity was about 5 to 10%. If we assume a mean ‘uniaxial’ compressive strength c of about 200 MPa, then a Q-value of about 2 to 3 is suggested, i.e. significantly jointed, perhaps with the following general character (see Appendix A): Q


50 2 0.66  
3 12 4 0.5

(11.10)

At 1000 m depth a velocity of the order of 5.5 to 6.0 km/s would be predicted, if the rock at this depth had unchanged character. Christensen, 1984, investigated pore pressure effects on basalts and dolerites and verified the strong effect of pore pressure variation on the velocities and on dynamic Poisson’s ratios. The latter increased significantly as a result of increased pore pressure. He discussed the possibilities of over-pressured zones due to seals caused by rapid accumulation of low permeability clays and shales, and also theorised that release of water accompanying low grade metamorphic reactions in basalts could result in excess pore pressure and resulting changes (reductions) in seismic velocities, and increases in Poisson’s ratios. The authors noted that the pore pressure coefficient was less than 1, and was not a constant for a given sample but depended on confining pressure and on pore pressure.

11.4.5

Sub-ocean floor attenuation measurements

Reportedly the first direct measurements of Upper Oceanic Crust compressional wave attenuation were

Velocity structure of the earth’s crust

269

Figure 11.41 Selected sub-ocean Qp profiles given by Jacobsen and Lewis, 1990. Variable attenuation, shows only partial consistency of increasing Qp with depth.

described by Jacobsen and Lewis, 1990, using seafloor hydrophones and large (56 to 116 kg) explosive sources. The site was on 0.4 m.y. old crust, 13 km SE of the Juan de Fuca Ridge. At the same site a seafloor velocity of 2.7 km/s increased uniformly to 5.6 km/s at 679 m depth, with gradients as high as 4.6 s1 at the surface and 4.1 s1 at depth. Values of seismic Q p obtained by Jacobsen and Lewis, 1990, varied from 4 to 275, but mostly clustered between about 10 and 20 in the upper 100 m, which was significantly lower than earlier estimates based on synthetic seismograms. They did not find a consistent increase of Q p with depth, but several sets of data for 1/Q p did show such a trend of 1/Q p reducing with depth. (Figure 11.41) The variations presumably might be connected with variable degrees of fracturing or cooling joints, and partial closure with effective stress increases. Their results showed that Q p was linearly related to frequency between 15 and 140 Hz, but frequency-independent components of attenuation were also evident. Pujol and Smithson, 1991, who analysed seismic wave attenuation from VSP measurements in the Columbia Plateau basalts, found values of Q p of about 50 (with Vp  5.0 km/s) that were close to the value of Q p of 40 found in Eastern North Sea basalt by Rutledge and Winkler, 1987. As has been argued in Chapter 10, there

is an implicit relation between seismic Q and the rock mass quality Q-based deformation modulus Emass, or M, when this is expressed in GPa. The above Vp of 5 km/s suggests a near-surface Q rock  32. Shallow, sub-ocean seismic Q of 10 to 20 might imply a significant degree of ‘structure’, if equivalent Q rock values were, say less than 5. Elsewhere, shallow ocean crust basalts have shown Q p values of between 20 and 50. Dry samples of oceanic basalts from layer 2, tested at (artificially elevated) confining pressures of between 40 and 100 MPa have given Q p in the range 5 to 85. Differences are attributed to crack content, degree of alteration and matrix porosity. These values are lower than the Q p values normally obtained for sound basalts, where values of between 100 and 600 can often be obtained (Wepfer and Christensen, 1990). Wepfer and Christensen, 1987, reporting the first laboratory measurements of Q p for dry and watersaturated oceanic basalts under appropriate pressure and temperature conditions, showed Q p varying from 8 to 100 at ultrasonic frequencies. The range was dependent on the state of alteration and porosity. The sudden steps up, and down from, very high in situ Q p values like 200–300, even negative 1/Qp steps, leads one to question whether the early ship-board triaxial test routines had an element of (local) correctness, meaning that some volumes of intact basalt can

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perhaps be subject to high 30 MPa plus-rock-depth confinement loads, interspersed by a majority of permeable and low effective-stress-loaded permeable blocks.

11.4.6

A question of porosities, aspect ratios and sealing

Shaw, 1994, using Kuster and Toksöz, 1974 theory, postulated that thin cracks preferentially close at shallow depth while lower aspect-ratio cracks do not. However, all crack populations were assumed to decrease with depth. It was pointed out that even 0.1% porosity in the

form of thin (  0.001) cracks significantly affect seismic velocities as these close, but this hardly affects overall porosities if thicker cracks and voids remain open. Near the surface (depth A in Figure 11.42), where both crack populations were assumed to be open, Shaw, 1994, estimated a Poisson’s ratio of 0.28. At intermediate depth (B), he postulated that only the thicker (  0.1) cracks and voids were open, resulting in an anomalously (and as observed) low Poisson’s ratio of 0.24. At greater depth (C), all cracks were assumed to be sealed, returning the velocities to that of the host rock, and Poisson’s ratio was again about 0.28. In older crust, hydrothermal deposition caused thin cracks to seal first. Thicker cracks

Figure 11.42 Top: a) For young crust: thin and thick cracks at depth A; thin cracks are sealed at depth B, leaving only the thick cracks. b) For old crust: all cracks are sealed. The above causes a Poisson’s ratio anomaly at depths of about 0.8 to 1.5 km, as shown in diagram d) in relation to Vp and Vs data. Shaw, 1994.

Velocity structure of the earth’s crust

could remain unclosed and unsealed until the crust was older, which then restored Poisson’s ratio to laboratory values.

11.4.7

A velocity-depth discussion

The strong focus on velocity-depth data in these investigations of the oceanic crust, in particular the supposedly ‘anomalous’ velocities and gradients discovered in the mid-ocean fracture zones, should lead us to consider the fundamental non-uniqueness of velocity-depth relations, as emphasised in a thought provoking article by AlChalabi, 1977. Figure 11.43a shows a smooth velocitydepth function such as: Vz  Vo  k.z

(11.11)

with actual small-scale fluctuations commonly seen in a sonic downhole log. In this simple equation which is attributed to Slotnick, 1936. Vo is the (P-wave) velocity at the surface and Vz is the velocity at vertical depth z. As pointed out by Al-Chalabi, 1977, the fluctuations shown in Figure 11.43a, which represent actual variability (and borehole effects) may not be seen in seismic work, when the seismic wavelength is greater than the scale of the fluctuations. The actual variations of sonic velocity with depth can be described by an extremely wide range of ‘parameter

Figure 11.43 a) A linear velocity-depth fit to a unit showing fluctuations at sonic log scale. b) Surface velocity-gradient trends for a unit logged at different depths in four wells. Al-Chalabi, 1997.

271

value combinations’, and these may well be parameters of convenience, as Al-Chalabi pointed out. In the rock quality Q-system the ‘convenient’ parameters are clearly those considered in the formulation of Q, rather than additional parameters not thought of. The non-uniqueness of the parameters in velocitydepth functions, and the lack of physical significance of any specific value of a given parameter had been overlooked up to then, according to Al-Chalabi, 1997. An investigation of the velocity-depth gradients that are synthesised in the Vp-Q-value-porosity-depth model of Barton, 1995 follows from Figure 5.36 (Part I), using a plotting format that can readily be compared with the oceanic crust fracture zone data of Layer 2A and 2B. Figure 11.44 shows the results which were extracted directly from Figure 5.36 for the case of six specific Q or Qc-values ranging from 0.001 (intensely fractured, thick clay-bearing discontinuities) up to 100 (quite massive, unweathered competent rock mass with few widely spaced joints, principally one set only). See Appendix A for relevant – but non-unique – parameter ratings. The very steep Vp-depth gradients typically seen close to the ocean floor, in the first few hundreds of meters of the new crust, could also be analysed with this near-surface based empirical method, developed mostly from civil engineering and engineering geological projects. Note

Figure. 11.44 Vp-depth trends for six specific rock quality Qc values, showing the assumed minor effect of porosity (n) when Qc is high. Influence of n% (the ‘hard’ porosity) increases with lower Qc-values. Gradient k  km/s/km  s1 is shown on the left-hand side. Trends of Vp-depth-Qc were derived from Figure 5.36 (Barton, 1995). Note similarity with oceanic crust fracture zone data for Layers 2A and 2B. The Qc-value represents mainly the ‘soft porosity’, i.e. jointing.

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Rock quality, seismic velocity, attenuation and anisotropy

the effect of porosities  1%, which increase strongly in influence as one moves from Qc  100 to the lower rock qualities (and larger ‘soft porosities’) towards the left-hand-side of Figure 11.44. In practice there will be a tendency for increased porosities close to the more weathered surface (arrow N trend), while with increasing depth, trend N will be reversed and trend J may dominate (i.e. reduced joint frequency, mineral healing, increased Q-value and Qc value, meaning that ‘curve-jumping-to-the-right’ will be necessary). This empirically-based, near-surface method could perhaps help to explain ‘anomalously high’ gradients through Layers 2A and 2B. Both trend N and trend J stimulate such an effect. Although ‘parameter value combinations’ in the rock quality Q-system (Barton et al., 1974, Barton, 2002) are definitely ‘non-unique’ (as per Al-Chalabi, 1997), a physically plausible situation is described by this empirically-based choice of increasing ‘hard porosity’ close to the surface, and reducing ‘soft porosity’ at depth (higher Qc-values). In a similar manner to the above, we can extract Vpdepth gradient (k) data from Figure 11.44, and express it in the simple form given by equation 11.11. The results are shown in Figure 11.45. Four sets of data are shown in Figure 11.45: A  mean gradient, 25 to 100 m (extreme) B  mean gradient, 100 to 500 m

C  mean gradient, 500 to 1000 m D  mean gradient, 25 to 1000 m In the case of D, giving the overall gradient from V0 to V1000, the separate effect of increased porosity is shown, which moves curves successively to the right. In each of these four cases, a uniaxial compressive strength of 100 MPa (nominal) has been assumed (giving Qc  Q in Figure 5.36). Higher values of c than 100 MPa, due to lack of weathering and low porosity would obviously give higher surface velocities and a lower gradient k (s1), thereby plotting to the left of these four sets of ‘100 MPa hard rock’ lines. The opposite would be the case with c  100 MPa (i.e. with younger rocks).

11.4.8

Fracture zones

The low velocity mid-Atlantic fracture zone studies reviewed in this section, show gradients of 3.0 to 3.5 s1 for the upper 0.5 to 0.8 km, and seabed velocities as low as 1.9 to 2.7 km/s. Reference to Figure 11.45 suggests that curves B and D with suitably increased porosities (nominal 1%) would fit such data very well. Data from mid-Atlantic Ridge fracture zone anomalies, discovered during the 1970s and 1980s, were assembled by Detrick et al., 1993. (e.g. Figure 11.46) These emphasise the extreme heterogeneity of their thickness and internal structure. In general, they consist

Figure 11.45 Analysis of Vp-depth gradients (k, s1) as a function of surface velocity Vo magnitudes, from the Vp-Q-value-depth-porosity model, Figure 5.36, from Barton, 1995). Based on the Al-Chalabi, 1997 plotting format, shown in Figure 11.43b.

Velocity structure of the earth’s crust

of thin intensely fractured and hydrothermally-altered basaltic sections, overlying a rather shallow Moho. The sites of some of these investigations are shown in Figure 11.46a, and a typical structural cross-section is shown in Figure 11.46b. Velocity-depth trends for four of the large Atlantic fracture zones are shown in Figure 11.47. Initial velocity-depth gradients to 2 km depth appear to vary from about 2 to 3 s1, though even steeper gradients are seen in the uppermost 100 to 200 metres. 11.5

The East Pacific Rise velocity structures

Following the forgoing summary of advances in understanding of mid-ocean ridges and fractured zones for the case of the mid-Atlantic ridge, we will now retrace some of the steps made in studies of the East Pacific

Figure 11.46 a) Simplified tectonic map of North Atlantic fracture zones. b) Generalised velocity-depth structural crosssection of a large Atlantic fracture zone. Detrick et al., 1993.

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rise. Many of the names of researchers will be familiar after reading or perusing the last section. Ewing and Purdy, 1982, both well known for their mid-Atlantic ridge studies, assumed a linear velocitydepth gradient in the upper 500 to 800 m of young (0 to 4 m.y.) oceanic crust on the flanks of the East Pacific Rise. The data shown in Figure 11.48 indicates an average gradient of between 3.0 and 3.5 s1 for the upper 0.5 to 0.8 km of oceanic crust, with seabed velocities ranging from as little as 1.9 to 2.7 km/s. Ewing and Purdy suggested that an even higher gradient might exist in the upper 400 to 500 metres. The evidence of very low velocities in the upper-most oceanic crust was reportedly consistent with visual/ submersible and photographic evidence of pervasive fracturing in mid-ocean ridge crustal regions, where the basalt layer was exposed, and it was consistent with drilling and logging results that showed high porosity (Hyndman and Drury, 1976; Kirkpatrick, 1979). Spudich and Orcutt, 1980a, had reasoned that a 10% porosity in the form of large fissures, added to a measured matrix porosity of about 8%, could readily produce a P-wave velocity of 2.6 km/s. For the case of rubble zones, Hyndman and Drury, 1976, had estimated a porosity of about 20%. The Vp-depth data interpretation shown in Figure 11.48 indicated to Ewing and Purdy, 1982 that ‘the percentage of cracks and voids’ diminished rapidly with depth, giving a Vp of about 5.2 km/s at 800 m depth. If we enter the Vp-Q-porosity-depth diagram shown in Figure 11.44, at a velocity of 2.5 km/s, and at a matrix porosity of 8%, we see a rock quality Qc value of about 1 (typical of weathered, heavily jointed rock). At 800 m depth, with assumed unchanged rock mass quality (but with higher effective stress), the P-wave velocity is predicted to be 5.3 km/s, almost the same as above, but without the linear-trend assumption. In other words, the effect of increased depth may have largely removed the porosity component created by the tectonic and thermal fracturing and jointing, but need not have removed (and indeed could not have removed) the matrix porosity of a competent volcanic rock which already had intruded into a pore pressure regime as high as 30 MPa, resulting from a 3000 m ocean depth. Ewing and Purdy, 1982 considered that their observed data showed a significantly lower gradient of about 1 s1 below 800 m, which would give a velocity of 6 km/s, appropriate for the ‘solid unweathered basalt’, at about 1.5 km depth. They reckoned that this might be a reasonable maximum depth of significant fracturing

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.47 Velocity-depth data from four of the large Atlantic fracture zones. Shaded areas are for ‘normal’ oceanic crust from White, 1984.

although it could be argued that initial fracturing extended to greater depth, and some healing has already occurred there by compaction and/or cementation’. Purdy, 1982, concurrently reported laterally homogeneous velocity-depth behaviour for two areas separated by 110 km on the flanks of the East Pacific Rise. The non-linear Vp-depth curves shown in Figure 11.49, which are averages for two areas of 20 to 40 km lateral extent, show, in this case, an inverse relation between age and velocity, since the youngest crust has highest velocity. Furthermore there was 100 m of sediment overlying the older of the two sets of crustal data, which would tend to add to the recorded velocity, yet it remains lower than the youngest Vp-depth curve. As a point of curiosity, the initial parts of the curves to the ‘knees’ at 400 and 600 m have gradients of about 4.2 and 4.4 s1. With reference to the

Q-Vp-depth-porosity-strength chart, in Figure 5.36, taking the nominal 25 m line as ‘surface’, the measured surface velocities of 3.05 and 2.4 km/s shown in Figure 11.49 suggest rock quality Qc values of about 0.5 and 0.08 (i.e. ‘very poor’ and ‘extremely poor’ engineering tunnelling qualities), following which at 400 and 500 m depths, Figure 5.36 predicts velocities of about 4.7 and 4.6 km/s, close to those measured. (Note that the empirical Vp-Q-depth-porosity-strength relationship was determined by trial and error, from land-based refraction seismic in jointed and faulted rocks, and from both shallow and very deep cross-hole tomography measurements, each with Q-logging of relevant core). The less steep gradients of about 2 s1 over the next 500 m depth to 1 km were the result of measured velocities of about 5.8 and 5.4 km/s. These compare to predicted velocities of about 5.5 and 5.3 km/s, from

Velocity structure of the earth’s crust

Figure 11.48 Linear Vp – depth assumptions for the shallowest fi km of East Pacific Rize oceanic crust (ROSE area), from Ewing and Purdy, 1982. They utilised a timedistance inversion method suggested by Dorman and Jacobsen, 1981, which required linear Vp – depth gradients in each layer. (OBH: ocean bottom hydrophone).

Figure 5.36. Differences in porosity and uniaxial strength between the youngest 0.5 m.y. and older 4 m.y. crust could be used to further distinguish and interpret the relative degrees of jointing, causing ‘curve jumping’ with increased depth, due to the likelihood of changed rock quality Qc values with age. Due to assumed aligned cracks, Shearer and Orcutt, 1986 found that travel times were affected by azimuth, in measurements performed during the Ngendei expedition to the South Pacific. They estimated 0.2 km/s difference in P-wave velocities and 0.1 km/s difference in S-wave velocities in the upper 1.5 km, caused by azimuth. In the upper mantle, from about 7 km depth below the sea bed (Figure 11.50), the difference in P-wave velocity was about 0.45 km/s, but a nearly isotropic S-wave was indicated. They interpreted the crustal anisotropy by a model involving aligned cracks parallel to the original spreading

275

Figure 11.49 Velocity-depth behaviour for 0.5 m.y.: crust (2E 2W), and 4 m.y.: crust (5E 6E 6W), from seismic refraction data on the flanks of the East Pacific Rise. Purdy, 1982.

Figure 11.50 Anisotropic velocity versus depth model which satisfies the Ngendei, South Pacific data. Solid line: NNE velocity, dashed line: ESE velocity. Shearer and Orcutt, 1986.

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ridge, resulting in a fast direction perpendicular to the fossil spreading direction. The upper mantle anisotropy was consistent with there being aligned olivine crystals, in which the fast direction was parallel to the fossil spreading direction. The problems posed by zero-age oceanic crust with Vp  2 km/s, compared to about 6 km/s for intact basalt continued to provide challenges for theoreticians and practitioners working on the origin, formation and structure of mid-oceanic crust. Studies resembling MidAtlantic Ridge theories about hard and soft porosity (low aspect ratios) and preferential mineral sealing, were also performed with East Pacific Rise data.

11.5.1

More porosity and fracture aspect ratio theories

Low aspect ratio cracks, and their reduced frequency of occurrence and reduction in aperture with depth, and probable sealing with hydrothermal minerals in the case of older oceanic crust, were some of the variables confronting those researching the variable structure of mid-ocean crusts. Using theories termed extended-Walsh and extendedKuster-Toksöz, Berge et al., 1992, utilised a range of crack aspect ratios ranging from extremes of 0.5 to 0.001, for depth zones ranging from 0 to 500 m below the sea floor, and succeeded in matching the Vp-depth trends for 0, 20 and 120 ka (1 ka  1000 years) oceanic crust from Christeson et al., 1991, and Purdy et al., 1991. These are shown in Figure 11.51. The method of Berge et al., 1992, was one of data fitting, not forward prediction. Berge et al., 1992 theorised that for 120 ka material with Vp  2.5 km/s, porosity should lie between 24 and 34%. Slower (Vp  2.2 km/s) zero-age crust was less well-bounded; a porosity of between 26 and 43% was predicted. The extended Walsh model used by Berge et al., 1992, required porosity-depth distributions for the various crustal ages, as shown in Figure 11.52. Wilkens et al. 1992 managed to match Ocean Drilling Program/Deep Sea Drilling Project (ODP/ DSDP9 Hole 504B and Hole 418A Vp – depth data, to 500 m depth, by modelling cracks of small aspect ratio that, in a ‘fast’ model became sealed if of sufficiently small aspect ratio, and in a ‘slow’ model did not seal. Deeper in the profile they ‘closed an increasing volume of lower aspect ratio pores’.

Figure 11.51 Vp-depth structure for zero-age crust, 20 ka crust (east and west) and 120 ka crust near the East Pacific Rise axial summit graben. Christeson et al., 1991 and Purdy et al., 1991.

Figure 11.52 Theoretical variation of porosity for matching Vp-depth data, with extended Walsh crack aspect ratio fit. Berge et al., 1992.

Velocity structure of the earth’s crust

11.5.2

First sub-Pacific ocean core with sonic logs and permeability tests

At the beginning of the 1980s, in a sub-ocean Deep Sea Drilling Project borehole in the eastern equatorial Pacific ocean, in the Costa Rica Ridge area, it was possible for the first time to correlate core (but usually of low % recovery) with downhole sonic logs, borehole televiewer logs, and permeability test results. This was first performed to a depth of 1 km, through layers 2A, 2B and 2C. A schematic section and downhole logging results from Newmark et al., 1985, is shown in Figure 11.53. Based on the vertical borehole logging (i.e. biased against vertical structure) the upper 50 metres contained numerous horizontal to sub-horizontal fractures, thick basalt flow units, and thin interbeds of pillow structures.

277

In general the uppermost 100 m was an aquifer of rubbly pillow basalts, breccias and a few massive flows, and greatest variability and largest velocity gradients occurred here. The next 0.5 km was composed of pillow basalts, flows and breccias with an abundance of minerals and alteration products. Basalt dikes were typical in the lower 350 m. Velocities, porosities and permeabilities varied approximately as shown in Table 11.4. The fact that average recovery of core was only 20% suggests many vertical and sub-vertical discontinuities were not sampled. Several of the well logs suggested the presence of zones of intense fracturing and open porosity, but the reducing permeabilities with depth clearly supported the general observation of increased mineral sealing with depth, and presumably increasing effective stress effects as well. (Of course the second leads to the first, if finest fractures are preferentially sealed).

Figure 11.53 Downhole (504B) sonic velocities and schematic structure of 1 km of oceanic 2A, 2B and 2C crust, from the equatorial eastern Pacific (Costa Rica Ridge area). Newmark et al., 1985. Note sediment and rock velocity contrast.

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Rock quality, seismic velocity, attenuation and anisotropy Table 11.4 Approximate velocities, porosities and permeabilities from downhole measurements in the top 1 km of Hole 504B, equatorial Pacific ridge. After Newmark et al., 1985. Zone

Vp

n%

k (cm2)


K (m/s)

Vp -depth gradients

Upper 100 m Middle 550 m Lower 350 m

3.7 4.8 5.6

4–10 – 1.5–4

109–1010 1011–1012 1012–1013

106–107 108–109 109–1010

Steepest Moderate Moderate

Figure 11.54 Principal permeability directions in layer 2B oceanic crust, showing anisotropic principal permeability magnitudes K1, K2 and K3. Interpretation based on observations of fracturing and mineralization of an (on land) ophiolite in Cyprus. van Everdingen, 1995.

The in situ bulk permeability of extrusive volcanic rocks measured in the Deep Sea Drilling Project (DSDP) drillhole 504B (Costa Rica Rift area), was subsequently quoted as 4  1014 m2 (or about 4  107 m/s) at 20°C, which corresponds to that of a well-jointed rock mass with a rock quality Q-value
0.25, based on a conversion of the above permeabilities to a Lugeon value of about 4 (see Chapter 9). In contrast, permeabilities of unfractured basalt, diabase and gabbro may lie in the range 1016 to 1023 m2 (or about 109 to 1016 m/s). Systematic investigations of jointing characteristics in ophiolitic (on land) remnants of oceanic lithosphere were used by van Everdingen, 1995, to infer the possible joint structure effects on permeability in layer 2B of the oceanic crust. A compilation of permeabilities measured or inferred for sub-sediment pillow lavas (from about 250 to 900 metres beneath the sea floor) and for the underlying sheeted dike complex (from 900 to 1600 m) showed a range from 1010 to 1018 m2 (or 103 to 1011 m/s). This happens to be comparable to the usual maximum range of measured land-based

permeability-depth measurements, e.g. to 1 km depth in igneous and metamorphic rocks. (Barton, 2002). The Troodos ophiolite estimates of van Everdingen, 1995, suggested a decrease in joint aperture and trace length with depth, and very marked anisotropy. The interpreted principal permeability directions in layer 2B oceanic crust given by van Everdingen, 1995, are illustrated in Figure 11.54. These land-based measurements appeared to have been at least partly based on the apertures indicated by epidote, quartz and later calcite fillings. Based on the usual inequality of hydraulic aperture (e) and the (rough-walled) average physical aperture (E) (i.e. E  e, Barton et al., 1985), the above method of estimating apertures could explain the higher estimates of permeability (e.g. 103 m/s), which would also be reflecting the negative effective stress episodes that would necessarily occur during hydrothermal penetration of fluids. Such was probably not typical of the effective stress conditions in operation when the above DSDP permeability measurements were made, since the permeabilities were of only moderate magnitude. (If effective stresses were locally negative during the DSDP permeability testing – a hazardous boundary condition for drilling of wells – then the resulting larger apertures, e.g. 1 mm or more, actually giving much higher permeabilities, would then have satisfied the assumed ‘mineral-filled opiolitic boundary condition’ of e  E.) A combination of deep sea crustal permeability measurements and interpretations of mineral-filled ‘frozen’ apertures from the Troodos ophiolite are shown in Figure 11.55. Similar, ophiolite observations of fossil flow porosities and permeabilities, based on cubic law calculations using mineral filling thicknesses (e.g. Norton and Knapp, 1977), were reported by Nehlig and Juteau, 1988. With apertures of 1, 2 and even 5 mm (e.g. of epidote), it is clear that artificially high estimates of ‘permeability’ are made, such as many estimates of 1010 m2, or about 103 m/s. These are exceptionally high. If many such

Velocity structure of the earth’s crust

279

Figure 11.55 An interpretation of possible permeability trends in the first 1600 m of ocean crust, based on parallel-plate modelling, with matrix addition, plus measured permeabilities from various sources. See van Everdingen, 1995, for references.

apertures were caused during negative effective normal stress episodes, as seems likely in sill and dike intrusions, they would not reflect ‘virgin’ permeabilities, as existing prior to the hydrothermal fluid injections. On the basis of this reasoning, the ‘fossil’ apertures observed in recovered core may not accurately reflect the porosity available at the time of hydrothermal fluid injection.

11.5.3

Attenuation and seismic Q due to fracturing and alteration

Swift et al., 1998a described the seismic attenuation, for the upper 1.8 km of Hole 504B (Costa Rica Ridge area: see upper 1 km of permeability data in Table 11.4 from Newmark et al., 1985). About 60% of the total observed

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Figure 11.56 VSP and sonic log measurements in upper 1.6 km of Hole 504B. VSP Poisson’s ratio log also shown. Qi (intrinsic) values are from Swift et al., 1998a with Qs (scattering) values at 10 m intervals from Goldberg and Yin, 1994. Note the very high dynamic Poisson’s ratios at shallow depth, derived from the VSP Vp and Vs values, due to thin flows, pillow lava, and breccia.

amplitude decay apparently occurred in the pillow basalt, due to geometrical spreading and impedance contrasts, and much of the remaining amplitude decrease was concentrated in two layers, about 500–650 m and 800–900 m below the ocean floor, as shown in Figure 11.56. Attenuation in these layers was described by low seismic Q of 10 and 8 respectively, due to intrinsic attenuation mechanisms. In the case of the upper zone the authors believed that alteration-mineralogy may have been responsible for the attenuation, as there was no crack-related reason for the high attenuation. In the past this may have been a zone of high porosity prior to pore-space filling by zeolites. In the case of the lower zone with seismic Q of only 8, the authors mention that this 800–900 mbsf interval coincided with features in core descriptions and logs that suggested the presence of an intracrustal deformation zone, or a sub-horizontal fault. Tectonically disturbed rock, a local minimum in resistivity, a maximum in inferred porosity, a decrease in Young’s modulus, increased fracturing in the wall of the borehole, low aspect ratio cracks containing fluid, are among the various descriptions of this low seismic Q zone. It could have been helpful to also know the rock mass quality Q, or at least RQD, among all these mostly qualitative descriptions. Attenuation studies in upper ocean crust cited by the authors, indicated a certain age relationship, with attenuation greatest and seismic Q lowest in the youngest rock, as reviewed by Swift et al., 1998a.

● ● ● ● ●

●

1 Ma Qseis
20 to 60 Near ridge axis Qseis
10 to 20 (near sea floor) Within first 0.4 Ma Qseis
50 to 60 (near sea floor) few Ma Qseis  300 (1 to 2 km depth) Lab samples of basalt at 50 MPa confinement: Qseis
55 to 120 Lab samples of diabase dikes at 100 MPa confinement: Qseis
70 to 370.

Other attenuation data from the upper crust in these mid-ocean ridge structures, show seismic Qp estimates varying from 35 to 80 in general (Harding et al., 1989; Vera et al., 1990; Wilcock et al., 1992) and dropping as low as 11 to 20 in the uppermost crust (Christeson et al., 1994). Kappus et al., 1995 found that their reflectivity synthesis computed with seismic Qp varying from 50 to 100, fitted original data very well. The high attenuation, low seismic Q zone described by Swift et al., 1998a, had sonic log velocities down to 1 km/s lower in this fractured interval. The Qi intrinsic attenuation and Qs scattering attenuation interpretation, the corresponding sonic and resistivity lows and the dynamic Poisson’s ratio determined from VSP, are each reproduced in Figure 11.56. Swift et al., 1998b also referred to the large-scale resistivity measurements at Hole 504B, giving parallel estimates of bulk porosity reduction with depth. The increase in Poisson’s ratio is caused by disproportional reduction in S-wave velocity compared to P-wave velocity, which theoretical studies by Shearer, 1988, have

Velocity structure of the earth’s crust

281

about 800m depth, failed to detect the low velocity that would ‘normally’, (nearer the surface), be an obvious feature of such a fault: see Figures 8.25 and 8.26 in Part I.

shown should occur with relatively thin cracks or joints, having aspect ratios less than 0,005 in an otherwise isotropic solid. Swift et al., 1998b gave an interesting comparison of laboratory data (open circles in Figure 11.57) obtained apparently from 100 MPa confinement, with Vp, Vs and dyn trends obtained from VSP. The 100 MPa confinement applied in earlier laboratory studies was an incorrect simulation of an actual much lower effective stress gradient, as discussed earlier in this chapter. Possibly some effect of a correct effective stress gradient might have been observed on the intact samples, if this had been applied. We can see that, in relation to this presumably unrealistic 100 MPa confinement, there is up to 2 km/s deviation (reduction) of in situ P-wave velocities due to structure, at the top of the hole. The difference is more than 3 km/s in the case of S-waves, presumably due to the water-filled structure close to the ocean floor. Swift et al., 1998b suggested that large-scale, welloriented vertical fractures (i.e. a joint set) formed tectonically, did not have a detectable effect on P-wave velocities. Presumably this is an expression of the effect of tight closure by stress, which has also been observed in the case of an obvious fault ahead of a (stuck) TBM tunnelling machine. (Seismic velocity tomography performed from diverging holes ahead of the particular tunnel face at

Some results of the first three-dimensional tomographic study of crustal seismic attenuation across the East Pacific Rise near 9°30
N, dating from 1988, was reported by Wilcock et al., 1995. The rather unique layout of 480 explosive charges distributed over an ocean-bottom 16  16 km grid is reproduced in Figure 11.58. Solid symbols are ocean bottom receivers, which included analogue and digital hydrophones and seismometers. Bathymetric contours (m) are also shown. The East Pacific Rise near 9°30
N is a fast spreading ridge, characterized by a sharp upper-crustal to mid-crustal velocity inversion some 1.5 to 2 km below the seafloor, presumed to be the roof of an axial magma lense. Small mid-crustal (i.e. 3 to 5 km deep) magma chambers appear to be a common feature of these fast-spreading ridges. Since a narrow lense of partly melted rock would solidify rapidly in a cooling environment dominated by hydrothermal

Figure 11.57 Comparison of VSP (in situ) velocity structures in Hole 504B on the Costa Rica Rift, with numerous researcher’s laboratory data (open circles), which show little effect of depth with the (artificial) applied effective stress of 100 MPa. Swift et al., 1998a.

Figure 11.58 A 16  16 km grid with 480 explosive charges (open circles) and the ocean bottom receiver array (sold symbols). Bathymetric contours (m) are also shown. Wilcock et al., 1995.

11.5.4

Seismic attenuation tomography across the East Pacific Rise

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.59 Results of the inversion for a vertical cross-section and an along-axis slice, showing the lower crustal, sub-ocean ridge, Qp1 attenuation structure. The along-axis result is at 4 km depth. The Qp values range from 25 to 100. Wilcock et al., 1995.

circulation, it is generally considered that the supply of magma from below must be relatively steady-state and uniform, deep beneath the axis of the ridge. The attenuation expressed as Q1, (or Q1 p ) for a central vertical section, and for a horizontal cross-section at 4 km depth is shown in Figure 11.59. The four attenuation (Q1) values give estimates of seismic Q  25, 33, 50 and 100 from the central lense (with an assumed few percent of melt) to 2 and 3 km off-ridge distances. In the upper 1 km by contrast, seismic Q averages about 35 off-axis, increasing to 65 near the axis rise. One may speculate that this might be due to a horizontal

stress enhancement above the lense, because 20 km off axis, seismic Q remains at only 45, despite greater age at increasing distance from the ridge. Inversions for individual receivers showed that seismic Q increased from average values of 40–50 in the upper 1 km, to at least 500–1000 at depth greater than 2 to 3 km. Results appear to be in agreement with other studies of attenuation in young oceanic crust. In an on-bottom refraction study near the centre of this tomography experiment, Christeson et al., 1994, measured seismic Q in the upper layer 2A of only 11 to 22. Wilcock et al., 1995, cited three dominant attenuation mechanisms in stable continental crust and marine sediments as: intrinsic attenuation as a result of Coulomb friction along cracks (Walsh, 1966), the flow of pore water (Biot, 1962) and scattering. They suggest that these mechanisms, together with scattering from the rough seafloor, may also be important in young, igneous oceanic crust. Laboratory measurements on oceanic basalts (Wepfer and Christensen, 1990) suggested that attenuation would also increase with porosity, degree of alteration and water saturation. One may append here the more specific and presumed ‘micro-shearing ‘and micro-flow’ terms to qualify the above ‘friction’ and ‘pore water flow’, since there are physicists who visualise only sub-atomic magnitudes of deformation across microcracks with the passage of seismic waves, and others who even deny that friction can be involved in attenuation. The subject of attenuation is indeed controversial, but there are clear indications, presented in Chapter 10, and further discussed in Chapters 13, 15 and 16, that micro-shear and micro-normal deformations along/ across attenuating cracks and joints (i.e. displacement discontinuities), as interpreted from seismic anisotropy field measurements, are closely following the stiffness (or compliance) magnitudes seen in the ‘static’ macrodeformation (stress-closure and shear-displacementdilation) testing of joints that is more common in rock mechanics. Dynamic compliances are often smaller than the inverse of ‘static’ stiffnesses, but only marginally so in the case of normal stiffness in rock masses of good quality. They seem to be of the same order of magnitude, or even closer. Dynamic shear stiffnesses may be up to two orders of magnitude stiffer than static shear stiffnesses. This seems hardly enough difference to prevent friction from being involved in attenuation. Since fractures are preferentially oriented parallel to mid-ocean rise axes, it has been postulated that attenuation should be higher for waves propagating

Velocity structure of the earth’s crust

perpendicular to the rise (Macdonald, 1982). Unfortunately there were insufficient axis-parallel paths in the tomographic investigation of Wilcock et al., 1995, to distinguish the two orientations.

11.5.5

Continuous sub-ocean floor seismic profiles

As time went by, investigations of the mid-oceanic ridge areas become even more extensive with the added possibility to compare new results with ever more numerous earlier studies. An integrating report of this nature by Kappus et al., 1995, also described a high-resolution seismic velocity profile of the uppermost 500 m of East Pacific Rise crust at 13°N, along a 52 km segment of the ridge crest. The continuous profile, synthesised from 70 individual 1-D models spaced at 750 m, showed remarkable lack of variation. The 53 km segment was however more than 100 km from the nearest first order transform

283

fault and over 10 km from the nearest second order discontinuity. The main features revealed were a thin low velocity layer 2A consisting of about 80 m of (nearly) constant velocity rock (2.45  3% km/s at the sea floor) followed by a steep gradient through 150 m of rock to the base of layer 2A. The thickness of the 4 km/s iso-velocity contour was mostly 130  20 m, increasing to 180 m towards the north. This implied a maximum Vp-depth gradient of about (4.0  2.45)/0.05
31 through a 50 m section compares with the also very steep gradients at shallow depth in jointed (sub-continental) rock masses shown in Figure 11.44, as derived from the Q-Vpdepth-porosity-strength model of Barton, 1995, 2002). Figure 11.60 shows the velocity of the top layer 2A (mean 2.45 km/s) and the thickness of the 4 km/s iso-velocity contour (mostly 130  20 m). Velocities at the top of layer 2A and at the top of layer 2B are shown in Figure 11.61. A reflection deeper in the crust (triangles) at a velocity of 5.5 to 6.1 km/s is also shown.

Figure 11.60 a) Velocity at top of layer 2A (mean 2.45 km/s) and b) thickness of layer 2A where the 4 km/s iso-velocity contour is found (130 to 180 m). Kappus et al., 1995.

Figure 11.61 Velocities at top of layer 2A (circles) and at top of layer 2B (squares). A reflection deeper in the crust (triangles) was interpreted as the lid of a magma chamber. Kappus et al., 1995.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.62 Seismic velocity structure of the upper 500 m of a 52 km long segment along the mid-oceanic ridge crest of the East Pacific Rise. Kappus et al., 1995.

(a)

(b)

Figure. 11.63 Average P-wave velocity-depth curve and standard deviation for 70 profiles covering a 52 km segment of the ridge crest, to a depth of 400 m. Kappus et al., 1995.

The relative uniformity of much of the 52 km long segment (measured at 70 locations) is further emphasised by the strikingly beautiful contoured velocities shown in Figure 11.62, which show rapid increases in velocity at first followed by slower increases due to longer depth intervals. The base of layer 2A was assumed to be the lower part of the steep velocity gradient at about 230 m below

the seafloor. This transition to an entirely different (2B) gradient is seen more easily in Figure 11.63, which shows the average velocity depth behaviour (solid lines) and the mean of N and S parts of the segment (dashed lines). A starting model of velocity versus depth, and various iterations is shown in Figure 11.64. For the purpose of estimating gradients, the average velocity-depth data is reproduced in Table 11.5. This data

Velocity structure of the earth’s crust

285

Table 11.5 Average velocity-depth data from 70 profiles along a 52 km segment of the East Pacific Rise ridge crest. Kappus et al., 1995.

Figure. 11.64 One of the starting models for Vp-depth inversion, to 1 km depth below the ocean floor. Successive iterations are shown, the fourth with asterisks. Kappus et al., 1995.

has been plotted among the ‘soft porosity’ (joint-related) curves of the Qc-Vp-depth-porosity-strength model, reproduced for easier comparison in Figure 11.65. The Table 11.5 data plotted in Figure 11.65, shows strong evidence of structural (and matrix porosity) effects, and much rock quality improvement with depth increase (i.e. curve-jumping), in the upper 250 m. Interestingly the Vp data below this depth suggests typical jointed rock Q-values (Barton et al., 1974; Barton 2002) in the range 2 to 8 down to 1000 m depth, with data paralleling the trends of Q  1 and Q  10 suggesting effective stressjoint-closure effects. A uniaxial strength of 100 MPa has been assumed in this example. If the basalt was closer to 200 MPa strength, a uniform shift to half as high Q-value (i.e. from about 5 to 2.5) would be involved. A plausible Q-parameter construction to explain such values of rock quality beyond 250 m depth could be the following: 60 3 0.5    3.8 12 4 0.5 Attenuation in the upper crust of these mid-ocean ridge structures is clearly quite strong, with seismic Qp

Depth below seafloor, m

P-wave velocity km/s

Standard deviation km/s

0 40 80 120 160 200 240 280 320 360 400 440 480

2.25 2.38 2.57 3.17 3.82 4.36 4.71 4.88 5.00 5.10 5.19 5.26 5.36

0.000 0.135 0.240 0.350 0.323 0.289 0.217 0.158 0.140 0.140 0.138 0.141 0.172

estimates varying from 35 to 80 in general (Harding et al., 1989; Vera et al., 1990; Wilcock et al., 1992). Kappus et al., 1995 found that their reflectivity synthesis computed with seismic Qp varying from 50 to 100, fit their original data very well. The low velocities of seafloor, age zero, mid-oceanic ridge crest materials from numerous studies in the period 1976 to 1994, reviewed by Kappus et al., 1995, had the following values in km/s: 2.5, 3.1, 2.1, 3.5, 2.35, 2.2, 2.0, 2.45, 2.4 and 2.7 (read from the zero-age end of eventual ranges of velocities). The mean value of 2.5 km/s implies a near-sea floor rock quality Q-value of only 0.1, as also roughly indicated in Figure 11.65. Velocity-depth gradients for layer 2A as a whole appear to have ranged from 3.5 to 5.5 s1, though they do not appear to have been quoted in many of the papers referenced by Kappus et al., 1995. These low velocity, zero-age, crustal values have to be contrasted to laboratory velocities for young basalts of at least 5.6  0.4 km/s (e.g. Hyndman, 1976). Information from drill holes (Alt et al., 1986; Nehlig and Juteau, 1988) reinforce the idea that the low velocities are strongly linked to structure (i.e. discontinuities, joints, fractures) and to matrix porosity, since there is evidence of strong circulation of hydrothermal fluids, mixing of cold and hot fluids and alteration, which could be intense at some levels. Collier and Singh, 1998, utilised wide-aperture seismic reflection data with much improved vertical resolution (shots and receivers placed every 100 m), and

286

Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.65 Comparison of Kappus et al., 1995, mean Wide Aperture Profile data with the rock engineering Q c-Vp -depth-porosity-strength model derived from Barton, 1995, 2002. A UCS value of 100 MPa gives Q  Q c.

Figure 11.66 Waveform inversion results from measurements on the East Pacific Rise near 14°S. Thinner lines show the one standard deviation error band. Collier and Singh, 1998.

applied full wave form inversion to interpret sub-ocean crustal structure beneath the East Pacific Rise near 14° S. They provided evidence of extremely high dynamic Poisson’s ratios as high as 0.48, with a sharp drop to 0.25 within 200 m of the ocean floor, across the 2A/2B transition. A very low Vs in the upper 50 to 100 m thick layer-2A (Vp 1.9 km/s, Vs  0.4 km/s) was responsible

for the initial high value of 0.48. Their results included an estimate of seismic Qp in the low range of 18–30 across layer 2A, with increases at greater depth, as shown in Figure 11.66. Their calculations suggested a porosity in excess of 30% in layer 2A, which reduced to 6–7% at the top of the 2A/2B transition, and further reduced to

Velocity structure of the earth’s crust

287

Table 11.6 Vp-depth data as a basis for rock quality Qc estimation. From Figure 11.66 data. Depth below seafloor

Vp (approx.)

Qc (approx.)

Gradient (s1)

10 m (nominal) 75 150 250 800

2.0 3.0 4.0 5.0 5.5

0.04 0.04 0.2 3 4

– 15 13 10 2

about 5% at a depth of 600 m below the seafloor, within layer 2B. Hydrothermal alteration seems to be mostly responsible for the reducing bulk porosity and for preferentially sealing low aspect-ratio cracks. They also cited the higher porosity of extrusives, i.e. pillow lavas, compared to the deeper intrusives, which consist of dikes and sills. The increasing lithostatic (effective) pressure also preferentially closes the cracks or joints with lowest aspect-ratios, which became predominant across the 2A/2B transition. As they and others have emphasised, this can have a dramatic initial effect on Vp gradients, until ‘seismic closure’ is achieved at sufficiently high effective stress. Table 11.6 gives the approximate indications of Vp-depth gradients. Referring to Figures 11.44 and 11.65, we see that, in rock engineering terms we need to ‘curve-jump’ from initially very low rock quality Q c-values, consistent with extremely fractured and altered conditions near the surface, to a typical poor quality jointed medium (Q c  3 to 4) at greater depth in layer 2B.

11.6

Age effects summary for Atlantic Ridge and Pacific Rise

Finally, this chapter will conclude with a broad review of age effects for both mid-Atlantic Ridge and Pacific Rise data. A very wide ranging assembly of seismic velocity data for uppermost oceanic crust (layer 2A), by Carlson, 1998, (with one and a half pages of referred authors) suggested that most of the age-dependent increase in seismic velocities occurred ‘rapidly’ with velocities nearly doubling in 10 million years. The apparently rather heterogeneous sets of data (Figure 11.67) when synthesised by Carlson, 1998, using mean and 9-point interval median values, showed much clearer trends of accelerated velocity increase with early age, and clear distinction from typical layer 2B velocities

(a)

(b)

Figure 11.67 Upper crustal velocities in the Pacific and Atlantic oceans for a) 0–150 m.y. b) detail of first 15 m.y. Typical layer 2B velocities (5.2 / 0.4 km/s) shown by dark band, from Houtz and Ewing, 1976 and Houtz, 1976. (OBS  ocean bottom seismometer, OBH  ocean bottom hydrophone, log  downhole, borehole  borehole seismic surveys). Carlson, 1998 and his numerous cited authors.

(shown by dark band). Layer 2A appears to persist as a low velocity capping of the ocean crust, even when 15 m.y. old, as shown in Figure 11.68. The trend for increased velocities as age increases is also shown clearly by the statistics for 1 m.y., 1–5 m.y. and 5 m.y. in Figure 11.69, also from Carlson, 1998. The link between hydrothermal alteration and seismic velocity increase, due to deposition of minerals first in

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.68 Mean velocities (black circles), and 9-point median velocities (open circles), as a function of median basement age. Mean velocities are from age intervals 0–1, 1–5 and 5–20 Ma. The data demonstrates that layer 2A persists as a low velocity (and low rock quality) layer, capping the crust. Hatched area is typical layer 2B. Carlson, 1998 and his numerous cited authors.

the thinnest cracks and joints, gives logical support to the notion of most rapid alteration when the hydrothermal activity has been most vigorous. However, a potential problem of interpretation exists as pointed out by Carlson, 1998, because hydrothermal void filling causes a simultaneous increase in velocity and reduction in hydraulic conductivity, therefore supposedly reducing heat flow to the ocean flow. Yet the heat flow has continued for far longer than the early period of velocity increase. When one considers the cubic flow law, suggesting that mineral sealing of small apertures will have less effect on hydraulic conductivity than sealing of large apertures, it seems reasonable to envisage that the sealing of smallest apertures first will not compromise the increase in seismic velocity and the maintenance of a reasonably high heat flow. Further interesting details of hydrothermal circulation and mineralization, as an explanation for seismic velocity increases with age, were given by Grevmayer et al., 1999. Their work was concentrated in Layer 2A, on the eastern flank of the East Pacific Rise at 14°S, along a 720 km by 25–40 km wide corridor, with only thinly sedimented seafloor of up to 8.5 Ma age. For 0.5 Ma and 8 Ma crust, they derived P-wave velocities

Figure 11.69 Distribution of seismic velocity in the upper crust (layer 2A) from age intervals 0–1, 1–5, 5 Ma. By comparison, layer 2B velocities generally range from 4.5 to 5.6 km/s. Carlson, 1998 and his numerous cited authors.

of 2.9 and 4.3 km/s, respectively. Over the last 8.5 m.y. there has been local ridge spreading at an average annual rate of 85 mm/year in this area. Their forward modelling of 17 (split) profiles on 0.5 to 8.3 m.y.-old crust for three age ranges is shown in Figure 11.70. When velocity is plotted versus age as in Figure 11.71, a rapid then gradually slowing rise in velocity is seen, which is similar of course, to the wider-reaching review of Carlson, 1998, shown in summary in Figure 11.68. Grevemeyer et al., data indicate a continuous decrease of the velocity gradient in layer

Velocity structure of the earth’s crust

Figure 11.70 Vp-depth models of upper oceanic crust from inversion of 17 OBH split profiles, on 0.5 to 8.3 m.y. crust, from the East Pacific Rise at 14°S. Note the three age groupings. Grevemeyer et al., 1999.

2A, with age up to 10 m.y. Their data only just reaches the plateau seen in Figure 11.68, beyond about 8 m.y. Grevemeyer et al., 1999, argued convincingly that hydrothermal mineral filling of open void spaces was the reason for age dependent velocities, and that velocities in layer 2A remained constant in crust older than
10 m.y. An 8 m.y. crust at the top of layer 2A, showed 4.3 km/s which is high for the Pacific. Even 110 m.y. crust and older, usually showed between 4.0 and 4.3 km/s. Interesting parallels to the above hydrothermal mineral filling of fractures, can be gleaned from civil engineering, where the sealing of jointed rock by pre-grouting with fine-grained micro-cements ahead of tunnels, or the use of industrial (coarser grain size) cements in dam foundations, are common ways of both sealing and improving properties. Quadros and Correa Filho, 1995, measured rotations (and magnitude reductions) of the three permeability tensors, when conducting multiple-borehole 3D hydrotomography before and after grouting. (Holes were redrilled after grouting, for the second round of permeability testing). These tensor or principal value rotations are interpreted as due to sealing of the most permeable and least stressed joint sets. This process can also be interpreted by small changes in five or six of the Q-value parameters (ratings in Appendix A), which has been shown by Barton, 2002, to cause some dramatic potential improvements in the rock mass properties such as modulus of deformation, seismic velocity, and frictional and cohesive

289

Figure 11.71 Layer 2A velocity as a function of age (at top of layer). New results (star-symbols) and various results from referred studies, including Carlson, 1998 (solid circles). Grevemeyer et al., 1999.

strength. These joint-grouting property-improvement aspects will be described at the end of this chapter. 11.6.1

Decline of hydrothermal circulation with age and sediment cover

It is well established that hydrothermal circulation naturally declines with the age of the crust. Anderson et al., 1985, and Evans, 1994, deduced on-axis (zero age) upper crustal permeability of about 6  1012 m2 (
6  105 m/s), this decreasing to about 7  1014 m2 (
7  107 m/s) within 6 m.y. Seismic velocities for crust of the same age were 2.2 km/s and 4.0 km/s according to the Grevemeyer et al., 1999, data. The same authors surmised that permeability may reduce to about 1014 m2 (
107 m/s) or less, by the time the crust is old enough to have reached a 4.3 km/s ‘plateau’. In thinly sedimented areas, sealing/plugging of crustal pore spaces appears to extend for 7 m.y., perhaps up to 15 m.y. However, in regions with significant sediment cover, the previously open seawater convection cooling system is hindered, and temperatures rise, thereby accelerating the formation of secondary minerals and porosity sealing. Rohr, 1994, used these arguments to explain 4.3 km/s velocities in only 1.5 to 2.0 m.y. crust at the Jan de Fuca Ridge. So Grevemeyer et al., 1999 concluded that basement temperature, which is a function

290

Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.72 The rock quality Vp-depth-Qc curves with rule-of-thumb estimates for the approximate permeability (m/s) caused by the ‘soft’ porosity (i.e. the jointing). As in the case of pre-grouting with micro-cements ahead of tunnels, one can argue for improvement of various Q-parameter ratings through sealing-mineralization, provided that clay and layer-lattice minerals are not involved. Harder minerals will have cumulative positive effects on Q-values, and therefore on permeability and other linked rock engineering parameters. ‘Curve-jumping’ or ‘Q-jumping’ can therefore occur. Based on Barton, 2002.

of heat flow, sediment thickness and sediment permeability, governed the evolution of the seismic properties of upper ocean crust. Since massive, non-vesicular basalt has a P-wave velocity of about 7 km/s (Wilkens et al., 1988), then mature sealed ocean crust, with velocities nearer 4 km/s, must have a residual porosity consisting of vesicules, fractures, breccia and inter-pillow voids. Most importantly, it is actually under a low effective stress, just as at the earth’s surface, despite (and because of ) 30 to 40 MPa hydrostatic pressure, and because of the shallow sediment and rock cover. In the rock quality world of Q and Qc (Qc  Q  c/100) there is a rough rule-of-thumb (Barton, 2002) that due to different degrees of ‘soft’ porosity caused by jointing, the Lugeon value (1L
107 m/s or 1014 m/s) is approximately inversely proportional to Qc. This applies in a central range of rock quality, uncomplicated by clay sealing of joints, which reduces both Q and permeability together, thereby defeating the inverse proportionality. In Figure 11.72, shown earlier in connection with velocity-depth gradients, the above rule-of-thumb permeabilities have been marked at appropriate depths

along the Q or Qc ‘isoquality’ curves. It is relatively easy to invoke this ‘jointed rock’ model as an analogue to explain a surface or near-surface permeability, as referred above, of about 105 m/s (1012 m2), with increases to 106 and 107 m/s (1013 and 1014 m2), as age allows the effective rock mass quality to rise, due to mineralization sealing in some of the ‘soft’ porosity. At the nominal 25 m deep ‘surface’ drawn in Figure 11.72, Qc changing from 0.01 through 0.1 to 1 (i.e. ‘curve jumping’ due to improving quality with age) implies permeability reducing from 105 through 106 to 107 m/s. We can express these analogues for rock mass quality improvement with age, due to sealing-mineralization (as opposed to clay-lubrication) in another way in the Vp-Qc-M-L interaction nomogram in Figure 11.73. Here we have marked the above analogue for permeability reduction with age (roughly 105 to 106 to 107 m/s) at the nominal near-surface depth of 25 m (central diagonal), and at 50 m. Also shown is the implied improvement of modulus of (static) deformation for the rock mass: 2 to 5 to 10 GPa, based on the simple empirical relation (units: GPa): M(or E mass )
10Q 1/3 c

(11.12)

Velocity structure of the earth’s crust

291

Figure 11.73 The rock quality Qc-Vp-M-L interaction nomogram, with appended ‘circles’ to mark the engineering consequences of ‘curvejumping’ on permeability, modulus and velocity. After Barton, 2002.

11.6.2

The analogy of pre-grouting as a form of mineralization

In this final section of Chapter 11, a possible rock engineering analogy to the hydrothermal mineral sealing of ocean-floor basalts will be demonstrated, using the analogy of high pressure (5 to 10 MPa) pre-injection pressures used in an ‘umbrella’ of numerous (20 to 40) boreholes, which are commonly drilled and injected ahead of leaking tunnels, or where there is environmental sensitivity at the surface and significant inflows to the tunnel cannot be allowed. The argument for improved rock mass quality due to the sealing (by micro-cement and micro-silica) of successive joint sets, is based on the evaluation of individual Q-parameter descriptions and ratings. Each small improvement, like the reduction of the number of effective joint sets due to sealing (i.e. Jn reduces, see Appendix A), may have cumulative effects on rock qualities Q and Qc. There exists in situ proof of improved qualities due to observations of improved stability, less deformation, less

need for rock support (bolting and shotcreting quantities are reduced), and of course reduced or negligible inflows. Permeability K (m/s) may reduce from 105 to 108, 106 to 108 or 107 to 108 m/s, the relative degree of improvement being related to the ‘severity’ of pre-treatment conditions. Higher pressure injection, from 5 to 10 MPa excess pressures (above joint water pressure), can cause permeabilities to reduce to between 108 and 109 m/s. There is an interpreted 1 to 5 litres of grout per 1 m3 of (locally-injected) rock mass in successful, highpressure grouting (Barton, 2004a). In other words there is the effect of some joint deformation close to the injection holes, made permanent by the subsequent hardening. Such would also be expected during hydrothermal episodes of injection, the subsequent ‘fossil’ mineral fillings therefore somewhat exaggerating the pre-injection apertures and permeabilities, despite some subsequent pressure adjustment prior to crystallization. Sealing of major channels is ‘a problem’ in both scenarios, because any continued flow will tend to hinder crystallization/ hardening in the two processes.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 11.74 Three-dimensional permeability monitoring (hydro-tomography) performed before and after grouting, showing rotation of permeability tensors, and reduction in principal magnitudes. Quadros and Correa Filho, 1995; Barton and Quadros, 2003.

Velocity structure of the earth’s crust

293

Table 11.7 A hypothetical model of potential Q-parameter improvements as a result of both pre-injection with microcement (in tunnelling) and through (hard, resistant) mineral sealing in sub-ocean crust. Improvement of rock mass properties with pre-grouting, as analogy to mineralization Effective RQD Effective Jn Jr Ja Jw

Increases Reduces Increases Reduces Increases

e.g. 30 to 50% e.g. 9 to 6 e.g. 1 to 2 e.g. 2 to 1 e.g. 0.5 to 0.66

(changed set)* (changed set)* (perhaps Jw  1 is achieved)

SRF would reduce only near surface, e.g. 2.5 to 1 (*it may be appropriate to qualify with the word ‘perhaps’ in these cases)

Before pre-grouting Q


After pre-grouting Q
Before pre-grouting

30 9 50 6





2 1

1 2





0.5 2.5

0.66 1


0.3 (i.e. prior to mineralization)


11 (i.e. after mineralization) After pre-grouting

Empirical equation

Q
0.3

Q
11

J J  r  w Jn Ja SRF c Qc  Q  100

Vp
3.0 km/s

Vp
4.5 km/s

Vp  3.5  log Qc km/s

L
3 (3  107 m/s)

L
0.1 (108 m/s)

L
1/Qc

M
7 GPa

M
22 GPa

Q


As referred to in Chapter 9, it has also been shown by Quadros and Correa Filho, 1995 and Barton and Quadros, 2003 that permeability tensors can rotate and reduce in magnitude as a result of grouting. This is shown in Figure 11.74. It appears to be evidence of successive sealing of the joint sets, starting presumably with the set that is under least normal stress (probably nearly parallel to max), or with the most permeable set (or sets) perhaps caused by (conjugate) shearing and dilation. This presumably could also govern the chronological order of deposition in hydrothermally opened fractures and major inter-connected pore space in the sub-ocean basalts. The mechanism by which rock mass quality and rock mass velocity increases, as a result of both successful pregrouting and ‘successful’ mineralization of sub-ocean crust (as it gets hotter due to sediment sealing), could be as in Table 11.7 (see Appendix A for descriptions and ratings of the six parameters). The hypothesised improvements in Q-parameters are very conservative particularly concerning the number of

RQD

M
10Q 1/3 GPa C

joint sets that may be sealed. More likely, the three sets represented by Jn  9, could be reduced to two sets (Jn  4), or even to one set (Jn  2). On the other hand, the grout is an ‘inferior’ fill in relation to hard rock, and may not then provide the expected increases in velocity and modulus, shown by the empirical equations in Table 11.7. So a greatly increased apparent Q-value, would not then give realistic velocity improvements. The exception would be the case of injection into weak rocks with comparable compressive strengths and densities (roughly 20–30 MPa and 1.5 gm/cm3). A beautiful example of an igneous intrusion into what was, or has since become a weaker rock is shown in Figure 11.75. This could act as a reminder that the injected hydrothermal fluids, and of course magma, if subsequently very stiff compared to the surrounding rock, will tend to be jointed due both to cooling and deformation, thereby maintaing a level of permeability at depth.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure. 11.75 An igneous intrusion (dike) tends to have elevated permeability due to the number of joint sets (typically four: Jn  15). Highmodulus mineralized veins may be fractured by subsequent tectonic deformation, helping to maintain some permeability despite the ‘sealing’ process. (see Plate 2)

12

Rock stress, pore pressure, borehole stability and sonic logging

By their very nature, hydrocarbon-bearing rocks rely on pore-space and permeability for the possibility of having recoverable reserves that can be produced at a well. The necessary entrapment beneath a shale-sealed anticline or by the juxtaposed impermeable layer caused by fortuitous faulting, are two basic scenarios for the presentday existence of the reserve. The necessary migration of the hydrocarbons from source rocks into potential entrapment structures, without escape to the atmosphere, adds to the adverse statistics of hydrocarbon exploration. Too close to the surface the sealing properties of shale, salt or clay-smear in faults, may have been compromised by lack of plasticity and too high permeability. Too deep, the pore space and permeability of the reservoir may be compromised, giving a reduced reserve and the need for permeability enhancement and gradient enhancement, or a decision for non-development. Following seismic interpretation of potential hydrocarbon-bearing structures, the need for expensive exploratory drilling and well-testing follows. Besides reservoir access for production testing, the hole is used for sonic logging and selected side-wall and regular core recovery, to better define the properties of the different lithologies, seals and reservoir rocks. Fortunately, or unfortunately according to viewpoint and tools available, rock reacts to the drilling of boreholes with a complex coupling of rock stress and strength magnitudes (plus the anisotropies of each), not forgetting the necessary subtraction of pore pressure for conversion of the three principal stresses to effective stresses. The appropriate selection of wellbore ‘temporary support’ in the form of mud pressure, using variable mud weight, determines the state of the borehole wall in the different lithologies, prior to setting and cementing the casing. Due to various opinions about an ‘alteration zone’ around the wells, there is now widespread acceptance of the need for logging while drilling (LWD) with monopole and dipole tools, to obtain ‘early’ velocity responses, which may differ significantly from subsequent wireline logging. The differences are probably due

to stress-fracturing, increased permeability, and accelerated mud-filtrate invasion. The frequent development of a near-wellbore, tangentially-distributed discontinuum, in cases of insufficiently mud-supported rocks, may perhaps have been overlooked, when modelling infiltration.

12.1

Pore pressure, over-pressure, and minimum stress

Before addressing the details of seismic signatures of reservoir rocks, caused by numerous environmental effects such as pressure, temperature and fluid type in Chapter 13 (at laboratory rock physics scale) and in Chapters 14 and 15 (at reservoir-scale), it is appropriate to consider the components and modifiers of the most fundamental of reservoir parameters, namely the effective stress magnitude. The rock stress and its variations with direction, depth and location, and the pore pressure and sometimes over-pressure which are influenced by compaction and also by fluid type, are the major boundary conditions. Their relative magnitudes affect both the laboratory test simulations, the drilling programme, the production planning, and the reservoir production and depletion, possibly for 50 years or more in a large reservoir.

12.1.1

Pore pressure and overpressure and crossdiscipline terms

Without attempting too much detail, since ‘pore pressure analyst’ has become a speciality career choice for numerous petroleum engineers, it is worthwhile following the helpful philosophy of Bruce and Bowers, 2002, and mentioning various cross-discipline differences for describing the effects of pore pressure and over-pressure. Reproducing selected diagrams from their practical article, we see

296

Rock quality, seismic velocity, attenuation and anisotropy

the following details in Figure 12.1a to d, and Figure 12.2 a to d. Most fundamentally, over-pressure and the presence of petroleum products, both increase the pore pressure. So the effective stress is reduced, which will have the effect of causing a reduction in P-wave velocity, as illustrated in Figure 12.3 from Bowers, 2002. Over-pressure commonly occurs where low permeability layers (as in shale) prevent fluid from escaping as rapidly as pore space compacts. Excess pressure in relation to hydrostatic then builds up as newly deposited sediments cause squeezing of the trapped pore fluids, which could be water, oil or gas or even two or three of these close together. To conclude this brief section on over-pressure effects, we may refer to more sophisticated considerations that over-lap with environmental effects discussed in the next chapter. Carcione and Gangi, 2000, reported results from their modelling of seismic attributes of gas generation and over-pressure. Their model for basin-evolution showed that pore pressure effects were seismically visible when the effective pressure was less than about 15 MPa, with oil-to-gas conversion of only 2.5%. Here they differentiated live oil containing gas, from the dead oil-free gas which may become seismically visible. They found that a small conversion of oil to gas was sufficient to make the pore pressure equal to the confining pressure. The large changes of predicted velocity, as shown in Figure 12.4, were the result of the fact that the dry rock moduli were strongly affected by low effective pressures. 12.1.2

Minimum stress and mud-weight

A complication for drillers when drilling through interbedded lithologies, or where hole stability is marginal due to limited rock strength or local ‘structure’, is their Figure 12.1 a) The basic gradients when there is over-pressure, considering min and the possibility of failure (hydraulic fracturing) by too high mud pressure. b) Depth-pressure gradients, showing equivalent mud-weights (in American units of lbs/gallon), where sea water  8.54 lbs/gallon. [1 lb/gal.  0.0519 psi/ft] c) Change from pressure-depth axis, to mud-weight-depth format (as preferred by drillers for obvious reasons). d) To prevent hydraulic fracturing by high mud-weights, as needed where there is overpressure, casing will be set to protect the overlying units from fracturing. Bruce and Bowers, 2002.

Rock stress, pore pressure, borehole stability and sonic logging

297

choice of mud weight. This heavy fluid acts as a temporary support of the walls of the well during drilling, until replaced by steel casing that is grouted into intimate, impermeable contact to the rock. Well testing, possible minimum rock stress estimation by mini-hydrofracing and subsequent production occurs through shapedcharge perforations of the casing in the reservoir intervals, and also in the cap-rock, if minimum stress is to be measured, to determine the minimum stress difference. Inter-bedded ‘brittle’ layers (like sandstone as opposed to ‘sand’), and ‘plastic’ layers (like shale or salt) will likely exhibit fluctuating minimum principal stress. Since the shale and salt-rocks may have insufficient shear strength to tolerate a significant stress difference, the minimum rock stress (the minimum of three principal rock stress directions) in the shale (or salt) will often exceed the minimum stress in the reservoir sandstone by up to several MPa. An example from measurements described by Barton, 1986, is shown in Figure 12.5. The shale (and the salt) may, if encountered at sufficient depth during drilling, require the support of an active mud-weight to prevent creep or squeezing, as graphically illustrated by Bradley, 1978, for the case of deviated wells, in Figure 12.6. So the drillers choice of mud-weight, or the setting of casing, becomes critical where support of the well is needed adjacent to a reservoir rock like sandstone or fractured limestone or chalk, which would tend to have a minimum rock stress less than that of these weaker, sealing ‘plastic’ layers. The reservoir horizons could potentially fracture, or have a permeable joint under lower normal stress than the mud-weight needed to keep the plastic materials from squeezing and jamming the drill-string. Invasion of mud (lost circulation), into any reservoir horizon is obviously very undesirable.

12.2

Figure 12.2 a) Overpressure in relation to normal hydrostatic pressure and its potential effect on effective stress-depth trends (in relation to vertical). b) Resistivity, velocity, density, depth trends with various degrees of deviation possible where over-pressure changes the effective stress. c) Pressure at well B is the sum of normal (hydrostatic) pressure, plus over-pressure, plus a buoyancy effect caused by the reduced density of the petroleum. d) The pressure components given in terms of depth-pressure gradients. Bruce and Bowers, 2002.

Stress anisotropy and its intolerance by weak rock

The local measured variations of minimum principal stress shown in Figure 12.5 are due to intolerance of stress difference in the weaker shale, as compared to the sandstone. As discussed earlier, such a mechanism also occurs in the case of salt. Swolfs, 1977 provided a graphic comparison of tolerance of stress difference (v  h min) for different rock types. Figure 12.7 shows data for v (overburden, calculated) minus h min (minimum horizontal principal stress) versus vertical stress. Rocks such as granite, stronger sandstones and

298

Rock quality, seismic velocity, attenuation and anisotropy

Figure 12.3 Example of high-pressure well from Bowers, 2002, where velocity (and resistivity) undergo reversals, due to ‘under compaction’.

Figure 12.5 Minimum principal (rock) stress in inter-bedded reservoir shales and sandstones, as recorded by minihydrofracing tests, to determine optimal stimulation by MHF (massive hydraulic fracturing), Barton, 1986.

Figure 12.4 A model of low frequency (25 Hz) P- and S-wave velocities versus excess pore pressure in the case of deep gas resources. The seismic visibility begins due to the sensitivity of Vp and Vs to reduced effective stress, especially in the dry state (dotted lines). From Carcione and Gangi, 2000.

stronger shales tolerate differential stress much better than weaker shales and salt rocks. Swolfs, 1977 compilation of vertical (over-burden) and minimum stress data for these typical North American reservoir rocks (and of some harder rocks like granite and gneiss) to depths of 5 km, shows greatest stress anisotropy near the surface, and in the harder rock types. Figure 12.8 shows a range of Ko from 0.35 to 2.9. Bedded salt in particular, plus weak rocks like Tertiary oil shale and Tertiary tuff showed h min/v close to 1.0. From the point of view of stress-azimuth dependent anisotropic velocity, the added influence of stressoriented jointing and the character of these joints will likely be more important than stress anisotropy effects on the matrix alone, due to the nature of ‘soft’ porosity (low aspect ratio) jointing. When shear wave splitting

Rock stress, pore pressure, borehole stability and sonic logging

Figure 12.6 The driller’s dilemma: avoidance of lost circulation (hydraulic fracturing or jacking), with the simultaneous need to support the rock walls of the well before casing is in place. Bradley, 1978.

299

Figure 12.8 Compilation of North American reservoir (and harder rock) and h min/v(Ko) ratios as a function of depth. Swolfs, 1977.

and joint shearing mechanisms are treated in Chapters 15 and 16, it will be found that the influences of anisotropic stress on the jointing will be of over-riding importance, since jointing may not always be parallel to the major stress direction, as traditionally expected.

12.2.1

Figure 12.7 Different degrees of stress difference (or shear stress) tolerance of reservoir rocks, compared to granite. Swolfs, 1977.

Reversal of Ko trends nearer the surface

As one approaches the surface, inter-bedded rock types resembling reservoir sequences, as illustrated in Figure 12.9, show the reverse of the previously discussed shear stress intolerance. Hydraulic fracturing tests reported by Barton, 1981 and Barton, 1986 generally showed low Ko ratios (h min/v) in the weaker materials like shale and siltstone, and maxima in the sandstones. This reversal of Ko trends (at a certain, unknown depth) if a general effect, may have certain ramifications when comparing stress-induced velocity anisotropy (and velocity ‘oscillation’) near-surface and at greater depth, for example when evaluating the applicability of ‘research-borehole’ seismic testing. There could be possible consequences for the relative magnitudes of attenuation, as low Ko (in addition to lower stress levels near

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Figure 12.9 A general tendency for lower Ko ratios (h min/v) in weaker rocks like shale and siltstone, according to hydraulic stress measurements at 100 to 300 m depth. Barton, 1981; Barton, 1986.

the surface) will tend to enhance attenuation, as seen in Chapter 10, as compared to the reduction of attenuation at depth due to higher stress and Ko values closer to 1.0 i.e. less anisotropy. Thus Q p and Q s values could be expected to be markedly lower and exhibit more anisotropy near-surface than at depth, as compared to rock sequences that did not show this Ko reversal. Whether such a trend has been recognised in seismic signatures, for these specific reasons, is uncertain. A possible modulus-related explanation for this Ko reversal was suggested by Barton, 1986. Figure 12.10 shows imaginary stress-strain curves for loading-unloading (i.e. sedimentation-erosion) curves for a stiff pseudoelastic sandstone and for a non-elastic, hysteretic shale. Imaginary deep-burial (but-on-the-unloading-curve) moduli of E2 (shale)  E1 (sandstone) and shallowburial (but-on-the-unloading-curve) moduli of E3 (sandstone)  E4 (shale) would give an explanation for the above depth-related Ko reversal. Whether the potentially different (unloading) moduli at these different depths would cause a part of an inhomogeneous velocity and attenuation structure, in addition to that caused by stress anisotropy and joint structure azimuth variations, remains an open question. Another open question, is perhaps whether the ‘oscillating’ minimum effective stress (min – pore pressure) in such alternating reservoir rocks is a significant reason for variable attenuation. In theory, it should cause ‘oscillations’ of Vp and Vs over-and-above those caused by the alternating media, with their different intrinsic properties like density, porosity, modulus and degree of fracturing or jointing. Possibly all the above cyclic properties of c, n% and Ko, and the different compliances of the

Figure 12.10 Imaginary stress-strain curves for loading-unloading (i.e. sedimentation-erosion) curves for a stiff pseudoelastic sandstone and for a non-elastic, hysteretic shale. Imaginary deep-burial (but-on-the-unloadingcurve) moduli of E2 (shale)  E1 (sandstone) and shallow-burial (but-on-unloading-curve) moduli of E3 (sandstone)  E4 (shale) would give an explanation for depth-related Ko reversal. Barton, 1986.

bedding planes and joints, could each play their role in the velocity-depth and attenuation (intrinsic and scattering) behaviour, and as we shall see in Chapter 15, influence shear wave splitting and anisotropy.

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12.3

301

Relevance to logging of borehole disturbed zone

The hydrocarbon reservoir exploration and production industry has found that the subject of borehole failure modes is an important ‘complication’ concerning the interpretation of sonic-logging of wells. There are now acoustic dipole and monopole logging devices that can be used in a logging while drilling LWD mode, that acquire responses from more than one hundred wave forms, in order to delineate formation fracturing response, and virgin conditions further from the walls of the wells, before additional ‘alteration’ has occurred from stress and/or mud-filtrate invasion, as often seen in subsequent wireline logging. There are possibilities for local velocity (and seismic Q) enhancement due to tangential stress increase in the case of competent rock like limestones, or low porosity sandstones. In the case of over-stressed, fracturing (‘dogearing’) sections of rock, and especially in the case of incompetent rocks like shales, reduction of velocity (and seismic Q) will occur, due to the mini-EDZ that form as a result of drilling. In the radial direction, stress reduction, which may be azimuthally varying, will tend to locally reduce the velocity, and thereby also the seismic Q. It is impossible to support each lithology with the ideal mud-weight, so some suffer the consequences, just as occurs in a tunnel where the contractor might be trying to reduce costs by under-supporting. In Part 1, Chapter 7, a range of effects that the EDZ (excavation disturbed zone) could have on seismic velocity inhomogeneity around tunnels was reviewed. Due to the smaller size of wells and the use of mud for hole support, the recognition of the behavioural data that can be extracted from anisotropic stress effects on small-scale EDZ round wells, seems to have come much later to the petroleum industry, than in tunnel engineering. This comment does not of course apply to borehole ellipticity, a much-used historical indicator of the minimum horizontal stress axis. The comment does apply to what lies behind the ellipticity. In tunnels it is all too easy to see, and occasionally even be killed by, the effects of structureinduced wedge release, or stress-fractured ‘lenses’ of rock. We are also able to install multiple-position borehole extensometers (MPBX), both in tunnels and in shafts, to measure the anisotropic radial-distribution of deformation, thereby giving deformation moduli as a function of direction and radial depth (e.g. 2.5 to 70 GPa variation of deformation modulus with radial depth, at

Figure 12.11 Shear and compressional sonic logs in ‘compacting shale’ between 1000 m and 2000 m depth in the South China Sea. Miller et al., 1994. ‘Substantial variation’ about the assumed (central) trends is taken by the writer as a possible indication of over-stress in numerous layers that, by the nature of the variation, were presumably insufficiently mud-supported.

1.6 km depth in steeply bedded quartzites: Barton and Bakhtar, 1983). Velocity variations and permeability variations as a function of position and radial depth around the tunnel or shaft, can also be determined, thereby relating these parameters to eventual stress anisotropy. (See Chapters 7 and 8) Plona et al., 1997, reported high frequency P-wave monitoring around a uniaxially loaded block of sandstone containing a borehole, and Figures 7.31 and 7.32 (and Section 7.4) gave indications of the significant velocity anisotropy (10 to 15%) due to unequal tangential stress concentration. They also suggested that the in situ detection of these azimuth-dependent velocity differences could be used to predict principal stress orientations, at stress levels below those needed for break-out. This was possibly signalling the early progress of important industry developments in dipole, loggingwhile-drilling, which will be illustrated later. Suspicion that wellbore effects must be important for logging results can be high-lighted by reference to Figure 12.11, taken from the sonic logging of a ‘compacting shale sequence’ in the South China Sea, reported by Miller et al., 1994. Should we really believe that the ‘substantial variation’ around the trends is a true reflection of different ‘virgin’ lithological properties? Are fluctuations of 500 to 1000 m/s about the mean ‘real’, or could they be due to accentuation of velocity changes, due to positive (m/s) or negative (m/s) mini-EDZ effects, as discussed, and illustrated above? Are the logging tools registering formation data, or wellbore effects?

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There is a strong likelihood that mini-EDZ in the weaker, less well mud-supported zones, have reduced, radial-dependent velocity, due to failure and deformation in the over-stressed zones. Stronger inter-beds could show an opposite trend due to tangential stress enhancement of the velocities. Mini-EDZ penetrating several diameters can in fact be detected, and circumvented by deeper sensing, shear-wave based, dipole logging tools. However the probable discontinuum reality (caused by log-spiral shearing, to be illustrated shortly), is only referred to as e.g. ‘shale alteration’. There is also the question of fabric and jointing and bedding plane effects, not least on the progress rates for mud-filtrate invasion. This seems not to be addressed, as yet. Fjæer and Holt, 1999 addressed the possible effects of the theoretical, isotropic, elastic stress distribution around a wellbore on sonic logging results. They suggested that with conventional long-spaced sonic tools, the zone of changed velocity due to the reduction in radial stress in relation to back-ground stress, would be mostly within a 1⁄2 well radius, and would not be detected, unless specially designed tools were used. They thought that the larger (and possibly also smaller) P-wave in the tangential directions would not be measurable by a conventional sonic logging tool. However, the authors referred to Plona et al., 1998 who had suggested use of a multi-pole logging tool capable of distinguishing between velocities in different azimuthal directions, close to the well. Plona and colleagues work, already referred to in Part I, is a central rock mechanics-based part of the newer well-logging developments that will be described shortly. Concerning processes important for well logging interpretation, we must consider modes of well behaviour, going strictly beyond elastic isotropic stressdistribution concepts. As we shall see shortly, the evidence to be presented for deeper penetration of mini-EDZ, presumably related with the ‘shale alteration’ referred to by Brie et al., 1998, is much in line with current industry interest. There turns out to be a serious potential contrast in logging results, when comparing the later (e.g. 1–2 weeks later) result of wireline logging, with the few hours delay represented by LWD, or logging while drilling. The more recent shear-wave anisotropy based logging, images a volume of up to several borehole diameters away from the wall, also beyond the stress-related fracturing and mud-filtrate invasion or ‘shale alteration’, thereby giving presumed ‘virgin’ formation attributes as well.

12.4

Borehole in continuum becomes borehole in local discontinuum

In mining and rock mechanics, there are well known, distinctive differences between stress-induced failure of hard dilatant brittle rocks like quartzites and hard sandstones (extensional splitting and crushing), and intermediate strength and less dilatant rocks, in which the traditional ‘dog-earing’ takes on a different shape due to log-spiral shear failure. These two basic modes were contrasted by a person with a broad experience of civil and petroleum related fields; Maury, 1987 (ISRM commission on failure modes). The two basic modes were linked to possible dilatant/non-dilatant rock failure behaviours by Barton, 1987. In Figure 12.12, various modes of continuum failure (of the previously intact matrix) have been assembled for comparison. They include a recently reported ‘tabular slot’ type of breakout, probably related with compaction band development during laboratory-scale drilling in porous blocks of sandstone. The more plastic model material, driven to the extreme of ‘well closure’ conditions, showed undrained strength mobilization and residual strength development reaching to many diameters. There was also a compacted zone. One may speculate that subsequent recovery (re-drilling) of such a zone would still leave permanent effects in relation to velocity reduction and seismic Q reduction. Local, dramatic changes of seismic properties should not deceive those interpreting well logging. The variable azimuth drilling described by Addis et al., 1990 was performed with the important threedimensional ‘detail’ of drilling while under 3D stress states, as happens in reality. The same result is not obtained when loading a block with a pre-drilled hole. The deep log-spiral development in the weak (0.5 MPa) cemented-sand tested by Addis et al., 1990, typically occurred when the major principal stress was about tentimes higher than the uniaxial strength, with the minor and intermediate principal stresses of 60% or 80% of the maximum. The borehole failure at the bottom of Figure 12.12 is probably a typical mode for not just non-dilatant, but actually contracting-with-shear clay-rich materials. Encountered in tunnelling situations, such fault-related, clay-rich materials may flow to form a weakly-inclined ‘delta’, flowing many tens of meters from the previous tunnel face (e.g. a Nathpa Jakri HEP headrace tunnel access drift, NE India). A case of 7,000 m3 of fault-zone

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Figure 12.12 A wide collection of failure modes for circular openings. Upper pair: from Maury, 1987 (ISRM commission on failure modes). Second pair: from NGI joint industry project and Addis et al., 1990. Third pair: left - deep log-spirals from NGI study by Rawlings, 1991, right – slotted breakouts sketched from Haimson, 2003. See Lee and Haimson, 2006 for recent results. Bottom pair: from NGI joint industry project: Bandis, 1988. Undrained shear strengths (in kPa) from centre: 0–5 (f ), 5–10 (p), 10–30 (p), 70–75 (c), 40–50 (s), and 50–60 (v). (f: flow, p: plastic, c: compacted, s: softening, v: virgin). See Zoback et al. 2003 for detailed theoretical analysis of break-out phenomena.

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Table 12.1 Failure and deformation modes typical in tunnels (after Barton, 2004b) may also apply at greatly reduced scale to the mini-EDZ that are likely to occur locally, where insufficient mud-weight has been applied. Description

Mode of behaviour

1. Hard, massive, brittle rocks that dilate during failure even when stresses are high. Stress-induced failure may be delayed as ‘strength corrosion’ occurs.

Extension failure, thin-walled stress-slabbing, dynamic ejection, bursting. The symmetric ‘dog-eared’ fall-out due to the anisotropic stresses may have a ‘nose’.

2. Hard or medium hard, bedded and jointed rock that can shear and dilate along structural planes, while under moderate to high stress levels.

Anisotropic response. Shear stress dissipates by slight shear on bedding planes and joints. Deformations are moderate. Block falls can occur.

3. Soft, massive, non-brittle rocks that may, or may not dilate during shear failure. Typical for young e.g. Tertiary rocks such as the mudstones and siltstones in Japan.

Failure may occur by log-spiral shear development and tangential strain. Radial deformations are large, and pressure on support is high. Multi-diameter influence.*

4. Very soft, plastic rocks (and clays) that contract when sheared under significant stress levels.

Post peak strength loss reaches an extreme of virtual ‘flow’, with in-rush of failed material.

(*Twin tunnels need pillars 4 to 5 times their span c.f. Japan, Taiwan, in order to minimise excavation interaction)

debris, filling a 70 m2 tunnel for 100 m has also been seen by the writer, in the Pinglin tunnels in Taiwan. Water pressures may of course be fundamental catalysts for such dramatic and sometimes tragic events. The ‘slotted’ failures described by Haimson, 2003, were obtained in polyaxially-loaded blocks of Berea sandstone, with 23 mm diameter hole-drilling while under stress, parallel to the intermediate vertical stress. Haimson’s samples with 17% porosity developed ‘conventional’ dog-earing, while the weaker 22% and 25% porosity samples developed increasing lengths of symmetric ‘slotting’ (see simple holes-with-slots traced from the experimental results, reproduced in Figure 12.12). The uniaxial strengths of the three sandstones were 53 MPa, 42 MPa and 22 MPa respectively. The depicted ‘slotting’ occurred during drilling, with principal applied boundary stresses of 50, 60 and 90 MPa, i.e. up to four-times the uniaxial strength of the weakest sandstone. Table 12.1, from Barton, 2004b, summarizes a quite complete range of failure and deformation behaviours for tunnels, with potential relevance to mini-EDZ development around boreholes, and possible consequences for sonic logging, and for bed-property enhancement or degradation, as discussed above. As emphasised by Barton, 2004b, the actual modes of physical behaviour experienced by boreholes and tunnels, are unlikely to be predictable when modelling with conventional Mohr-Coulomb type (c  tan ) shear strength criteria, because rock tends to fail first by loss of continuity at small strain, caused by loss of local tensile or cohesive strength, followed by frictional mobilization at larger strain. In modified Mohr-Coulomb

terms it is a case of ‘c then tan ’, not ‘c  tan ’. Numerical models that are programmed, or manuallysteered, to dissipate cohesion while mobilizing friction are capable of matching observed behaviour. The BEM (Boundary Element) fracture mechanics code FRACOD (Shen et al., 2002) seems to model log-spiral fracture development, and over-stress dissipation, in a particularly realistic way. If stress anisotropy (and stress magnitudes in relation to rock strengths) are sufficient to cause break-out, then clearly the principal horizontal stress direction is easy to predict from calliper logs, it being at right-angles to the largest well diameter in the case of a vertical well. This ‘simple’ situation may be disturbed by break-out caused by structure, i.e. steeply dipping jointing causing wedgeshaped fall-outs assisted by local bedding. Such mechanisms are a sign of a mini-EDZ that is in progress around the well, and one that could be used in dedicated, azimuthal, short-base, well-logging. The influence of stress fracturing on velocity anisotropy, including but beyond the pre-failure states investigated by Plona et al., 1997, means that there will be anisotropically distributed fracturing around eventual over-stressed part of a well, that had not been adequately supported by mud pressure. To emphasise (and probably exaggerate) the likelihood of possible serious differences in EDZ-potential down a well in alternating hard/soft rocks, one may refer again to some of the borehole stability studies reported by Addis et al., 1990. These were performed in the late 1980s at the Norwegian Geotechnical Institute, in a joint oil-industry study. Figure 12.13 shows one of the

Rock stress, pore pressure, borehole stability and sonic logging

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Figure 12.14 Closed-form elasto-plastic analysis of an internallysupported well, compared to the physical-model reality of log-spiral shear-failure surfaces, that help to dissipate the highest stresses further into the rock mass. NGI contract report, 1990.

Figure 12.13 One of a series of log-spiral-type failures around heavily stressed model boreholes that were drilled at different deviation angles in relation to a moderate 3D stress anisotropy. Addis et al., 1990, and NGI contract report, 1990.

‘symmetric’, double-cusp, intersecting log-spiral modes of shear failure that was exposed around the borehole, following polyurethane-foam hole-stabilization, while still under stress. Cubic 50  50  50 cm blocks of model sandstone (c  0.5 MPa) were used for 3D

application (via flatjacks) of three equal or unequal principal stresses, with drilling performed into the modelled block of rock while under stress, either as a ‘vertical’ well, or at different deviation angles with respect to any of the principal stresses, as shown in this case. Application of an analytical closed-form elastoplastic isotropic continuum model to a heavily stressed, drilling-mud-supported well, shown in Figure 12.14 suggested that a narrow, deeply-penetrating, elliptical ‘plastic’ zone would develop, where the Mohr-Coulomb shear strength criterion was exceeded. The reality – as far as a physical model represents reality – was for one

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of earth science’s favourite continuum theories to be ignored, and instead we witnessed the development (in every case), of a 1 to 2 diameter wide zone of log-spiral failure surfaces, making in effect a discontinuum, which actually allowed the wall-rock to dissipate the highest shear stresses further into the surrounding rock, just as occurs in tunnelling through over-stressed ‘squeezing’ rock. A ‘radial’ strain is observed in the opening – there is measured radial closure – but the reality is tangential strain due to the log-spiral shearing. This mechanism has been well documented by Aydan et al., 1992. These three-dimensional failure surfaces ‘followed the borehole’, and also curved in front of the face of the hole, whenever the holes were drilled into the highly stressed blocks of rock simulant. This was seen following sectioning. Such an EDZ, developed in an insufficiently mud-supported weakness zone, or in a bed of shale adjacent to a reservoir sandstone (with insufficient hmin to tolerate higher mud weight), would tend to locally accentuate both the expected low seismic velocity, and an expected low seismic Q value, that could be obtained from seismic logging. Before leaving rock failure mechanisms in the intact matrix around boreholes, a hybrid (intact plus jointed) result will be shown from modelling with the FRACOD fracture mechanics BEM code of Shen, described in Shen et al. 2002. The two models shown in Figure 12.15, performed by Shen for the case of a deep excavation under high stress, had deliberately sparse jointing. Different levels of ‘log-spiral-type failure are demonstrated, depending on the ‘disturbance’ to stress distributions, caused by jointing, which dissipates some of the highest, near-wall tangential stresses. The resultant ‘dispersed’ fracturing (as opposed to jointing) would presumably be a strong source of scattering attenuation – and velocity reduction. Note that the principal applied stress levels in the case of this strong rock were only about 35–38% of the uniaxial strengths. A brittle sandstone of 50 MPa UCS would be acted on by an equivalent ratio of effective stress beyond about 1200–1300 m depth, with standard density and pore pressure assumptions, considering a H max value no larger than the vertical effective stress. Of particular interest to the frequent velocity discrepancy between LWD and later wireline logging of the same formation (see later examples), is the possible development of fracturing over time, and the result this has on the ‘factor of safety’ against further shear failure. Figure 12.16 shows two episodes of fracture development over time from the same FRACOD model, and

demonstrates a distinct rotation of the dark grey-scale, from a ‘NNE-SSW’ to ‘E-W’ azimuth. The grey-scale represents F. of S.  1.0.

12.5

The EDZ caused by joints, fractures and bedding-planes

Due to the influence of deformation of ‘soft’ as opposed to ‘hard’ porosity, a borehole for hydrocarbon exploration that penetrates variably jointed and faulted ground, will actually experience variable small amounts of deformation, due to different degrees of joint closure, joint opening, and joint shearing. There will also be the pseudo-elastic response, due to both loading (at the diametrically-opposite  max locations) and potential unloading (at the diametrically-opposite  min locations) of the matrix as well as the joints, the latter usually dissipating some of the theoretical (isotropic, elastic) peaks of maximum and minimum tangential stress. This process will occur even with a constant mudweight, since the mud – unlike rock bolts in a tunnel – cannot prevent joint movements of unequal magnitude at different points around the opening, although the mud may help to make them very small. Figure 12.17 shows four idealized, two-dimensional models of circular hole excavations in anisotropically loaded ‘blocky-rock’, with four successively reduced block sizes. There are 250, 1000, 4000 and 10,000 blocks in the respective models. Two of the coarsest block geometries are shown in the top of the figure, while all four of the joint-shearing fields are given. The reducing block sizes can be glimpsed within the two lower models. These models represent ‘crushed zones’ at borehole scale, i.e. gross approximations to fault-zone-crossing stability problems. Figure 12.18 demonstrates analytical Mohr-Coulomb formulations used by Shen to produce the general result for zones of shearing on differently inclined, conjugate or perpendicular joint sets. The four-sector EDZ, at roughly 45°, 135°, 225° and 315° is bisected by the two applied boundary principal stresses, e.g. a ‘N-S’  H and an ‘E-W’ h. Shear displacements occur on the joints in these four sectors, even when stresses are isotropic, as shown by UDEC-MC or UDEC-BB modelling of tunnels through horizontally and vertically jointed rock. A more realistic model of ‘fractured rock’ (such as might be found in the neighbourhood of fault zones), actually representing slightly random jointing in tuff, is shown in Figure 12.19. The model represents a bored

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(a)

(a)

(b)

(b)

Figure 12.15 Fracture mechanics BE modelling of circular openings in high over-burden environments, using the FRACOD code developed and demonstrated by Shen. The modelled rock mass was hard and of high modulus (UCS  160 MPa, M  50 GPa), with assumed shear strength of c  40 MPa,   35° and appropriate fracture toughnesses at the modelled effective stress levels of 30 to 60 MPa. a) EDZ with sparse jointing and 1 (‘NS’) of 55 MPa and with 2 (‘EW’) of 40 MPa. b) EDZ with significant jointing and 1 (‘EW’) of 60 MPa and with 2 (‘NS’) of 30 MPa. Note: deformations do not track subsequent fall-out/loosening. Nick Barton & Associates contract report, 2005.

Figure 12.16 Fracture development over time in a FRACOD model of a circular opening in a jointed zone. Note the ‘rotation’ of the diametral-pair of red regions, which represent low factors of safety against shear failure. Further fracturing dissipates and displaces the low F. of S. zones, suggesting that more fracturing could occur across the ‘E-W’ diameter. Changed seismic response over time is easy to imagine, also a mudfiltrate invasion speed that could be highly non-uniform, due to developing permeability in the partly connected discontinuum. Nick Barton & Associates 2005 contract report. See Figure 12.15 for input data. (See plate 3).

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Figure 12.17 Shear deformation zones developed around circular openings, as a result of slip along both joint sets, when excavated under anisotropic stress, and when with limited joint strength, e.g. due to clay-smear or general smoothness. Cundall’s distinctelement UDEC-MC code (with Mohr-Coulomb sub-routine), was used for the analyses, with four successively reduced block sizes. Note the increasing multi-diameter EDZ, as block size and therefore rock quality reduces. Line thickness depicts joint shear magnitude. Shen and Barton, 1997.

Figure 12.18 Theoretical, Mohr-Coulomb based solutions for shear displacement zones involving slip on conjugate joint sets. Note that the largest joint-shearing EDZ is for the 60° case, in which shear stress is maximized relative to the joint directions. The smallest joint-shearing EDZ is for the 90° case, in which the shear stress is minimized relative to the joint directions. Shen and Barton, 1997.

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Figure 12.19 UDEC-BB modelling of a TBM tunnel EDZ in jointed tuff, at a simulated 650 m depth. Note far-field h  fiv. This model is assumed to represent a generic case of heavily fractured (faulted) and sheared rock close to a vertical borehole. Clockwise (with 8 m full-scale excavation diameter): principal stresses (max. 30 MPa), deformations (max. 11 mm), joint shearing (max. 8 mm), and joint (and block-corner channel) conducting apertures (max. 2 mm). Hansteen, 1991 (NGI contract report), and Barton, 2000.

excavation at 650 m depth, and had the predicted, closeto-the hole EDZ behaviour. (Note that the model’s loaded boundaries extended some 10-diameters from the hole, and the hole was also close to a simulated claybearing fault.) Four basic EDZ components are shown: ●

●

●

●

Principal stresses (‘N-S’), and redistributed tangential stress Displacement vectors: maximum parallel to ‘N-S’ stress maximum Joint shearing (clockwise or anticlockwise) and proportional to line thickness Joint (and block corner channel) conducting apertures

The modelled rock was actually jointed tuff, with input data from index testing of numerous joints from

each set, as recovered from deep boreholes at the UK Nirex Sellafield’s site in NW England. A second model, this time representing a horizontal bored tunnel at 400 m depth through inter-bedded sandstone and shale, is shown in Figure 12.20. If we scale the roughly 5–15 mm range of deformations from 8 m tunnel size in hard rock, to a nominal, and convenient, 16 cm well size, with correspondingly reduced rock strengths, the magnitudes become 0.1 to 0.3 mm. The deformations, although small (i.e. submillimetre size when the hole is stable), are probably up to a few orders of magnitude larger than the displacement discontinuities that are sufficient to generate joint compliance changes (normal and shear), that are of recognisable (inverted) magnitude, in relation to the joint stiffnesses familiar in rock mechanics. The lower

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Figure 12.20 UDEC-BB modelling of a TBM tunnel EDZ at 300 m simulated depth, in inter-bedded sandstone and shale. Note far-field h  v. This model is assumed to represent a generic, shallow horizontal well. From top: principal stresses (max. 50 MPa), deformations (max. 15 mm), joint shearing (max. 8 mm). Note that ‘buckling’, or cracking of thin beds, does not occur in UDEC, unless the necessary failure surfaces are discretized before-hand. Chryssanthakis, 1991 (NGI contract report), and Barton, 2000.

dynamic compliances will signal the reduced velocity and the reduced seismic Q, via the reduced dynamic (and static?) moduli. Since both isotropic and anisotropic stresses, but especially the latter, can (indeed must) cause a minidisturbed zone around a well, it is likely that this could influence dipole sonic logging down the well. In the case of the sedimentary rock model, with shale beds, at a moderate 300 m depth, the joint shearing and deformation EDZ are each of several hole-diameters in extent. Is it not possible that the mini-EDZ illustrated here, can be the root cause of much of the intense fluctuation seen in the sonic logging results presented in Figure 12.11? Low Vp and low seismic Q zones could be depressed further by an accentuated EDZ. Conversely, high Vp and high seismic Q could be further elevated by the effect of high tangential stresses close to the borehole wall, where there was no failure or joint deformation (or joint presence) to speak of. Consider the following cross-discipline parallels. When assessing the rock quality of the walls and arches of tunnels, the observed rock, which is the visible part of the tunnel-scale EDZ, is classified (using the Q-system: see Appendix A), in order to select appropriate rock reinforcement (grouted rock bolts) and tunnel support (sprayed, steel-fibre-reinforced concrete). The latter is the equivalent of the borehole mud pressure, and is badly needed in a complete load-bearing ring, in the rapidly deteriorating and deforming clay-bearing zones, in order to control deformation and prevent local tunnel collapse. Outside the tunnel EDZ, the rock mass would be characterized as a better quality rock mass. If one performed both sonic logging and azimuthal dipole sonic logging – a development described by Brie et al., 1998 (see later), the borehole mini-EDZ can be classified by the one tool, while the hydrocarbon-bearing or reservoir sealing formation away from the immediate influence of the hole, can be characterized with higher velocity by the other tool. The same arguments as above apply to seismic Q. As we shall see, at least part of this rock mechanics logic is being applied in modern well logging, with multi-wave-form acquisition. A layered model, consisting of a ‘thinly-bedded’ model sandstone and micaceous inter-layers that was expertly fabricated by Bandis while working at NGI, is shown in Figure 12.16, to emphasise again that if one starts with a discontinuum, the possibility of deformation is increased. In contrast to the jointed UDEC models shown earlier, this steeply inclined bedding

Rock stress, pore pressure, borehole stability and sonic logging

allowed a buckling mode of deformation to develop, causing an elliptical yielding zone, with a long-axis of several diameters. It is easier to imagine this case when rotated through 45°. A mud-pressure capable of preventing the buckling action can readily be imagined causing unwanted hydraulic fracturing, as depicted in Figure 12.6. Such buckling mechanisms are common in thinly-bedded coal-measure rocks, and presumably can compromise the integrity of horizontal wells, if drilled where beds are very thin. In the foregoing, the possible effects of the weakness of formations, in the face of drilling with insufficient mud-pressure, have mainly been addressed. Accompanying potential shear-failure, there is a tendency for dilation, unless stress levels are high enough to suppress this expansion. The local and bulk dilation is of course part of the ‘alteration’ zone phenomenon, and is a basic reason for an initial velocity reduction (e.g. under LWD), followed intuitively by increasing permeability, therefore accelerated mud-filtration weakening, with a possible spiral into lower velocity territory, by the time of wireline logging. The permeability of a damaged borehole wall is unlikely to remain constant in the interval between LWD and wireline logging.

Figure 12.21 A buckling mode of deformation when penetrating horizontal or steeply dipping thinly-cycled beds, would also tend to compromise the ‘correct’ value of logging-based Vp and seismic Q, in the case of dipole azimuthal-logging. Model fabricated by Bandis, 1987 (pers. com.).

12.6

311

Loss of porosity due to extreme depth

Loss of porosity with pressure or depth is well documented in sandstones recovered from sedimentary basins such as the North Sea and the US Gulf Coast. These basins typically have porosity versus depth curves with mean porosity of about 23 to 27% at 2 km depth, decreasing to 3 to 7% at 7 km depth. This change in porosity signals changes (increases) in mechanical strengths and of course increases in seismic velocities, and, all other things being equal, would suggest reduced attenuation or higher values of seismic Q. In a downhole or reservoir environment, inhomogeneity caused by structure, for example more intense fracturing or jointing in the resulting stiffer sandstone might have a reversed effect on the above assumption of reduced attenuation with depth. An assessment of the onset of the brittle ductile transition of sandstones reported by Scott and Nielsen, 1991, has relevance here in the case of increased depths of burial, and possible components of behaviour around deep wells, in view of the approximate doubling of the field effective stresses in the tangential stress arch around an initially non-yielding borehole wall, i.e. when still responding ‘elastically’ with horizontal stresses of similar magnitude, giving  (max and min)
31  3. The authors Scott and Nielsen, subjected sandstones with a wide range of porosities (6.0%, 13.9%, 19.9%, 20.9%, 22.0% and 27.6%) to triaxial confinement (0.1, 5, 10, 30, 50, 70, 90, 110 and 130 MPa), and also reviewed tests at much higher confining stresses. All their tested sandstones had similar grain size, shape, orientation and composition, and all were cored from fresh unweathered blocks, without strong bedding plane anisotropy. Figure 12.22 shows how the higher porosities were readily driven to the brittle-ductile boundary; solid circles representing ductile (non-dilatant) cataclastic flow, while open circles represented brittle, dilatant, shear fracture. On the shear strength development at reservoir stress levels are shown in Figure 12.23 subject of extreme burial effects, Chuhan and Bjørlykke, 2002 contrasted the normal mechanical compaction of sandstones down to 2–2.5 km depth, with grain crushing phenomena at greater depths. The ‘limits’ of normal mechanical compaction appears to correspond to the ‘knee’ seen in velocity-effective stress tests in the laboratory up to about 25 MPa. They mentioned the precipitation of quartz cement at greater depth, where temperature was higher,

312

Rock quality, seismic velocity, attenuation and anisotropy

causing enough strengthening of the grain framework to prevent further compaction. According to Chuhan and Bjørlykke, grain fracturing is commonly seen in North Sea reservoirs, in coarsegrained sandstones, but rarely in fine-grained sandstones. Some deeply buried sandstones (5 km) at Haltenbanken showed evidence of more extensive grain crushing, because grain coatings had apparently delayed quartz cementation. Deeply buried reservoir sandstones (6 km) from the Azerbaijan area, that were subject to rapid subsidence and a low geothermal gradient had very little quartz cement and showed evidence of intense grain fracturing. This was assumed to have occurred when the effective stress was about 40–50 MPa, at 4–5 km depth.

12.7 Figure 12.22 High pressure triaxial tests on sandstones of various porosities, showing the approximate limit of brittle behaviour. Scott and Nielsen, 1991 and cited authors. Note the extreme confining pressures. Solid circles represent cataclastic flow, open circles represent brittle shear fracture.

Figure 12.23 Shear strength envelope separating brittle and ductile behaviour for sandstones of various porosities. Scott and Nielsen, 1991 and cited authors. Solid symbols represent cataclastic flow, open symbols represent brittle shear fracture, and half-black represents transitional behaviour.

Dipole shear-wave logging of boreholes

Brie et al., 1998, in a multi-authored, major contribution to ‘new directions in sonic logging’, provided a fascinating glimpse of the newer techniques of well logging, and of the challenging conditions that were met in different types of formations. Their article confirms many of the foregoing suspicions that what we have termed mini-EDZ, are indeed a source of concern in certain formations, and more importantly, that these deeper ‘alteration zones’ can be detected and seismically characterized, and avoided, with the help of novel dipole transmitter tools, that generate flexural waves. Flexural waves are shear waves that are polarized into fast and slow directions, and penetrate several hole-diameters into the formation, thereby revealing potential stress-induced ‘alteration’, and/or drilling mud-induced alteration. As we shall see in much greater detail in Chapter 15, shear wave measurements seem to be the most useful mode for fractured reservoir interpretation at many scales. The amount of sophisticated equipment that well drillers may now connected to ‘follow’ the drill-bit, using a down-hole mud motor in the bottom-hole assembly (or BHA), is impressive for its sophistication and necessarily compact nature. It resembles in some ways the several hundreds of meters of generally much less sophisticated back-up that are set to be pulled (on rails), behind a large tunnel boring machine. Consider this paragraph from Brie et al., 1998, concerning an interval of drilling down an Angolan (West African) offshore exploratory well: ‘A long single-bit run was conducted over a 7-day period that covered a depth from 1000 to 8000 ft. The wellbore

Rock stress, pore pressure, borehole stability and sonic logging

was deviated 20° in this interval. The BHA consisted of a PowerPak mud motor, a CDR Compensated Dual Resistivity tool, a PowerPulse MWD (measurement while drilling) telemetry system – for real-time transmission – and an ISONIC sonic-while-drilling tool. The ISONIC tool, placed above the PowerPulse system, was approximately 104 ft (32 m) away from the bit. At the average rate of drilling, the LWD (logging while drilling) measurements were made fewer than four hours after the formation was first cut. Wireline sonic logging was run after the 7-day drilling run was completed, and then only after circulating the well for several hours.’ Brie et al., 1998 emphasised that LWD logging while drilling sonic logs, acquired in freshly drilled rock, show ‘remarkable differences’, compared with wireline measurements that are usually taken many days, or a week or two, after the drilling has exposed the formation. They pointed out that both well surveys bring important but different information about wellbore rock properties. The cause of these fundamental differences is summarized in a helpful diagram from their publication, shown in Figure 12.24. Since the ‘altered zone’ around the borehole may continue to develop during the week or so that may separate the two types of logging, the later wireline log may be influenced by a reduced modulus in an annular zone around the borehole, particularly in soft formations. Water uptake in this zone (from mud-filtrate), as well as the initial over-stress, will also reduce the modulus in shales and shaly sands, according to Brie and co-authors, lending support to our initial question concerning the real meaning of the South China Sea log shown earlier in Figure 12.11. A so-called ‘bi-compressional arrival’ may be registered – a phantom arrival too fast to be a shear wave – actually caused by trapping of the wave-front by the low-modulus damage zone. Figure 12.25 illustrates the novel dipole transmitter principle. During logging, flexural waves are generated by sequential firing in two perpendicular directions (see bottom of tool), first along the tool x-axis, then along the tool y-axis. These induced shear waves are split and polarized into fast (qS1) and slow (qS2) directions, respectively parallel and perpendicular to dominant fracturing or to the principal (horizontal) stress direction (if the tool is in a vertical hole, and more distant response is analysed). The shear waves are registered by the dipole receiver pairs shown at the top of the tool. The important property of shear-wave splitting is illustrated in Figure 12.26. In the example shown, the shear wave splitting is caused by the y-axis aligned

313

Figure 12.24 Stress-related damage, possibly compounded by subsequent water or mud-filtrate weakening, have the potential effect of reducing the modulus in the several days or one week delay between LWD (logging while drilling a few hours behind the drill-bit), and the subsequent wireline sonic logging. Entrapment of wave-fronts in the lower modulus damage zones results in ‘bicompressional arrivals’: i.e. second arrival compressional waves. Brie et al., 1998.

fracturing, with fastest velocity (as also with P-waves), in the direction parallel to structure, possibly also aligning with the major principal stress direction. (In Chapter 15, numerous examples of this exceptionally fortuitous property of S-waves will be given, from fractured reservoir analysis). The slow direction (as also with P-waves) is perpendicular to the fracturing – which could be microcracks, cracks, joints or faults – according to the scale of example considered. Shear-wave splitting, and polarization is one of the most valuable of all seismic anisotropy properties for fracture and fracture-fluid investigations, perhaps matched by the anisotropic and dispersive attenuation of P- and S-waves (see Chapters 14 and 15).

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 12.26 An illustration of the shear-wave splitting and polarization phenomenon, from Brie et al., 1998. Note the longer wave length of the fast shear-wave. Figure 12.25 Dipole transmitter tool for sequential firing in x- and y-directions, to generate flexural (shear) waves that become split and polarised due to dominant fracturing or stress, thereby becoming fast (with longer wavelength) parallel to structure, and slow (with shorter wave length) perpendicular to structure. Brie et al., 1998.

The two orthogonal dipole transmitters, and the multiple receiver pairs, which are aligned in orthogonal directions, measure the components of slowness in any direction within planes perpendicular to the borehole. In fact four sets of waveforms are recorded. By minimizing (with Alford rotation), the cross-receiver amplitude-based energies, the rotated direction of the fastest shear waves becomes the fast-shear tool azimuth. A magnetometer relates this direction to true north. The logging tool results are converted to graphic read-out of the two contrasting velocities, together with the energy anisotropy, the slowness anisotropy, and the time anisotropy. Large energy differences, with the minimum staying low, signal strong anisotropy. Both the acoustic time anisotropy and the slowness anisotropy

are sensitive to properties deeper within the formation than the surface effects of drilling. A significant finding regarding the distinction between stress-related anisotropy around boreholes, and fracture related anisotropy, is shown in Figure 12.27 from Winkler et al., 1998 (his co-authors Sinha and Plona were also contributors to Brie et al., 1998). Borehole stress concentrations (in competent rock like the tested Berea sandstone) caused radial stress gradients that were different in the two principal directions, thereby causing frequency dependent (dispersive) effects such that the shear-wave that is polarized parallel to the major stress, is fastest only at low frequency (25 Hz). The fact that shear wave anisotropy allows the investigation of a volume of the formation up to several diameters from the borehole axis, means that it can sense jointing, and stress-induced fracturing, that are missed by conventional logging tools. This means that it is particularly useful for registering the additional jointing and fracturing that tends to be present on either side of a fault. (Endo et al., 1997)

Rock stress, pore pressure, borehole stability and sonic logging

315

Figure 12.27 Dipole dispersion cross-over of fast and slow shear waves, demonstrated by modelling, and by testing unloaded and loaded blocks of Berea sandstone containing a borehole. Caused by unequal radial stress gradients in the two principal stress directions, when uniaxially loading one of the blocks of sandstone containing an instrumented borehole. Winkler et al., 1998. This study should ideally be performed on a borehole drilled while the block is under stress, e.g. following Addis et al., 1990, Haimson, 2003.

A case was described from an Egyptian oil-producing well drilled in basement granites. With the shear-wave anisotropy logging, the fault signature was clear, with the fast azimuth starting to change slowly when about 20 m from the fault, with a rapid change of nearly 65° across the fault, followed by a return to an intermediate azimuth some 30 m beneath the fault, and a final return to background azimuth at greater distance. The particular fault had high permeability. A final mention will be made of two other very useful applications of LWD with dipole shear-wave anisotropy analysis, which is available almost in realtime (some hours behind the drill-bit). The first is the application to drilling of horizontal well sections, designed to intersect a maximum amount of structure, and simultaneously avoid the less favourable parallel to H max hole direction. The second is early warning while drilling in formations with rapidly changing pore pressure. LWD is then an important aid in choosing appropriate mud pressures. When porosities are no longer maintaining a normal trend of increased compaction

with depth, the slowness data will tend to diverge from the expected trend (Brie et al., 1998). By the beginning of the 21st century, it has become more common to use dipole sonic logs to help interpret AVO or amplitude variation with offset anomalies, and to help tie in ocean bottom seismic surveys (OBS) with four-component (4C) acquisition. These techniques will be briefly described with case examples, in Chapter 14. The use of both wireline dipole logging in vertical holes, and pipe-conveyed dipole tools for deviated and horizontal wells has now given reservoir geophysicists improved means of calibrating the responses of their rock physics based reservoir models, against small-scale measurements.

12.7.1

Some further development of logging tools

More recent descriptions of mechanical damage and anisotropy evaluation using a new modular dipole sonic

316

Rock quality, seismic velocity, attenuation and anisotropy

logging tool developed by Schlumberger, were given by Pistre et al., 2002. This tool provided a complete seismic characterization in radial, axial and azimuthal directions. Improved monopole and cross-dipole technology, together with 13 axial levels, each with 8 azimuthal sensors, with each of the 104 receivers individually digitised, resulted in 104 waveforms per transmitter firing. Five transmitters are used. As the authors emphasised, radial rock property variations arise because of non-uniform stress distributions and mechanical and chemical near-wellbore ‘alteration’ due to the drilling process. The development of a discontinuum close to the wellbore is not mentioned, but perhaps implied in the word ‘alteration’. The authors emphasised that radial gradients of acoustic slowness arose due to wave speeds being a function of stress. (To this could be added the velocity reducing effects of a discontinuous medium, due to rock failure and various possible deformation mechanisms, as illustrated earlier). The authors pointed out that anisotropy could also be caused by intrinsic shale anisotropy, possibly combined with external differential stresses. Inversion for these anisotropic, radial and azimuthal rock properties could now be achieved from the various acoustic behaviours, and from use of broadband dispersion curves. A particular feature of the new tool was that profiling of radial variations in compressional slowness could be achieved through monopole acquisition with a wide range of transmitter-receiver spacings, from very short to very long. Radial inversion of shear slowness was quantified through inversion of the broadband dispersions of the dipole flexural (Figure 12.25) and Stonely wave modes. When radial gradients were detected, in e.g. sandstones, there could be an increased risk of sanding, while lack of radial property gradients suggested mechanically intact rock, far from failure. The question of tangential-stress enhanced velocities and moduli, capable in principle of adding to the velocity oscillation seen in Figure 12.11, was not mentioned. (As shown in Chapter 5, Figure 5.36, the modulus that is influenced by cracking or jointing, shows strong stresssensitivity). An example of part of a log display from an exploration/development well, is reproduced (in grey-scale) in Figure 12.28, from part of a very comprehensive, colourful log display given by Pistre et al., 2002. This shows the result of the dipole flexural wave split into fast (left) and slow (right) shear directions. The six-tone curves represent slowness (expressed as s/ft) at different

Figure 12.28 Part of a dipole-generated flexural wave monitoring log, here split into fast (left) and slow (right) shear directions by stress and/or fracturing. Differences are expressed here as slowness, for different radial depths behind the wellbore wall. Pistre et al., 2002.

radii from the wall of the borehole. The upper half of the profile shows a large radial gradient, from high slowness near the wellbore, to a lower slowness at a radius of 24 in, or 63 cm. At the base of the profile the individual curves tend to overlay, indicating a sounder rock with negligible radial gradient of shear velocity.

12.8

Mud filtrate invasion

The related themes discussed and illustrated in the forgoing pages: ●

intensely fluctuating sonic log velocities in interbedded (sandy?) shales

Rock stress, pore pressure, borehole stability and sonic logging

317

invaded zone would be important for processing and interpretation of logs. The problem is caused by the invaded (or ‘altered’) zone being deeper than that illuminated by the logging tool, meaning that the velocities will not reflect those of the formation, but of the damaged zone, therefore requiring corrections. They used multilayer velocity models to interpret well measurements, for example the following layer depths and velocities for the case of a slow and fast formation: Figure 12.29 Conceptual mud-filtrate invasion in a permeable rock formation. After Chi et al., 2004. ● ●

●

●

mini-EDZ around experimental boreholes log-spiral shear surfaces observed in physical and numerical models deformation (shearing, opening) of joints close to numerically modelled wells damage zones confirmed by bicompressional arrivals in real wells

suggest that mud-filtrate invasion modelling may perhaps need to also consider flow through local discontinua, such as interconnected log-spiral shear surfaces in softer rocks, or less well- connected tensile and shear fractures in harder rocks, and flow along bedding planes and joints in general cases without over-stress. Chi et al., 2004 mention the fairly common finding, based on LWD and subsequent wireline logging differences, that near-wellbore formations are often altered by stress, stress release and an assumed mud-filtrate invasion, as envisaged, schematically in Figure 12.29. However, a relatively uniformly-paced invasion, based on porositypermeability conversion may perhaps be compromised by an actual permeability enhancement, based on the central thesis of this book that rock quality, i.e. degree of jointing, stress-induced fracturing, deformation moduli, velocity and permeability, are quantitatively linked. According to the authors, the ‘alterations’ cause the physical properties in the near-wellbore region to be different from those of the uninvaded rock formation. In addition, stress concentration may cause formation anisotropy, and an azimuthally varying radial variation of velocities. As they point out, in well-consolidated hard rock formations, mechanical damage is less pronounced than in soft formations, so mud-filtrate invasion would then be more localized. Formation properties inferred from wireline logging measurements may not reflect the true properties, so their opinion was that a realistic description of the

Layer

Radius

Vp slow m/s

Vp fast m/s

1 2 3 4 5 6

0 0.10 0.18 0.26 0.34 0.42

1500 2300 2350 2400 2450 2500

1500 4390 4512 4634 4756 4878

These differed in a realistic manner from a more commonly assumed sharp-interface model. In some ways this small-scale gradational model mirrors the early controversy concerning stepped or gradational sub-ocean spreading-ridge velocity modelling, also applying to an unchanged rock type, in that case basalt, and applying to kilometre-scale depths. (Chapter 11) Both phenomena are reflections of the changing degree-of-fracturing, and of its interaction with the local effective stress. Chi et al., 2002, emphasised that synthetic seismograms often did not correlate with measured seismograms, when correlating seismic data with acoustic logs. It appeared that the standard approach here was to ‘correct’ the acoustic logs via a Biot-Gassmann fluid substitution, to ‘free sonic logs from mud-filtrate invasion effects’. Doing this, it was assumed that the measured velocities were those of the invaded zone, saturated with mud filtrate. By ‘displacing the saturation fluid’ theoretically, new velocities were obtained, and taken as the virgin formation velocities. However, there is a potential problem here, if the near-wellbore is stressfractured, despite ‘removal’ of the saturating fluid. In the example they described, surprisingly, only of the order of 2 to 3% velocity changes resulted from the Biot-Gassman fluid substitution, showing that a reduction of Vs and an increase for Vp had occurred in relation to true formation properties. This magnitude of change seems immaterial in relation to the total effect of potential wellbore damage, clearly mostly caused by

318

Rock quality, seismic velocity, attenuation and anisotropy

‘rock mechanics’ effects (i.e. stress induced fracturing of some form). In addressing the needs of a multi-physics approach to the complex question of formation evaluation, based on time effects registered by well logging (LWD followed by wireline), Torres-Verdin et al., 2003 utilised a variety of modelling approaches. In Figure 12.30 they show the result of a four-days mud-infiltrate invasion model, using constant-permeability-with-radius assumptions, but with a 1:10 ratio of Kvertical and Khorizontal in the formation of interest. The figure shows the calculated formation resistivity distribution, due to the unequal rates of invasion in the central formation. This anisotropy modelling gives an improved vision of possible realities, but due to wellbore damage, modellers and analysts should perhaps also consider a radius-dependent distribution of permeability, related with the radius-dependent velocity caused by the (also radius-dependent) degree of stress-induced fracturing and stress redistribution. Such will only be necessary of course, when the formation characteristics, in relation to the stress levels and mud-pressure applied, cause unwanted ‘alteration’ of properties, both immediately, and exacerbated by time effects. Infiltration rates seem likely to be accelerated at smaller radius, due to the possible presence of a miniature, failure-related discontinuum. (Revealing velocity-versus-radius measurements in tunnels were reviewed in Chapter 7, see for instance the circular tunnel cross-hole seismic results in Figure 7.5). Briggs et al., 2004 in research at MIT, compared LWD and wireline data that was collected over the

same interval in the same well. Both monopole and dipole logs were measured by the wireline tool, which was run some 10 days following completion of the drilling. The LWD tool provided dipole measurements.

(a)

(b)

Figure 12.30 Modelling of four-days mud-infiltrate invasion, using constant-permeability-with-radius assumptions, but with a 1:10 ratio of Kvertical and Khorizontal in the formation of interest. Torres-Verdin et al., 2003.

Figure 12.31 Scatter plots comparing higher frequency (shallowerviewing, more disturbed) LWD tool velocities, with the lower frequency (deeper-viewing, less disturbed) wireline tool velocities. Briggs et al., 2004. In the case of the higher velocities, the earlier LWD measurement possibly views a less cracked and/or less invaded borehole wall, both tools registering relatively high velocities.

Rock stress, pore pressure, borehole stability and sonic logging

The authors found that for this well, there was on average about 5% discrepancy in shear wave data, and about 3% in compressional wave data. These trends suggested higher average velocities from the subsequent, deeperviewing wireline logs. A short section of the formation showed velocity differences of just over 10%, with an opposite trend. Significantly, both tools measure in different frequency ranges, and had different offsets between source and first receiver. The authors pointed out that as a general rule-ofthumb, a tool sees 1 inch into the formation for every foot separating the source and first receiver. Furthermore, low frequencies (1–3 kHz) see 2 to 3 borehole diameters, while the higher frequencies see less than one borehole diameter. Consequently, the higher frequency LWD tool was assumed to see the formation nearer to the borehole wall than the lower frequency wireline tool. This would mean that the damage zone would tend to be seen by the LWD tool, while the virgin formation would tend to be seen by the lower frequency wireline tool. However, the deeper penetration of split shear waves nevertheless detects fracturing and anisotropy in the formation, outside the damage zone, as we saw earlier. The overall scatter plots of LWD versus wireline P- and S-wave velocities shown in Figure 12.31 support this radius-bias, with the wireline velocities sometimes 1 km/s faster in Vp, and 0.5 to 1.0 km/s faster in Vs.

319

The authors emphasised that in poorly consolidated zones that would be susceptible to damage by drilling, the slower velocities should be accounted for, either by making a sufficient correction, or by using lower frequencies and/or larger offset, in order to see deep enough into the formation to register undisturbed velocities. Material reviewed in this chapter has demonstrated that geomechanics/rock mechanics wellbore stability studies have an important place in improved understanding of well-logging anomalies (e.g. Fjaer et al. 1992). However, the existence of a miniature, but potentially up to several diameter EDZ discontinuum, which cannot be modelled in conventional Mohr-Coulomb based continuum modelling (Barton, 2004b), due to incorrect addition of the cohesive and frictional components, is perhaps the root cause of the phrase ‘alteration zone’ being used to describe the complex, time-dependent interactions occurring in the over-stressed, near-wellbore zone. The use of logging tools that illuminate to greater depth, due to low frequency, but that can also give information about the discontinuous zone, are clearly of importance for improved understanding of this cross-discipline region that surrounds wellbores. The mini-EDZ theme will be terminated with two photographs from a large ‘borehole’, namely one of the world’s first TBM tunnels, excavated by a 7 ft (2.1 m) diameter steam-driven machine credited to Beaumont,

Figure 12.32 One of the world’s first TBM tunnels, from 1880, credited to Beaumont. Excavation in chalk marl of UCS  4 to 9 MPa, close to the Channel Tunnel between England and France. Note structurally controlled and (vertical) stress-controlled breakout to at least one-radius on diametrically opposite sides of the tunnel. Barton and Warren, 1996.

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Rock quality, seismic velocity, attenuation and anisotropy

for ‘pilot-drilling’ towards France, in an early (1880) effort to examine the feasibility of a sub-sea link between England and France. The four pictures shown in Figure 12.32 are very informative for this chapter. They show: a) structurally controlled, three joint set fall-out, which would be a source of calliper-log ‘noise’ in other (vertical well) circumstances, disturbing the assumption of hole-ellipticity parallel to  h min. Photos b) and c) show progressive stress-controlled ‘break-out’ at least doubling the effective diameter, caused in this case by tunnel loading under a 50–60 m chalk cliff along the S. England Folkestone Warren coast line. The weak (UCS  4 to 9 MPa) chalk marl at tunnel level, has failed in combined shear and compression, due to a vertical stress of only about 25% of UCS, possibly with some bedding plane influence in the ‘break-out’. The discontinuum lies on the tunnel floor and behind what we see at the tunnel wall. In a ‘mud-filtrate invasion’ scenario, the fluid would not penetrate in an isotropic or linear manner, but faster into the haunches, or ‘E-W’. In a further possible illustration of unwanted hole collapse, this time due to ‘over-pressure’, photograph d) shows failure due to successive bedding plane opening under the sea section of this tunnel. The original circular 2.1 m diameter hole has ‘migrated’ with time, into the collapsing, bedded rock above the crown. Could this be the occasional fate above and below horizontal sections of wells waiting for casing installation, in case of thinly bedded strata with overpressure?

12.9

Challenges from ultra HPHT

The drive to discover more petroleum, which is especially relevant at the time of publication (2006) with oil prices above 70 US $ per barrel, is stimulating the exploration of deeper petroleum reserves, with all the associated difficulties of high temperatures, high fluid pressures, and high rock stresses. Some of this is so-called ‘infrastructure-led exploration’, searching deeper or laterally and deeper from developed fields with their existing production facilities. Since a 1990 accident report (the Piper Alpha platform disaster in the UK sector of the North Sea), there have existed formal definitions of high pressure high temperature (HPHT) wells. With time this has been extended to the following three-tier system for classifying these extreme conditions.

Table 12.2 Definitions of maximum HPTP pressure and temperature tiers (after Willson, 2006). Tier

Reservoir pressure

Reservoir temperature

Tier I Tier II Tier III

15,000 psi (103 MPa) 20,000 psi (138 MPa) 30,000 psi (207 MPa)

350ºF (177ºC) 400ºF (204ºC) 500ºF (260ºC)

The Tier II and Tier III categories are termed ultraHPHT and extreme HPHT for obvious reasons. The current record for the offshore environment is reportedly Mobile Bay, off the coast of Alabama, at 138 MPa and 215°C. There are now several North American deep gas reservoirs both onshore and offshore that would classify as Tier III. As might be expected, there are operating temperature limits for ‘conventional’ LWD logging while drilling components, and for steerable downhole drilling motors. Even Tier I temperature limits may be reached at well depths in excess of 6 or 7 km, meaning that real-time data may no longer be available while drilling. However, subsequent wireline logging can presently be performed at temperatures up to the Tier III ‘limit’ of 260°C. As we shall see in Chapter 13 on rock physics phenomena at extreme levels of confining stress, the high state of compaction at great depth means that the porosity and seismic velocity of typical reservoir rocks may exhibit little sensitivity to changing depth. The prediction of fluid pressures and fracture gradients (e.g. Figure 12.1) is then more difficult. A related problem of extreme rock pressure is that the Terzaghi, 1943 theory of effective stress: 
  – p

(12.1)

may no longer give a correct description of the magnitude of the three effective principal rock stress components that would normally define the likely stability or instability of a deep well. At great depth, the rock skeleton may bear a greater proportion of the total rock stresses due to an effective stress parameter  that is less than 1.0, following the Biot, 1956b generalized theory of poroelasticity: 
  – p

(12.2)

A ‘moderate’ example from Hettema and de Pater, 1998 is a clay-rich sandstone with an unstressed porosity of 20%, which demonstrated an -value of 0.9 under zero differential pressure, reducing to 0.6 at 36 MPa

Rock stress, pore pressure, borehole stability and sonic logging

differential pressure. A more extreme example is a limestone tested by Laurent et al., 1993, with -values reducing from 0.8 to 0.2 as porosity decreased from 23% to 4.5%. Such effects may increase the effective stress components by tens of MPa, which leads, as also in TBM tunnelling (Barton, 2000) to reduced drilling penetration rates as the rock is stronger. However it also leads to the opposite effect of a potentially increased likelihood of stress-induced fracturing or (log-spiral) shearing, depending on rock type. (In the world of TBM tunnelling there are extremes of 0.1 m/hr and 10 m/hr penetration rates, the former due to extremely hard rock at great depth in an Idaho mine, with a TBM giving insufficient thrust. Practical measures for reducing the double impact of both high effective stresses, and the additional thermoelastic effect of high drilling mud temperatures were proposed by Maury and Guenot, 1995, by introducing mud cooling systems. When the circulating mud is cooler than the formation, thermoelastic contraction means lower tangential stresses, with the dual effect of reducing the likelihood of compressive stress-induced fracturing, but an increased likelihood of mud pressure induced tensile cracking, due to the reduced minimum tangential stresses on opposite sides of the well, and rotated 90° from the potential compressive fracturing locations. The tensile cracking allows mud loss, but some is returned when the temperature subsequently rises. The apparent wellbore ‘ballooning’ represents the mud loss, prior to the subsequent gain of fluid. The subject of mud temperature management is of great current interest for ultra deep wells, for extending fracture gradients,

321

as discussed by Pepin et al., 2004 and others, in recent literature. As pointed out by Willson, 2006 in a helpful technical review of the subject (‘Feeling the heat, can’t stand the pressure?’), manipulating the mud temperature during the drilling process, before formation temperature is re-established, can also be used ‘in the opposite direction’ to positively influence the hydraulic fracture (mudloss) gradient if there is no risk of formation well-bore compressive failure. This would be done by increasing the mud temperature. However, in the case of shale, an initially undrained condition when exposed by drilling means that the greater thermal expansion coefficient of the contained water will have greater influence on the stability than the rock’s response to increased or lowered mud temperatures (Li et al., 1998). There are reportedly particular problems when penetrating salt rocks at high temperature and pressures (Willson and Fredrich, 2005), due to the particular sensitivity of the creep rates of salt to high temperature. There is a so-called ‘undefined mechanism’ of creep at lower temperatures, and a ‘dislocation climb mechanism’ at high temperatures, which can result in orders of magnitude increased rates of ‘creep’. Already between 60°C and 230°C there is a reported 200 increase. Clearly this is of particular concern to petroleum companies who are developing reserves beneath thick bedded salt formations or next to salt dome structures. A review of drilling problems, and an emphasis of the need for high pressure and high temperature creep tests for salt is given by Maia et al., 2005.

13

Rock physics at laboratory scale

King, 2005 recently summed up the major explorationrelated goals of rock physics research. They are ‘to understand how lithology, porosity, confining stress and pore pressure, pore fluid type and saturation, anisotropy and degree of fracturing, temperature, and frequency influence the velocities and attenuation of compressional P- and S-waves in sedimentary rocks’. At the end of this list the author added ‘and vice versa’, presumably emphasising the interactive and complex nature of the reality. Isolation of just two or three of these variables for intense, high quality investigation, clearly gives just a small increment to the overall understanding. His review article ended by emphasising the remaining challenges: relationships between attenuation, anisotropy, fractures and fluid flow – and determining these relationships across the frequency spectrum of core, log and seismic measurements. In this chapter we will review some of the important increments in this understanding, mostly by first treating velocity-related experiments, then attenuation-related experiments. Description of various matrix behaviours will be followed by description of laboratory tests that include jointing or induced fracturing. There was early recognition (e.g. Birch and Bancroft, 1938), that seismic velocities of rocks were strongly influenced by microcracks, and that seismic attributes representative of the intrinsic mineralogy and porosity, could only be obtained by applying pressure to the rocks. Much of the rock physics understanding of reservoir rock behaviour (of both matrix and joints), has therefore to be achieved at elevated pressure, and the importance of temperature is also well recognised, but less frequently an experimental variable. Mavko, 2002 pointed out that because of the growing complexity of recently discovered oil fields, a major shift had taken place in the use of seismic methods in the last decade of the 20th century. Interpretation of the increased spatial variability due to heterogeneous distributions of porosity, clay content, fracture density and permeability, was now more strongly based on rock physics understanding. Gradually, more order had been discovered in relations that once seemed scattered, such

as velocity-versus-porosity, porosity-versus-permeability, Vp/Vs-versus-saturation and lithology. The author discussed the seismic signatures of cementation, sorting, shaliness, lithology, fluid content, and compaction. Both the well-established porous matrix behaviours, and several of the newer areas of knowledge such as joint and fracture behaviour, will be reviewed in this chapter, before moving to reservoir-scale in Chapters 14 and 15. Of necessity the selection of material is subjective, but designed to be informative, and broad-based, within the confines of one chapter. A lot of supplementary data will be found concerning seismic Q, to add to the introductory material of Chapter 10. In this chapter it is presented together with the velocity data. A ‘shallow perspective’ of this subject, certainly in relation to depth of observation, will be found in Chapter 2, based mostly on civil engineering related investigations. A certain relation to many of the high-pressure velocityparameter trends presented in the present chapter will be noted. The reader is referred to some particularly interesting assemblies of low-stress data. The particular effects of variable weathering and fissuring common to the nearsurface is documented, which is absent in reservoir-related studies, with the possible exception of related effects from alteration close to fault zones, that may exhibit hydrothermal alteration of their various mineral assemblages. 13.1

Compressional velocity and porosity

In the petroleum industry there is a history of at least half a century for inferring porosity from well logs, and for indicating pore fluid type. Among the oldest, and most popular expressions was that put forward by Wyllie et al., 1956, based on time-averaging in the solid and fluid phases. Using Tp to represent the total travel time of a P-wave, and Ts and Tf to represent the travel time components expected in the solid and fluid phases respectively, it is assumed that: Tp  Ts  Tf

(13.1)

324

Rock quality, seismic velocity, attenuation and anisotropy

A ‘reservoir rock’ selection of P-wave velocity versus porosity data for saturated samples, is reproduced in Figure 13.2 for ready reference. This limited Vp- selection, from Mavko et al., 1998 appendices, is also credited to original authors in the figure caption. Chalk, two sets of limestone data of widely different porosity ranges, dolomite, and two sets of sandstone data are reproduced. As we shall see shortly, explaining some of the wide scatter in the data requires specification, as a minimum, of effective stress level, degree of cementation, and claycontent. Examples of such discrimination are shown in Figure 13.3, from Dvorkin and Nur, 1998.

13.2 Figure 13.1 P-wave velocity versus porosity for compact clean sandstones, and for a suspension of component grains, behaviour that is separated by the critical porosity c concept. Nur et al., 1991, and Mavko et al., 1998.

Density, Vs and Vp

A close variant of this Wyllie et al., 1956 time-average prediction, is the popular velocity-to-porosity equation of Raymer et al., 1980, for   0.37:

The age-depth relationships derived for numerous wells in sandstone-shale units by Faust, 1951 (see beginning of Chapter 14), had a certain grouping of velocities with age, due to variations of porosity and the resulting densities. Hard porosity in the form of pores tended to decrease with age and depth, while (soft) porosity in the form of joints tended to increase with age due to tectonic influences, but reduced strongly with depth. Only the hard porosity will have a significant effect on density. Gardner et al., 1974, showed simple velocity-density trends for reservoir rocks, which on a log-log plot were almost linearly distributed. Figure 13.4 shows the trends for sandstone/shale/limestone/dolomite, where the central relationship (dashed line), as in equation 13.4 is:

Vp  (1  )2 Vps   Vpf

g  0.23V

Inserting the fractional porosity () of the rock, and Vp for measured velocity, the component velocities Vps and Vpf contribute as follows by substitution in equation 13.1:  1 1    Vp Vps Vpf

(13.2)

(13.3)

However, as pointed out recently by Dvorkin and Nur, 1998, in an appropriately titled note: ‘Time-average equation revisited’, there is actually only a limited theoretical scope for such time-average equations, requiring arrangement of the two components in layers normal to the direction of propagation, with a wave length small compared to the thickness of an individual layer. Nur et al., 1991 championed the concept of a critical porosity that separates both the mechanical and acoustic state of a rock and its component grains. At lower porosities than c the mineral grains are loadbearing, giving correspondingly higher velocities, while at porosities greater than c a fluid phase will be loadbearing, the particles being in suspension, with the obvious consequences of a very ‘flat’ velocity-porosity response. An example of this concept, for the case of clean sandstones, is given in Figure 13.1.

1

4

(13.4)

where   bulk density in gm/cm3, and velocity Vp is ft/s. (Note: density  velocity  impedence  gm/cc  m/s) We can visualise more familiar (km/s) velocities and densities by estimating  when Vp is 3, 4 or 5 km/s (9,840, 13,120 or 16,400 ft/s). The three results for  according to this equation are approximately 2.29, 2.46 and 2.60 gm/cm3 respectively. When Vp  6 km/s a density of 2.72 gm/cm3 is predicted. Each of the above is a realistic reflection of both mineralogy and porosity differences, as density and velocity increase. Several sets of seismic data that included the fundamental effect of density were presented in Chapter 2, but these were not specifically related to reservoir rock, and were usually at ‘near-surface’ stress levels, related to civil engineering projects, and often had the density- and velocity-reducing influences of weathering.

Rock physics at laboratory scale

325

Figure 13.2 An assembly of Vp-porosity data for saturated chalk, two limestones of widely different porosity, dolomite, and two sandstones of medium and high porosity. a) Chalk: from sonic log and porosity log, Urmos and Williams, 1993. b), c) Limestones: ultrasonic, 10 to 50 MPa effective pressures, Cadoret, 1993, Lucet, 1989, Yale and Jamieson, 1994. d) High porosity sandstone: ultrasonic, 35–40 MPa effective pressures, Strandenes, 1991. e) Sandstones (with yet-to-be-defined clay-content): ultrasonic, 30–40 MPa effective pressures, Han, 1986. f ) Dolomites: ultrasonic, 10–35 MPa effective pressures, Geertsma, 1961, Yale and Jamieson, 1994. After Mavko et al., 1998.

A ‘reservoir rock’ selection of P-wave velocity versus density data, is reproduced in Figure 13.5a for ready reference. This limited Vp- selection, from Mavko et al., 1998 appendices, is also credited to original authors in the figure caption. Chalk, limestone, dolomite, and three sets of sandstone data are reproduced. Again for reference purposes, both the shear-wave and compressionwave velocities, for the same six groups of rocks, are shown in Figure 13.5b. The relatively ‘ordered’ density-Vp trends for the chalk, limestone and dolomite reflect the simpler mineralogy. The contrast to the widely scattered density-Vp data for the three groups of sandstones is evidence of the variable

mineralogy of ‘sandstones’, with 10–15% variation in density possible for the same velocity, particularly in the case of the tight gas sandstones, which gives a correlation coefficient of only 0.39. In contrast to these variations, the Vs  Vp trends are consistently uniform, as befits characterization by seismic waves. In Chapter 14, an early introduction to the age and depth effects on velocity is reproduced from Faust 1951, who analysed well survey results from some 500 petroleum wells in the USA and Canada. Faust used data from about 300 kilometres of well sections. The great majority of data was for mixed shale/sandstone sections.

326

Rock quality, seismic velocity, attenuation and anisotropy

A non-systematic comparison of shale and sand (sandstone) velocities revealed an average discrepancy of only 350 ft/sec, or 106.7 m/s in velocity between these two, frequently inter-bedded units, the sandstone having the highest velocity by this small average margin. We will present the also remarkably close Vp versus Vs trends for water-saturated sandstones and shales, from Castagna et al., 1993, as reproduced in Mavko et al., 1998, at the appropriate location in Chapter 14 (Figure 14.4), to emphasise the remarkably similar Vp and Vs signatures of these two ‘dissimilar’ lithologies, when in a compacted state. The necessity of using impedence (gm/cc  m/s), attenuation, and anisotropy, for seismically distinguishing these two most essential reservoir ‘partners’ is clear.

13.3

Figure 13.3 Specification of sandstone condition: quartz-cemented, clay-cemented, uncemented, and specification of effective stress level (applied on uncemented Troll sand), helps to sort P-wave velocity data that displays ‘unexplained’ scatter. Dvorkin and Nur, 1998. The subenvelopes beneath the Troll sand data are from Dvorkin and Nur, 1996.

Figure 13.4 Log-log trends for Vp (ft/s), and . Gardner et al., 1974.

Velocity, aspect ratio, pressure, brine and gas

An important early paper in the area of theoretical modelling of porous rock behaviour was presented by Toksöz et al., 1976, who examined the numerous factors affecting seismic velocities of intact samples of porous rocks with emphasis on sandstones. They developed theoretical formulations to represent the solid matrix, and assumed spherical to oblate spheroidal pores, of widely varying aspect ratios, to match numerous laboratory data. As one would expect, they found that small aspect ratios (flatter voids) caused greatest reductions to elastic moduli and velocities. They also predicted and confirmed that the properties of the saturating fluid (gas, oil or water) produced greater effects on the compressional velocities than on the shear velocities. The P-wave velocities were predicted, correctly, to be higher when the rock was saturated with water, than when dry or gas-saturated. When fitting their theoretical model to P- and S-wave velocities that were measured at different pressures, they required pore shape spectra ranging from spheres to very fine cracks (aspect ratios from 1 to 105) for sandstones, limestones and granites, both under dry and saturated states. As igneous rocks have low porosities, the pore shape has great influence on the elastic and seismic properties, and dry and water-saturated behaviours are markedly different, as was also seen in Chapter 2. Compressional velocities were highest with brine saturation and lowest with gas saturation, but the difference declined with increasing pressure. Poisson’s ratios for gas saturated rocks were lower than for those with

Rock physics at laboratory scale

327

(a)

Figure 13.5a An assembly of Vp-density data for saturated chalk, limestone, dolomite, and three sandstones of low, medium and high porosity. a) Chalk: from sonic log and porosity log, Urmos and Williams, 1993. b) Limestone: ultrasonic, 10 to 50 MPa effective pressures, Cadoret, 1993, Lucet, 1989, Yale and Jamieson, 1994. c) Dolomites: ultrasonic, 10–35 MPa effective pressures, Geertsma, 1961, Yale and Jamieson, 1994. d) Tight gas sandstones: ultrasonic, effective pressures 40 MPa, Jizba, 1991. e) Sandstones: ultrasonic, 30–40 MPa effective pressures, Han, 1986. f ) After Mavko et al., 1998. f ) High porosity sandstone: ultrasonic, 35–40 MPa effective pressures, Strandenes, 1991. After Mavko et al., 1998.

brine saturation, and this difference persisted to great depths according to their model. Figure 13.6, from Toksöz et al., 1976, is a good example of their modelling predictions, showing the relative predicted effects on Vp of brine-filled and gas-filled cracks in a 16% porosity sandstone model. The fluid occupying the smaller aspect ratio cracks has more influence on velocities at low pressures, due to the greater pressure sensitivity of the fine cracks. Figure 13.7 shows the same authors’ predicted Poisson’s ratio variations, with varying degrees of brine or gas saturation, and also as a function of differential pressure to

50 MPa. Greatest sensitivity, as one would expect, was shown when pressure or depth was smaller. From summaries of the numerous experimental and theoretical trends given by Toksöz et al., 1976, Table 3.1 was developed. The effects of the dry or brine-saturated states, and the influence of effective stresses, as predicted theoretically by Toksöz et al., 1976 so long ago, were nicely illustrated by more recent testing by King and Marsden, 2002, who tested numerous sandstones both dry and brine saturated. Ultrasonic P- and S-wave measurements were made on ten sandstones with porosities less

328

Rock quality, seismic velocity, attenuation and anisotropy

(b)

Figure 13.5b An assembly of Vs - Vp data for the same saturated chalk, limestone, dolomite, and three sandstones of low, medium and high porosity, that are presented in Figure 13.5a. a) Chalk: from sonic log and porosity log, Urmos and Williams, 1993. b) Limestone: ultrasonic, 10 to 50 MPa effective pressures, Cadoret, 1993, Lucet, 1989, Yale and Jamieson, 1994. c) Dolomites: ultrasonic, 10–35 MPa effective pressures, Geertsma, 1961, Yale and Jamieson, 1994. d) Tight gas sandstones: ultrasonic, effective pressures 40 MPa, Jizba, 1991. e) Sandstones: ultrasonic, 30–40 MPa effective pressures, Han, 1986. f ) After Mavko et al., 1998. f ) High porosity sandstone: ultrasonic, 35–40 MPa effective pressures, Strandenes, 1991. After Mavko et al., 1998.

than 10%, and thirty-four specimens with porosities in the range 20 to 30%, under hydrostatic effective stresses up to 60 MPa (in the case of the stronger, lower porosity samples), and up to 40 MPa in the case of the higher porosity set. Figure 13.8 shows the Vp and Vs results for the dry and saturated specimens to a common hydrostatic stress of 40 MPa. Equations relating Vp and Vs are shown in the figure. King and Marsden, 2002, also presented their Vp and Vs results as a function of the effective stress (10, 20, 40 or 60 MPa). Figure 13.9 shows both the Vp-Vs-effective stress trends, and the dry-saturated trends. The addition of a ‘Gassman predicted’ result for the saturated

state, given by the authors, has been omitted from these figures for the sake of clarity.

13.4

Velocity, temperature and influence of fluid

Although far from exhaustive, a limited set of data for temperature effects on hydrocarbon-saturated samples will now be presented to illustrate some of the geophysical changes that can be used to monitor producing, stimulated reservoirs. Nur, 1989, referred to the new ‘four dimensional seismology’, in other words the ability to monitor in three dimensions the effect of time during

Rock physics at laboratory scale

329

Table 13.1 Typical relative effects of environmental conditions for porous reservoir rocks (derived from Toksöz et al., 1976).

Figure 13.6 Theoretical variations of Vp with differential pressure (0 to 50 MPa) and different aspect ratio cracks, for various brine or gas saturation levels. Toksöz et al., 1976.

Lower velocity (Vp) if

Higher velocity (Vp) if

Low water saturation Dry or gas saturated (if flatter pores) Some immiscible gas (in brine) Higher porosity Over-pressured Shallow depth Thin pores After several cycles of freezing Room temperature Extremely high temperature

High water saturation Dry or gas saturated (if rounder pores) Saturated with brine No immiscible gas Lower porosity Under-pressured Greater depth Rounded pores Frozen Low or moderate temperature

Lower velocity (Vs)

Higher velocity (Vs)

If water saturated

If dry or gas saturated (and highly porous)

Figure 13.7 Toksöz et al., 1976 model predictions for Poisson’s ratio as a function of pressure or depth, and as a function of the degree of saturation with brine, gas or a mixture of the two.

various flooding methods. The basis for such an ability would be the strong dependence of velocity on temperature, (water-flooding causing local cooling, steam flooding the opposite), plus the significant influence of the relative hydrocarbon and brine saturations. The six sets of results shown in Figure 13.10 show an easily detectable effect of temperature, with greatest effect when 100% oil saturation, and least effect (almost zero effect) when 100% gas saturated or 100% brine

Figure 13.8 Vp and Vs as a function of condition (dry or brinesaturated), at a common hydrostatic effective stress of 40 MPa. King and Marsden, 2002.

330

Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.9 Vp and Vs as a function of effective hydrostatic stress, for a) ten lower porosity sandstones, b) thirty four high porosity sandstones. Dry and brine-saturated results are shown. Redrawn from King and Marsden, 2002.

Figure 13.10 Vp behaviour as a function of relative hydrocarbon saturation and temperatures up to 150°C. Top: Kern River oil sand: P  100 bars, PP  0 bars, Bottom: Venezuelan oil sand: P  100 bars, PP  30 bars. Nur, 1989.

Rock physics at laboratory scale

saturated. This temperature effect on velocity reduces to about half strength when 50% oil/50% gas or 50% oil/50% brine are present. In other words, when the oil is removed from these sands, the velocities successively become independent of temperature, with roughly half the effect when 50% oil remains. Nur, 1989, also referred to a pilot steam flood experiment in viscous tar sands in Canada, conducted by Amoco. Changes in travel-time caused by heating effects reducing Vp were readily detected. A differential traveltime plot revealed the areas closest to the wells (and partly between the wells) where velocity had been reduced by the change in viscosity. Laboratory tests of the tar sand showed an S-shaped reduction in velocity from Vp  2.4 km/s at 25°C, to a final plateau of about 1.1 km/s at 150°C. (Den Boer and Matthews, 1988). In their review of acoustic velocity and attenuation in porous rocks, Winkler and Nur, 1995 refer to the work of Wang and Nur, 1990 who measured the temperature dependence of compressional and shear wave velocities in sandstones that were either dry, saturated with water, or saturated with crude oil. Figure 13.11 shows the quite widely differentiated results, due again to the temperature

331

dependence of the viscosity of the oil. The phenomenon was described as follows by Winkler and Nur. At low temperature the higher viscosity means that the oil cannot flow easily, so the dynamic measurement is on the high-frequency, high velocity, unrelaxed side of the localflow mechanism. As temperature increases viscosity reduces, so fluid flows more easily, and velocity therefore decreases since measurement is on the relaxed side of the absorption/dispersion mechanism. 13.5

Velocity, clay content and permeability

A comprehensive series of laboratory tests reported by Klimentos, 1991, were designed to investigate the influence of clay content on the P-wave velocities of saturated sandstones under varying confining and pore fluid pressures up to 40 MPa. Forty-two samples of sandstones were investigated, having the following range of characteristics, in order to see their combined and individual effects on velocity: ● ● ●

Porosity: 2 to 36% Permeability: 0.001 to 306 mD Clay content: negligible to 30%

The principal results are shown in Figure 13.12, with sorting according to clay-content, shown in Figure 13.13.

Figure 13.11 Compressional and shear wave velocities in Boise sandstone, as a function of temperature and saturating fluid. The samples were dry, or saturated with water or saturated with crude oil. A common effective stress of 15 MPa was applied. Wang and Nur, 1990 in Winkler and Murphy, 1995.

Figure 13.12 P-wave velocity at 1 MHz frequency and 40 MPa confining pressure, showing clay contents and porosities. Klimentos, 1991.

332

Rock quality, seismic velocity, attenuation and anisotropy

where   porosity (fraction), c  clay content (fraction) and K is permeability in millidarcies. The effect of permeability alone on the P-wave velocity is seen to be negligible. In fact a misleading, weak increase in Vp with increasing permeability arises due to the velocity-clay content and clay content-permeability interrelations. Clearly these equations can be reformulated to give estimates of (matrix) permeability. Klimentos and McCann, 1990, also drew attention to the complex nature of permeability – depending as it did on porosity, pore size distribution, inter-connectedness of the pores, and tortuosity – the latter two presumably being especially compromised by clay content. They also posed as an open question, what the relative effects would be of frequencies of 10 Hz to 1 kHz (as used in seismic exploration) or frequencies of 10 to 20 kHz (as used in borehole logging), when clays were present in the in situ sandstones.

(a)

13.6

(b)

Figure 13.13 a) P-wave velocity as a function of clay content for porosities of 6 to 36%. b) P-wave velocity as a function of clay content with average 15% porosity (squares) and 28% porosity (circles), each at 1 MHz and 40 MPa confining pressure. Klimentos, 1991.

From Figure 13.13, where porosity differences were used to distinguish the effect of clay content. Klimentos, 1991, gave the following multivariable linear regression equations for estimating Vp: 1. at ultrasonic frequencies (1 MHz): (r  0.96) Vp  5.66  6.11  3.53c  0.0007K 2. at seismic frequencies: (r  0.93) Vp  5.27  5.40  2.54c  0.001K

(13.5)

(13.6)

Stratigraphy based velocity to permeability estimation

Gutierrez et al., 2002, also addressed the question of clay-content, referring to the initially undifferentiated data set of Han, 1986 for sandstones. Figure 13.14 shows the undifferentiated Vp versus porosity data of Han, 1986: top-left, and the stratigraphy-guided, clay-content differentiation: top-right, that makes the nearly 2 km/s variation in Vp at one porosity, understandable. Jan, 2003 presented a finer clay-content break-down of Han’s data, including some additional data, which is included in Figure 13.14c and d. Both the P-wave and S-wave velocities were measured at 40 MPa confining pressure and 1 MPa pore pressure. In order to emphasise the potential of some stratigraphyguided lab-to-field velocity-porosity-permeability correlations, Gutierrez et al., 2002 presented a well log for La Cira-Infantas Oil Field (LCI). This is reproduced in Figure 13.15. The left-hand velocity log applied to the highly variable (also laterally) clean-to-shaly, loosely consolidated, Tertiary sandstones, lying in a highly faulted, asymmetrical anticline. Well-logged Vp ranged mostly from 2.5 to 4 km/s, while core-based porosity was mostly between 10 and 30%, and there was a four order-ofmagnitude range of core-based permeability. The corebased results are plotted in Figure 13.15b and c. The authors plotted a series of velocity-porosity diagrams, starting with an 850 m interval with a few thousand data points for the undifferentiated deposition

Rock physics at laboratory scale

(a)

(c)

333

(b)

(d)

Figure 13.14 a) Unsorted Vp – n% data for sands with 35% clay. b) Logical differentiation of Vp – n% trends when grouped by clay-content. Gutierrez et al., 2002. c) and d) A more detailed presentation of Han, 1986, data given by Yan, 2003.

cycles of the Tertiary basin. Successively smaller deposition cycles were then considered, first down to a specific operational zone, then so-called ‘fining-up’, giving successively higher Vp-n% correlation coefficients, reflecting the more uniform sedimentary environment and diagenetic nature of the smaller cycles. An essentially linear plot was shown for one of the fining-up cycles: in a 5 m section Vp was 3.5 km/s at n  10%, and 2.5 km/s at n  30%, with correlation coefficient r  0.973. The authors found that due to a large fraction of silt (whose mineralogy is close to that of clean sand), the clay-content in 100% shale intervals could be as low as 20–30%. Poor sorting in the shale caused a reduction in total porosity, which caused an increase in the velocity in relation to existing models, and in relation to the data sets in Figure 13.14, which show lower velocities with these amounts of clay. The concept of sorting data into common categories, using stratigraphy and other matching techniques, was also the theme in Prasad, 2003, who showed that by grouping and sorting rocks into hydraulic units, it was easier to establish relationships between velocity and

permeability, through a more relevant match of porosity and permeability with common sediment compaction and cementation history. This work followed the permeability-porosity matching of Amaefule et al., 1993, who showed the importance of separation into hydraulic units. Possibly we can draw a parallel here to the common separation of rock mass qualities into classes (Q  1  4: poor, Q  4  10: fair, etc), for different structural domains, which is the basis for prediction of similar behaviour, such as particular reinforcement needs in a tunnel, a particular range of deformation moduli or P-wave velocities. Amaefule et al., 1993 and Prasad, 2003 used the following simple ‘classification’ relations: RQI  0.0314 (k/)

1

(13.7)

2

FZI  0.0314/ (k/)

1

2

(13.8)

RQI is known as the reservoir quality index, with permeability (k) in units of millidarcies, and () is the

334

Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.16 Porosity-permeability correlation from core of a second well in the LCI Tertiary sands, which allowed sonic-logging data to be used for permeability prediction. Gutierrez et al., 2002.

13.6.1

Figure 13.15 a) A well log from the heterogeneous Tertiary sands of the LCI field, showing Vp, with stratigraphyguided core data for b) porosity and c) permeability. Gutierrez et al., 2002.

fractional porosity. The term () is the void ratio, given by /(1-). It thus links FZI the flow zone indicator with RQI, using the ratio of pore volume to solid volume. Rocks with FZI values within a narrow range belonged to one hydraulic unit: they had similar flow properties. A semi-log plot of porosity versus permeability showed similar FZI values plotting together. Prasad first tested this older method, showing unsorted data (left), then data sorted by FZI (right) in Figure 13.17. This demonstrated that the FZI concept could be extended to seismic parameters, giving a strong correlation between velocity and permeability, when using the appropriate FZI grouping. She used a laboratory-test data base, which included porosity, permeability, velocity and attenuation data from tests at similar confining pressures. Figure 13.18 shows a much larger set of data with Vp – k correlation through FZI.

Correlation to field processes

Prasad, 2003 also provided a practical illustration of the effect of depth-of-sediment on porosity, velocity and permeability development to 500 m below sea floor, using marine logging results from ‘Site 977, ODP Leg 161 (Shipboard Scientific Party, 1996). In the parallel diagrams reproduced in Figure 13.19, the scattered downhole log data is shown beneath the smoothed trend lines A-B in each case. Curves D-D' represent the hypothetical trend if porosity is ‘frozen’ by a cementation episode from point D. Note the FZI-predicted maintenance of high permeability, and the ‘non-correlating’ increase in velocity (but one that can be explained by FZI). Curves C-C' represent the hypothetical effects of an ‘opposite’ trend – an influx of pore-filling materials from point C. There is a rapid reduction in porosity. This can be used to give an estimated reduction in velocity followed by an FZI-predicted reduction in permeability. Prasad, 2003 calculated the permeability scatter-curves directly from assumed FZI values of 0.1 (left curve), and 0.25 (right curve), using the log data for porosity and velocity. Note the similar scatter-shape of porosity data, and FZI-calculated permeability, due presumably to the use of (porosity)0.5 and (void ratio)1.0 in the FZI estimate.

Rock physics at laboratory scale

(a)

(b)

(c)

(d)

335

Figure 13.17 a) Unsorted log k versus ␸ data on the left, and b) sorted data using the expression for FZI with measured matrix parameters on the right c) Unsorted log k versus Vp data on the left, and d) sorted data using FZI on the right. Prasad, 2003.

13.7

Figure 13.18 Permeability estimated from velocity data, using FZI values from a larger data base of reservoir sandstones, marine reservoir sand and a tight sandstone. Prasad, 2003.

Velocity with patchy saturation effects in mixed units

Knight et al., 1998, showed that uniform or smooth variations of velocity with degree of saturation were strictly a function of an assumed or actual homogeneous distribution of saturation due to lithological uniformity. They investigated the more complex (and common) effects of having mixed lithological units, which tended to create a heterogeneous or patchy, saturation distribution, with different signatures during imbibition and drainage. With a more complex distribution of saturations due to lithology differences, it was only when close to saturation of 100%, that there was a consistent steep rise in velocity. (From another field, and for harder rock types, see Saito, 1981, in Figure 2.17a, b in Chapter 2 of this book). The authors found that pore-scale and sample-scale fluid distribution effects, and of course capillary effects, caused different Vp response (in degree but not general

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.19 An illustration by Prasad, 2003 of the possibility of predicting permeability from log data of porosity and permeability, using a relevant, logging-based FZI-value. Marine logging results from ‘Site 977, ODP Leg 161 (Shipboard Scientific Party, 1996). Hypothetical mineralization from D (curve D-D’) , and hypothetical pore-filling from C (curve C-C').

style) when draining as compared to imbibing. The drainage process creates a more heterogeneous distribution of saturation. Local full saturation of the crack-like regions of the pore space tend to stiffen these regions in relation to high frequency, but at low frequency these ‘patches’ can drain to the less saturated pore space. The phenomenon appears to be shifted in frequency at ‘macroscopic-patch’ scale. Such results clearly impact poroelastic modelling with different frequencies, which is discussed in Chapter 15. Knight et al., 1998, found that the pore fluid relaxation time increased as the size of the volume occupied by the fluid increased. They argued that the size of a patch (or partly drained rock joint?) may be orders of magnitude larger than a compliant pore. So if pore fluid is arranged in patches, the apparent (Vp) stiffening of partially saturated rock in response to a dynamic wave may occur even at low frequencies. Examples of frequency-dependent differences in Vpsaturation response, for the case of carbonate samples, are shown at lower frequency (1 kHz) in the first example, in Figure 13.20a. Presumably the lower frequency allows the wave-induced pressure changes in the pore fluid to dissipate, so that the pore fluid pressure is very close to that of the high-compressibility gas in the dry pore space, as described by Knight et al., 1998. As a result, the pore fluid lying in thin, compliant pores can flow freely into the dry pore space, in a squirtflow type of attenuation response. It does not therefore

allow reinforcement of the compliant part of the rock, so velocities are low. At high frequencies, (Figure 13.20b), this pressure equilibrium cannot occur because the pore fluid relaxation time is greater than the seismic wave period. Pore fluid in the thin compliant pores is then effectively ‘trapped’, and it therefore reinforces the otherwise compliant pore spaces, resulting in higher apparent modulus and velocity. Knight et al., 1998 described a comprehensive investigation with a controlled distribution of (10) lithologic units, an assumed state of capillary equilibrium, and calculated the saturation level in each unit from corresponding capillary pressure curves. Their contrasting calculations for shaley and clean sand, shown in Figure 13.21, demonstrate the effect of saturation heterogeneity. The effect of ‘patchiness’ (of saturation), compared to homogeneous conditions is nicely demonstrated in Figure 13.22. The two parallel lines defining ‘patchy’ Vp-saturation response, are two different theoretical solutions given by Knight et al., 1998, in which just two different lithologies have been combined. In Figure 13.23, the ‘extremes’ created by mixing the ten lithological units are shown. (Properties were given in Figure 13.21a). The smooth, conventional result (Figure 13.23a) was obtained by a pore-scale mixture of the ten sand-to-shaley-sand units, while the ‘multistepped’ response shown in Figure 13.23b was obtained using a patchy mixture of the ten lithological units.

Rock physics at laboratory scale

337

Figure 13.21 a) Properties of 10 lithological units, showing clay content and permeability versus porosity. b) and c) P-wave velocity (calculated) versus saturation for mixtures of shaley and clean sand. Knight et al., 1998.

Figure 13.20 P-wave velocity responses to a) lower and b) higher frequency in the case of a carbonate sample of 30% porosity studied by Cadoret, 1993. Note ‘hardening’ at high frequency, and the different imbibition and drainage responses with changing levels of water/air saturation, as described by Knight et al., 1998.

13.8

Dynamic Poisson’s ratio, effective stress and pore fluid

Carcione and Cavallini, 2002, described modelling in relation to Poisson’s ratio (the dynamic value), as a function of ‘differential pressure’ and pore fluid type. (The ‘differential pressure’ is the hydrostatic confinement minus pore pressure, and is referred to as effective stress in soil and rock mechanics.)

Figure 13.22 P-wave velocity versus saturation in a 40% mixture of clean sand and shaley sand. The two lithologies were combined in a patch arrangement and as a homogeneous mixture. Knight et al., 1998.

The authors highlighted the fact that Poisson’s ratios are anomalously high for cases of over-pressure, where effective stress can approach the fracturing (negative) side of the usual lithostatic and pore pressure gradients (as approached in Figure 12.1 of chapter 12).

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.24 Some experimental results for dynamic Poisson’s ratio, as a function of effective stress (hydrostatic confinement minus pore pressure) and fluid type. Khazanehdari et al., 1998, as reproduced by Carcione and Cavallini, 2002.

stiff, equi-dimensional pores does not show major variations of  with effective stress. However, closure of low aspect ratio (compliant) microcracks and pores will tend to increase the bulk modulus K more than the shear modulus , having the following effect on () :    1  1    1  1  K  2   3



Figure 13.23 P-wave velocity versus saturation for a) a pore-scale ‘homogeneous’ mixture of ten units, b) a patchy mixture of ten units, from sand to shaley-sand. Knight et al., 1998.

Dynamic Poisson’s ratio, as we have seen in Part I, can be calculated from: 1 1    1  , 2  a  1 

 Vp 2 where a     Vs 

(13.9)

Carcione and Cavallini emphasised that it was the aspect ratio of the cracks and pores and the nature of the saturating fluid that determined . Rock containing mainly

(13.10)

Therefore, in dry rocks, dynamic Poisson’s ratio increases with differential or effective stress. However, in saturated rocks the compliant pores have become stiffened in relation to high frequency waves, so () changes less as effective stress increases. However, at low effective stress, or when pore pressures are very high, the effective stress sensitivity is marked, and () increases. Some experimental results that the authors quoted, from tests by Khazanehdari et al., 1998, are shown in Figure 12.24, and indicated the increasing sensitivity at low effective stresses. Carcione and Cavallini were particularly interested in the responses of () close to the hydraulic fracturing limit when sealed over-pressured beds were under-compacted, and where there could be excess pressure due to oil-to-gas conversion, as investigated by Carcione and Gangi, 2000. As they pointed out, at zero effective stress, Vs is (locally) zero as the rock mass is hydraulically fractured and load is born by the fluid. However Vp is not zero, therefore the ratio (a) in equation 13.9 tends to infinity and  : 0.5.

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339

Figure 13.25 Dynamic Poisson’s ratio  versus differential stress (hydrostatic confinement minus pore pressure). The squares and open circles are from Winkler, 1985. Curves marked 1, 2 and 3 were calculated results for full oil saturation, 50% oil saturation and full brine saturation, respectively. Carcione and Cavallini, 2002.

Carcione and Cavallini used the theory of Carcione and Gangi, 2000, to develop theoretical trends for Poison’s ratio increase when approaching zero effective stress, showing in Figure 13.25, similar trends to the available experimental results.

13.9

Dynamic moduli for estimating static deformation moduli

In engineering fields that involve design for building foundations, dams or tunnels, or indeed wellbore stability for hydrocarbon exploration and production, it is well documented that static moduli of deformation can be significantly lower than the dynamic moduli predicted from P- and S-wave velocities. (See Chapter 6, for extensive rock engineering based comparisons of these quantities.) Such differences will also tend to be greater in jointed in situ rock, as opposed to microcracked lab samples. Such differences in moduli are of obvious interest to the petroleum industry. Tutuncu et al., 1998, expressed the opinion that knowledge of non-linear elastic properties (that are largely responsible for the differences between dynamic and static moduli) is essential for optimal drilling, effective well completions and efficient reservoir management. For example, when applying distinct element modelling to the Ekofisk reservoir subsidence in the mid 1980s, (Barton et al., 1986), it was appreciated that there were obvious uncertainties about the choice of moduli of deformation for the various layers of

Figure 13.26 Non-linearity and hysteresis observed in uniaxial cycling (with constant differential stress). The rock was a tight gas sandstone, tested dry. Tutuncu et al., 1998.

the 3 km of overburden, which were inevitably velocitybased at that time. Only the reservoir itself (chalk) was core-sampled and laboratory tested. Based on laboratory observations of the elastic nonlinear behaviour for sandstones as illustrated in Figure 13.26 a and b, Tutuncu et al., 1998, showed that the frequency of measurement was all important for the geophysical estimate obtained, since Eultrasonic  Elog  Elow freq.  Estatic. Their ultrasonic laboratory measurements were conducted at 1 MHz, 180 kHz, 100 kHz and 50 kHz, and their low frequency measurements at 2 kHz to 1 Hz, and their static measurements at 0.05 Hz to 0.001 Hz. To understand the frequency dependence of the various ‘dynamic’ moduli, it was necessary to see the effect of frequency on the velocities of the P- and S-waves. Firstly, for the case of dry porous sedimentary rocks, it was generally concluded by the authors that dynamic

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.27 Ratios of Vp static/Vp dynamic, and Vs static/Vs dynamic, and attenuation, each as a function of strain magnitude. Tutuncu et al., 1998.

tests gave results that were independent of frequency below ultrasonic frequencies. However, when ultrasonic frequencies were approached (0.1 MHz) the wave length could become comparable to the grain size and scattering became an important attenuation mechanism, which increased with frequency and when heterogeneities were present. In fluid saturated porous rocks, Vp, Vs and attenuation depend on frequency even when scattering is negligible. Since Vp increases with frequency more than Vs, the resulting Vp/Vs increase may give a pronounced increase in the dynamic modulus estimate. Under the more rapidly oscillating loads, the fluid in the pores and grain boundary cracks are not allowed sufficient time to (micro-) flow or ‘squirt’, and the rock acts as if unrelaxed so the properties measured will be undrained and

Figure 13.28 Young’s modulus as a function of strain amplitude at two different confining stress levels, and a comparison of E dynamic/E static. Tutuncu et al., 1998.

stiffer. By contrast, low-frequency measurements give sufficient time for fluid transfer and squirt to occur from microcracks, so that a relaxed, drained or less stiff behaviour is registered. Squirt flow appeared to be the dominant mechanism for attenuation and velocity dispersion at frequencies from 100 Hz to 10 kHz. When strain amplitude was increased (as in static measurements), the good agreement between wave propagation models and experimental data broke down, and large discrepancies were experienced between measured and predicted velocities and attenuations. One of the main objectives of the Tutuncu et al., 1998, study was to develop a methodology to predict

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341

hard-to-measure static (low frequency) moduli and attenuation from the relatively easy to measure dynamic moduli. They therefore conducted stress cycling measurements at various stresses and cycling frequencies. The fact that Vultrasonic  Vlog  Vstatic is emphasised by their plots of Vp ‘static’/Vp dynamic versus differential strain amplitude. A typical set of Vp, Vs, Young’s modulus and attenuation data plotted in this format is shown in Figure 13.27 a, b and c. For the above general reasons, when comparing dynamic Young’s modulus to ‘static’ Young’s modulus, Tutuncu et al., 1998, were able to show large discrepancies, since the ‘static’ measurements (0.05 to 0.001 Hz) were at so much higher strains than low strain dynamic measurements. Results are shown in Figure 13.28, which resemble rock engineering data shown in Chapter 6. 13.10

Attenuation due to fluid type, frequency, clay, over-pressure, compliant minerals, dual porosity

In this section we will trace parts of the development of attenuation as a means of improved characterization of reservoir rocks. The dispersive, frequency-dependent nature of seismic Q, and the greater sensitivity of the ratio of Qs/Qp to fluid and partial saturation than Vp/Vs, as already reviewed briefly in Chapter 10, will be illustrated by interesting cases reported in both past and recent literature. 13.10.1

Comparison of velocity and attenuation in the presence of gas or brine

Some of the subtle differences between velocity and attenuation (in the form of seismic Q) were shown by Frisillo and Stewart, 1980 tests with variable gas/brine saturations. The tests on Berea sandstone (n  19.7%, k  376 mdarcy) shown in Figure 13.29 give Vp and Qp on the vertical axes, and percent gas saturation on the horizontal axes. Zero percent gas saturation corresponds to 100% brine saturation. Frisillo and Stewart’s data represented by black circles, is shown supplemented by some reasonably consistent data (also for Berea sandstone) reported by Spencer, 1979 (squares), and by Toksöz et al., 1971 data for dry or full saturation (triangles). The expected reduction in Vp by reduced brine saturation (and increased gas

Figure 13.29 Compressional wave velocity and seismic quality factor Qp as a function of gas/brine saturation for sandstone at 10.3 MPa effective stress. Frisillo and Stewart, 1980.

saturation) was matched initially, by greater attenuation (a Qp of 33, reducing to approximately 9). At the far end of the saturation scale, when the samples become ‘room dry’ and reached 100% saturation with nitrogen, the attenuation reduced sharply, and Qp reached a value of about 50. Clearly this is related to the eventual absence of squirt flow with increased dryness.

13.10.2

Attenuation when dry or gas or brine saturated

In 1979, Toksöz et al. presented ultrasonic laboratory data on dry and water- or brine-saturated rocks, investigating how the attenuation varied with ‘differential’ pressure. Pore fluid pressure (Pf) and confining pressure (Pc) on their specimens was controlled independently, Pc  Pf giving their quoted ‘differential’ pressures. In a companion paper, reviewed in Chapter 10, Johnston et al., 1979, presented the assumed mechanisms of attenuation, and formulated theoretical models that fitted this laboratory data. The present data was obtained at ultrasonic frequencies (0.1 to 1.0 MHz), using a Berea sandstone with 16% porosity. Toksöz et al., 1979 used a frozen rock (limestone), showing very small attenuation and very high Qseis, as a

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(a)

(b)

(b)

Figure 13.30 Qp and Qs values as a function of confining (or differential) pressure, in a) dry (Pf  0) and b) methane saturated (Pf  0.465 Pc) Berea sandstone. Toksöz et al., 1979.

reference standard. Their subsequent detailed studies of environmental effects such as dry, methane-saturated, or brine-saturated, were conducted on Berea sandstone. At zero pressure, the P-wave velocities of their dry and brine-saturated Berea sandstone were about 3.3 and 3.8 km/s respectively, rising rapidly to about 4.1 and 4.2 km/s at 3000 psi (about 21 MPa). At the highest differential pressure used there was little difference between the dry and brine-saturated Vp in relation to the differentiation of the dry or brine-saturated condition. These and similar velocity trends for methane and for other brine concentrations were used in their calculation of seismic Q, which are shown in Figure 13.30 and 13.31, for the case of dry, methane-saturated, and two NaCl concentrations.

Figure 13.31 Qp and Qs values as a function of differential pressure (Pf  0.465 Pc) for brine-saturated Berea sandstone, with NaCl concentrations of a) 67.2 ppm and b) 161.3 ppm respectively. Toksöz et al., 1979.

The anomalous high value of Qp at highest differential pressure in Figure 13.30a was assumed to be due to some pore collapse and locking of grain boundaries. Several important trends can be seen in the Q data. Firstly, Qp and Qs were both higher (less attenuation) in the dry or methane saturated states, than in the case of brine saturation. Furthermore, Qs was more often larger than Qp in the case of the dry and methane-saturated sandstone. In contrast, there was a consistently wide separation of Qp and Qs of some 100 to 150% (Qp  Qs) in the case of the brine saturation. 13.10.3

Effect of frequency on velocity and attenuation, dry or with brine

Winkler, 1983, provided a remarkably detailed collection of velocity and attenuation data for three sandstones

Rock physics at laboratory scale

when tested in triaxial compression, over a range of frequencies (400 to 2000 kHz) in a dry or brinesaturated state. Effective stresses were increased in the sequence 2.5, 5, 10, 20 and 40 MPa in the case of the dry samples. The three sandstones had the following basic physical properties:

Porosity % Permeability (mD) Grain size ( m) Quartz %

Massilon sst.

Berea sst.

Boise sst.

24,6 1425
200 94

20.3 107 150–200 80

24.9 286 150–200 46

(Note: 1 Darcy  1012 m2 or 105 m/s, approximately)

The three ‘sandstones’ were of Mississippian age (first two) and Pliocene (last), with geological descriptions quartose sandstone, greywacke and arkose, respectively. Grain densities varied only from 2.68, 2.65 to 2.63 gm/cm3, respectively. The frequency-dependent, saturation-dependent and effective stress-dependent variations of Vp and attenuation (1/Q) measured by Winkler in this study, are reproduced in Figure 13.32 (a to f ). The dry samples all showed negative velocity dispersion, meaning velocity decreasing with increasing frequency, while the attenuation increased as the third to fourth power of frequency. This was taken as evidence of scattering within the pore spaces between the grains. (Inter-grain scattering in aluminium reportedly also results in f 4 attenuation.) The brine-saturated ‘sandstones’ mostly showed slight, positive, velocity dispersion (at least at the lower confining pressures) while attenuation varied with only the first or second power of frequency. This change in attenuation-frequency dependence was taken as evidence of local fluid-flow loss mechanisms. The saturated rocks always showed much stronger attenuation (lower Qp ) than the dry samples. All the data sets showed the strong influence of effective stress, which had greatest influence on attenuation when the samples were brine-saturated and at the lowest levels of effective stress, as we have seen earlier in this chapter. Parallels to compliant joints affecting rock mass behaviour (Chapters 15 and 16), were the observations by Winkler, 1983, that the nature of the grain contacts was all important. Compression and dilation of relatively compliant contacts (and strong pressure dependence)

343

in the case of the three sandstones could readily induce fluid flow into and out of the contact regions. Interestingly, the reported behaviour of fused glassbead samples was entirely different, as the sintered contacts between the glass beads were very stiff and lacked pressure dependence, and would not therefore generate local (micro) fluid flows (squirt) which would have increased the attenuation. Figure 13.33 shows this contrasting Vp and attenuation behaviour for the fused glass-bead samples, which had spherical 177–210 m beads (initially) that were fused by heating to give a porosity of 26.6% and a permeability of ‘several’ Darcies (1 Darcy  1012 m2), i.e. it was significantly more permeable than the three ‘sandstones’, yet could not generate squirt-related attenuation. 13.10.4

Attenuation for distinguishing gas condensate from oil and water

On the basis of the differentiation of Qp values, listed below, Klimentos, 1995, suggested a way of distinguishing gas and condensate from oil and water in sandstone reservoirs, but at the same time questioned whether the method could also be used in carbonate reservoirs. 1. in perfectly dry rocks, Qp is very high 2. in fully liquid saturated rocks Qp is at an intermediate level 3. in partially saturated rocks Qp is low Ranges of Qp and Qs for sandstone reservoirs were reportedly as follows based on well log, i.e. sonic frequencies: ●

●

●

Gas and gas5  Qp  30 15  Qs  30 condensate bearing sandstones Oil bearing 8  Qp  100 15  Qs  50 sandstones Water bearing 9  Qp  100 15  Qs  50 sandstones

Cross-over of P-wave and S-wave attenuation (or crossover of Qp and Qs, due to the increase in attenuation of P-waves by gas (lower Qp) and the absence of effects on the S-wave attenuation (as above), was the basis of the

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.32 Compression wave velocities and attenuations (1000/Qp) as a function of frequency, and whether dry (dashed line) or brine saturated (solid line), for three ‘sandstones’. Numbers on the curves represent the applied effective pressures (MPa), Winkler, 1983. Note interpreted Qp scale added on right-hand axis for convenience.

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Figure 13.34 Indication of a gas zone in a well, due to Qs  Qp. Klimentos, 1995.

A specific set of data for Qs and Qp as a function of porosity in a gas zone in one of the wells analysed is shown in Figure 13.34. The low Qp value for the gasbearing sandstone suggests the presence of partial saturation with a liquid phase, and possibly higher pore pressure as well.

13.10.5

Figure 13.33 Vp and attenuation as a function of frequency, and effective stress, for dry (dashed line), or brinesaturated (solid line) fused glass beads. Winkler, 1983.

method suggested. Typical sets of well data such as the following were cited:

1. 2.

Gas-bearing sandstone Water-bearing sandstone

Vp km/s

Qp

n%

(2.5 km depth)

4.0

5

15

(2.5 km depth)

4.2

40

15

Attenuation in the presence of clay content

It has previously been established that compressional wave velocities are inversely proportional to the clay content of sandstones (see previous section), with softening of the sandstone matrix and reduced dynamic deformation modulus as a result. (Han et al., 1986). In the study of Klimentos and McCann, 1990, the first systematic study of intrapore clays on compressional wave attenuation seems to have been made. These authors noted that there was a general lack of correlation between porosity and permeability for clay-bearing sandstones, but in general low permeability was associated with high clay content, and high permeability with low clay content. Although the Biot, 1956a and Biot, 1956b theory accounted well for attenuation in clay-free sandstones, it apparently failed by an order of magnitude to account for the attenuation effect of the clay. Klimentos and McCann suggested, as others since then, that this strong clay-related attenuation was due to viscous interaction between the clay particles and the pore fluid. Since the permeabilities were strongly dependent on the

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.35 shows the strong influence of clay content (% by volume) on Qp, and a less clear relation of Qp with permeability. The data set excluded the few samples with zero clay content, as they could not be plotted on the logarithmic scale. Qp and clay content showed excellent correlation. The best fit statistical relationship was: Qp  179C0.843

(13.11)

where C was the percent clay content by volume. The correlation coefficient was 0.91.

13.10.6

Figure 13.35 Top: Seismic quality Qp versus volumetric clay content for 39 sandstones with porosities from 6 to 36%. Bottom: Permeability (which is dominated by clay content) versus Qp . Confining pressure was 40 MPa in each case. Klimentos and McCann, 1990.

clay-content, the dependence of the attenuation on the permeability arose from the over-riding influence of clay-content. One may also add here that any possible thin layering of clay-rich horizons could, in an in situ environment, cause an increase in the shear compliance. Clay-bearing discontinuities tend to have low (‘static’) shear stiffness and high (dynamic) shear compliance. Klimentos and McCann, 1990, measured the attenuation of compressional waves in 42 sandstones under a confining pressure of 40 MPa. The frequency range was limited to 0.5–1.5 MHz, using a pulse-echo method. The objective was to investigate the role of porosity, clay content and permeability on the attenuation. Intrapore clays were naturally found to be important in causing attenuation and in modifying the permeability.

Attenuation due to compliant minerals and microcracks

A number of important trends of behaviour regarding potential mechanisms of attenuation behaviour in the presence of compliant minerals and joints under the effect of confinement, have been revealed by researchers at Imperial College, using
260 m deep research boreholes, located in Northern England. The near surface sedimentary series of rocks (sandstones, siltstones and limestones)have been extensively investigated, both in laboratory, and with multi-frequency field surveys. The water-saturated microcracked clean sandstones, and their in situ counterparts (bedded/jointed sandstones) exhibited strong pressure dependence/depth dependence respectively, with strong decreases in attenuation, and increases in Qp at higher pressures. (Best and Sams, 1997; Best, 1997). This effective stress dependence was attributed to reduced squirt flow as pressure rose, due to partial closure of joints and bedding planes. Other sandstones and siltstones at the site had varying proportions of clay and kerogenic organic matter, which seemed to reduce sensitivity to pressure; Qp was quite low even at high pressure, which was attributed to ‘clay squirt flow’, Best 1997. Data from Best et al., 1994 and Best, 1997, combined in Figures 13.36 a and b, shows systematic reduction of Qp (from 80 plus to about 20) as the percentage of compliant minerals in sandstones and siltstones increased from a few percent to nearly 80%. Best and Sams, 1997 speculated that clay squirt flow would be an important mechanism at both seismic and sonic frequencies, if larger scale geologic features were involved, such as inter-bedded permeable and impermeable layers.

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347

(a) (a)

(b)

Figure 13.36 Ultrasonic data for siltstones and sandstones; Qp versus compliant mineral content, showing the effect of confinement. Best, 1997 and Best et al., 1994.

From a rock mechanics/rock engineering point of view it would seem important to measure the deformation properties imparted by these increased contents of compliant minerals. In the Q-value world of rock mass engineering quality, increased compliant mineral content would mean reduced uniaxial strength c and therefore reduced Qc (Q  c/100) and modulus. There were clearly significant differences in the elastic deformation properties of the siltstones, sandstones and limestones as intact materials. Best, 1974, mentioned a maximum range of instantaneous sample shortenings of 0.74% (siltstone), 0.18% (sandstone) and 0.05% (limestone) as a result of applying the 60 MPa confining pressure. Moduli of 8.1, 33.3, and 120 GPa are implied. P-wave velocities for the laboratory samples were about 3.4 to 3.7, 3.6 to 4.6 and 6.0 to 6.3 km/s respectively. In the case of a clean, saturated sandstone pervaded by microcracks, Best and Sams, 1997 and Best, 1997, showed that Qp was a more sensitive indicator of the effect of confining pressure than Vp. The comparative ultrasonic responses of velocity and attenuation to

(b)

Figure 13.37 Comparative Vp, Vs and Qp, Qs responses of a saturated, microcracked sample of sandstone to confining pressures varying from 5 to 60 MPa. Best, 1997.

confining pressures of up to 60 MPa are compared in Figure 13.37. The sensitivity shown alerts one to the possible complication of sampling-induced microcracking (i.e. related to the initial stress release when coring), which is everpresent in laboratory samples acquired from anisotropicstress environments, if tested at artificially low confining pressures. At 5 MPa confining pressure (close to the estimated in situ confining pressure at the borehole site), Qp was 24  2, increasing to 83  29 at 60 MPa. The grain contact microcracks were apparently closing beyond about 40 MPa, with a consequent reduction in squirt flow related attenuation. The most interesting set of data from the point of view of rock mass quality (as opposed to rock matrix quality), and in relation to attenuation behaviour is shown in Figure 13.38. This strictly field data (belonging to

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.38 Comparison of core (Whitchester sandstones) and downhole sonic log measurements, at equivalent pressures and depths. Best and Sams, 1997.

Chapter 14) is presented here for the sake of continuity. Presumably an ‘altered zone’ (stress-fracturing and mudfiltrate invasion: Chapter 12) that tends to affect sonic logging data at reservoir depths, would be only a very minor factor at this shallow 260 m deep well. The figure shows the stress dependence of the microcracked laboratory specimen (mild) and the stronger response to pressure of the bedded/jointed in situ structures. Best and Sams, 1997 did not comment on the relative bedding/jointing frequency at the different depths in the borehole. However, the pressure/depthvelocity gradient shown in Figure 13.38 can be estimated to be approximately: 3.6  2.7 (km/s) 0.9

10 s1 (MPa) 3.0  0.8 0.09 In the above, the pressure increment 2.2 MPa has been converted to an approximate 90 m depth (0.09 km) to give the conventional Vp-depth gradient in s1 units. This steep gradient suggests quite a low rock quality Q-value, representing the soft porosity in this bedded sedimentary strata, which responds strongly to pressure increase at shallow depth. In Chapter 11, Figure 11.72, an empirical Vp-Q c-depth trend was shown, that suggests,

for velocity-depth gradients to 250 m that are in excess of 5 s1, that Q c  0.1. A typical finely-layered sequence of limestones, sandstones, siltstones and mudstones, with bedding and perhaps a set of bed-limited joints, could be expected to have a ‘poor-quality’ rock quality Q-value, lowered by bedding planes (counted as one set, as is customary, and possible cross-bedding, giving a moderate RQD. Softer inter-beds would effectively increase Ja (See Appendix A for a description of these terms.) We may estimate Q
20/4  1.5/4  0.66/1, or about 1, certainly to the nearest order of magnitude. Together with a rough estimate of uniaxial strength of closer to 10 to 40 MPa than either 1 or 100 MPa, the resulting Q c value would be very roughly 0.1–0.4, making velocity of about 3.5 km/s at about 250 m depth easily understood, if the matrix porosity was about 10% (refer to Figure 11.73). A medium low rock quality Q-value, typical for sedimentary inter-bedded strata, and a correspondingly lower rock quality Q c value, would give significantly reduced rock mass static modulus of deformation Emass (or M), Barton, 1995, from the relation: M  10  Q 1/3 c

(13.12)

Values of M would be in the range 4 to 7 GPa, for the case of Q c  0.1–0.4. This ‘static’ modulus actually has the appearance of correlating, in broad terms, with the lowest values of seismic Q p obtained at lowest frequency. In Chapter 10 we saw frequency-dependent seismic Q values as low as 9 to 12 for this in situ site (Figure 10.35), from sonic log based (8 to 24 kHz) measurements. 13.10.7

Attenuation with dual porosity samples of limestones

Assefa et al., 1999, conducted ultrasonic (0.7 to 0.85 MHz) compressional and shear wave attenuation measurements on forty, 5 centimetre-sized samples of water- or oil-saturated oolitic limestones, at 50 MPa effective hydrostatic confining pressures ('  55 – 5 MPa pore pressure  50 MPa). They found that attenuation reached a maximum value in the samples which had the most fully developed ‘dual-porosity’. This dual porosity consisted of inter-particle macro-pores (dimensions up to 0.3 mm) and micro-pores (with dimensions of 5 to 10 microns). They interpreted this increased attenuation (low Q seis) as evidence of a squirt-flow mechanism, as

Rock physics at laboratory scale

349

Figure 13.40 Compressional-wave seismic quality factor (Q p) versus shear-wave quality factor (Q s), showing a dominance of Q p over Q s when there was less attenuation. Assefa et al., 1999.

Figure 13.39 Attenuations (1/Q p and 1/Q s) for water saturated limestones, as a function of (helium) porosity (range 3 to 17 %) and a roughly three-orders-of-magnitude permeability scale. Assefa et al., 1999.

found in shaley sandstones. They also suggested that conventional dual porosity (i.e. joints and pores) present in the case of, for instance, in situ limestones, could similarly cause seismic attenuation due to squirt flow. Modelling these dual porosity aspects will be addressed in Chapter 15. Klimentos and McCann, 1990, and others had previously shown how attenuation in sandstones was dependent on the pore-filling minerals, particularly the clay content. They had shown how the attenuation was significantly higher in clay-rich sandstones, than in clean clay-free sandstones of identical porosity. Klimentos, 1995, had later measured compressional- and shear-wave attenuation from sonic wave forms in three gas and oil reservoir wells, and was able to show that Q p/Q s was about 1/3 in gas bearing sandstone, while Q p/Q s

was about 5 in water/oil saturated sandstone. The combination of Q p/Q s and Vp/Vs with other well logs enabled differentiation of gas-bearing from oil-bearing reservoirs, as we have seen in other research. Assefa et al., 1999, found that their ‘dual porosity’ (or bimodal porosity) limestone specimens showed higher attenuation (lower seismic Q) when permeability and (total) porosity were also larger. Their results are shown in Figure 13.39. Both distributions of pore size were important, and the attenuation was shown to be the sum of Biot-type fluid flow and squirt flow to/from the larger, moderately interconnected inter-granular pores, which sometimes contributed about 90% of the total porosity. Assefa et al., 1999 also presented results for the ratio of Q p and Q s, sorted by mineralogical differences in their samples. Figure 13.40 shows the generally larger magnitude of Q p consistent with the general effect of saturation, as referred to above. They also compared Q seis values (Q p and Q s) for oil-saturated and water-saturated, showing in Figure 13.41 how the water saturated specimens generally showed less attenuation (higher Q p in particular). The authors posed the question of whether the ultrasonic data (0.7–0.85 MHz) for these small ‘intact’ dual-porosity limestone samples, were of any value to geophysicists trying to interpret propagation through dual-porosity (porous and jointed) limestones in the field, at frequencies in the 50 Hz to 30 kHz ranges, as used in seismic and sonic log surveys.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.41 Comparison of oil-saturated and water-saturated seismic quality factors, for bi-modal porosity limestones, at 50 MPa effective hydrostatic stress. Assefa et al., 1999.

Concerning in situ jointed, dual-porosity chalk (with higher porosity than the limestones), Newman and Worthington, 1982, measured Q p and Q s values as low as 4.0 and 5.2, and 3.5 and 5.9, in two near-surface fissured (jointed) chalks, using seismic frequencies. Assefa et al., suggest that when interpreting the propagation of low frequency seismic waves, the potential for squirt flow attenuation in a large scale dual porosity system such as jointed limestones will clearly be present. Possibly this is why a certain correlation is being noticed between seismic Q and the ‘static’ modulus of deformation, expressed in GPa and readily estimated from rock quality Q (equation 13.12). The components of the rock quality Q-value reflect many potential attenuation-causing factors, e.g. RQD/Jn for scattering due to relative block size, Jr/Ja concerning frictional and conductive properties of the joints expected to be relevant for squirt flow (also including mechanisms in clay), Jw as a direct link to permeability, and SRF related to increased attenuation where stress is low, and reduced attenuation where stress is high. 13.10.8

Attenuation in the presence of over-pressure

Establishing wells in deep sea environments, where there may be over-pressured zones due to rapid sedimentation of alternating sands and shaly sediments, presents a

potential hazard due to the risk of so-called shallow water flows (SWF). Sands in the Gulf of Mexico can present problems for these reasons, at water depths of between 400 and 2100 m, and depths below the mudline of as much as 1200 m. As the name implies, SWF can also be a hazard in shallow water drilling, where effective stresses and compaction of sediments can be minimal, and progressive instability during drilling at a new well can potentially engulf neighbouring wells. Prasad, 2002, used rock-physics principles involving velocities and attenuation, to study this problem. Older data on sands tested at very low effective stresses (in Prasad, 1988), were added to by new data, by performing 1 MHz pulse generator testing of jacketed, lightly confined, clean beach sands of grain size 250–550 m. Due to very low values of shear wave velocity at low effective stresses, for example 400 m/s at 1 MPa, while equivalent compression wave velocities were closer to 1,800–1,900 m/s, there was an exponential increase in the ratio of Vp/Vs to values beyond 5 and 10, and even beyond 100 at negligible effective stress. This trend, which became very noticeable below 2 MPa, is shown in Figure 13.42a, with a log scale for effective stress shown in Figure 13.42b. Prasad showed that there was a dramatic change in the S-wave signals when testing at extremely low effective stress levels, with high attenuation of the shear waves at the lowest pressures, indicating the sand was close to a state of suspension, with low shear strength. The amplitude of the S-waves decreased dramatically below 1 MPa. In contrast, P-wave attenuation reduced marginally at very low effective stress. Due to the decreasing S-wave velocity, Poisson’s ratios increased rapidly to just below 0.5 at negligible effective stress levels. The diagnostic use of the velocities and seismic Q values for registering over-pressure, and the presence of gas can conveniently be ‘tabulated’ as follows, based on the author’s summary text: Detecting over-pressure Reduction in Vp may be ambiguous, as both over-pressure and gas reduce Vp Vp/Vs increases with over-pressure Vp/Vs and Poisson’s ratio both increase exponentially, when sediment approaches a state of suspension Detecting gas Reduction in Vp may be ambiguous, but Vs will be unaffected by presence of gas Vp/Vs decreases with gas saturation

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351

Figure 13.43 Distinguishing between sand and sandstone is very clear using the ratio of Q p/Q s in combination with (Vp/Vs)2. The effect of increasing pore pressure, and reducing effective stress is suitably accentuated. Prasad, 2002.

Figure 13.42 Ratio of Vp/Vs showing exponential increase at low effective stresses (Note: differential pressure Pd is effective stress, defined as Poverburden – Ppore). Prasad, 2002. An empirical prediction from work by Hamilton, 1971 is glimpsed beneath the recent data in the upper diagram.

Carcione and Gangi, 2000, added another important aspect to the understanding of over-pressure effects on seismic attenuation, by considering and modelling, the relative effects of pore-space compressibility, and the compressibility and thermal expansion coefficient for the fluid mixture filling the pore space. Their model consisted of reservoir sand that was buried at a constant sedimentation rate, under a geothermal gradient which was constant both in time and depth. Their model (Figure 13.44) showed realistic reductions of velocity and quality factor with reducing differential (or effective) pressure, especially when less than 15 to 20 MPa, as commonly observed in numerous studies reviewed in this book.

They pointed out that rocks saturated with fluids of high compressibility and low thermal expansion coefficient were generally under-pressured, while rocks saturated with fluids of low compressibility and high thermal expansion coefficients were generally overpressured. The latter could therefore be seismically ‘visible’. Of course at high differential pressures, the velocities (and quality factors) became almost constant. The authors’ model was able to predict pore pressure from seismic properties, if reliable wave velocities and quality factors could be obtained. 13.11

Attenuation in the presence of anisotropy

A further combination of interesting rock physics test data and sophisticated modelling abilities were described by Carcione, 2000, concerning petroleum source rock containing kerogen and different amounts of water. The objectives of the study were to obtain a model for source rocks that would be capable of relating seismic anisotropy (of velocity and attenuation) to kerogen content, pore pressure and water saturation. The author succeeded in demonstrating that anisotropic velocities and attenuation could be used as strong indicators of kerogen content and maturation, which depends on pressure change. Some test data, from the North Sea Kimmeridge Shale, is shown in Figures 13.45a and b. The author’s model, shown as solid curves, was based on a viscoelastic transversely isotropic medium composed of illite and smectite

352

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c)

(d)

Figure 13.44 Modelling of low frequency (25 Hz): a) and b), and ultrasonic (1 MHz): c) and d) P-wave seismic Q versus differential pressure, or versus excess pressure, for a water-saturated model sandstone reservoir. Experimental squares for bedding-parallel Q of Berea sandstone, from Prasad and Manghnani, 1997. (Dotted lines correspond to 0 to 2 km, where the rock is normally pressured, and the continuous lines to the range 2 to 8 km where the rock is over-pressured.) Carcione and Gangi, 2000.

and organic matter. The data for Vp and Vs versus kerogen content, was presented from measurements in bedding normal (0°) and bedding-parallel (90°) directions. The marine Kimmeridge Shale was from the Draupne Formation, located at between 3480 and 3580 m depth, in the central Viking Graben of the North Sea. The modelled seismic Q p and Q s trends, shown in diagrams d) and e), demonstrated an attenuation anisotropy that was higher than the velocity-based stiffness anisotropy. The largest anisotropies were at 18% kerogen content for the case of attenuation, and 30% kerogen content for the case of stiffness or velocity. In Figure 13.45, diagrams e) and f ), Carcione demonstrated the modelling of Vp and Vs for the case of a fixed kerogen content of 35%, and several water saturation levels (Sm  0 to 0.7), again for the case of bedding normal (0°) and bedding parallel (90°) directions. A key variable in these plots was the strong effect (in the case of the bedding-normal (0°) direction of measurement), of an excess pore pressure of up to 50 MPa, giving as expected, successively lower velocities, with greatest reductions for the highest saturation levels. The different maturation stages of this source rock were modelled by evaluating the kerogen to oil conversion and the excess pore pressure, with fracturing estimated if a change of pore pressure of as much as 48 MPa occurred,

compared to the calculated lithostatic minus hydrostatic pressures of 82 MPa and 34 MPa. A kerogen content of 35% was assumed here. The sonic log result for Vp showed a typical reduction from about 4 km/s to a fairly constant value of only 2.6 km/s for the 100 m thick section of this valuable over-pressured source rock.

13.11.1

Attenuation for fluid front monitoring

In 4-D, time-lapse seismic monitoring of reservoir processes, several 3-D seismic surveys of the same reservoir locations made at different times are compared. Differences in reflection amplitude or impedance indicate changes in the reservoir. There is an increasing move to have permanent down-hole sources and receivers for obtaining greater detail of the movement of fluids during production and injection (Ziolkowski, 1999), and for enabling the periodic performance of high frequency cross-hole imaging (e.g. see Chapter 14). Wulff and Mjaaland, 2002 studied time-dependent fluid-front 4-D seismic effects, using a large scale laboratory test, in which a block of lower Triassic sandstone of 17% porosity, was successively submerged in a

Rock physics at laboratory scale

(a)

(b)

(c)

(d)

(e)

(f)

353

Figure 13.45 Experimental velocity data for Kimmeridge Shale source-rock samples from three and a half kilometres beneath the North Sea, with comparison to viscoelastic, transversely isotropic model results. Anisotropic velocity, attenuation, and velocity dependence on excess pore pressure was demonstrated, when measured or modelled in bedding-normal (0°) and bedding parallel (90°) directions. Carcione, 2000.

water tank in four stages, with immediate and long term (300 days) seismic monitoring of the effect of the intermittent ‘water-flood’ and capillary effects. They used P- and S-wave transducers, with centre frequency of 500 kHz. Transmitted and reflected waves were used for the monitoring, with six transducers glued to the top and (submerged) bottom of the block. The water-flooding caused the velocity, amplitude and frequency of the transmitted waves to diminish significantly, with reversal upon final drying of the block. The authors evaluated both the attenuation coefficient (), where 1/Q  V/f, and the attenuation 1/Q, relative to the signals obtained for the dry rock. Seismic Q was also estimated by the spectral ratio method. At maximum saturation of the block, the spectral ratio method indicated a very high maximum 1/Q p of 0.5, and

1/Q s of 0.3. The authors therefore preferred to use the attenuation calculated from (). This gave 1/Q p of 0.065 and 1/Q s of 0.07. Attenuation had increased very rapidly, such that maximum attenuation was reached prior to full saturation, followed by a quite fast decline in the three following months. This was assumed to be due to the decline in local fluid flow (squirt) effects which were dominant prior to full saturation, prior to full flooding. The authors assumed that the velocity reductions were due to water adsorption effects causing a reduced modulus (strictly a laboratory, as opposed to an in situ reservoir effect, unless gas replaced by water-flooding could be considered?). They concluded that improved interpretation of reservoir processes required not only P- and S-wave measurement, but also amplitude and attenuation measurement.

354

Rock quality, seismic velocity, attenuation and anisotropy

13.12

Anisotropic velocity and attenuation in shales

Anisotropy in shale has not been frequently studied due to difficulties with sample disturbance when handling fissile materials. The set of data from Johnston and Christensen, 1995, (Figure 13.46), shows the effect of Vp measurement direction, and the effect of confining pressure, and is a useful summary of the effects of preferred clay mineral orientation. Data sets reviewed by Johnston and Christensen, 1995 showed Vp anisotropy of 20 to 30%, and Vs anisotropy of 32 to 35%. The maximum velocity was always parallel to bedding and the minimum perpendicular to bedding,

Figure 13.46 Effects of confining pressure and direction of velocity measurement for shale. Anisotropy is caused by the preferred orientation of clay particles in the fabric of the shale. (Vsh is the velocity of the shear wave vibrating parallel to bedding, and Vsv is the velocity of the shear wave vibrating perpendicular to bedding). Johnston and Christensen, 1995.

just as it is for the case of rock joints, as reviewed in Chapter 3. Figure 13.47 shows the complete distribution of velocities, with the vertical/horizontal axes showing respectively the perpendicular to bedding and parallel to bedding magnitudes (units km/s). Domnesteanu et al., 2002, measured the anisotropic velocity and attenuation of fully saturated shales under overpressured conditions, Figure 13.48, apparently for

Figure 13.47 Velocity anisotropy caused by the preferred orientation of clay particles in the fabric of the shale: sample New 7. Note shear-wave splitting when making an increasingly acute incident angle to the direction of bedding. (Vsh is the velocity of the shear wave vibrating parallel to bedding, and Vsv is the velocity of the shear wave vibrating perpendicular to bedding). Johnston and Christensen, 1995.

Rock physics at laboratory scale

355

Figure 13.48 a) Propagation and vibration directions with respect to foliation, and relevant to shale sample number. b) Seismic qualities for P- and S-waves through over-pressured shales, as a function of differential pressure, and as a function of propagation direction relative to the foliation. c) One set of examples of P-wave and S-wave attenuation as a function of over-pressure, where PP/Pc  0.46 corresponds to over-pressure. Domnesteanu et al., 2002.

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Rock quality, seismic velocity, attenuation and anisotropy

the first time in the laboratory. They used an ultrasonic reflection technique. The shale cores were from the North Sea. Confining and pore pressures were applied that were relevant to in situ conditions, giving differential pressures from 5 to 60 MPa. (In view of the low permeability of the shale, the use of the rock mechanics adjective for 1  3  differential stress, will not be questioned, as the actual effective stress is uncertain, due to test rate dependency). The seismic signature of the shale was explored by taking the samples through cycles of over-pressured and normally pressured states, whilst increasing the overall confining pressure. The authors found that each incremental increase in pore pressure caused the shale to expand slightly, counteracting the opposite effect of increasing the confining pressure. It was found that the shales behaved elastically at confining pressures higher than 35 MPa. As expected, the compressional and shear wave velocities and seismic quality factors increased with increasing differential pressure (i.e. with reduced over-pressure. The plane of circular symmetry was parallel to the foliation (see Figure 13.48a). The degree of sample anisotropy was found to be related to the depth of origin of the shale. Both Vs and Vp decreased with increasing over-pressure. Nevertheless, the ratio Vp/Vs decreased with increasing differential pressure. As expected there was a general increase in seismic Q p and Q s with differential pressure, but with lowest values showing least increase with stress. Under a fixed differential pressure, an increasing pore pressure was found to reduce Q p by about 16%, or up to 8 units. An anisotropic pattern of wave attenuation is evident from Figure 13.48b. The authors found that the relative proportions of Biot ‘fluid-past-frame’ attenuation, and local squirt flow attenuation were different in the plane parallel to foliation, and in the plane perpendicular to the layering. Squirt flow, localized between compliant and noncompliant pores, was considered a predominant loss in the bulk modulus, and a small loss in the shear modulus. It was naturally considered to be more active in the plane of the foliation, than perpendicular to it. Biot flow was considered a predominant loss in the shear modulus, and a very small loss in the bulk modulus. Since arising from fluid movement in the open pores, it was considered to be related to the macro-permeability. The authors found that at differential pressures 20 MPa, compressional waves propagating perpendicular to the layering (Vp33) were attenuated by squirt flow, and hence more attenuated than the compressional

waves propagating parallel to the layering (Vp11). Q p reduced with overpressure, regardless of propagation direction, while Q s was highly dependent on propagation direction, and depended less on pore pressure than Q p. Perhaps predictably, the results suggested a strong link between the rock framework, the pore geometry and connectivity, and therefore the response of pore fluid to the propagation of seismic waves, in specific directions.

13.12.1

Attenuation anisotropy expressions E, G and D

At a seismic Q workshop in Madrid, Best et al., 2005, described an ultrasonic pulse-echo technique for investigating both velocity and seismic Q anisotropy of P- and S-waves in finely inter-bedded reservoir-type rocks. They had modified the earlier version of the equipment, so as to be able to study shear wave anisotropy, using a 360° rotating S-wave transducer, for observing the shift of arrival time. This will be described here because of obvious relevance to attenuation in finely bedded reservoir rocks, which will be partly addressed in the next section. Their studies were performed at effective stress levels of 5 and 40 or 50 MPa, on vertically or horizontally aligned samples of Carboniferous sandstone, siltstone or limestone obtained from the Imperial College experimental borehole site in northern England. Following Thomsen (1986) velocity anisotropy expressions for ,  and  in weakly transversely isotropic media, and because of the excellent stability of their pulse-echo data, they gave equivalent expressions for attenuation (Q1), and derived relevant results for these new parameters: 1

(Q 1 )



1

Q p (H )  Q p ( V ) 1

Q p (V ) 1

1

(Q 1 ) 

Q sh (H)  Q sh ( V )

((Q 1 )

Q sv (H)  Q sv (H)

1

Q sh ( V ) 1



(13.13)

(13.14)

1

1

Q sv (H)

(13.15)

where V denoted vertical, H horizontal, and the sub-scripts p, sh and sv denoted P-waves, S-waves with horizontal polarization, and S-waves with vertical

Rock physics at laboratory scale

357

shear wave splitting for revealing attenuating and fluidconducting joint structure, in hydrocarbon reservoirs.

13.13

Figure 13.49 Orientation of laboratory (sub-core) samples, with bedding features (dashed lines) either perpendicular or parallel to the shear wave transmission. Shear wave polarization is shown by the Sv and Sh components. Best et al., 2005. Table 13.2 Q 1 anisotropy parameters for thinly bedded sandstone samples. Best et al., 2005. Lithology

Pressure (MPa)

(Q1) %

(Q1) %

((Q1) %

Sandstone

5

Sandstone

40

11.8 (/3.3) 42.5 (/5.1)

0.0 (/1.2) 75.0 (/4.6)

27.3 (/1.0) 7.7 (/1.9)

polarization (see Figure 13.49). The authors introduced the parameter ␨, to describe the anisotropy between the fast and slow S-wave polarizations in the H sample. (The subjects of shear wave splitting and polarization are treated in detail in Chapter 15). A brief sampling of Best et al., 2005 results for sandstone, using these new expressions, is given in Table 13.2. The samples exhibited visible sub-millimetre, fine horizontal layering of clay/organic matter. At an equivalent 500 m depth (for the case of low density, porous rock), the effective stress of 5 MPa indicates that there is sig1 nificant Q 1 p anisotropy (), none for Q sh (␥), and 1 strong anisotropy for Qsv (␨), i.e. consistent with transverse anisotropy. At 40 MPa, roughly equivalent to effective stresses at 4,000 m depth in porous sedimentary rock masses, there was a dramatic increase in anisotropy for Q p1 and 1 Q sh (the latter perhaps surprising), while the Q 1 sv anisotropy reduced, as would be expected at higher stress. A second sample showed significantly different 1 results, except in the case of Q sv behaviour (reduction with increased stress). The anisotropy of seismic Q will be addressed in much more detail in Chapter 15, due to the importance of

Permeability and velocity anisotropy due to fabric, joints and fractures

A very interesting laboratory study of velocity and permeability anisotropy, for the case of tight gas sandstones containing sub-vertical, conjugate-type jointing, was reported by Dürrast et al., 2002. The individual joints were either ‘open’, open-and-mineralized, or mineralized. The sandstones were of very low matrix permeability (30 d), and had a sedimentary layering consisting of fine clay layers. Production from a reservoir in such tight sandstones naturally depends on the jointing (i.e. the natural fractures). The authors were able to study the three-dimensional P-wave velocity of spherical samples machined from the core, in at least 100 directions, to obtain Vp symmetry without prior assumptions. Some selected results of the P-wave anisotropy measurements, plotted stereographically on lower-hemisphere Schmidt net projections (perpendicular to the core axis), are shown in Figure 13.50a. Their results for six spherical samples, under the first condition of zero confinement, showed a range of maximum Vp (saturated) of 4.6–5.2 km/s and minimum Vp (dry) of 3.7–4.0 km/s, with the difference plots (saturated minus dry) showing a maximum range of 0.51.1 km/s for the six samples, under zero confinement. The sedimentary layering and cross-bedding tended to dominate the Vp distribution, with jointing (open or mineralized) having less effect on Vp, but tending to change the symmetry of the Vp distribution, giving a more monoclinic symmetry. Permeability and P-wave velocity measurements were performed on spherical samples of the same sandstones, some containing both the sedimentary fabric and the steeply dipping jointing. Vp under four levels of confinement, up to 100 MPa are shown in Figure 13.50b. These tests demonstrated several important trends of behaviour. Naturally, in the absence of jointing, the higher permeability and velocity values were recorded in the plane of the nearly horizontal layering, perpendicular to the core axis. Figure 13.51a shows the permeability in three orthogonal directions, as a function of confining pressure, with results dominated by the successively reducing porosities of the five selected samples. Note the low values of the vertical (Z-axis)

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.50 a) Three-dimensional P-wave velocity measurements on spherical samples in more than 100 directions, in the dry and saturated states. Two of the six results (k3 and k5) for the tight gas sandstones are shown. These illustrated cases were under zero confinement. b) Confined tests with sedimentary layering (ss) and sometimes jointing (r1 and r2), provided an anisotropic, confining pressure-dependent mix of effects on velocities. (Note: sample porosities are listed in Figure 13.51). Dürrast et al., 2002.

permeabilities in each case, due to the thin dark-clay layers obstructing vertical flow. However where discrete jointing occurred, with subvertical orientation, as in the case of sample k5, the highest permeabilities were recorded parallel to the core axis, i.e. vertically. This clear trend is shown in Figure 13.51b. With confining pressure below 50 MPa, there was a mono-clinic symmetry of the P-wave velocity distribution caused by the combination of sedimentary layering, jointing, and cross-bedding, while at higher confinement, the sedimentary layering was virtually the only remaining feature, resulting in a more transversely isotropic symmetry.

The authors commented on the significance of the surface roughness of the joints providing a significant fluid path, even at higher confining pressures. From 50 to 80 MPa confining pressure, corresponding to depths of several kilometres, the permeabilities parallel to the fractures were up to nine times higher than those parallel to the sedimentary layering. In view of the possibility of conjugate shearing of such joint sets, one may speculate that in a reservoir environment, with anisotropic stress, there would be a possibility of relative maintenance of joint permeability despite high effective stresses. These possibilities, and the influence of joint-surface related

Rock physics at laboratory scale

(a)

paper, by one of the above co-authors, from the Institut Français du Pétrole, see Rasolofosaon and Zinszner, 2002. The new equipment, based on that developed by Arts et al., 1996, now allows independent application of pore pressure and confining pressure, while measuring P-wave velocities in multiple directions as we have seen. These two authors described interesting comparisons of the anisotropic 3D permeability and elasticity tensors of various reservoir rocks. The permeability tensors were obtained by a tracer injection and X-ray technique. They found that in some cases, the elastic property anisotropy, and the hydraulic anisotropy were closely related in terms of symmetry directions – this occurred when the two mechanisms shared the same cause, such as layering or jointing. Good agreement was seen between the two types of anisotropy for a North Sea sandstone of 16% porosity (Figure 13.52), while in the case of a dolomite of 23% porosity, there were marked differences due to the influence of small-scale disconnected fissures. Cases where there was no correlation, highlighted the challenges faced in estimating permeability and monitoring fluid flow from seismic measurements in the field. In an earlier study with the same equipment, Rasolofosaon et al., 2000 had shown a comparison of crack and fabric analysis with inversion of the multidirectional ultrasonic data.

13.13.1

(b)

Figure 13.51 a) Orthogonal permeabilities of five spherical samples, having successively reducing porosities. Vertical permeability (Z) is least due to dominance of sub-horizontal dark-clay layers. b) Orthogonal permeabilities of jointed sample k5, which had a porosity of 10.2%. Note effect of sub-vertical jointing on the higher vertical (Z) permeability in this case. Dürrast et al., 2002.

properties, like roughness (JRC), and wall-strength (JCS), in assisting permeability maintenance (unless each are too low), are mentioned in Chapter 14 and addressed in detail in Chapter 16. The large, spherical-sample test equipment used in the above studies, was also described in a companion

359

Seismic monitoring of fracture development and permeability

An important experimental testing facility at Imperial College, described by King et al., 1995, Shakeel, 1995, and King, 2002, allows the application of extremely high (hundreds of MPa) polyaxial stress states to small (40 to 50 mm) cubical specimens of rock. Figure 13.53 illustrates the loading frame and principal loading and velocity measurement directions, with definition of the nine components of P- and S-wave velocity, and the vibration directions of the S-waves. Pietzo-electric transducers were used to produce and detect the pulses of compressional waves (450–800 kHz), and either of two shear waves (350–750 kHz), polarized at right-angles, and propagating in one of the principal stress directions. By holding the minimum principal stress very low (e.g. 2 or 3 MPa), and increasing 1 and 2 in unison, to high levels, it was possible to create a set of closely spaced extension/tension fractures perpendicular to the minimum stress direction. Shakeel and King, 1998 and

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.52 Comparison of elastic anisotropy, measured on a spherical North Sea sandstone sample, and hydraulic anisotropy, measured by a tracer-injection X-ray technique in the same rock sample. ISO: isotropic, TI: transversely isotropic, MON: monoclinic symmetry, ORT: orthorhombic symmetry. Rasolofosaon and Zinszner, 2002.

King, 2002 described dynamic hydro-mechanical (ultrasonic and flow) measurements both before fracturing, during fracturing, and in load-unload cycles after fracturing. Figure 13.54 reproduces some of the very interesting experimental results of principal P-wave and S-wave velocities that were recorded during the initially almost biaxial loading of a 6% porosity, and almost isotropic sandstone up to fracturing. Diagrams a) and b) show Vp1 and Vs1 increasing steadily parallel with the high ‘biaxial

loading. At approximately 100 MPa, the set of ‘biaxial’ extension fractures started to develop (point F), and the perpendicular velocities Vp2 and Vs2 indicated rapidly declining velocities due to the presence of the new fractures. Figure 13.55 indicates what happened when the newly fractured cube was reloaded with equal hydrostatic stress. There was a more rapid increase in Vp2 and Vs2 as the fracture set was (nearly) closed, while parallel with the fractures, the velocities Vp1 and Vs1 behaved almost as

Rock physics at laboratory scale

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(a)

(b)

Figure 13.53 a) Section through the 3D static and dynamic loading facility at Imperial College. Permeability can also be measured in the presence of a high pore pressure. b) Principal loading and velocity measurement directions, with definition of the nine components of P- and S-wave velocity, and the vibration directions of the S-waves. King et al., 1995, King 2002.

362

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(a)

(b) (b)

Figure 13.54 Ultrasonic P- and S-wave components from tests performed across a 6% porosity, isotropic cube of Crossland Hill sandstone, when loaded in a polyaxial facility. Pre- and post-fracturing results are shown, and compared with excellent modelling results, from Shakeel, 1995. Measurable permeability (1 md) parallel to the pending fractures, did not develop until velocities reduced at fracturing point F. King, 2002.

before. The very closely matching analytical modelling results by Shakeel, 1995, using a method developed for a transversely isotropic cracked medium by Nishizawa, 1982 are virtually identical with the experimental result, in terms of velocities. King et al., 1997 reported several interesting results concerning the attenuation of various of the nine velocity components (calculated by the spectral ratio technique), in an equivalent series of three test cycles on a cube of Penrith sandstone of 13% porosity. Figure 13.56a shows selected results for the ‘3’ direction, perpendicular to the pending fracture set, which presumably started to initiate at point F, when the major stress was increased beyond 100 MPa to initiate fracturing. Note the reduction of seismic Q from about 20 before fracturing, to

Figure 13.55 Ultrasonic P- and S-wave components from tests performed across a 6% porosity, isotropic cube of Crossland Hill sandstone, when re-loaded in a polyaxial facility in parallel and perpendicular-to-fracturing directions, upon subsequent hydrostatic loading to 90 MPa. Note the almost unchanged velocities measured parallel to the fracture set that was developed. King, 2002.

less than 5, somewhat resembling a reduction in deformation modulus, when expressed in units of GPa. Figure 13.56b shows the hydrostatic loading test phase for the same set of fractures, with a low stress seismic Q increasing from 10 to about 29 with hydrostatic (therefore normal) loading to 70 MPa. The ‘before-fracturing’ result is also shown for comparison, indicating seismic Q increasing from 20 to 40, as a result of loading to 70 MPa. These again resemble increase in moduli, expressed in units of GPa. In Figure 13.57, the attenuation for P- and S-waves in the same perpendicular ‘3’ direction, are plotted against permeability measured parallel to the fracture. King, 2002 described the less demanding development of a set of parallel (cleavage) fractures in slate, simply by axially loading a cylindrical sample in a conventional triaxial cell. These easily formed, smooth, planar cleavage

Rock physics at laboratory scale

363

(a)

Figure 13.57 Attenuation for P- and S-waves in the ‘3’ perpendicular to fracture set direction for the same cube of Penrith sandstone of 13% porosity, plotted against the permeability to flow parallel to the fracture set. Results apply to the hydrostatic loading case, as in Figure 13.56b. King et al., 1997.

(b)

Figure 13.56 a) Fracturing test cycle on a cube of Penrith sandstone of 13% porosity, with attenuation results for the ‘3’ direction, perpendicular to the pending fracture set, which presumably started to initiate at point F. b) Hydrostatic loading test phase for the same set of fractures, with comparison to ‘beforefracturing’ phase. King et al., 1997. Note: seismic Q values have been added on the right-hand axes, as the geophysicists tradition for expressing attenuation as ‘1000/Q’ is perhaps hiding a physically viable mechanism related to attenuation, namely a certain modulus increase due to normal loading, of unknown but similar magnitude to seismic Q, when the former is expressed as GPa.

fractures had a spacing of about 1 mm, while in the sandstone, fractured in the polyaxial cell, the rougher fractures were spaced many mm to 1–2 cm apart, based on a photograph of a fractured cube, provided in King, 2002. A particularly interesting, and possibly challenging result was obtained from the dynamically monitored permeability measurements. King and his colleagues had found that the low permeability (1 md) sandstone, started to develop measurable permeability once the velocities Vp2 and Vs2 started to reduce (at point F in Figure 13.54), indicating crack development.

In the subsequent hydrostatic loading, the velocities tended to converge indicating near-closure, but the permeabilities of three similarly fractured sandstones, shown in Figure 13.58 reduced much more slowly with stress increase than the smooth cleavage fractures in the slate. The shear wave velocity Vs2 showed a continuous rise. King, 2002 reported ‘considerable hysteresis’ in Vs2 – permeability behaviour, with subsequent crack-closing cycles. An example is shown in Figure 13.58b. King was of the opinion that the reason for the significant differences in velocity – permeability behaviour between the smooth and the rough fractures was ‘unclear’, but of course cited the difference in roughness. For some reason, rough fractures closing due to stress increase contributed to increased velocity, but suffered a less-than-expected reduction in permeability. The reason for the different behaviour of the rough fractures compared to the smooth, may be that E (physical aperture)  e (hydraulic aperture), for the case of rough fractures (or joints), and E
e for smooth fractures (or joints). (Barton et al., 1985). This would mean faster physical closure than hydraulic closure for rough joints. The greater inequality with increased roughness JRC, of the average physical aperture (E), compared to the theoretical, smooth-wall hydraulic aperture (e), described more fully in Chapter 16, means that a fracture or joint with an assumed (low) aspect ratio, say 104, may have a permeability equivalent to an even smaller aspect ratio

364

Rock quality, seismic velocity, attenuation and anisotropy

empirical equation of Barton et al., 1985 was as follows:

e

(a)

(b)

Figure 13.58 Shear-wave monitoring of fracture closure and permeability reduction, due to increased normal loading in the Imperial College D-H-M polyaxial cell. a) Three cubic samples of different sandstones, each with a set of parallel, rough extension fractures, display quite different behaviour to smooth (cleavageparallel) extension fractures in slate. b) Stress-closure cycles for the fractures in Crossland Hill sandstone, show strong hysteresis on the first cycle. King, 2002 and Shakeel, 1995.

e.g. 105. This means that a 100 m physical aperture may have a 10 m hydraulic aperture. So the physical aperture (E) of a rough joint or rough fracture, with a typical JRC  10–15 for a well controlled extension fracture, closes much faster than the hydraulic aperture under stress, perhaps helping to explain the strong velocity response and the weaker permeability response. When on the other hand the fracture has the lowest JRC of 1, typical for cleavage joints in slate, there will be no inequality between E and e. JRC  1 is the practical limit to the following relation, implying ‘table-top’ planarity and smoothness. The

E2 JRC 2.5

(13.16)

where JRC, the joint roughness coefficient of Barton and Choubey, 1977, is fully explained in Chapter 16. With E  100 m, and JRC  15, e  11.5 m. With JRC  1, E  e  e.g. 10 m. Such a fracture offers no resistance to closure: it closes to a significant degree under even a very low normal stress. Possibly the above result is one of the reasons that in a jointed or fractured reservoir, the performance of 4D seismic can be quite successful if effective stresses are not too high, as the velocity (and particularly the attenuation) are relatively sensitive indicators of small permeability changes. By the nature of jointed reservoirs, there are unlikely to be commercially viable hydrocarbon-bearing fractures or joints with very low JRC values, as joint closure under stress would preclude both permeability and ‘storage’, if such was needed due to low porosity matrix. Hydraulic fractures, or widely opening joints, due to the cooling and pressure-drive effect of water-flooding, could be expected to show a ‘first-closing’ cycle showing large hysteresis, when heat flow returns (see Bandis et al., 1983 ambient tests). Velocity anisotropy due to a set of fractures, parallel or perpendicular to principal loading axes, as beautifully illustrated in the above polyaxial experiments is, inevitably, only a part of the information needed when trying to interpret field data from a jointed or fractured reservoir. Gibson and Toksöz, 1990 addressed the important question of crack orientations ranging from 0° to 90° in relation to the stress axis. Cracks of small aspect ratio (roughly 104) were modelled, applying the theory of Walsh, 1965 concerning crack closure under stress applied obliquely to the crack normals. The variation of the quasi compressional velocity with orientation, and the important link to permeability variation with crack orientation and stress level were each addressed. Some difficulty in closely matching the sparse experimental results was indicated, including matching the more rapid closure at low stress. The reality of fracture sets having different properties affecting the stress-closure behaviour, and the possible influence of intersecting or interconnecting fractures also altering the stress-closure behaviour were discussed, but these difficulties could not of course be modelled analytically. In this complex rock mechanics area, there were by that time promising advances in distinct element modelling

Rock physics at laboratory scale

365

Table 13.3 ‘Rule-of-thumb’ for order of magnitude estimates of seismic Qp, based on the empirical scheme linking the jointed rock mass quality Q, Vp, Emass – and in very approximate terms – the rock mass permeability. (Barton, 1999). Water at 20°C assumed in mD to m/s conversion Vp km/s Qseis (est.) K mD K m/s

1.5 2 1000 105

2.0 3

2.5 5 100 106

3.0 7

3.5 10 10 107

with the two-dimensional UDEC and three-dimensional 3DEC codes of Cundall, allowing dynamic wave transmission and attenuation through intersecting joint sets of any desired orientation or block size. Various numerical modelling methods are discussed in Chapter 15. 13.14

Rock mass quality, attenuation and modulus

This chapter will be concluded by bringing an empirical rock mechanics scheme into consideration, as justification for the tentative, repeated conclusion, first launched in Chapter 10, that seismic Q very much resembles the static modulus of deformation expressed in GPa, strictly for the case of jointed or fractured rock, for which a good data base exists. The special fracturing tests of King and his colleagues at Imperial College, have given repeated support for this simple hypothesis. Deformation moduli are almost always in the range of 5 to 100 GPa, and seismic Q seems also to be most frequently in this range in the case of near-surface rock masses (to 1 kilometre depth?), as frequently suggested by attenuation data presented in Chapters 10 and 13. The empirical expression for static deformation modulus: Emass  10 Qc1/3, and the expression linking velocity and rock quality: Vp  3.5  log Qc can be merged, by elimination of Qc into the form: E mass  10(Vp0.5)/3 (GPa ) (
Q seis ?)

(13.17)

The Vp scale on the left-hand side of Figure 13.59 can be followed across the diagram (‘ignoring’ the rock mass quality Q c), all the way to the right-hand side deformation modulus estimates, giving (in Table 13.3) proposed Vp – Emass (GPa) or seismic Q ‘first-pass’ estimation of (better than) order of magnitude values of seismic Q, specifically where jointed or fractured rock masses are involved. For good measure, a very rough estimate of permeability is also given, based on the Lugeon value (1 L
107 m/s, and with 1 Darcy  1012 m2
105 m/s, for water at 20)C, we have 1 Lugeon
10 millidarcies).

4.0 15

4.5 22 1 108

5.0 32

5.5 46 0.1 109

6.0 68

6.5 100 0.01 1010

There is something quite familiar about these estimates of seismic Q in relation to Vp, based on the large number of cases in fractured rock, reviewed in Chapter 10, and in relevant parts of Chapter 13. Note that Vp2 in Figure 13.54a is 2.5 km/s at the end of the cracking phase, just as the reported seismic Q of a second sandstone was 5 at the same stage of loading, following the same method of fracture development. Beyond the ‘jointed rock’ modulus limit of roughly 150 GPa, the question of seismic Q value estimation is problematic, but remarkably it starts to resemble the rock mass Q and Qc value, i.e. 500, 1000, 2000 – the latter representing completely intact hard rock at moderate, deep and kilometre-depths, or relevant to hard, very hard and extremely hard unjointed rock at moderate depths of say 1⁄2 to 1 km. In case of knowledge of the approximate uniaxial compressive strength (c) of the rock where the P-wave velocity measurement is made, the improved linkages between (c) and deformation modulus (and therefore an approximate seismic Q ) can be applied, as shown in Figure 13.60. Example: Vp measured at 2 km depth in fractured sandstones  5.0 km/s. Uniaxial strength of sandstones
50 MPa. Estimate of ‘static’ deformation modulus is 25 GPa. A first estimate of seismic Q, specifically Qp is therefore 25. The possible relative differences in frequency effects on Vp and seismic Q is of course a source of additional error in this simple method. Porosity effects not captured by direct effects on (c) may be subtracted from the estimates of modulus, using the graphical adjustments suggested in Figure 13.59. These are empirical by nature and have an insignificant data-base at high rock quality Qvalues, since high n% seldom accompanies high Q-values. In Chapter 7 concerning excavation disturbed zones, we reviewed the very thorough seismic studies of the Basalt Waste Isolation Project (BWIP) conducted by King et al., 1984 and 1986, and several other researchers. The review included EDZ effects on P- and S-wave velocities in the columnar basalt, using cross-hole seismic measurement at different depths into the tunnel wall in horizontal, diagonal (inclined), and vertical directions.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 13.59 For the case of jointed or fractured rock, there is a strong resemblance of the magnitude of seismic Q, to the ‘static’ deformation modulus expressed as GPa. The figure shows the inter-relationships developed from an empirical expression linking the rock mass quality Q-value with the ‘static’ deformation modulus Emass (or M) and velocity Vp. Permeability, in Lugeons (1 L
107 m/s
10 millidarcies for water at 20)C) is also roughly linked, in the absence of clay-sealing of the joints. In this chart a nominal uniaxial compressive strength of ‘hard’ rock, namely 100 MPa forms the basis of the graphics, but using the Q c  Q  c/100 relation, other compressive strengths can be applied, as shown in Figure 13.60. Barton, 1999a.

Figure 13.60 A rough method for estimating seismic Q from P-wave velocity and uniaxial compressive strength linkages to ‘static’ deformation modulus. By implication, and also in practice, the trend when moving downwards-and-to-the-right is for increased depth and reduced porosity, thereby reaching values of Emass in the higher range of 50 to 100 or more typical for crystalline rocks or hard limestones or well-cemented sandstones.

A very interesting result of relevance to the possible link between seismic Q p and the static deformation modulus determined from Q rock is shown in Figure 13.61. This is not laboratory data for Q p, but it is normalized by laboratory data, on the assumption that the relative

Q p value in situ cannot be more than that of an intact sample of the same rock at the same stress level. King et al., 1986 normalized their in situ estimates of Q p, using an assigned maximum value of 50, where the highest value of Q seis was recorded, 9 m from the tunnel face, in

Rock physics at laboratory scale

Figure 13.61 Relative Qp values interpreted from seismic crosshole measurements in the face of a shallow (46 m) tunnel. Measurements in horizontal (strongly jointed) and vertical (sparsely jointed) directions, in thincolumn basalts of 0.15 to 0.36 m thickness at BWIP. King et al., 1986.

367

a vertical direction (not crossing any columnar joints, and probably few if any horizontal cross-column joints). The value of 50 corresponded to the laboratory test value at appropriate low stress levels. Note the horizontal ray-path relative Q of about 5 to 8, measured in a direction crossing the maximum number of joints (sinuous six-sided basalt columns of 0.15 to 0.36 m thickness), and possibly under the influence of a low horizontal stress, typical of many near-surface columnar basalts. The depth of the tunnel was only 46 m. In the vertical direction, with theoretical vertical tangential stress effects perhaps more clearly imprinted, due to the relative lack of horizontal joints, there is an unmistakable similarity of the increase in relative Q to the deformation modulus increase (and magnitude, when expressed as GPa) that one often interprets from tunnel and shaft extensometer arrays. For example Barton and Bakhtar, 1983, back calculated static deformation moduli from extensometer measurements in a deep (1.6 km) shaft in steeply bedded and jointed quartzites, obtaining moduli from 2.5 to 60 GPa from near the shaft wall to one diameter depth. There is also an unmistakable similarity of these numbers to expected Qp ranges, as also in Figure 13.60.

14

P-waves for characterising fractured reservoirs

The ability to detect the presence of viable hydrocarbonbearing structures, with sufficient porosity, and with tolerable matrix and mass permeability, are among the challenges of the petroleum geologist, petrophysicist, and geophysicist, whose joint role may last far into the reservoir engineers’ production phase. In this chapter we will give examples of some of the basic ways of ‘seismically illuminating’ reservoirs at larger scale, sometimes extending over 100’s of km2 to depths of 5 km. (Small-scale dipole and monopole sonic logging was described in Chapter 12, because of its intimate connection to rock stress, borehole stability and mud pressure). The larger scale techniques illustrated in this chapter range from cross-well tomography, VSP 2D and 3D multi-azimuth walk-away surveys, 4C multicomponent surveys, AVO and AVOA for detecting fracture orientation, and 4D repeated surveys for tracking reservoir changes over time. One of the causes of such changes is the use of water flooding, which causes various coupled mechanisms, besides an advancing oil/water contact. 4D can also be used for monitoring the effects of compaction, and subsidence. In general, apart from a brief treatment of C-waves or converted P-S waves, we will leave a detailed description of the use of shear wave splitting and polarization for Chapter 15. This remarkable method for characterization of fractured reservoirs is a suitable finale, and a good introduction to the need for more geomechanics (in Chapter 16), for improved understanding of fractured reservoir behaviour.

14.1

Some classic relationships between age, depth and velocity

The most fundamental and earliest means of interpreting possible reservoir conditions at kilometre depths was the use of seismic P-wave velocity well surveys, using a simple VSP concept. There was early recognition of velocity increase with depth, with the following smooth

velocity-depth function attributed to Slotnick, 1936: v z  v o  Kz

(14.1)

where vo is the (P-wave) velocity at the surface and vz is the velocity at vertical depth z. There was also early recognition of a quite systematic trend linking velocity to the geological age, in combination with the present depth of occurrence. The interesting empirical method of Faust, 1952 will be summarized as a ‘geological’ and ‘stress-effect’ introduction to hydrocarbon reservoir investigation. Faust discovered that the greatest rate of velocity increase occurred at shallow depth in the oldest units, which is fundamental early proof of the importance of dual porosity. The likelihood of more joints in the stiffer, older units make these units more sensitive to stress change. However, with only Vp as a dynamic indicator of conditions, acoustic closure represented a limit to the sensitivity, especially for the weaker, younger reservoir rocks. Faust, 1951, used data from almost 1 million feet (or about 300 kilometres) of well sections, in 500 petroleum well surveys, mostly from the USA and some from Canada. The great majority of data was for mixed shale/sandstone sections. A non-systematic comparison of shale and sand (sandstone) velocities had revealed an average discrepancy of only 350 ft/sec, or 106.7 m/s in velocity between these two, frequently inter-bedded units, the sandstone having the highest velocity by this small average margin. The ironic similarity of velocities for these two basic dissimilar as ‘chalk-and-cheese’ units, is a reminder of the potential ‘non-uniqueness’ of P-wave velocity, and the recognised need for alternative interpretation methods, such as impedance and attenuation, to distinguish the different lithologies and their fluid-bearing signatures. The potential closeness of velocities for shale and sandstone is actually surprising, in view of the greater tolerance of the stronger sandstone to stress anisotropy, often resulting in several MPa greater minimum stress

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Rock quality, seismic velocity, attenuation and anisotropy

Table 14.1 Mean depth-velocity data from Tertiary and Pennsylvanian shale-sandstone units, selected from Faust, 1951, from wells in the USA only. Mean depth Z (ft)

Mean velocity of Tertiary (ft/s)

No. of wells of Tertiary

Mean velocity of Pennsylvanian (ft/s)

No. of wells of Pennsylvanian

1 025 2 500 3 500 4 500 5 500 6 500 7 500 8 500 9 500 10 500 11 500

6 800 7 660 8 160 8 670 9 220 9 520 9 860 10 220 10 670 11 090 11 300

71 63 63 64 54 53 48 31 23 13 2

9 420 11 110 11 720 12 230 12 650 12 710 13 320 13 390 13 020 14 030 14 500

18 14 18 18 14 7 5 4 4 3 2

in the shale, which is frequently a fluid barrier for the hydrocarbon-bearing sandstone. Faust minimised lithological variations by averaging all measurements at the same depth and age. At the outset he assumed that velocity (V) could be expressed as a function of depth (Z), age (T) and lithological variables (L). Since L was considered too problematic (i.e. how to compare the separate units limestone, shale and sandstone) shale and sand were accepted as representing equivalent sections, as they alternated too frequently in relation to the usual interval of down-hole velocity measurement, which then was as much as 500 feet (or 152 m). Table 14.1 gives an extract of the data for the two most frequently represented geologic ages, namely the Tertiary and the Pennsylvanian, which follows the Permian. The oldest units were Devonian (15 wells) and Ordovician (3 wells). Although reproducing very ‘smoothed’ data due to the averaging process, Faust, 1951, was careful to point out that the maximum deviations from the velocity averages could be great. Nevertheless both minimum and maximum values also demonstrated increased velocity with depth. Comparison of same-age same-depth data from different regions of the USA, reportedly showed little systematic deviation of the mean from one area to another. However the Devonian of the Appalachian Basin and the Eocene and Cretaceous of SW Texas had velocities more typical of data 3000 ft (915 m) deeper. This was thought to be due to unusually high degrees of cementation. Figure 14.1 is derived from the extensive data that was partly sampled in Table 14.1. It shows the quite systematic average trends of velocity, age and depth. The greatest rate

of velocity increase occurs at ‘shallow’ depth in the oldest units, which is presumably a function of more joints that therefore make the older units more sensitive to stress change. The steepest velocity-depth gradients occur, of course, in the 300 m to 1 km depth range, 1000 ft being the approximate limiting depth of measurement. The trend of the data is given by Faust, 1951, as: V  m Z

1

n

(14.2)

which was reportedly similar to a current weathering correction method known as the ‘Blondeau weathering’. Z is depth in feet, m is a constant with units of velocity (that proves to be age-dependent) and n is a constant, independent of age. Faust plotted the same data in log-log format, as shown in Figure 14.2. The velocity at each depth could then be represented as: log V  log m  1 n log Z (14.3) To the extent that equation 14.2 is correct, m represents the velocity for a particular geological age at 1 foot depth (0.3 m). The relevant geological ages and the ‘zero depth’ velocity constants (m) are given in Table 14.2. The constant n  6, applies for all the curves in Figure 14.2. By plotting m against age, shown in Figure 14.3, a linear log-log plot was obtained of the form: am  T1/6

(14.4)

where T is geologic age in years and  is a constant. Equations 14.2 and 14.4 could therefore be combined as: V  (TZ)1/6

(14.5)

In Faust, 1951,  is given as 125.3, and is numerically equal to velocity in feet per second when TZ  1. From the literature of the time, values of  of 121.5 and 127.2 were also quoted by Faust. A mean value of 124.7 from these three results suggests that   125 would be an acceptable constant. An example will now be given to illustrate this simple, early technique. Assume Evaluating equation 14.5 at

Pennsylvanian  220 106 years (Table 14.2) M  3,047 ft/s  929 m/s (Table 14.2) Z  1,000; 1,500; 2,000; 3,000 ft, we obtain: V  9,712; 10,391; 10,900; 11,663 ft/s  2.96; 3.17; 3.32; 3.56 km/s

P-waves for characterising fractured reservoirs

371

Figure 14.1 Velocity-depth trends for in situ reservoir rocks of various geological ages (linear scales). Faust, 1951.

Figure 14.2 Velocity-depth trends for in situ reservoir rocks of various geological ages (log scales). Faust, 1951.

Figure 14.3 Mean values of m (Velocity in ft/s at nominal 1 ft depth) for different ages. Faust, 1951.

Table 14.2 Geologic age and ‘zero depth’ velocity constants. Faust, 1951.

Geologic age

Geologic time

Velocity constant m ft/s

Tertiary Eocene Cretaceous Jurassic-Triassic Permian Pennsylvanian Mississippian Devonian Ordovician

26 106 yrs 43 106 yrs 93 106 yrs 152 106 yrs 192 106 yrs 220 106 yrs 245 106 yrs 284 106 yrs 390 106 yrs

2 190 2 332 2 607 2 823 2 866 3 047 3 235 3 380 3 439

Velocity constant m m/s 668 711 795 861 874 929 986 1 030 1 048

These predicted velocities at 305 m, 457 m, 610 m and 915 m depth, are apparently much less sensitive to stress increase than jointed rock would be to sub-horizontal wave paths, from refraction seismic or cross-hole tomography. Perhaps this is because we are looking at an inter-bedded sandstone-shale unit of Pennsylvanian age, with the predominant measurement direction in a subvertical direction, with shot points only some 1,000 ft (305 m) from the well, and with downhole receivers to record the approximately 0.09 to 0.08 s average arrival time, limited to each 1,000 ft depth interval (in the case of the Pennsylvanian age sediments).

372

Rock quality, seismic velocity, attenuation and anisotropy

from 4% to 39% porosity, with clay volume fractions spanning 0 to 55%, and over a confining pressure range of 0 to 40 MPa, equivalent to depths up to roughly 3 km.

14.2

Figure 14.4 Remarkable similarities of Vs versus Vp trends for water saturated sandstones and shales, according to ultrasonic testing in the laboratory at effective pressures of up to 40 MPa. Castagna et al., 1993, as reproduced in Mavko et al., 1998.

The natural suspicion that the ‘coarse’ VSP-style well logging available at this time may have been the cause of the poor differentiation of the shale and sandstone in terms of their relative P-wave velocities, as referred to at the beginning of this review of Faust, 1951, is definitively not supported by confined ultrasonic laboratory data for shales and sandstones. Figure 14.4, from work by Castagna et al., 1993, and reproduced by Mavko et al., 1998, shows that the three given empirical relationships for Vp and Vs seem to fit both data sets very closely. Han’s easy to remember 1986 relationship: Vs  0.79Vp  0.79

(km/s)

(14.6)

was shown by Mavko et al., 1998 to give a very good fit to a wide variety of (water saturated) shaly sands,

Anisotropy and heterogeneity caused by inter-bedded strata and jointing

Fine layering of alternating porous and impermeable strata is obviously one of the basic sedimentary systems that contribute to the existence of potential reservoir rocks in sedimentary basins. Sandstones with their usually elevated porosities, may be the recipients of the hydrocarbons, and the variously aged shale facies may contribute both as the deeper and or laterally occurring source rocks, and as the elevated seals or cap-rocks. Some form of deformation of the recipient strata, through folding or faulting, is usually necessary to ensure that a trap is formed. Petroleum may therefore be found within anticlinal structures containing favourable jointing, if capped by impermeable shales or salt rock. Frequently it is the larger scale faulting that is responsible for the porous reservoir rocks and sealing layers to be juxtaposed, or sealed by shale-smear if sufficiently plastic. The final requirement is a favourably tilted dip direction. Fine layering of sedimentary strata means that the dominant wavelength of a seismic or sonic pulse is long compared to the thickness of individual layers. The medium will nevertheless exhibit effective (and real) anisotropy, with a vertical symmetry axis in the case of horizontal layering. In the presence of hydrocarbons this layered medium may show substantial attenuation and velocity dispersion, which will be compounded with the additional (or separate) presence of jointing or fracturing. The authors Helbig and Thomsen, 2005 emphasised that anisotropy, and the associated new techniques: primarily shear wave splitting and polarization, bought with them a new exploration concept: neither exploring for the presence of reservoir rock, nor for the presence of hydrocarbons, but for the presence of crack or fracture permeability. In 4D repeated surveys, changes of fracture permeability due to flooding and production has also become a modern goal in the use of seismic and attenuation anisotropy. Following Lynn, 2004, a ‘thin bed’ is 3 8 of a wave length, the limit for a discrete reflection both from the top and bottom of the bed. Wave scattering, attenuation and dispersion occur when the ordered heterogeneities have scale lengths of about 0.3–0.01 of the

P-waves for characterising fractured reservoirs

wavelength, while the smallest scale of ordered heterogeneity, less than 0.01 of the wavelengths, may be the cause of most of the azimuthal and offset dependent velocity. Conventional seismic wavelengths are much longer than the scale lengths of either of the features that govern dual-porosity flow in a reservoir. As pointed out by Williams and Jenner, 2002, the earth does not care which tools or frequencies we use; it still knows it is anisotropic. Strong P-wave velocity anisotropy is being observed in every geologic environment, with the possible exception of basins under primary deposition and burial. P-wave azimuthal anisotropy was previously ignored, and left to the research and technology group, but is now known to be one of the most significant properties of the acquired seismic data. Unfortunately, in the marine environment, fully populated offsets in each azimuth class are less common than on land, but Williams and Jenner emphasised that even narrow azimuth data gave an opportunity to see the effects of azimuthal anisotropy. Hand-in-hand with the basic anisotropy caused by sedimentary layering, and deformation processes, is marked heterogeneity, occurring at many scales and for many reasons. As Nur, 1989 pointed out, reservoirs are much more heterogeneous than anybody likes to believe, and as time goes by more and more reservoirs are re-classified as severely heterogeneous, due to a multitude of dynamic flow-related cyclical events during their formation, and due to fracturing and faulting in subsequent geologic eras, each of which become better understood as time, and seismic developments, advance. An appropriate quotation from Lynn, 2004, also has relevance here. ‘Fractures are like cockroaches. There is no such thing as one cockroach. If you see one, a whole family of all scale lengths is hiding nearby.’ In a survey of one hundred fractured (i.e. jointed, not MHF) oil reservoirs from around the world, it was found convenient to divide the reservoirs into four groups (Allan, 2002): 1. Type I: little matrix porosity and permeability – fractures provided both storage capacity and fluidflow pathways. 2. Type II: low matrix porosity and permeability – matrix provides some storage capacity – fractures provide fluid-flow pathways. 3. Type III: micro-porous reservoirs with high matrix porosity but low matrix permeability – matrix provides the storage capacity – fractures provide the fluid-flow pathways.

373

4. Type IV: macro-porous reservoirs have high matrix porosity and permeability – matrix provides both storage capacity and fluid-flow pathways – fractures merely enhance permeability. The author warned that Type I and Type II reservoirs could be easily damaged by excessive production rates (due presumably to the rather strong sensitivity of permeability to unnecessarily high effective stress levels), but many performed well under unassisted primary recovery when managed properly. In Type III reservoirs the recovery factor was dependent on lithology, wetability, and fracture intensity. The choice of appropriate EOR (enhanced oil recovery) was essential for optimal exploitation. In Type IV reservoirs, the recovery factor was most sensitive to the selected drive mechanism. The sophistication of investigation methods, using multi-component and multiple-frequency methods, gives the capability of revealing heterogeneity and fracturing at many scales, even if indirectly, thanks to some remarkable and fortuitous dynamic wave properties. A good analogy to the developing heterogeneity of a better understood reservoir, is all the adverse faulting gradually revealed by successive drilling at a potential nuclear waste disposal site, perhaps causing its eventual rejection, after many years of costly investigations. With huge quantities of petroleum in place at a potential or existing reservoir, rejection is seldom an option, and better understanding through improved seismic and enhanced production techniques, are the obvious ways forward.

14.2.1

Some basic anisotropy theory

For reference purposes we need to summarize some basic elements of isotropic and anisotropic behaviour, since various categories of anisotropic behaviour will now be treated in somewhat more detail than in earlier chapters. A linear elastic isotropic medium requires only two constants to specify the stress-strain behaviour, either Young’s modulus (E) and Poisson’s ratio (*), or alternatively Lamé’s constants ( ) and ( ), where ( ) is the shear modulus. These pairs of parameters can be derived from each other using standard equations of elasticity (see Chapter 1, and refer also to the Rock Physics Handbook by Mavko et al., 1998, and Birch, 1961).

374

Rock quality, seismic velocity, attenuation and anisotropy

Matrix format (6  6) is used to represent the threedimensional elastic tensors, which in the isotropic case, requires only two parameters, as follows:   2

  2

  2

  

0 0 0

0 0 0 0

0  0  0  0   

●

(14.7)

where the term  2 can be expressed as c11, as c12, and as c44. Figure 14.5 shows the contrasting elastic tensors for three classes of anisotropy: ●

●

Transversely isotropic with vertical axis of symmetry (TIV) typical of fine layering in shales. (Five independent constants, since c66  1⁄2(c11 – c12). Tensor elements 1,3 and 2,3 are the same term c13)

Figure 14.5 Elastic tensors in 6  6 matrix format, for two single ‘geological’ classes of symmetry (TIV and TIH), combined as more realistic orthorhombic material in the third diagram, and requiring nine instead of five independent constants. Typical of bedded or layered rock with anisotropic horizontal-stress related, aligned vertical jointing, fracturing and/or microcracking.

Transversely isotropic with horizontal axis of symmetry (TIH) perpendicular to the vertical layers, but typically caused by stress-related aligned, vertical jointing, fracturing, and/or microcracks. (Also five independent constants: tensor elements 1,2 and 1,3 are the same term c13) Orthorhombic symmetry typical of horizontally bedded rock containing a set of vertically aligned joints, fractures and/or microcracks. (Nine independent constants).

Symmetry, as above, is an important property, if found, as the wave fronts will be similarly symmetric. When processing orthorhombic data (which can have a second perpendicular fracture set and still be termed orthorhombic), if fast and slow directions have been identified, then azimuth sectoring can be applied in these directions, and according to Lynn, 2004, most ‘isotropic’ processing codes can function fairly well on these azimuth-sectored data.

14.3

Shallow cross-well seismic tomography

For consistency of presentation we may start this brief review of reservoir characterization, by referring to an interesting shallow 3D tomographic imaging of both seismic velocity and attenuation, given by Brzostowski and McMechan, 1992. This was based on a 1989 3D survey shot by Peko Oil USA, and by Texaco in SE Oklahoma. Figure 14.6 (a to d) shows the surface geology and Vp tomograms for the first, second and third constant-thickness slices centred at depths of 32, 96 and 106 m. The corresponding seismic Qp tomograms are shown in Figure 14.7. As is readily noted from this interesting set of data, the alluvium (e.g. unit Qal) had both low velocity (2.25 km/s) and low Qp (6) at 32 m average depth, while the lithified sandstones had velocities between 2.5 and 3.5 km/s at 32 m average depth and Qp values of about 7 to 10. Clearly the Vp values for all units and the corresponding Qp values increase with depth. However, more lateral variation is shown in the Qp tomogram. As we have seen both in Chapter 1 and in Chapter 11, this lateral variability is also common at much larger scales. The suggested link between Vp and Qp developed at the end of Chapter 13 (Figure 13.60) suggests Qp values lower than 2 to 3, in the case of weak materials in the presence of velocities lower than 2.25 km/s. Where velocities climb to 3.5 km/s in much of layer 3 (centred

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Figure 14.6 3D P-wave velocity tomograms for mid-depths of 32, 96 and 106 m depth in quaternary sediments, alluvial stream beds and sandstones. Brzostowski and McMechan, 1992.

Figure 14.7 3D Qp tomograms corresponding to Fig. 14.6 slices. Brzostowski and McMechan, 1992.

at 106 m depth), the measured Qp was predominantly from 5 to 10, and Figure 13.60 suggests Qp of at least 5 to 7, in the case of moderately weak materials, such as ‘shallow’ sandstones. Since both Vp and seismic Q contain a certain level of information about the pore space and degree of jointing or fracturing, and the saturating fluid, the trial combination of these parameters in the form of tomographic plots of Qseis/Vp, possibly offers the possibility of a closer estimate of transport properties. In an interesting study using tomographic imaging between a total of six wells with known lithology, but unknown transport properties, Liao and McMechan, 1997 showed what might be delineated by the combination of tomographic images of Vp, seismic Q, and their ratio Qseis/Vp. Figure 14.8 shows the 210–400 m deep shale/sandstone sequence. The Gypsy sands were high porosity (mean 20%), high permeability (mean 560 mD), water-saturated, clean sand channels lying within a silty flood-plain. High-resolution cylindrical piezoelectric bender transducers were used as both sources and receivers, over a band width of 300–1300 Hz. From the diamondpattern of six wells, the data between wells 1, 5 and 7 were selected for Qseis and Vp tomographic analysis. Overall full-depth, three-hole, results are shown in Figure 14.9, while a detailed 90 m section between wells 7 and

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Figure 14.8 Sand, shale and sand-shale lithology at the three-well tomographic site described by Liao and McMechan, 1997.

5 is shown in Figure 14.10. This has a marked shale-rich upper 40%, and a sand-rich middle-to-lower section. The typical in situ values of the parameters were as follows: sandstone shale

Vp 3.0 km/s 3.6 km/s

Qseis 45 30

Qseis/Vp 15 8.3

The low velocity was a consequence of the high porosity (mean 20%) of the channel sand. The relatively low attenuation (Qseis as high as 45) was reportedly due to its full water saturation, and high porosity. The authors considered it likely that high values of the ratio Qseis /Vp would correlate with the most porous and most permeable zones, and low values with reduced flow such as the shale-rich layers. They considered that a thin and a thick shale barrier did show appropriately low values of the ratio (i.e. light colours in Figure 14.10, panel c). The authors cited Castagne et al., 1993, who had suggested that sandstones often have higher velocity and show less attenuation than shales in the same environment. In these channel sands the low velocity (3 km/s) is clearly a function of lack of cementation and their high porosity, while the full-saturation makes

Figure 14.9 Fence diagrams of seismic tomography analysis between wells 1, 5 and 7 to full depth. The wells were 99 m, 141 m and 105 m apart. Liao and McMechan, 1997. Note Vp, Qseis and Qseis/Vp tomograms. Liao and McMechan, 1997. Reproduced by kind permission.

them less attenuating (no squirt flow losses), giving a relatively high Qseis of 45. This combination (ratio  15) is many times higher than the modest ratios of Qp /Vp suggested in the jointed rock model suggested in Figure 13.60, at the end of Chapter 13. Perhaps, on reflection, this contrast in Qseis/Vp ratios, being so marked, could delineate the difference between unconsolidated sands and jointed sandstones, and between weak plastic shales, and the less desirable fissured/jointed, or indurated variety.

P-waves for characterising fractured reservoirs

Figure 14.10 Selected tomographic images of Vp, Qseis, and their ratio Qseis/Vp, between well 7 (left) and well 5 (right), for contrasting shale-rich (top), and sand-rich (lowermiddle) zones within a 90 m section between the wells. When dominated by shale, ratios of Qseis/Vp are low, and when dominated by sand they are high. Sand/shale proportions for each borehole are shown. Liao and McMechan, 1997. Reproduced by kind permission.

14.3.1

Shallow cross-well seismic in fractured rock

The question of resolution levels necessary for fracture detection was illustrated by Majer et al., 1997. Working at the Conoco Borehole Test Facility, their goal in

377

shallow (15 to 35 m) water saturated limestones, was to image gas filled fractures in wells with 50 to 100 m separation. The authors had started out using standard low resolution VSP and surface reflection methods, which yielded little information on the individual fractures, but did indicate P-wave anisotropy due to a N70°E trending set of joints. Cross-well, high frequency (1 to 10 kHz) surveys using piezoelectric sources, were later used with success, to image an individual fracture zone in the limestone, before, during, and after air injection. The air followed the hydrologically-predicted pathway, and helped to seismically ‘illuminate’ the zone. Subsequent slant-hole coring verified the presence of a conducting, vertical fracture 1 m from the seismically located position. The wave-lengths used were of the order of fi to 1 m, and the fracture aperture reportedly as large as 1 mm. The P-wave velocity of the limestones determined from earlier near-offset VSP varied from about 3.8 to 4.2 km/s between the shallow depths of 16 and 26 m, which suggests a rock quality Q-value of 2 to 5 from the empirical relation Vp
3.5  log Q derived in Part I, relevant to nominal 25 m depth, ‘100 MPa, low-porosity’ rock. Q  2–5 is typical for rock masses with three sets of joints, moderate block size, and with possible weathering of the joint walls: i.e. from Appendix A: Q
90/9  2/2  0.66/2.5
2 to 3. A seismic Q of the order of 5–20 times higher than Qrock, as suggested from numerous cases reviewed in Chapter 10, suggested an ‘order of magnitude’ estimate of Qseis  10–25, at this shallow, jointed site. The method suggested in Figure 13.60, and Table 13.3, linking Qseis to the ‘static’ deformation modulus estimate, suggests a Qseis value of about 13–14 from Qrock  2 to 3, if the uniaxial compressive strength of the limestone was around 100 MPa. Alternatively, utilising Figure 13.60, for evaluating the possible effect of lower uniaxial strengths, we see that Qseis for this jointed (i.e. fractured) limestone might be about 12 to 16 with the given Vp range of 3.8–4.2 km/s. 14.3.2

Cross-well seismic tomography with permeability measurement

A new poroelastic analytical model called ‘super – k’ was described by Yamamoto, 2003, who was working not in petroleum provinces, but on a limestone aquifer. Pointing out that extraction of permeability from velocity and

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Table 14.3 Seismically derived, frequency-dependent cross-well data for Vp and Q, with the seismically derived (super-k) prediction of permeability and porosity. Limestone section at 462 m depth. Yamamoto, 2003. Frequency (kHz)

Vp (m/s)

Q

k (d)



2 4 8 12

3545 3580 3616 3652

14.0 18.1 31.0 49.0

33.7 33.7 35.0 35.7

0.34 0.35 0.36 0.34

Note: k from pumping test  33.2 d k from packer test  36.3 d porosity from neutron log:   39%

attenuation data had been one of the important unsolved problems in seismic exploration, the author was able to demonstrate good correspondence between acousticallyimaged permeability and hydraulic pumping (extraction) and packer (injection) tests. An unusual close, 11 m horizontally-spaced cross-well set-up was used for deriving 4 kHz velocity and attenuation tomograms. Data was also acquired at five other frequencies (1, 2, 3, 5, and 0.250 kHz). Permeability was measured in four packered intervals down the same 300–480 m deep test section. His model reportedly coincided numerically with the combined Biot and squirt flow mechanism (the BISQ model of Dvorkin et al., 1994), when permeability was 100 md, and when the frequency was 100 kHz (the so-called super-k regime, where the pore fluid is always relaxed). The limestone where the author performed these studies had extremely high permeability (10–250 d). He described a large wave attenuation and velocity dispersion in this highly permeable limestone. This in situ data is reproduced in Figure 14.11. The author divided the 180 m  11 m imaged crosssection into seven, mostly 25 m long sub-sections, for the purpose of velocity and attenuation inversion. His analytical inversion model for permeability involved a quadratic equation for a non-dimensional permeabilityfrequency parameter, with attenuation as a polynomial constant. It may be noted that although the porosity and permeability were of exceptional magnitude, the seismic velocities of 3.5 and 3.6 km/s obtained at the two lowest frequencies of 2 and 4 kHz, were matched with seismic Q values of 14 and 18, which are quite close the jointed rock model potentially linking Vp and Qp, if the assumption is made that the uniaxial strength of the limestone is high, and that the high porosity and permeability is due to solution channels. (If porosity was distributed

Figure 14.11 Comparison of models (K  super – k, B  Biot, and D  BISQ ) with cross-well velocity and attenuation data from 300–480 m depth at a permeable aquifer site. Data from Yamamoto and Kuru, 1997. Yamamoto, 2003.

it would presumably resemble chalk more than limestone). Significantly, the mismatch with the Qseis modulus-model (Figure 13.60) increases strongly at higher frequencies.

14.3.3

Cross-well seismic in deeper reservoir characterization

A special issue of Geophysics was devoted to cross-well methods in 1995, due to the large number of unsolicited papers on the subject, following strong oil industry interest in use of cross-hole tomographic methods since the late 80’s, for imaging below the resolution of surface seismic, for such purposes as steam injection front imaging. An important discovery from the early period of cross-well research, was that very high frequency could be propagated over distance of several hundreds of metres, when both source and receiver were down-hole, in deep boreholes. The additional discovery of very high bandwidth with downhole receivers and sources apparently confirmed the phenomenon that seismologists also have to live with, if without downhole instruments (Chapter 10), that most of the surface-based frequency loss is due to attenuation in the near-surface low-Q zone. Rector, 1995, mentioned an order of magnitude improvement in subsurface resolution, with many investigators now using secondary arrivals, such as reflections, to obtain

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379

very high resolution images. As at the surface, where refraction imaging was gradually replaced by reflection imaging, the same occurred with VSP, and now was occurring when receiver and source were downhole. Mathisen et al., 1995 gave an example of the use of time-lapse cross-well data in heavy oil sands, using a cemented multiple-receiver cable in one hole. Twenty seven cross-well surveys were acquired between two wells, during a 31⁄2 month period, before, during, and after a 34 days steam injection cycle. Vp and Poisson’s ratio tomograms were used to track the changes caused by both the temperature and viscosity reduction. Stratification with a dip of 20° controlled the flow of steam, which caused progressive reductions in P-wave velocity of up to 90 to 270 m/s adjacent to and above the injectors. Poisson’s ratio tomograms showed a corresponding decrease (0.1), in the same areas. Time-lapse S-wave tomograms demonstrated great stability with time, showing only very slight change (i.e. shear waves not registering fluid viscosity changes), and therefore demonstrating that the reservoir ‘rock’ was stable despite the fluid changes.

14.4

Detecting finely inter-layered sequences

Remaining at shallow depth for the moment, namely a 250 m deep research well through finely inter-layered limestone, shale, and sandstone sequences in the Imperial College Borehole Test Site, one may note the important work by Sams, 1995, who showed how the combined use of a borehole compensated (BHC) sonic logging tool, a compensated formation density tool, and a Formation Micro Scanner (FM) could resolve much of the detail of finely interlayered rock sequences. Figure 14.12 shows the success of multiple borehole logging tools in resolving some details of finely interlayered rocks. Sams, 1995, pointed out that the minimum detectable layer thickness using standard sonic tools may be no less than 15 cm. In the limit when the layers become thin with respect to the wavelength, the particular layer will be transparent. Standard logs will tend to underestimate the effects of layering on measurements of attenuation and anisotropy. Consequently, intrinsic attenuation and dispersion may be incorrectly assessed. Any distorted frequency dependence of the intrinsic attenuation would subsequently adversely affect estimates of the physical rock properties and of the contained fluids. This is because the intrinsic attenuation is

Figure 14.12 a) The results of multiple borehole logging tools in resolving the velocities and densities of finely interlayered rocks. b) The relative velocities of the shales, sandstones and limestones from laboratory tests of Vp, and an assumed Vs correlation. Sams, 1995.

important for remote detection of fluids, such as kerogen rich shales and their state of maturation. As discussed at length in Chapter 12, the probability of a variable, mini-EDZ in the walls of a well that penetrates inter-bedded strata of different stiffnesses, may mean accentuated fluctuation of velocities when sonic logging, if the well is of sufficient depth. Both Vp and an associated Qseis, are intuitively likely to move in the direction of lower values if the mini-EDZ takes the form of shear fracturing and additional joint and fissure displacements and loosening, as it apparently can in shale, in the so-called ‘alteration’ zone. Both parameters may move in the opposite direction of higher values, when the tangential stress concentration (e.g. 3H – h) makes a positive contribution to the

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Rock quality, seismic velocity, attenuation and anisotropy

‘tightness’ of both a stiff matrix (like limestone) and any local joint structure in these stiffer facies. The velocity-facies definition given in Figure 14.12, with implicit and definitive separation of shales, sandstones and limestones, leads one to suggest the potential for facies or strength based estimates of Qseis, using such differentiated velocities. With appropriate ranges of uniaxial strengths and velocities for the three rock types (shale, sandstone, limestone), one might arrive at ‘representative’ Qseis values of 6–7, 10–15, and 20–40 for the less frequent limestone layers, using the modulusmodel of Figure 13.60. The key question is then whether the inter-bedded mix of facies will create a ‘weighted average’ response, concerning the high frequency, best definition of layering when well logging. In Chapter 10, where Qseis was treated in detail, one may note from Figure 10.34, from the multi-frequency investigations of Sams et al., 1997 in these same experimental boreholes, that the 8–24 kHz sonic logging gave the lowest Qp range of about 6–14, with a mean Qp of 10.4 and a mean Vp of 3.48 km/s. (See Table 10.4). These fit the modulus-model predictions. Figure 14.13, a virtual copy of Figure 10.35, is repeated here with the important Qp scale firmly in place, to supplement the somewhat misleading ‘1000/Q’ typically found in numerous publications. If Qseis is accepted as potentially being ‘a rock mass property’ (i.e. pores and joints and saturating fluid included), it apparently helps to give a very believable range of Qp of about 5 to 12, with sonic velocities ranging from 3 to 4 km/s as shown in the figure. The lower frequencies of cross-hole of 0.2–2.3 kHz, gave a mean Qp of 15.7. Interestingly, the lowest frequency 30–280 Hz VSP, giving poorest definition of the fine inter-layering, gave a mean Qp of 31.3. At first sight it would appear possible that this is because of the dominant effect of higher velocity layers (limestone) and the relative invisibility of the low velocity layers to longer wave-lengths, thereby ‘biasing’ the weightedaverage picture that applies most fully at higher frequency when ‘all’ layers are illuminated. However, in relation to velocity, this argument does not hold, as Figure 14.13 shows VSP velocities to be somewhat lower (range of approx. 2.8 to 3.6 km/s). The higher core velocities, ranging from 3.4 to 4.4 km/s, are for matrix without bedding or cross-bedding joints, naturally giving higher Qp, they do not fit the modulusmodel well since they are not representative of the jointed, bedded rock mass.

Figure 14.13 Sams et al., 1997 multi-frequency results for four scales of seismic illumination. The highest frequency sonic logging, giving a form of weighted-average of the numerous rock layers present, seems to be quite well matched by the modulus-model of Figure 13.60.

14.4.1

Larger scale differentiation of facies

Larger scale differentiation of facies described by Kabir and Verschuur, 2000, is shown in Figure 14.14. In this synthetic Picrocol data set, which nevertheless was based on real data shot over a salt dome, the model assumed constant velocity layers, which was a simplification.

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381

Figure 14.14 Estimated velocity models based on an IFP Picrocol data set from a southern North Sea salt dome and surrounds. Note lateral velocity variations in individual layers. Kabir and Verschuur, 2000. Reproduced by kind permission.

Nevertheless each layer was described with an average velocity and a vertical velocity gradient. Overburden stress and fluid pressure were assumed to increase linearly with depth. The authors discussed the sometime need for lateral velocity gradient in addition to vertical velocity gradient, in interpreting variations. They suggested the use of well velocities to improve depth conversion and geological interpretations.

Fracturing or jointing caused by anticlinal structures can be a key to effective drainage of oil and gas from a porous but low permeability matrix such as tight sandstone or chalk. Depending on the efficiency of the caprock, often shales, there may also be over-pressured shale layers in the reservoir. Fracturing or jointing causing reduced velocities may be seen as a seismic time-sag. This can be accentuated by the presence of gas rather

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Rock quality, seismic velocity, attenuation and anisotropy

than oil, and can also be accentuated by the effect of over-pressure.

14.5

Detecting anisotropy caused by fractures with multi-azimuth VSP

In the same way that we had to reject earlier assumptions about elastic isotropic rock mechanics behaviour, the sedimentary rocks containing hydrocarbons have also proved to be neither isotropic nor homogeneous, but heterogeneous and anisotropic. Besides detecting azimuthal velocity anisotropy, signalling aligned fracturing and/or anisotropic rock stress, there are now needs for spatial resolution of variable structure, and also for resolution of temporal changes. A more recent challenge is the resolution of azimuthal variation in attenuation as an indicator of horizontal permeability anisotropy. All seismic data are now known to vary with the offset (angle in relation to the well), and with the azimuth. Since all seismic data also varies with frequency, there is an increasing recognition that 3D multi-component, multi-mode and multi-azimuth acquisition may be required and economically justified. The seismic wavelength at which the measurement is made, determines what seismic attributes can be measured, and whether the rock looks homogeneous and isotropic or heterogeneous and anisotropic. According to Lynn, 2004 when the cause of the ordered anisotropy replicates itself across different scale lengths, or exhibits fractal tendencies, the anisotropy measured in modern dipole well logs at kilohertz frequencies, may match the anisotropy trends that are detected at another scale, with 10–100 kH reflection seismic. A given set of vertically aligned fractures will therefore cause anisotropy with low frequency measurement, signal distortion with mid-frequency measurement, and lead to reflections by the highest frequency waves. The practice of VSP (vertical seismic profiling), walkaway VSP, multi-azimuth VSP, and numerous other techniques related to VSP are so fundamental in exploration that a diagram for illustrating the technique is probably superfluous. Nevertheless, since a figure is worth a thousand words: Figure 14.15 shows the principle of e.g. walkaway VSP, with surface shot points shown along a single azimuth, and downhole receiver positions. There is also a technique for performing VSP for horizontal well sections, using geophones clamped to the formation, and hydrophones suspended in the borehole

fluid. Subtraction of seismograms for the down-going and the up-going pulses leaves an enhanced reflection. (Christie et al., 1995). There is a growing trend to instrument some petroleum wells on a ‘permanent’ basis, so that 4D seismic can be used ‘more easily’, to monitor changes bought about by different water-flood and production practices, using rock physics principles to assist in the interpretation. As we saw in Chapter 10, the in-well installation practice apparently started in the late 80’s and early 90’s in the case of permanent installations in deep holes adjacent to the San Andreas fault in California.

14.5.1

Fracture azimuth and stress azimuth from P-wave surveys

The original goal of a seismic study reported by Lynn et al., 1999a, for the US Department of Energy, was to evaluate and map fracture azimuth and relative fracture density throughout a naturally-fractured gas reservoir interval. P-waves travelling in the plane parallel to aligned vertical fractures (thus giving transverse isotropy with a horizontal axis – known as HTI media), have higher velocity than the P-waves travelling perpendicular to the fractures. The latter direction corresponds to the high attenuation direction, due to the lower frequency of the P-waves, and therefore a lower seismic Q. The advantages of using of both travel time and amplitude, or travel time and frequency, for detecting permeability was emphasised. As the authors pointed out, the detection of relative crack density and crack orientations was not the final goal, rather it was the detection of azimuthal anisotropy that was attributable to structure that controlled the fluidflow properties at reservoir scale. With sufficient fracture density, connectivity and permeability anisotropy were likely. A threshold value of anisotropy would probably be involved. The detection of permeability anisotropy could be considered as one step beyond the detection of vertically aligned fractures, and/or the detection of unequal horizontal stresses. The authors emphasised the importance of knowledge of the orientation of maximum horizontal stress, due to the commonly assumed strong correlation between directionality of reservoir flow and the local, presentday orientation of the maximum horizontal stress. Typically, oriented four-arm calliper logs show a long axis that is oriented parallel to the minimum horizontal stress

P-waves for characterising fractured reservoirs

(a)

383

(b)

(c)

Figure 14.15 a) Simple illustration of the principles of walk-away vertical seismic profiling (VSP). The usual practice will be the use of shot points along multi-azimuth lines, preferably symmetrically distributed, such as in two perpendicular arrays related to the dominant fracturing direction (e.g. Grimm et al., 1999), or as illustrated by b) with a more complete double-orthogonal coverage for the case of the hypothetical fractured reservoir (Liu, 2003). A walk-around lay-out at constant offset or radius, for improved characterization of fractured reservoirs has also been used (Horne, 2003). Use of wide aperture layouts, extending on the surface to at least the target depth is recommended, e.g. Lynn et al., 1999. c) Zero, or limited offset VSP with the direct and reflected wave-paths explained (Christie et al., 1995).

direction, if there is stress-induced break-out. (However, as mentioned earlier in this chapter, and discussed in more detail in Chapters 15 and 16, there may be jointor fracture-related reasons for a careful evaluation of this commonly-held viewpoint.) Interestingly for later discussion of this topic, the authors mention the ‘problem’ of a NW-oriented production trend at a neighbouring well, yet with a

WNW-oriented fracture strike (based on oriented core and impression-packer results). The WNW fracture direction also agreed with the maximum stress indicated by break-out analysis from calliper logs. A plausible explanation of enhanced dilation of the WNW fracture set, due to structural flexure of the anticlinal structure, mentioned improved connectivity as a possible explanation of the (roughly 20°?) rotated NW production trend.

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Rock quality, seismic velocity, attenuation and anisotropy

Analyses at the Rulison Field by Lynn et al., 1999b, using just two azimuthal bins of data, also showed a ‘discrepancy’ of orientations: a similar present day stress as above (N 70–80° W), but principle P-wave velocity directions of N30W and N60E. The authors continued to assume that the direction of H max would be the direction of open cracks or fractures, but did not discuss the possibility of the interaction of e.g. two sets of joints or fractures, or the possibility of conjugate shearing as an explanation of ‘open’ fractures. This topic is treated in detail in Chapter 16, following analysis of the shear strength of rock joints and fractures, and analysis of what has been learned by Zoback and coworkers, about water conducting joint (or minor fault) directions relative to H max directions. Their findings should have special relevance in petroleum reservoirs where rock strengths are limited, yet fractures are assumed to be ‘open’, despite ␴h min magnitudes of tens of MPa. In Chapter 16, (and Barton, 2005), a further reason is discussed for such minor angular discrepancies, namely a dilation-related contrary-rotation of fluid lenses contra rock-to-rock contacting asperities, when nonplanar joints (or fractures), are actually under significant shear stress, and therefore significantly ‘open’. This geometric effect could possibly rotate shear wave splitting mechanisms. Interesting observations on the subject of ‘open’ fracture orientations were made by Laubach et al., 2002. They cited comparisons of measured stress directions and orientations of open, flow-controlling fractures that showed that open fractures in the sub-surface were not necessarily parallel to maximum compressive stress (H max). Fractures perpendicular to this direction could also be ‘open’ if partially filled with mineral cements, and for this reason, sealed fractures parallel to H max were numerous. They pointed out that a determining factor for fluid flow was the degree of mineral cements deposited within the fractures, either ‘at the time of fracturing’ (synkinematic), or as post-kinematic cements precipitated after fractures ceased opening. They suggested, from experiences in both compressional and extensional provinces, with production data from 2,400 to 6,400 m depth, that the divergence between H max and ‘open’ fractures demonstrably contributing to flow was ‘from a few degrees to 90 degrees’. Grimm et al., 1999 also chose a relatively simple (two-azimuth bin) method of estimating the spatial distribution of gas-producing natural fractures in a tight gas reservoir. This relatively large P-wave survey was divided into two volumes, with ray-paths parallel and perpendicular (/45°) to the assumed dominant

fracture direction (based on structural geology). This method was used in order to construct azimuthally differentiated, and azimuthally limited seismic attributes, that would highlight the formation’s fracture and matrix response, respectively. A rough measure of fracture anisotropy was given by the resulting P-wave interval velocities, measured in two such azimuthal bins. (Two-azimuthal binning is however blind to anisotropy near 45° to the principal chosen directions). The authors found that when the anisotropy exceeded 5 to 10% using this simpler approach, there was good agreement with the principle directions obtained by more sophisticated methods. There was correspondingly robust correlation and identification of zones of high fracture density and permeability. The authors reported that reflectivity and frequency were also anisotropic, and actually had better correlations with gas productivity than P-wave velocity anisotropy. Ray paths travelling parallel to fractures giving increase in frequency may have been due to squirt flow mechanisms parallel to the fractures. The authors used the neural network technique (with 85% success), to infer commercial prospectivity over undrilled areas, using the available geological, geophysical and engineering attributes. The authors advised full-azimuth 3-D P-wave surveys for such analyses, with maximum offsets equal to, or greater than target depth, using azimuthally isotropic source and receiver arrays. Naturally they also recommended processing in as many azimuths as allowed by cost, with independent velocity analyses in each azimuth. An admirably detailed integration of structural orientation data with near-offset VSP at the Conoco Borehole Test Facility, was given by Queen and Rizer, 1990, based on the surface outcrop joint orientations, rock fabric orientation (from point-loading), and from the results of joint orientation using a borehole televiewer and oriented core. Figure 14.16 shows the principal orientation data at these different scales. The two joint sets seen at the surface proved not to be as consistent as expected with the three sets of jointing in the sub-surface. The quite consistently oriented point-load fracturing traces could not apparently be related to any observable microcrack directions or to fabric, and would then seem likely to have some relation to residual stresses in the samples. The seismic anisotropy measurements consisted of near-offset VSP in twenty three 30 m intervals from 183 to 853 m depth, and azimuthal VSP uniformly spaced at 15° intervals around a 120° quadrant, with nine sources on a 290 m radius centred on the Conoco 33–1 well.

P-waves for characterising fractured reservoirs

385

Figure 14.16 Top left: surface outcrop and joint rosette. Top right: superimposed tensile-fracture traces from point-load (steel ball) indentation testing of the limestone. Middle: left and right: cumulative induced-fracture lengths and orientations from 35 tests on oriented surface samples of the limestone, and from 9 tests on oriented indurated shale core from 734 m depth down the Conoco 33–4 well. Bottom left: Joint rosette concerning accumulative length of sub-surface jointing of given strike, interpreted from BHTV and oriented core (with bias against non-vertical jointing). Bottom right: Polar histogram for all levels and azimuths of all the ninecomponent VSP data, with lengths weighted by travel time. Queen and Rizer, 1990.

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Rock quality, seismic velocity, attenuation and anisotropy

The results of shear wave splitting and polarization, from this multi-component survey (strictly also belonging in Chapter 15), suggested closest correspondence with the ‘middle’ set of (ENE) fractures, which was close to the BHTV-interpreted break-out analysis indication of the (perpendicular) major horizontal stress. Alternatively, the ENE direction could be the theoretical and therefore practical resultant of shear wave splitting influences from the other sets, which strike to each side (NE and ESE). The point load fracturing, perhaps responding to a residual stress (since no microscopicallyvisible oriented microcracks, nor aligned fabric were seen), was also in the conforming ENE direction. The authors were of the opinion that their data, although consistent, did not have enough resolution for detailed engineering analysis of fluid flow.

14.5.2

Sonic log and VSP dispersion effects and erratic seismic Q

The authors De et al., 1994, from Chevron, compared P- and S-wave velocities and seismic quality factors (Q p and Q s) using vertical seismic profiling (VSP) and sonic log measurements in five wells, which were situated in California, Texas and Alberta. The expected bias (VSP transit times were greater than sonic log times) were attributed to normal velocity dispersion, due to which higher frequency (sonic) waves travel at higher velocities than lower frequency seismic waves. Differences in average P-wave travel times ranged from 2.5% to 7% in the different wells, giving velocity differences between the two methods that were consistently in the direction predicted by dispersion. The authors discussed additional potential causes of the systematic velocity differences, citing local stress concentrations around the boreholes, altered zones and velocity anisotropy or lateral inhomogeneity. In fact stress concentrations around the wells, will cause a magnification of (tangential) stress, in the same direction as major principal stress, and diminution of (tangential) stress in the perpendicular direction. If these effects are strong enough in relation to rock strength, shear surfaces may develop, first giving break-out, subsequently a log-spiral-fractured discontinuum. Various forms of borehole wall disturbance are possible, as emphasised in Chapter 12. De et al., 1994, calculated seismic quality factors (Q p and Q s) both from a velocity dispersion formula and

from spectral ratios. When the two Q seis values agreed, they concluded that velocity dispersion resulted solely from absorption. They showed logs of Q p down a 1000 m deep borehole that showed an average difference of Q p (dispersion formula) minus Q p (spectral ratio method) of 13. Typical ranges of Q p were 10 to 50 (again reminding one of the expected magnitude of deformation moduli, as expressed in GPa). They found that VSP (i.e. seismic) Q p were systematically smaller than those from sonic Q p, therefore suggesting a bias between VSP and sonic log Vp that could not be explained by intrinsic attenuation alone under a constant Q seis assumption. Besides these observations, the authors observed that individual values of Q p or Q s changed ‘erratically with depth’ unless depth averaging was used. The authors suggested that the validity of seismic Q ‘does not always correlate with the data quality or with the rocks themselves’. Since there is a potential relation between rock quality Q c and seismic Q p via the empirically derived ‘static’ modulus of deformation (Figures 13.59, 13.60), it must be emphasised that the rock mass quality Q-value also usually varies rapidly down any given drill-core, unless rock mass conditions are unusually uniform. So on that basis it would not then be surprising to see ‘erratically’ varying Q p or Q s with depth. An example of rock mass (core-logged) Q-value variations and an alternative rock mass rating RMR from Bieniawski, 1989, down a recovered core is shown in Figure 14.17. It is unfortunate that such logs of rock quality are never (?) a part of the geophysicists’ reporting of seismic attributes. There is after all, a strong empirical relationship between Q rock and Vp, and there is an implicit similarity in the variable values of Q rock with both rock quality (obviously), and also with depth, as we saw in Chapter 10.

14.6

Dispersion as an alternative method of characterization

Seismic attenuation has come to be recognised as potentially very sensitive to reservoir properties. This is because of its sensitivity to fractures, joints or bedding planes, and in turn, due to sensitivity to changes of effective stress. Attenuation levels are also sensitive to the saturating fluid and petro-physical properties. However, as emphasised by Hackert et al., 2001, field measurements of in situ attenuation are complicated due to reflections, geometrical spreading losses and varying formation stiffness.

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California. They found that high dispersion (and low Q seis) values correlated with thin sand and carbonate beds within the shale. These beds were at least ten times as permeable as the host shale formation. A velocity and density log for the part of the formation (3950 to 4300 ft depth) is shown in Figure 14.18. The main Antelope Shale (lower half of log) contained more than 100 thin sand and carbonate layers: the most visible ones marked with (S) and (C). These contrasted with the uppermost Brown shale, and Upper Antelope shale that contained no sand or carbonate layers. High frequency measurements differ from low frequency measurement due to elastic scattering and intrinsic attenuation. Based on work by Marion et al., 1994, and Brown and Seifert, 1997, the authors of this reservoir study gave the following equation for rationalising their two-frequency approach: Vsonic (
10kHz ) Figure 14.17 Examples of rock mass quality variability in terms of Q-values and RMR, down a 600 m section of the UK Nirex Ltd borehole RCF1, at Sellafield. This was the planned site for a 500–700 m deep shaft, to develop a Rock Characterisation Facility, for nuclear waste disposal feasibility studies. NGI contract report, 1994. The rock was tuff and ignimbrite, of (obviously) varying quality due to jointing and faulting. These Q-values, modified to Qc using UCS, correlate with Vp, Emass and depth.

It has recently been discovered that dispersion, or the well known dependence of seismic velocity on frequency, can be used for reservoir characterization, as dispersion is mathematically related to seismic attenuation. Sams et al., 1997 (reviewed earlier in this chapter, and also in Chapter 10), compared velocities and attenuation from four frequency regimes: vertical seismic profiling (VSP), cross-well measurements, sonic logging and core measurements. They established dispersion and attenuation profiles as a function of these different frequency measurements. A distinct peak in attenuation versus frequency was observed at about 20 kHz, related to a crack relaxation mechanism (Aki and Richards, 1980) with realistic crack aspect ratios according to the crack model of Jones, 1986. Hackert et al., 2001, used a similar multiple-frequency (cross-well: 1 kHz and sonic log: 10 kHz) investigation to create logs of intrinsic dispersion and attenuation for a shale formation in the Buena Vista Hills reservoir in

 Vwell  Vsc  Vi (
1kHz )

(14.8)

where Vsc  change of velocity due to elastic scattering, and Vi  change of velocity due to intrinsic attenuation. The former is related to geometric effects including the natural anisotropy (layering) of the medium, while the latter is caused by inelasticity of the rock matrix and/or viscous losses of saturating fluids in compliant pores. They also defined a term (VES) from the above terms: VES  Vsonic  Vsc

(14.9)

As can be noted in Figure 14.19, VES is significantly higher than Vwell, particularly in the anisotropic sand and carbonate section. Hackert et al., 2001 conducted forward modelling of their cross-well set-up in this layered medium, first assuming Q seis values roughly proportional to the dynamic elastic moduli, as follows: Shale Q seis  34 Sandstone Q seis  66 Dolomite Q seis  88 They used the difference between the VES and Vwell curves to derive the predicted Vi, which yields the intrinsic Q seis, using a method described by Aki and Richards, 1980. The results of this analysis indicated Q seis values in the thin sand and fractured carbonate beds of between 10 and 50 (appearing to potentially match our modulus-model logic), while the bulk shale had Q seis 50 in general, which appears not to be well matched by

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Figure 14.18 P-wave velocity and density logs in relation to the location of non-shale layers (sand and carbonate) in the Antelope shale. Hackert et al., 2001.

Figure 14.19 Cross-well velocity data compared to computed VES. Hackert et al., 2001 computed Qseis, finding lower Q seis with multiple sand and fractured carbonate layers as shown earlier in Figure 10.69b.

modulus-model logic, suggesting other attenuation mechanisms than fracturing and contained fluid effects. 14.7

AVO and AVOA using P-waves for fracture detection

AVO (amplitude variation with offset) and AVOA (amplitude variation with offset and azimuth) will be

briefly described in this section. Azimuthally dependent variation of P-wave amplitude can be related, both theoretically, and clearly in practice, to the presence of fracturing, and gives reasonable estimates of the orientation of the fracturing, particularly if only one set is involved, or if one set is dominant. Two studies related by Pérez et al., 1999a and 1999b will be briefly summarized, as they illustrate the method, and they also compare results with shear-wave related studies, using C-wave (P to S converted waves), and the shear-wave splitting mechanism. Although the use of shear waves are theoretically favoured for fracture set detection, using the shear wave splitting and polarization mechanism to be described in Chapter 15, there has apparently been a certain reluctance to use shear waves, due to more expensive acquisition and more expensive processing routines. For these reasons, the use of P-waves for fracture set detection and estimation of orientation, has attracted a lot of interest, even though P-wave travel times need to be detected in many directions to obtain the necessary information. AVO analysis using P-waves, is based on some principles that can best be illustrated by the practical example, given by the authors. If seismic data acquisition is conducted parallel to the fracture orientation, the fractures will have minimal influence on the reflection properties, regardless of the angle of incidence, or offset. This is because the P-wave particle motion is parallel to the fractures. If the line is instead oriented more perpendicular to the fractures, at larger angles of incidence than zero, the reflection coefficients will be affected strongly. In fact at the largest angles of incidence, especially when

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Figure 14.20 Survey geometry for Pérez et al., 1999a and 1999b analyses of 3D AVO and converted (C) wave P-S shear wave splitting analyses. Small inward-facing arrows indicate H max direction interpreted from break-out orientation logs, from wells 16, 17, 20 and 23. The (unconventional) rose diagrams, which have been blackened for clarity, indicate the various fracture orientations, and their density, based on FMS logs at these boreholes.

perpendicular, the P-wave velocity is expected to also be affected by the acoustic properties of the fluids filling the fractures. So in the presence of anisotropy, the reflection amplitude will vary with offset, due to changed angle of incidence, and also will change with azimuth (AVOA). The authors used data acquired from three, intersecting 10 km, three-component seismic lines, with three different azimuths. The three lines intersected at one of the wells, where there were results of FMS (formation micro-scanner) and caliper logs for estimating both the dominant fracture strike and the direction of H max. The latter was oriented NW-SE, and the authors assumed that the fracture set in approximately this direction (one of several sets), would be the one most likely to be ‘open’, and therefore most detectable. In this study the far offset extended to 3600 m, a bit more than the depth of the target zone: a 35 m thick fractured limestone at approximately 3000 m depth. This had a P-wave velocity of only 3513 m/s, and an S-wave velocity of 1890 m/s, with a density of 2.5 gm/ cm3. In other words it would seem to have been extremely well fractured or over-pressured. A geophysical term NMO (normal moveout) is relevant here, as the so-called NMO stretch decreased frequency at far offsets, which therefore affected the amplitudes. This distortion was most significant at shallow depth and large offset. During processing, the authors observed a higher frequency (and velocity), along the offset line that had an azimuth parallel to the assumed dominant (‘open’) fracture set, which agrees with other studies.

The authors opinion at this time was that there were few studies that related AVO attributes to fracture or crack parameters. However they were convinced that P-wave AVO gradients were affected by fractureinduced azimuthal anisotropy. Analysis involved calculating reflection coefficient curves in two azimuths, one parallel, the other perpendicular to fracture orientation (implying the need to know the expected result). They found that the AVO gradient was larger for the lines perpendicular to fractures than for the line parallel to fractures: this direction showed a somewhat higher reflection coefficient. In a companion paper, Pérez et al., 1999b compared their local 2D AVO study of the fracture effects at the intersection of their three azimuthal lines (with tie-in to well data at this point), with more comprehensive 3D azimuthal AVO analysis, and with analysis using converted (C) P-S waves, using shear wave splitting and polarization (see Chapter 15). The converted P-S waves have the advantage that they can be generated by compressional ( i.e. explosive) sources, yet are expected to contain the same information as pure S (or SS) waves. These comprehensive studies were finally used to assist reservoir engineers in exploiting the fractured limestone layer at 3 km depth, using horizontal wells oriented perpendicular to the densest (or the assumed more ‘open’?) fracture set. Figure 14.20 shows the layout of the three survey lines relative to the wells, with details of some fracturestrike orientations from FMS logs. Figure 14.21 shows the results of two of the three fracture direction analyses,

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Figure 14.21 Fracture orientations within the investigation area, projected to the 35 m thick fractured limestone at 3 km depth. Interpretation from a) Converted P-S based shear wave analysis, b) 3D azimuthal AVO analysis. Note that the result using converted P-S waves was relatively closer to H max. Pérez et al., 1999b.

which were described by Pérez et al., 1999b. The upper one is from the converted (C) wave P-S analysis, using the shear wave splitting and polarization method (qS1 parallel, and qS2 perpendicular to jointing – see Chapter 15).

The second fracture orientation plot was derived from the 3D azimuthal AVO analysis. The ‘independence’ of the plots was guaranteed by the sequential timing of the surveys. The authors estimated that the azimuth of the maximum AVO gradient was 56°, based on a Rüger, 1996 formula for calculating the reflection coefficients in TIH (transversely isotropic media with a horizontal symmetry axis due to a vertical fracture set). Consequently, since this is assumed to be perpendicular to fracture orientation, the 3D AVO based fracture azimuth estimate was 146°, which was shown to be as much as 36° from the interpreted H max direction. When based on the converted P-S shear wave splitting, the deviation was less. This brings us to a topic introduced later, when reviewing water-flood analyses summarized by Heffer, 2002. Heffer’s results from water flood case records, may suggest to those with rock mechanics background, the possibility of conjugate-shearing of joint sets that are intersected by the H max direction. This topic is treated in more detail in both Chapters 15 and 16, as it both contradicts the ‘standard industry’ assumption of ‘open fractures parallel to H max’, at the same time helping to explain real angular discrepancies between dominant ‘open’ fracture azimuths, and the perpendicular-to-break-out based H max direction. (Refer to Figure 16.71 for visualization of this shear mechanism, and the potentially important fluid lense rotation phenomenon). The authors Pérez et al., 1999a and 1999b felt that their analyses of fracture orientation trends from 3D AVO and from converted P-S (and also from 3D NMO ellipticity: not shown here due to much ‘poorer’ stressdirection fit), had ‘captured the regional orientation of maximum horizontal stress in the field’. They also concluded, significantly, that even though the reservoir had several fracture systems, most of the applied methods picked ‘the one that is closer to the maximum horizontal stress’. See also Tingay et al., 2005 (Fig. 8c) As we shall see in Chapter 16, this may not be a necessary condition for maximum permeability direction – most likely this will be found sub-parallel to the dominant set of a conjugate pair that has suffered more shear and dilation than its neighbouring set. At shallow depth however, the standard ‘industry assumption’ (also in civil engineering) is more correctly focussed on maximum permeability (and Vp) being parallel to the H max direction. This is because this joint direction has verifiable apertures and permeability near the surface.

P-waves for characterising fractured reservoirs

Figure 14.22 a) Exaggerated vertical cross-section of faulted anticline defining the Valhall reservoir. The small-scale fracture sets are thought to be related to the domal faulting, which has principal directions of NW-SE and NE-SW. b) Schematic of orthogonal 3D-4C ocean bottom cable (OBC) data acquisition over Valhall. Source lines were 7.8 km long at 600 m spacing, with shots every 25 m over pairs of receiver lines. Each receiver cable of 6 km length, also at 600 m spacing, had receiver arrays at 25 m spacing, each with seven four-component sensors at 1.5 m spacing in each group. Note: patch shooting, over pairs of receiver lines, using air guns at 7.5 m depth. c) Details of a single, multi-component receiver unit, which are uniformly spaced along the cables, Hall and Kendall, 2003.

14.7.1

Model dependence of AVOA fracture orientation

As described later in this chapter, a 3D-4C (threedimensional, four-component) ocean bottom seismic

391

(OBS) survey was performed at the Valhall field in 1998. (See details in Figure 14.22, from Hall and Kendal, 2003). This, and previous 2D-4C studies had shown the ability of shear waves, derived from converted P-S waves, to penetrate through a gas cloud and illuminate the target fractured zones, otherwise invisible to P-waves in these locations. As part of the seismic studies using the new 3D OBS data at Valhall, Hall and Kendall, 2000 and subsequently Hall and Kendall, 2003, addressed the problem of modeldependence in AVOA analyses of the multi-azimuth OBS-acquired, vertical P-wave part of the data (i.e. component Z in Figure 14.22c). The authors suggested that the fracture strike direction could be ambiguous, since the azimuthal variation in the near-offset AVO gradient, could be positive or negative, relative to the fracture direction. They found, unfortunately, that the direction of the most positive AVO gradient could correspond to either the fracturenormal, or the fracture strike direction, depending on the character of the fracturing, i.e. depending on whether brine-filled or gas-filled – which were the ‘end-member’ models. They therefore recommended forward modelling in order to constrain the interpretation of AVOA. The objective was to predict the near-offset AVO gradient anisotropy for equivalent medium models, based on the different elastic properties of the different fracture models, and compare this with observed AVOA in the data. The effective medium models were based on the additional fracture compliance terms (ZN and ZT) allowing poroelastic modelling of the (micro) hydraulic connectivity between fractures and pore space (as discussed in more detail in Chapters 10 and 15). Log-based data for the fractured chalk were as follows: Vp  3134 m/s, Vs  1534 m/s, density 2300 kg/m3. Permeabilities related to production were an order of magnitude higher than core data, due to the significant amount of fracturing. Hall and Kendall, 2003 mentioned that azimuthal anisotropy was also observed from the dipole sonic logging in the producing horizon, using the flexural shear-wave splitting principle, as described in Chapter 12. Their comparison of model and field data suggested that a large crack density (about 0.1) and thin fractures, were needed to match the high anisotropy, and this matching also suggested liquid-filled rather than gasfilled fractures, unless aspect ratios were 0.00025. Low matrix permeability was also suggested. They considered a most important finding was that the high

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 14.23 Fracture pattern map, assuming that the high levels of observed anisotropy could only be modelled if the most positive nearoffset AVO gradient was in the direction perpendicular to dominant fracturing. Hall and Kendal, 2003.

levels of observed anisotropy could only be modelled if the most positive near-offset AVO gradient was in the direction perpendicular to dominant fracturing. Hall and Kendal 2003 emphasised that in other situations, the reverse could be true, i.e. the direction of the most negative AVO gradient could be in the direction perpendicular to the dominant fracturing. The principal fracturing directions interpreted from the AVOA studies described, were NNW-SSE to N-S, the former nearly resembling the ‘compartmentallike’ NW-SE component of faulting, as shown in Figure 14.23.

14.7.2

Conjugate joint or fracture sets also cause anisotropy

From experiences of domal-structure jointing at Ekofisk, one may pose a tentative question: could the above images of dominant, fracturing directions actually be images of the similar strike of conjugate, steeply dipping sets? If so, then an important mechanism of compaction and production-maintenance could also be at work, namely down-dip shearing, despite the one-dimensional strain boundary condition. (Barton et al., 1988). The modified apertures caused by slight shearinduced dilation, could perhaps have influence on the above aspect ratio assumptions, where the inequality of physical aperture (E) and conducting aperture (e) (Barton et al., 1985), actually results in two possible aspect ratios, whose individual relevance may depend on

the mechanism being modelled, i.e. squirt flow attenuation would actually be governed by a different aspect ratio to that determining the fracture compliances – if these mechanisms were being modelled in poroelastic models that required aspect ratio as input. The standard assumption that maximum permeability in a rock mass tends to be parallel to a dominant set of vertical joints or fractures, which themselves usually trend parallel to the maximum horizontal stress, is a simply understood concept for which there is also theoretical support (e.g. Sayers, 1990). The arguments clearly extend also to the P-wave and S-wave velocities. The concept and the theory are defensible, when the rock is of sufficient strength in relation to the effective normal stress, to provide (partly) ‘open’ joint apertures in the major stress-parallel direction. This generally applies at least to near-surface rocks, and it may apply at reservoir depths in the case of harder rock types. However, if stress-closure modelling that is based on empirical rock mechanics data, can demonstrate virtual closure of the set under discussion, at effective normal stress levels of several tens of MPa, then other mechanisms are likely to be operating, in order to explain a viable production rate, assuming that matrix permeability is insufficient to explain production, as for instance at both the Valhall and Ekofisk jointed chalk reservoirs. The conjugate shear mechanism, and an important detail of this mechanism for the common case of nonplanar joint or fracture surfaces, is introduced in Chapter 15, and further quantified in Chapter 16, with

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Figure 14.24 a) Two synthetic models of jointed or fractured reservoirs, with one set, or two intersecting sets of joints. The modelling of overlying shale (Vp  3700 m/s) and reservoir matrix (Vp  5877 m/s and density 2.4 gm/cm3), was supplemented by compliance additions to account for the joints, but with neglect of complex joint-set interaction (as modelled in UDEC). b) Azimuthal P-wave reflection coefficients as a function of angle of wave incidence at four selected azimuths for models 1 and 2. c) Equivalent coefficients for split shear waves: P-SV for model 1 and P-SH for model 2. Note greater azimuthal sensitivity of a single set of joints, and greater azimuthal separation of the reflection coefficients for the case of polarized shear waves. Sensitivity of P-waves to azimuth is limited, below angles of incidence of 25°. Chen et al., 2005.

particular reference to the ‘shearing critical crust’ concept of Zoback and co-workers. So far little recognition of the importance of this mechanism is evident in reservoir geophysics literature. Sayers and Dean, 2001, and also Chen et al., 2005, addressed the question of the effect of additional fracture sets, in particular non-orthogonal vertical sets, on the AVO response. The first authors showed sinusoidaltype P-wave reflection coefficient trends, when plotted versus azimuth (0 to 360°), with variations depending on the assumptions for the ratios of fracture normal and shear compliance, and whether these ratios were equal or unequal for the different sets.

Some of the theoretical assumptions concerning the ratio of compliances being 1.0 for the case of ‘open, gasfilled’ fractures seem not to match engineering concepts, due to the entirely different mechanisms involved in closure and shear. However a lower ratio of ZN/ZT (or Bn/Bt) for the case of clay filled fractures seems reasonable. Chen et al., 2005 presented reflection coefficients as a function of both angle of incidence and azimuth for two very ‘tangible’ images of single-joint set and twojoint set models, as illustrated in Figure 14.24. The authors set up synthetic jointed reservoir models with the model 1 and model 2 jointing, intending to have a fracture density of 0.1 in each case.

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14.7.3

VP anisotropy caused by faulting

Concerning anisotropy in the neighbourhood of faults, Williams and Jenner, 2002, warned of the possibility for multiple fracture directions, with the fast velocity no longer equal to the matrix or bulk rock velocity. The normal elliptical Vfast and Vslow distribution is then replaced by superimposed multiple ellipses, which have the effect of reducing the observed velocity, and the previous directionality with a single set of joints or fractures will be lost. Due also to rapid changes in fracture frequency, rapid changes in velocity are also seen – in fact responding to the rapid changes in rock mass quality Q close to, and across faults, as frequently observed in tunnelling, and when logging fault-zone core for rock quality purposes. The authors showed a velocity difference tomogram of Vfast – Vslow, with velocity differences of up to 150 m/s in the neighbourhood of known faulting, due not to bulk velocity changes, but due to changes in fracturing frequency and directions. Since even 2-D offset lines cross the earth’s azimuthal velocity field, a case was made for dense sampling near fault and fracture zones. Mostly, azimuthally varying P-wave velocities are attributed to fractures, but the authors suggested that stressaligned microcracks, as always suggested by Crampin, may also be responsible, and that the fractures did not need to be ‘open’.

14.7.4

Poisson’s ratio anisotropy caused by fracturing

A useful contribution to the question of seismic anisotropy caused by fracturing is found in a description of geothermal development in the Olkaria field of the Kenya rift. This incipient caldera structure has had a number of injection episodes. It was monitored with a seismic network comprising 18 stations. Simiyu, 2000 gave Vp, Vp/Vs, and  data from 2613 well-located micro-earthquakes, 45 quarry blasts and 25 calibration shots. Velocity-depth data, extending beyond 4 km depth, for six geothermal fields in the area (identified by initials) are reproduced in Figure 14.25. The well distributed stations made possible the presentation of less frequently seen, azimuthally dependent dynamic Poisson’s ratio data, as shown in Figure 14.26. For the case of geothermal reservoirs, Vp/Vs and  are more controlled by Vp than Vs due to the various fluid-phases in the reservoir. Vp/Vs ratios increase when

going from a vapour-saturated (low pore pressure) condition to a liquid-saturated (high pore pressure) condition. Water-dominated geothermal fields tend to have higher values of  (i.e. 0.2–0.3), while steam-dominated fields have lower values of  (i.e. 0.15–0.2). NW-SE and NESW trending structures associated with reservoir fluid channelling were suggested by the anisotropic distribution of , according to Simiyu, 2000.

14.8

4C four-component acquisition of seismic including C-waves

There is a multitude of technical jargon in the geophysical industry, not least because of the advanced developments, the large number of practitioners, and the complex processes of seismic data gathering, and methods of interpretation. One of the simpler sources of confusion is double use of C – which singly used refers to converted waves (i.e. P-wave converting to S-wave mode, at the sea floor), and the 4C term meaning fourcomponent seismic recordings, typically using oceanbottom-cable (OBC). A helpful diagram, illustrating each term, and also presenting an important ‘new’ seismic acquisition method, was found in Yuan, 2001, who analysed four-component seafloor data to determine the possible presence of vertical (TIV) or horizontal (TIH) transverse isotropy, in the presence of mode-converted shear waves. The illustrated acquisition technique consists in principle of implanting four-component (4C) sensors into the seabed. These consist of one hydrophone, one vertical geophone, one in-line horizontal geophone, and one cross-line horizontal geophone. (See also Figure 14.22c). Conventional air gun arrays (P-wave generating sources) are used, towed by a shooting vessel, while a recording vessel stays above the receiver array. The receiver (OBC) array must of course be relocated, to give multipleazimuth data if not already installed in multiple azimuth directions. There is a potential tendency for 3D OBC to give ‘patchy coverage’ in offset and azimuth (e.g. Hall and Kendall, 2003), though not in the case of the extensive survey illustrated in Figure 14.22. An interesting proposal by Thomsen, 2002, based on imminent plans at BP, was to ‘fuse’ 4D (repeated surveys for reservoir management), with 4C. Although 4C technology had proved an economic success, e.g. for imaging beneath gas clouds, and helping to delineate anisotropic structure, it had not according to Thomsen caused a revolution. He also considered that 4D, though very useful

P-waves for characterising fractured reservoirs

Figure 14.25 Vp and Vs-depth trends and Vp/Vs histograms for six geothermal fields in the Kenya Rift. Simiyu, 2000.

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Rock quality, seismic velocity, attenuation and anisotropy

for enhancing reservoir management, was expensive as each new survey cost as much as the previous one. Thomsen’s vision was to make subsequent 4D surveys much cheaper than the first, so that re-shoots could be

Figure 14.26 Dynamic Poisson’s ratio as a function of azimuth and depth. Simiyu, 2000.

done frequently. The key was to accept the investment of permanently installed receivers in the seafloor, so that the marginal cost increase for making 4D receivers also 4C, would be born by the economic gains made from ‘dozens’ of 4D re-shoots. Management needed to become confident in the gains to be made from frequent 4D4C surveys. Such a philosophy, based on huge investment until prices were driven down by marketplace economics, could revolutionize the practice of reservoir management according to Thomsen, with ‘history matching’ replaced by ‘parameter estimation’ and prediction of performance. The consequence of frequent full-field 4D4C re-shoots, providing full-field estimates of all required reservoir parameters, would result in much more efficient exploitation of reserves, a production increment coming sooner, and also possibly larger, than discovery and exploitation of new fields. Regarding penetration of gas clouds, referred to by Thomsen, Granger et al., 2000 referred to the fact that even 2D-4C surveys at the Valhall reservoir in the North Sea, had been able to penetrate through a gas cloud using the converted or C-waves, since the resultant shear-wave component could illuminate a target otherwise invisible to P-waves. In 1998, a 3D-4C seismic survey was performed at Valhall with the intention of improving the structural imaging of the crest of the field, and for establishing the potential for jointly using P-wave and C-wave data for reservoir characterization, lithology prediction, and for stress and fracture orientation.

Figure 14.27 Configuration of four-component (4C) seafloor seismic, for P-wave and mode-converted S-wave acquisition, using ocean-bottom-cables (OBC). Companie Général de Géophysique (CGG) diagram, from Yuan, 2001.

P-waves for characterising fractured reservoirs

The P-wave part of this work was briefly reviewed earlier, see Figures 14.22 and 14.23. 14.9

4D seismic monitoring of reservoirs

In recent years, many more oil companies have been utilising Ocean Bottom Cable (OBC) acquisition methods to make repeated three-dimensional measurements over time, so-called four-dimensional or 4D seismic. (e.g. Bull-Gjertsen, 1998). This has made it possible to track reservoir depletion phenomena, such as changing pore pressure, and especially to track water-injection fronts in water flood treatments. Experiences from several North Sea oil and gas reservoirs have shown that the higher velocity of reservoir zones saturated with water allows operators to register where the oil-water contact is moving, and where oil may be by-passed by the water flooding. In this section we will see a brief selection of uses for 4D seismic, including the mapping of oil saturation changes over time, the monitoring of water-flooding, and the detection and quantification of reservoir compaction, and even near-surface, sub-sea subsidence. Reservoir monitoring with 4D seismic in its most basic form is the inversion of seismic data to obtain (dynamic) reservoir properties, which can subsequently be used to predict pore pressure change at a distance from the wells due to the assumed, laboratory-sample-based effective stress sensitivity of the reservoir rocks. While there is high sensitivity to effective stress in shallow reservoirs, the typical ‘plateau’ that may be reached at high effective stresses (i.e. beyond roughly 25 to 50 MPa, depending on rock type), suggests that the fluid compressibility effects may become more important at greater depth. 14.9.1

Possible limitations of some rock physics data

There is unfortunately a basic complication that the more compressible grain-boundary cracks with their low aspect ratios may be partly the result of stress unloading when drilled and bought to the surface (Holt et al, 1996, 1997, Nes et al., 2000), and it is such samples that are the basis for much of the collective assumption of a given stress sensitivity. There is in addition the possibility that joint sets that are under lower levels of effective stress may still be contributing to some of the (anisotropic) sensitivity to effective stress change, and they certainly contribute,

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through finite compliances, to attenuation, as already seen in Chapter 10. This emphasises the need for both velocity and attenuation monitoring in 4D seismic. In addressing stress sensitivity questions related to 4D seismic, MacBeth, 2004, developed semi-empirical pressure-sensitive bulk-moduli and shear-moduli formulations using the concept of excess compliance, which was designed to capture all categories of weakness in the rock, specifically in numerous types of sandstones. He found that the bulk and shear modulus pressure-sensitivities (i.e. sensitivities to effective stress change), lay between 1 and 10% per MPa. This meant that a 5 MPa pore pressure decline in a reservoir could produce from 5 to 50% increase in bulk modulus, depending on sand/sandstone type. Rocks of higher porosity tended to show higher pressure sensitivities, and the reverse behaviour was also shown, as intuitively expected. MacBeth pointed out several potential problem areas related with using ultrasonic core measurements for interpreting changes of reservoir seismic velocities in 4D seismic monitoring. Some of these are summarized below: 1. In saturated rock, higher velocities are generally measured at higher frequencies. 2. Saturated samples containing microcracks would project a lower stress sensitivity with laboratory ultrasonics, than with seismic waves. 3. Cores loaded back to their original in situ stress state do not recover their original velocities, and due also to the possible microcracking caused by sampling, may show increased sensitivity to effective stress relative to in situ. 4. On the other hand, jointing is not a part of the laboratory sample response. 5. Cores may be selected from the most productive and competent part of the reservoir. 6. Subsequent core-to-log correlations, and interpretation using long wave-length seismic averages may cause underestimation of pressure sensitivity. Most of the rocks studied by MacBeth were predicted to have only 1% per MPa sensitivity to stress change (at 24 MPa effective stress). However, elevated temperature testing may be needed; see Chapter 16. 14.9.2

Oil saturation mapping with 4D seismic

An impressive and very clear indication of the utility of 4D time-lapse seismic analysis of producing reservoirs

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was provided by Eide et al., 2002. The authors described quantitative mapping of changes in oil saturation over a 30 km2 area in the northern part of the Gullfaks field in the North Sea. A base survey dating from 1985 before the start of production, was supplemented by monitoring surveys in 1996 and 1999, for assisting well planning, and these reportedly had a large economic impact on production. The oil saturation mapping project utilised a rock physics model to compute changing density from P-wave and S-wave velocities at the three survey times, with porosity, percentage of clay, saturation and pressure effects extracted from a flow simulator. Synthetic seismic amplitude and amplitude difference volumes were generated by forward modelling, based on time-dependent elastic parameters. The change in reflection strength at the top of the reservoir horizon, and the change in oil saturation in the upper cells of the reservoir simulation model, using segments with high correlation of seismic changes and saturation changes, were used to generate maps of saturation change. Statistical analysis indicated that the relationship between the change in reflection strength and the oil saturation change, depended on the height of the original oil column. Coloured maps of saturation change from 1985 to 1996, were contrasted with those from 1996 to 1999, showing as expected, significantly larger areas and stronger changes (i.e. So approximately as high as 0.35 to 0.5 in 4 to 5 regions) in the first 11-year period, compared to the less well distributed, small areas and small changes in the second, 4-year period. Probability maps of large, medium and low saturation changes based on a stochastic simulation were also developed.

14.10

4D monitoring of compaction and porosity at Ekofisk

Landrø and Stammeijer, 2002, described two seismic methods for monitoring compacting reservoirs, based on seismic data acquired in 4D surveys at Ekofisk. One was based on prestack travel time changes, the other on poststack travel time and amplitude changes. Velocity-porosity relationships were not required. The authors emphasised that 4D time-shifts in a compacting reservoir were a combined result of increased velocity due to compaction, and reduced layer thickness, i.e. reinforcing effects. They referred to measurements of time-shifts of as much as 12–16 ms, between 1989 and 1999, related to an

Figure 14.28 Uncertainty in estimated velocity and compaction magnitudes, as a function of reservoir depths, with assumed excellent 4D data yielding a time-shift error estimate of only 0.5 ms (solid-lines). With poorer data, and 1.5 ms error (dotted-lines). Maximum offset assumed limited to 3000 m. Compaction: black, Velocity: grey. Landrø and Stammeijer, 2002.

estimated 6 m of additional compaction at 3 km depth. The authors related time shift, thickness change, and velocity change with the following normalized relation: t z v
 t z v

(14.10)

The authors assumed a 4D time-shift error of 0.5 ms at near-offset, and 2 ms at far-offset, and a reservoir at 3000 m depth, with 9 m of compaction. A major challenge here, was to discriminate between compaction and velocity changes, both in the 300 m thick reservoir, and in the 3 km of overburden. Figure 14.28 shows a set of their compaction and velocity-change estimates for a more general case. As reservoir depth increased, the magnitude of uncertainty increased for both components. Smith et al., 2002 described some of the detailed operating problems caused by the Ekofisk subsidence, including the difficulty of extrapolating seismic depth conversion from known horizon-depths at existing vertical wells, to predict depth structure away from the wells. Two hundred wells in the main field area, giving excellent depth control, contrasted with limited downflank control, above this large domal structure. The authors found that simply scaling seismic interval velocities to well interval velocities, suggested larger structural variation than expected. Extrapolated depths

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Figure 14.29 Comparison of a) detailed seismic-based (4D time-shift) compaction interpretation (with adjustment for the velocity reduction caused by a subsiding overburden), with b) geomechanics-based one-dimensional strain compaction model, that included porosity reduction due to weakening effect of water saturation, seen in the next figure. Smith et al., 2002. Note gas cloud effect in centre of seismic model. (See Plate 4). Reproduced by permission from NPF.

down-flank were deeper than nearby exploration wells. The authors therefore developed a method for improving the seismic depth structure match to the horizontal sections of wells that penetrated far down-flank. The authors mentioned that a straightforward timelapse comparison between the 1989 3D seismic survey, with the newer 3D seismic survey in 1999, had given unrealistically large values for compaction and subsidence. Subsequently a geomechanics-based model was developed, based on vertical uniaxial strain behaviour for (intact) chalk, that related porosity changes to layer thickness changes. The authors mentioned use of a linear porosity-velocity relationship for the chalk, to compute depth conversion from velocity change. An example of the good general fit between the seismic time-shift compaction model, and the geomechanics-based compaction model, is reproduced in Figure 14.29. (see also Plate 4). The water-weakening porosity-reduction model used at Ekofisk is shown in Figure 14.30, from a companion

paper by Guilbot et al., 2002. The water injection programme, designed to compensate for the big pressure draw-down following about 20 years of production, had side effects, well known from early rock mechanics testing, of reducing the strength of the chalk. Figure 14.30 shows how this water-weakening was tied to assumed porosity reduction, due to accelerated pore-collapse, based on tests of ‘water-flooded’ triaxially confined chalk. In fact the water weakening effect, although not positive in terms of arresting settlement of the sea-bed, has given a strong boost to the compaction drive mechanism, resulting in exceptional recovery of the reserves. The extensive casing damage to numerous wells at Ekofisk is one set of evidence of discontinuous behaviour, due to stretching of the overburden and differential bedding plane slip. A new source of evidence for discontinuous behaviour during the compaction at Ekofisk can be seen in the results of the 4D seismic. A 1989 to 1999 ‘time lapse’ comparison (Geo, 2001),

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(a)

(b)

Figure 14.30 The water-weakening model for estimating porosity reduction as a function both of vertical effective stress, and degree of saturation. Guilbot et al., 2002.

appears to show fault related discontinuities in the estimated ‘tomogram’ of compaction magnitudes, and also a somewhat larger compaction (8 m in the central 1.5  2.0 km), as compared to the ‘smoother’ continuum calculations of the geomechanical model reported by Smith et al., 2002. 14.10.1

Seismic detection of subsidence in the overburden

It is interesting to note from Smith et al., 2002 that subtle overburden velocity changes had occurred due to

the ‘stretching’ of the overburden in response to the 10 years of incremental compaction. Apparently the abovementioned, initial over-estimates of compaction given by the initial 4D comparison of 3D-1989 and 3D-1999 data, did not account for this reduction in velocity. Large-scale, 2D axi-symmetric modelling with 3  10 km ‘layered-jointed-and-faulted’ models with UDECMC (Barton et al., 1986, 1988), add support to possible reasons for a velocity reduction mechanism, as they showed a lot of locations in the over-burden with horizontal shearing, due to velocity-based moduli-contrasts between different layers. These events could presumably affect velocities determined from VSP, at most offsets. The combination of bedding plane shear and the stretching caused by the overburden possibly subsiding nearly as much as the compaction, were presumably also the inherent source of numerous casing collapses mentioned by Ekofisk authors in the past. At the Wilmington field, where hundreds of casings collapsed, seismicmagnitude events were recorded due to bed slip, one of which measured 24 cm. Stretching causing slight opening of numerous subvertical, bedding limited joints, and a general horizontal stress reduction on sub-vertical faults, would presumably only affect velocities determined from wide-offset (large aperture) VSP. At Ekofisk there was inevitably a mismatch of 3D isotropic continuum based subsidence modelling (mostly giving S/C ratios of about 0.6, and 2D discontinuum modelling, which suggested S/C ratios as high as 0.75, increasing to beyond 0.85 as compaction progressed. (Barton et al., 1988). The ‘simpler’ 2D discontinuum modelling matched the steep 1985 subsidence bowl better than the 3D continuum models, which is understandable considering the 150 km3 of (obviously discontinuous) rock involved. This total volume of deforming rock, has required billions of dollars of extra investment, due to the late 1980’s need to jack all platforms and risers 6 m, protect the central storage tank with a 100 m diameter concrete wall, and finally establish new platform facilities away from the central subsidence during the 1990’s. However, the compaction is fortuitously giving much more in return, with greatly increased recovery. The huge volume of rock that is deforming, happens to be some 1015 times larger than the core-plugs used for uniaxial strain testing. Possibly the high stress levels are responsible for a relative lack of scale effect, when these small tests are used for compaction modelling. Alternatively, the effects of joint deformation in the

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compaction, are in some way ‘cancelling’ a possible scale effect.

14.10.2

The periodically neglected joint behaviour at Ekofisk

Ekofisk is a classic jointed (or fractured) reservoir, having too low matrix permeability for production without the jointing. Yet jointing tends to be ‘ignored’ when modelling, due to the large scales involved (possibly as much as 15 km3 of chalk, with 300 m thickness). A more complex aspect that is inevitably missing from large-scale geomechanical models, which due to size constraints, are usually isotropic elasto-plastic continuum in nature, is the actual jointed nature and possible coupled behaviour of the Ekofisk joints, and their special behaviour during compaction, especially when stimulated by HTM effects during water-flooding (i.e. cooling, reduced shear strength, greater permeability). The joints are typically in the form of conjugate sets of steeply dipping joints, making small block sizes of e.g. 15 to 40 cm, whose roughly common strike reportedly ‘rotates’ around the pear-shaped flanks of the anticlinal structure. The rotation is associated with the rotating directions of maximum horizontal stress, also shown by Teufel and Farrall, 1992, which is reproduced in Figure 14.31. Two-dimensional distinct element (jointed) modelling with UDEC-BB performed for the Norwegian Oil Directory, soon after the seabed subsidence was discovered (e.g. Barton et al., 1986, 1988), had shown that down-dip shearing could occur with various joint geometries and with the higher porosities. The onedimensional compaction modelling was performed using the effect of a 20 MPa reduction in pore pressure experienced prior to water flooding, causing a 20 MPa increase in effective stress. In subsequent more comprehensive UDEC-BB modelling at NGI, performed by Gutierrez in the 1990’s, 24 MPa was used, confirming the joint-shearing trends of the earlier modelling. The horizontal stress acting in all these models was, in effect, the rotating major horizontal stress shown in Figure 14.31. Input data for the 1985 models were obtained from tests on jointed core recovered from Ekofisk, using joint index testing (e.g. joint wall roughness and tilt tests), direct shear tests, and coupled-shear-flow-temperature biaxial tests (CSFT, Makurat et al., 1990), using hot Ekofisk oil or carbonate-equilibrated sea water. The

Figure 14.31 The anticline-related rotation of the maximum horizontal stress directions at reservoir levels at Ekofisk. Teufel and Farrell, 1992 and Bruno and Winterstein, 1994. These stress rotations relate also to the rotating strike of the steeply-dipping conjugate joint directions, which give a rotating trend for principal permeability directions. A rotating trend for P-wave anisotropy, and for polarized shear waves would also be expected. (See Chapter 15 for rotation effects measured in the overburden).

Barton-Bandis joint strength and stiffness parameters derived from JRC, JCS and r, were scaled from assumed in situ block sizes, for each set of conjugate joints. The less than obvious discontinuum component of the compaction mechanism, was due to matrix contraction providing ‘space’ for the down-dip shear, despite the onedimensional (‘roller-boundaries’) constraint. Significantly, the down-dip shear mechanism caused the development of a higher ko (ratio of horizontal to vertical stress), than in the case for ‘1-D’ compaction of unjointed chalk, thereby helping to stabilize the mechanism. (Some of this modelling is shown in the joint behaviour related geomechanics material, treated in Chapter 16).

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It seems highly likely that the multitude of (inevitably) shearing joints in this pear-shaped 9  14 km and 300 m thick reservoir, may be an important reason for the rapid weakening by water during water flooding, due to the huge increases in surface area exposed to water, caused by the multiple joint surfaces, with strength loss and increased shear, following mechanisms interpreted at larger scale by Heffer 2002, reviewed shortly. The ‘several-micron’ sized apertures modelled in the 1980’s, were apparently almost maintained by shearing due to joint-surface non-planarity, even without subsequent 1990’s and present cooling effects from waterflooding. Sufficiently permeable jointing (and fractured rock near faults), will also be potential causes of faster water break-through to producer wells. Faster breakthrough of the water front close to faults was referred to by Guilbot et al., 2002. These authors reported that about 9 ms of time-shift had occurred at the top of the reservoir in the 10-year period between the two 3D surveys, but mentioned a range of 0–20 ms in the water-flood areas. Strongest compaction (i.e. largest time-shift) was usually interpreted where reservoir thickness and porosity was highest. As a possible corollary to this, the above joint-shearing mechanism was also found to occur with most strength where modelled porosity was high (e.g. 40%) rather than low (e.g. 25%). There are undoubtedly multiple reasons for the higher compactions where porosity and thickness was greatest, and also multiple reasons for the continued reservoir compaction, despite (or because of?) extensive water-flooding from 1990. Barton, 2002b suggested the following: ● ● ●

●

accelerated pore collapse joint shearing compaction joint permeability maintenance (due to dilation counteracting effective normal stress increases) water-weakening (accelerated through a vast area of joint planes)

Maury et al., 1996 have pointed out the inevitability of compaction increase when water-flooding watersensitive reservoir rocks. Strength reduction actually applies to the majority of rocks, according to the experimental data reviewed by Barton, 1973, but perhaps is more extreme for a very porous weak material like chalk. From a change-of-seismic-velocity point of view, the effect of each of the above mechanisms must be extremely complicated, possibly only pore collapse

Figure 14.32 The conventional and frequently occurring fracture and fault opening parallel to the Sh min direction with water flooding. Heffer et al., 1997, Heffer, 2002.

causing potentially increased velocity, assuming breakdown of the rock frame is not itself a source of velocity reduction: probably it is initially.

14.11

Water flood causes joint opening and potential shearing

In water-flooding, for stimulating petroleum production, indeed for driving production, there is both a local increase in pore pressure at the injector wells, and a reduction in temperature, causing some contraction of the matrix, both of which help to dilate and indeed create, fractures. Gutierrez and Makurat, 1997, have demonstrated these effects in fully-coupled MHT modelling. Heffer, 2002, referred to earlier studies of waterflood effects in eighty reservoirs, both fractured and unfractured (Heffer et al., 1993, 1995), and discussed the important question of flood directionality in relation to the major horizontal stress level. The conventional and expected mechanism of fracture or fault opening exactly in the direction of Sh min, as shown in Figure 14.32, was not in fact so common as one might expect. Figure 14.33 shows the important statistical spread of observations, from 33 cases of reservoirs known to be fractured, and from 47 cases thought to be unfractured, at least prior to the water-flooding. There are in fact subtle and important indications in these two ‘joint rosettes’ (in this case fault or fracture

P-waves for characterising fractured reservoirs Unfractured reservoirs (47 cases)

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Figure 14.33 Statistical data for water flood directionality effects in relation to Sh max directions in 47 unfractured reservoirs, and in 33 fractured reservoirs. Heffer et al., 1997, Heffer, 2002. See also extensive data sets in Tingay et al. 2005.

rosettes), that the unloading caused by the two waterflood effects mentioned above, are in many cases stimulating shear-failure (of ‘intact’ rock), or shear displacement, and therefore further dilation, of existing joint or fracture sets, or faults. The direction of H max shows a frequent tendency to have bisected the geologic features that are the basis for the rosettes shown in Figure 14.33. The mechanism may (often?) be one of conjugate shear, in which case showing strong parallels to the findings of Townend and Zoback, 2000 concerning the frequency of water conducting features being under shear stress. These topics are addressed in detail in Chapter 16. 14.12

Low frequencies for sub-basalt imaging

Many prospective ocean margins are covered by large areas of basalts. These tend to be extremely heterogeneous, and scatter and attenuate the seismic energy of conventional seismic reflection surveys, making it difficult to obtain seismic images from deeper reflectors. Ziolkowski et al., 2003, argued that since high frequencies were scattered more than low frequencies, it would be logical to emphasise low frequencies, by using much larger air guns, towing the source and receivers at greater depths than usual, i.e. 15–20 m. This was done in 2001, over an area of the NE Atlantic margin that holds promise of very large accumulations of hydrocarbons in the Mesozoic and Palaeozoic sediments, which are covered by higher velocity Cenozoic flood basalts.

The new sub-30 Hz data was shown to suffer significantly less attenuation due to scattering, and revealed deep reflections not previously seen in conventional surveys. One of the problems identified in numerous previous attempts had been the scattering and attenuation from the rough basalt surface, and absorption due to faults and joints, plus interference from inter-bedded units of e.g. claystone and siltstone. Strong sea-surface reflections had also been a problem. Basalts of this region are very heterogeneous at scale lengths of tens of metres, approximately an order of magnitude less than the seismic wavelength when of 10 Hz. So use of the long wave-lengths could avoid the problems of thin inter-layering and lateral inhomogeneity. The authors generated synthetic seismograms, using an available sonic well log in basalt, and assumed a single deep reflector. They used the following model: 1. 0–400 m Vp  1500 m/s 2. 400–1000 m Vp  2500 m/s 3. 1000–1800 m Vp  3500–5500 m/s (strong oscillation in basalt flows, greater extremes) 4. 1800–5000 m Vp  3000 m/s (assumed sedimentary basin) 5. 5000–6000 m Vp  4000 m/s The modelled basalt was 800 m thick. Their subsequent field survey, using large air guns towed at 15 m depth, were able to image deep reflectors in a much clearer manner than achieved in a conventional survey. We may conclude this section with an exotic use of reflection seismic imaging, described by Dypvik et al.,

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1996 and Tsikalas et al., 1998, namely the imaging, in the Barents Sea, of the 40 km diameter Mjølner impact structure, originating some 145 million years ago, which involved an 850–1400 km3 disturbed volume of rock, possibly caused by ‘only’ a 0.9 to 3 km diameter meteor. A transient crater of 16 km diameter and 4.5 km depth, and ejecta of some 175 km3, were interpreted from the seismic images. Large amplitude tsunami waves, and energy release of some 1020 or 1021 Joules, equivalent to an 8.3 magnitude earthquake were estimated by the authors.

14.13

Recent reservoir anisotropy investigations involving P-waves and attenuation

Mapping the azimuthal velocity anisotropy of P-waves, to reduce risk of drilling low-productivity wells in relatively unfractured parts of the UK offshore Claire Field, west of the Shetland Islands, was described by Smith and McGarrity, 2001. Their company, BP, had performed multi-azimuth walk-away (‘float-away’) VSP in an offshore well to attempt a calibration with oriented core data and with FMI logs. Three 4 km walk-away lines were performed, using a downhole triaxial accelerometer sensor array, both in the overburden (1486–1535 m) and in the fractured reservoir (1850–1906 m). They described the obvious importance of ‘open conductive fractures’ with producing-well intersection of these features as the goal. The authors cited azimuthal variation in the shear modulus of the fractured rocks as the reason for the P-wave velocity anisotropy. ‘P-waves travelling obliquely to the fractures can be influenced by the shear properties of the rock’. This is perhaps an alternative way of acknowledging the theoretical contribution of the shear stiffness (and normal stiffness) of the fractures to the anisotropy, which also causes shear wave splitting, as we shall see in Chapter 15. The authors also mentioned the more conventional dominance of one fracture set orientation, with an orthogonal subset, and mentioned variation of fracture density in this unequal two-set system, as a reason for variations in the degree of seismic anisotropy. We will investigate fracture density in detail in the next chapter, mostly in connection with the interpretation of shearwave anisotropy. A schematic classification of fracture types in the Claire reservoir, shown in Figure 14.34, suggesting considerable complexity, reduced nevertheless to the predominance of

Figure 14.34 Fracture-type schematic for the Clare field reservoir, given by Smith and McGarrity, 2001.

Figure 14.35 Polar plots showing orientation from core, FMI fracture orientation, and maximum stress orientation (90° to calliper-log elongation?), compared with travel time inversion (Vp anisotropy) and polarization inversion, using postulated velocity models to fit the direction of wave front motion at VSP downhole receivers. Smith and McGarrity, 2001

(almost) H-parallel ‘open’ fractures as the clear source of preferred orientation for both the travel time and the polarization inversion, as shown in Figure 14.35. The magnitude of the (P-wave) velocity anisotropy, typically 6%, actually ranged from 0 to 15%, and the authors were able to demonstrate reasonable correlation of highflow wells with higher (P-wave) velocity anisotropy and low-flow wells with lower anisotropy.

P-waves for characterising fractured reservoirs

(a)

(b)

Figure 14.36 a) Density of shading represents degree of P-wave velocity anisotropy at reservoir (unit V) level. b) Well flow rates versus estimated P-wave velocity anisotropy. Smith and McGarrity, 2001.

(a)

405

The very rough correlation between velocity anisotropy and well flow rate, are shown in Figure 14.36b. It was therefore suggested that conventional P-wave seismic acquired by towed arrays in marine environments may help characterize fractured reservoirs, thereby maybe avoiding the need for expensive multi-component shearwave acquisition. Following on from the above azimuthal anisotropy of P-waves at the Claire Field, as discussed by Smith and McGarrity, 2001, a later study by Maultzsch et al., 2005, with BGS colleagues from Edinburgh, addressed the question of attenuation anisotropy at this field. They also used the multi-azimuth walk-away VSP, and demonstrated that the fractured, oil-saturated reservoir also showed a consistent azimuthal variation in attenuation. These authors first demonstrated the 1/Q seis related modelling abilities of the Chapman dynamic poroelastic matrix-and-aligned-fractures model, which is reviewed in Chapter 15. A simulation of P-wave attenuation in the case of a modelled rock mass with vertical fracturing is shown in the polar diagram reproduced in Figure 14.37, showing in b), a maximum attenuation 1/Q  0.15 for the vertical direction of fractures. First they measured a zero-offset Q seis, using data from all source offsets and azimuths. They obtained Q seis  18 for the reservoir which was fractured (again a very plausible match to deformation modulus in GPa), and Qseis  35 to 40 for the overburden, which they assumed was relatively unfractured. Secondly they analysed attenuation as a function of azimuth for each offset, both in the reservoir and in the overburden, utilising two tool settings. In the reservoir, minimum attenuation lay between N70°E and N100°E. But at the shallower receiver setting in the overburden the

(b)

Figure 14.37 Two examples of attenuation modelling with a set of vertical aligned fractures, using Chapman’s dynamic poroelastic matrixand-fracture-set model. See Chapter 15 for a description of this model. (Reproduced by kind permission, Maultzsch pers. comm. 2005). (see Plate 5).

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Figure 14.38 a) Fracture rose diagrams for all fractures, and b) open fractures at the Claire Field. c) measured minimum attenuation direction from multi-azimuth walk-away VSP. d) major horizontal stress estimate. (Maultzsch et al., 2005, and Smith and McGarrity, 2001).

minimum attenuation was scattered between wider azimuths, as shown in Figure 14.38a. Rose diagrams of all the fractures and of the open conducting fractures, from others’ logging of cores and borehole images are reproduced in Figure 14.38a and b. Maultzsch et al., 2005, also provide, in Figure 14.38c, their measured azimuth of minimum attenuation, which although close to a match with the open fractures, is actually some 20° oblique to these. Curious to see where the major horizontal stress is oriented, we can add this as in Figure 14.38d, from Smith and McGarrity, 2001, just reviewed. It is close to parallel to the open fractures, yet the minimum attenuation was 20° different. A possible explanation is that the ‘open fractures’ are open due to limited (but sufficient) shear dilation episodes in the past, when H max was perhaps not parallel to these joints. From a rock mechanics point of view, and armed with several experiences of measuring a considerable h min magnitude at reservoir depths

Figure 14.39 A sheared, rough fracture analogue for ‘open’ fractures, that shows the dilated parts (white) as having a different average orientation compared to the black, contacting (partly crushed, load-bearing) parts of the asperities. Barton, 1973.

using hydraulic fracturing, one must question whether there can be ‘open’ fractures in a petroleum reservoir at right angles to h min, unless: a) the rock is unusually strong and that joints are rough, b) there exists a close-to-fracturing pore pressure, c) that shearing has occurred, d) there is a suitable quantity of hard mineralization to ‘bridge’ and maintain an earlier porosity. Fractures can presumably be conceived as ‘open’ if they have good connectivity and reasonable apertures (for example 10 to 100 m conducting apertures?) with respect to the gradients that are operating. If limited shearing and therefore dilation has occurred in the past, and if there are limited influences from a second set of fractures, then Figure 14.39 can be a possible explanation for the apparent 20° rotation in the above case. Note the possible influence of a rotation of the fluid-bearing parts of the fractures (black), in relation to the contacting parts taking the load. This model will be developed further in the last two chapters of this book.

15

Shear wave splitting in fractured reservoirs and resulting from earthquakes

In this chapter the effect of structural anisotropy on shear wave splitting and polarization phenomena will be treated in some detail, due to its extreme importance in helping to characterize jointed or fractured reservoirs, and due to the improved insight it is giving into earthquake phenomena. The structural anisotropy may be stress aligned, and there are then logical ties to the principal permeability or drainage directions. Dominant jointing and natural fractures are of increasing interest to petroleum companies, both for production and for aiding stimulation, where matrix permeability is low but hydrocarbon storage high. This vitally important structural feature is notoriously poorly sampled by vertical core and well-bore scanning, since itself often sub-vertical or vertical. The ‘miracle’ of shear-wave splitting (with assistance from azimuthal AVO P-wave surveys) has provided the means of detecting the presence of these compliant, fluid-bearing fractures. Contrary to the classic wisdom of porous media fluid substitution theory, in situ fractures also seem capable of signalling to the shear-waves, whether they contain gas or brine, through subtle velocity reduction of the slow S-wave, due to the fluid-compressibility-altered fracture compliance magnitudes. Geophysicists utilise an unfortunately ambiguous way of describing fracture density: as number per unit volume times radius cubed. This ambiguity, meaning that millions of microcracks or a hand-full of fractures can give the same magnitude, nevertheless seems to have a remarkable proportionality to shear-wave anisotropy, but clearly this can be altered by changed compliances. The need to define a specific volume of fractures for reservoir understanding is urgent. Consequently, recent numerical dual-porosity poro-elastic modelling developments have become increasingly important for exploring the frequency-dependent velocity and attenuation resulting from the various potential scales of anisotropy. Case records both from seismology and petroleum engineering will be used to show recent trends in analysis of seismic survey data. Relevant rock mechanics experience with coupled stress-deformation-flow testing of

rock joints will be referred to in several contexts, where deemed appropriate. There will also be a strong focus on the possible links between the joint or fracture shear and normal compliance used by geophysicists, and the macro-deformation, and inverted stiffnesses used for many years in rock mechanics models of jointed media. The need for compatible measures of volume-defined fracture densities and in situ values of compliance (as opposed to those obtained from hand-sized joint samples or roughened plates of Lucite) is necessary for further development.

15.1

Introduction

In view of the very widely accepted knowledge that vertical and sub-vertical jointing is extremely common in most rock masses (due to such diverse effects as cooling, bed-flexure and tectonic influences of horizontal stress), it is unfortunate to say the least, that vertical boreholes are usually the first, and seemingly also the second choice, for sampling and gaining access to the sub-surface. As pointed out by numerous authors, and also quantified by R. Terzaghi, 1965, the sampling bias caused by the mismatch of borehole diameter and horizontal spacing of vertical structure, and the vertical borehole itself, is extreme. Our vertical boreholes provide such a poor sample of the jointed sub-surface, that P-wave azimuthal anisotropy on the one hand, and shear-wave splitting caused by the presence of vertical or aligned structure on the other hand, are truly god-given means for rectifying our poor sampling strategies. If the ‘economy’ of a vertical well as opposed to a steeply inclined one, and the subsequent ‘cost’ of an extensive seismic survey were combined, there would perhaps be more reason for rapidly deviating our boreholes at least 10° or 15°, in order to sample the increasingly understood relevance of vertical and subvertical structure on hydrocarbon production. As emphasised by Laubach, 2003, a central challenge of sub-surface

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fracture characterization is obtaining data on essential fracture attributes where direct observation is (remarkably) unlikely. Recently, five boreholes inclined just 30° from the horizontal, with a combined length of 1.4 km were used to investigate the steeply folded geology and structure along the route of a rail tunnel in Norway. The value and relevance of the core logging and permeability measurements was thereby increased 10- or 100-fold in relation to the equivalent length of vertical holes. Of course this is not a recipe for deep oil-field wells, but a fairly early deviation of 10° or more would greatly improve understanding of both the overburden jointing and the reservoir jointing. The potential anisotropy of the overburden cannot be ignored in seismic inversion. As Barkved et al., 2004 pointed out in their review of multicomponent data, countless reservoirs have been discovered, characterized, and monitored by P-waves. However, P-waves cannot solve every seismic imaging or reservoir description problem. With the addition of S-waves, (usually in the form of converted PS-waves, see Chapter 14), oil and gas companies have found an enormous quantity of new reserves that could not have been found with P-waves alone. The new reserves have been more effectively exploited by better identification of fracturing, and therefore better placement and deviation of the wells. Not infrequently, shear-wave technology provides information where shallow gas has obscured P-wave imaging over central parts of a field. A particularly good example is the Ekofisk reservoir. Shear waves bring additional knowledge to a seismic study due to the different rock mass properties that are sampled. The traditional view is that shear-wave velocity remains unchanged whether a formation contains gas, oil or water. However, as we shall see, because of the effects of fluid compressibility on the normal stiffness of fractures (or its inverse: compliance), the shear waves passing through a fractured or jointed medium, will give the ability to distinguish between oil (low compressibility) and gas. (Van der Kolk et al., 2001). There is possibly a small point of controversy here, concerning whether the fractures and shear-waves can both be vertical, when theoretically only shear compliance is sensed. It is uncertain if shear compliance will be sufficiently affected by the fluid compressibility. A more certain effect of fluid compressibility – i.e. the ability to distinguish between oil and gas is when normal compliance is involved in the case of sub-vertical fractures (or sub-vertical shear-waves) giving a finite incidence angle (Sayers, 2002b).

Shear waves were once considered just noise and had to be filtered out. Now, with proper multicomponent recording, S-waves can deliver important information both concerning rock and fracture properties, and concerning fluid type in the case of shear-wave splitting.

15.2

Shear wave splitting and its many implications

A landmark paper on the relatively new technique of shear wave splitting, summarising the first ten years of developments, was given by Crampin and Lovell, 1991. Following theoretical developments of Keith and Crampin, 1977, and the suggestions of Crampin, 1978, shear wave splitting was positively identified above small earthquakes by Crampin et al., 1980, and many times subsequently. Shear wave splitting had already been noted in a number of sedimentary hydrocarbon basins, with Lynn and Thomsen, 1986, and Willis et al., 1986, reporting at the 56th SEG (Society of Exploration Geologists) meeting in Houston. A simple schematic of the shear wave splitting principles, given by Crampin and Lovell, 1991, is reproduced in Figure 15.1a. When a steeply inclined shear wave meets sub-vertical, aligned discontinuities, the shear wave splits into two components, which have different arrival times and different, usually orthogonal polarization. Both these aspects are shown in Figure 15.1. A more complete version of this simple diagram, from Barkved et al., 2004, is also reproduced in Figure 15.1. This shows, depending upon ones preference for microcracks or joints, the simplest source of polarized shear waves: a set of vertical joints or fractures. These, like microcracks, cause the transmitted shear-wave to split into a fast and slow component, registered as time delay, due to the attenuating effect of fracture compliance on the S-wave component that has particle motion perpendicular to the fracture strike. The difference in traveltime between the fast and slow waves (termed qS1 and qS2 elsewhere in this book), is strongly related to fracture density, and also to fracture compliance, since both have an attenuating effect. An often referred aspect of shear wave splitting and polarization is that the faster of the two polarized components is parallel or sub-parallel to the direction of maximum horizontal stress and/or to the preferentiallyoriented fluid-filled microcracks, cracks or sets of subvertical joints or fractures. The shear-wave velocity anisotropy is often in the range 0.5 to 5%, sometimes

Shear wave splitting in fractured reservoirs and resulting from earthquakes

(a)

(b)

Figure 15.1 a) Simple schematics of shear-wave splitting principles, as a direct or indirect result of the principal stress and the associated stress-aligned, fluid-filled cracks. Crampin and Lovell, 1991. An updated version of this classic diagram, from the BGS Anisotropy Project in Edinburgh, shows larger ‘cracks’, signifying not just aligned microcracks, but perhaps an aligned joint set, also assumed to be roughly parallel to maximum stress. b) A more comprehensive diagram of the principles of shear-wave splitting, from Barkved et al., 2004. The fast qS1 particle motion is polarized in the average direction of fracture strike, while the slow qS2 particle motion is polarized perpendicular to the average fracture strike. Note the ‘formation fast axis’ substitution for major horizontal stress. They may of course be synonymous.

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much more. The distribution of stress-aligned cracks or inclusions is referred to by many authors as ‘extensivedilatancy anisotropy’ (or EDA), following Crampin’s publications. Fracture (or joint) characterization using seismic methods is considerably more complicated than for the isotropic case, due to the existence of the three distinct body waves, which propagate with different velocities and polarizations. Following general convention, these waves are referred to as the qP (quasi-compressional), qS1 and qS2 (fast and slow quasi-shear) modes, or simply S1 and S2. At the time of the Crampin and Lovell, 1991 review of the first ten years of recordings (which accelerated rapidly with the development of digital, three-component geophones in the late 1980s) it was still not known exactly what caused the shear-wave splitting, because aligned pore space, layering and consistently aligned microcracks and joint (or fracture) sets could each cause the phenomenon. Shear-wave splitting had been identified by this time, in a wide range of rock types. It was considered remarkable that, with all the different scales and characters of aligned fluid-filled cracks, inclusions or fractures in sedimentary, metamorphic and igneous rocks (with their wide differences in strength and modulus), the differential shear-wave anisotropy varied only within narrow limits (0.5 to 5%). Since that time, with increasing application at well-fractured reservoirs, this range has been greatly exceeded, as we shall see later. The magnitude of shear-wave anisotropy appeared already to correlate well, with the amount of hydrocarbon production where there was larger-scale jointing or fracturing. There was also evidence, e.g. from Lewis, 1989, that the delay between the split shear waves appeared to decrease with increasing depth, yet an accumulative delay with increasing depth had been expected. Crampin and Lovell identified several difficulties with shear wave splitting interpretation in the case of earthquakes. Because of the relative steepness needed for the incident wave to make an acute angle to (typical) subvertical structure, there was a need for the recording site to be within a so-called ‘shear wave window’. The epicentral distance from the recording sites needed therefore to be considerably less than the focal depth of the earthquake. Another limitation with interpretation of shear wave splitting from earthquakes was the combination of the large scale and the generally complex geology and tectonic structure between the source and the recordings.

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Rock quality, seismic velocity, attenuation and anisotropy

The shear waves would likely pass through a range of rock types with different ages. Velocity, fracturing style and individual fracture-set properties would therefore likely vary, and each split shear wave could therefore split again, giving multiple splitting, with the influence of the joint structures near the recording site as one of the prominent results. Multiple splitting obviously makes time delay estimation more difficult. Crampin and Lovell emphasised that the fluid filled features (cracks, inclusions, fractures) being the most compliant (i.e. with least stiffness, as referred in rock mechanics), would potentially be most sensitive to pore pressure changes or deformation, and thereby modify the way that the shear waves pass through the rock mass.

15.2.1

Some sources of shearwave splitting

Crampin and Lovell, 1991, listed five possible scales of azimuthal anisotropy that could cause shear wave splitting: 1) 2) 3) 4) 5)

aligned crystals direct stress induced anisotropy lithological anisotropy (e.g. aligned grains) structural anisotropy (fine layering) stress-aligned crack-induced anisotropy

Subsequently, much evidence for larger-scale fractureor joint-set alignment effects on shear wave splitting have been obtained, which is a very important ‘addition’ for shear wave splitting, in view of the importance of these structural alignments for hydrocarbon production from fractured (naturally jointed) reservoirs. The larger scale features dominate drainage potential from the matrix to the joints, and thence to the wells, while the smaller scale EDA(extensive dilatancy anisotropy), popular with Crampin in many subsequent papers, would logically dominate drainage from the pores to the microcracks. However, Crampin and Lovell emphasised that it was the stress-aligned vertical fluid-filled cracks that were most likely to cause more uniform splitting. That the two shear wave components will be oriented (polarized) parallel (or sub-parallel), and perpendicular (or subperpendicular) to the present most permeable fracture set directions, that may themselves be parallel (or subparallel) to the present major horizontal stress is the logical extension from crack-scale to joint or fracture scale. But

as we shall see in Chapter 16, there are other joint or fracture alignments (caused by shearing), that are of major importance too. Temporal changes of shear wave splitting were referred to already in Crampin and Lovell’s ‘10 year review’ paper. These had occurred before and after earthquakes, and after hydraulic pumping in granite. Changes in the aperture of the fluid-filled, aligned features (cracks, joints or fractures) would presumably have changed the aspect ratio of these features, and changes in Kn/Ks ratios would be a macro-deformation rock mechanics consequence of such changes. In the case of earthquake source investigations, it is unfortunate that shear-wave polarizations tend to be determined by the anisotropic joint or fracture structure close to the recorder, which of geometric necessity is likely to be much nearer the surface than the source. However, in the petroleum industry with its more limited depths, down-hole recording as in VSP, can focus on the structural domain of interest. For this reason, many of the important developments up to the time of Crampin and Lovell’s 1991 ‘10-year’ review, had been made with VSP configurations. Two further important practical details concerning the potential uses of shear-wave splitting technology were emphasised by Crampin and Lovell, 1991. Firstly that the shear-wave-train likely contained many times the information carried by the P-wave-train, and that this was in the wave forms themselves rather than just in arrival times. Secondly that the multiplicity of sourceto-geophone ray paths required to analyse P-wave arrival times, was not needed to obtain information from shear waves. The problem of relative scale was also emphasised by Crampin and Lovell, 1991. The likely dimensions of the different phenomena (from extension-dilation cracks perhaps of microns to fractions of millimetre size, to fractured reservoir features of many metres size) were each much smaller than the wave-lengths of most shear waves (i.e. tens of metres in reflection experiments to several kilometres in teleseismic shear waves). It was emphasised that multi-offset, multi-azimuth, three-component VSP was likely to be the best way to attempt to analyse the geometrical aspects. Some of these investigations will be reviewed later. In Chapter 10 concerning the phenomenon of attenuation, the inverse trends of velocity and attenuation magnitudes were seen. High velocities only occur where attenuation is low or Qseis is high. Links to rock mass qualities Q and Q c through deformation moduli were

Shear wave splitting in fractured reservoirs and resulting from earthquakes

also cited, i.e. high velocities only occur where rock qualities Q and Q c are high. Q seis was likened, numerically, to the rock engineering static deformation modulus in the first kilometre (when expressed in GPa), and to the Q c value itself at extreme depth, since both seem to depend on the degree of jointing, clay-content, and rock hardness, despite the micro-displacements involved in seismic loading. Crampin and Lovell made the interesting observation that the reciprocal relationship between velocity and attenuation (e.g. Crampin, 1981) was one of the reasons why the leading split shear wave was such a stable phenomenon; because it was travelling in the fast direction and was less attenuated than the slower split shear wave. The oriented rock mass quality Q o described by Barton, 2002, also has its maximum value in this same direction, i.e. sub-parallel to dominant structure, due mainly to higher RQD in this direction. (The use of oriented RQD, termed RQDo, gives Q the directional dependency Q o, together with the changed Jr/Ja ratio representing the frictional strength of the joints across the sampling direction. See Appendix A for description of these terms). Crampin and Lovell, 1991, concluded their ‘10-year review’ by claiming that ‘progress in understanding shearwave propagation is the most fundamental advance in seismology for some decades’. They also speculated on the future uses of shear-wave splitting, including monitoring of hydrocarbon production and monitoring the stability of major civil engineering works in rock. The former is now much used.

15.3

Crack density and EDA

Na 3 V

Let us examine some orders of magnitudes to get a ‘feel’ for this actually rather ambiguous geophysics parameter: 1) Microcracks: Assume 106 microcracks of radius 100 microns in a 10  10  10 cm rock sample. This gives e  106  (104)3/(101)3  0.001. If the ‘microcracks’ were of 1 mm size, the crack density would be 1.0. The ‘crustal range’ is contained within these ‘extremes’. (The microcracks would need to be 330 to 465 m to lie in the mid-range of e  0.01 to 0.05) with the above frequency. 2) Fractures (or joints): Assume 10 joints of 1 m radius in a 10 m3 block of rock in situ. We have: e  10  13/10  1.0. (This represents a well-connected rock mass if for instance there were on average 3.3 joints in each principal direction of the 2.15 m ‘cube’. If there was only one aligned set, the spacing would be close to 20 cm, if two conjugate sets, the spacing of each would approximate 40 cm. This fracture density is significantly less than much of the jointed chalk at Ekofisk, as we shall see later. If there was only one such joint per 1000 m3 (10 m on a side), the ‘crack density would be the same as our more extreme microcrack example with e  0.001. (We would need 10 to 50 joints of 1 m radius per 10 m cube to lie in the mid-range of e  0.01 to 0.05). 3) Fault swarm: Assume 10 medium-sized faults of 464.5 m radius in 1 km3. In this case e  10  464.53/109  1.0. If we veer to the other extreme, we would require only one minor fault of 100 m radius in 1 km3 to give e  0.001. (We would need 10 to 50 minor 100 m faults per 1 km3 to lie in the mid-range of e  0.01 to 0.05) To a non-geophysicist, it is difficult at first viewing, to see why so much seismic interpretation is related to this parameter when it is so ambiguous. To check again:

The geophysicist’s crack density is defined as: e

411

(15.1)

where a is the crack radius, cubed due to the argument that this relates to the energy of elastic deformation associated with the crack. (O’Connell and Budansky, 1974). N is the number of such cracks in volume V. According to the authors Leary et al., 1990, crack density is often in the range of e
0.01 to 0.05 in widely different geological and tectonic regions. This opinion seems to stem from the articles of Crampin, several of which will be reviewed here.

1) microcracks. e  107  (104)3/(101)3  0.01 (ten million @ 100 ␮m/10 cm cube) 2) fracture e  10  13/103  0.01 (ten @ 1 m/10 m cube) 3) minor fault e  10  1003/10003  0.01 (ten @ 100 m/1 km3) These three very unequal scenarios with their equal ‘crack density’ would inevitably have totally different mechanical and fluid-conducting properties. Yet surprisingly, they are supposed to generate equal shear wave anisotropy, as we shall see.

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Rock quality, seismic velocity, attenuation and anisotropy

The Leary et al., 1990 review of the 1988 Chapman conference (and 3rd International Workshop on Seismic Anisotropy) papers on ‘Seismic Anisotropy of the Earth’s Crust’, gave a useful broad-brush reflection of some of the earlier opinions on fracture and crack induced anisotropy and its measurement, prior to the great advances in data acquisition and computer processing, that occurred mostly during the 1990s, that has given ‘anisotropy’ a central role in earthquake interpretation and fractured reservoir exploration and subsequent production monitoring. Aligned fracturing may be detected and monitored over a huge range of length scales, using polarized shear waves. Dimensions may range from crustal dimensions of 10–100 km, through 1–1000 m reservoir scale fractures and faulting, to millimetre and micron-sized microcracks. The potential of fluid-filled microcracks to react to crustal stress and strain led Crampin et al., 1984 to propose the ‘extensive-dilatancy-anisotropy’ (EDA) concept. The EDA hypothesis is that crustal fluids prop open a population of high-compliance voids or inclusions that are nevertheless capable of remaining open against the least principal stress. The implication of 3D principal stress anisotropy at depth is that EDA cracks will tend to be aligned in a vertical plane, striking parallel to the major horizontal stress. With this configuration, Crampin 1978 had reasoned that a microcracked but otherwise isotropic crust was transversely isotropic, with a horizontal symmetry axis. Shear waves polarized parallel to the microcracks, and also travelling parallel to them, hardly sense the presence of the cracks, and travel at almost the wave speed of the unfractured matrix. However, the shear waves travelling in this same parallel-to-structure direction, with polarizations normal to the microcracks, sense the reduced shear stiffness caused by the cracks and are slowed, in a similar manner to shear waves that might be travelling along the (perpendicular) axis of symmetry. As a result of the differential wave speeds, the shear waves travelling parallel to the aligned microfractures, with their two different polarizations, separate in time in proportion to the length of travel path and the density of the crack population. The majority of polarized shear wave observations show the fast wave polarized parallel or sub-parallel to the accepted local or regional maximum stress field. EDA can in principle refer to a wide range of crack sizes, including fluid-conducting fractures. However, it seems that because many of the observed seismic properties can be simulated by propagation through distributions of microcracks, Crampin appears to have

focussed on this scale of EDA for many years, while others have now demonstrated dispersive effects caused by fractures of entirely different dimensions, using double-porosity or triple-porosity poroelastic models, with pore-microcrack-fracture-fluid interaction. The ‘problem’ is that the delayed, approximately orthogonal shear-wave arrivals are also consistent with a feasible density of aligned vertical microcracks. However, the relative stiffness of microcracks, having much higher aspect ratios than inter-locked fractures or joints, means that they cannot respond in the same way as fractures, to a given change in fluid pressure – at least according to classic geophysics teaching. Furthermore there is the crack density definition, which is a source of confusion (for non-geophysicists).

15.3.1

A discussion of ‘criticality’ due to microcracks

According to Crampin, 1993b, several oil companies were already reporting shear wave splitting in almost all their three-component reflection surveys in sedimentary basins. Furthermore, perhaps contrary to Crampin’s expectations, the splitting, as he observed, was assumed to be due to large fractures within fractured reservoirs. Shear wave splitting was also visible in reflections from layers above the reservoirs, apparently suggesting to Crampin that exclusive dependence of splitting on large fractures seemed unlikely. In fact as we will see later in this chapter, shear wave splitting is also seen to follow the saucer-shaped subsidence bowl far above a compacting North Sea jointed chalk reservoir, with correlation to the exact location of increased sea depths. Joint-stretch in the overburden seems likely to be the cause, but if unconsolidated sediments were the actual source of the splitting/polarization, microcracks or even macro-cracks in the sediments would need to be invoked to explain the polarization match to the subsidence bowl. It is not quite clear why, but Crampin, 1993a was of the opinion that fluid-filled microcracks were the most compliant elements of the rock mass. If this opinion was because of the assumption that larger scale (and lower aspect-ratio) fractures and joints would be closed at depth, then indeed the usually less compliant microcracks could remain as perhaps the most compliant element of the rock mass. But here we run into difficulties concerning the interpretation of 4D repeated surveys over producing reservoirs.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

Rock physics provides evidence of effective stress sensitivity of e.g. S-waves, P- and S-wave attenuation, and of their anisotropy and dispersive nature. (Chapter 13). When changes of oil saturation in producing parts of a reservoir are monitored, or water/oil front progression is monitored (see examples in Chapter 14), it is surely the fractures that are the primary targets for the diagnostic seismic waves. Do the pore-to-microcrack responses to production-caused pore pressure, occur fast enough to be ‘in-step’ with the responses in the probably more compliant fractures and joints? After all, the fractures have far higher permeability in general, than the matrix. As we have seen in the earlier critique of ‘crack density’, this parameter does not seem to help in answering this question, because of its basic ambiguity. In his paper ‘Arguments for EDA’, Crampin, 1993a also addressed the meaning of the typical 1% to 5% differential shear-wave anisotropy, reportedly measured in a wide range of rock types, but as we shall see, there are many exceptions in fractured areas. Crampin considered that the 1% to 5% was also equivalent to the generally limited range of effective crack densities, which he assumed were usually 0.01  e  0.05. Crampin noted that the percentage of differential shear wave anisotropy was usually about e  100, for a Vp/Vs ratio of about 1.7 (1.732 was quoted). Crampin, 1993a avoided mentioning specific rock-volume dimensions regarding crack density (e) in the following paragraph, which will be quoted in full, as it reveals an unexpected way of viewing rock mass stability and the fluid-bearing nature of rock masses, which is difficult to match with rock mechanics and hydraulics experiences. ‘A crack density of e  0.05 (shear-wave anisotropy about 5%) is equivalent to a crack of diameter 0.7 in each unit cube. A crack density of e  0.1 has a crack diameter of 0.93 in each unit cube (check: e  1  0.4653/1  0.100), and this is clearly near the critical crack density at which an intact rock fragments, as very close cracks begin to coalesce to form through-going fractures. Thus the upper limit of crack densities (e  0.05, with occasional excursions to 0.1) is probably due to the limit of the number of fractures for an intact rock mass to remain intact. If this limit is exceeded the rock mass fragments and the pore fluid would disperse and, once dispersed, the cracks would tend to close and crack-healing occur which would lead to a lower crack density of open cracks. The only other occasion when substantially larger crack densities (up to e  0.4) have been claimed for field observations are reported by Crampin et al., (1980a) for observations on the surface of limestone

413

pavements, where the pavements are characterized by massive jointing and the rock cannot be considered as intact.’ In a later article, Crampin, 2000 relates e  0.055 to ‘fracture criticality’, and states that ‘almost all rocks are (then) marginally close to the ‘critical percolation threshold in a stressed fluid-saturated solid, when shear strength is lost and fracturing occurs’. It has to be emphasised that these are foreign concepts to rock engineers: extensively jointed rock masses with far higher crack densities have perfectly adequate strength to tolerate e.g. tunnelling. Rock stress and joint roughness helps retain both strength and permeability. If there are two or three joint sets contributing to ‘e  0.055’, there is actually little cause for concern about ‘loss of shear strength’, or ‘dispersion of fluid’. Three joints of 52 cm diameter, intersecting (or avoiding each other) in a 1 m3 block of rock also gives e  0.055. This would be a rather stable rock mass compared to near-surface experiences. When blasting one would see most of the remaining ‘half-pipes’ of the blast holes, but with occasional ‘block-corner’ overbreak beyond the half-pipes. If the same 1 m3 block was (almost) divided into eight component smaller cubes by three typical, near-surface, mutually perpendicular joints, each of 1 m diameter, the crack density would have increased to: e  3  0.53/1  0.375. We regularly construct tunnels in such rock, and if stress and joint roughness are adequate, and there is no clay, there may be no need for immediate rock support of the exposed perimeter of such a tunnel. That the tunnel may leak is a different problem. It does not signal ‘criticality’, rather ‘normality’. In a reservoir, ‘leakage’ is desirable when in the right direction. After all, where will the fluid go, and where will the rock blocks go when surrounded by neighbouring fluid and neighbouring rock blocks at 3 km depth? They will continue to contribute their coupled roles in supporting the weight of the over-lying 3 km of rock, and they will continue to provide (limited) void-space for oil storage, and allow percolation towards producing wells. There is surely nothing critical about this, just normality. 15.3.2

Temporal changes in polarization in Cornwall HDR

An interesting phenomenon was observed by shear-wave splitting when monitoring the Cornwall hot-dry-rock HDR project. Crampin and Booth, 1989 reportedly found that there were 7° to 10° rotations in the polarization directions as a result of deep-well injection of (cold)

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.2 (a) The Cornwall joint-shearing mechanism visualized by Barton, 1986 as a result of cold water injection and effective stress reduction in a joint set not perfectly aligned parallel to the major stress, and under a differential (shear) stress. (b) An exaggerated diagram of (conjugate, or single-set) joint shearing, showing the possibility of opposite rotation of the rock-to-rock contacts (R), and open (O) fluid-filled sections during shearing of the usually non-planar joints needed to give joint permeability in reservoirs. This shearing-mechanism could possibly be the source of polarization rotation, both here and elsewhere, where ‘deviation’ with respect to H max has been noted.

water into the jointed and (possibly) microcracked granite, which was also AE monitored to several kilometres depth, during the pumping. Batchelor and Pine, 1986. They considered that this consistent change in polarization was a stable, reliable and significant result. Although the title of the Crampin and Booth paper suggests an ‘explanation’ that could have been consistent with the writer’s joint-shear-dilation hypothesis (Barton, 1986, see below), Crampin 1993a actually suggests the following mechanisms: ‘The results suggest that before the dilation of the incipient joints by pumping, the fluid-filled EDA cracks are aligned parallel to the in-situ stress field. After the joints have been dilated by pumping and the stress field modified, the EDA cracks close to the joints are realigned parallel to the joints.’ There follows a reference to opening and closing of microcracks and sub-critical crack growth, that seem not to relate directly to any well explained joint-dilation

mechanism. Was the dilation considered to be a normal expansion of the apertures, or was there sufficient, inclined, differential stress, for shearing to occur as a result of the pumping? The answer would have a direct effect on how the stress field was modified. Figure 15.2a, illustrates an alternative interpretation of the Cornwall polarization rotation of 7° to 10°, referred to above. The jointing at depth was under some shear stress, as it was not aligned parallel to the major horizontal stress. With cold water injection there is both contraction and effective normal stress reduction, allowing for some slight shearing that is likely to be part of the source of microseismic ‘clouds’ that propagated to greater depths down the presumably dilating, slightly shearing jointing. (Batchelor and Pine, 1984 and Barton, 1986). The hypothesis that slight joint shearing can lead to polarization rotation is illustrated in Figure 15.2b. The details of this mechanism are described in Chapter 16.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

415

Crampin, 1993a emphasised many times the (reportedly) remarkable ‘uniformity’ of the mostly 1% to 4% (but occasionally 10%, and even 30%) shear-wave anisotropy, reportedly from a multitude of rocks and from a wide range of scales of investigation, i.e. near-surface: 10’s of meters, sedimentary basins: 1–2 km, mixed geology above earthquakes: 5–15 km, and whole crust: 30 km. Focus on the 1% to 4% range, if generally justified, is implying limited EDA dimensions of a few microns to a few meters. Crack density does not need to be 0.015–0.045 to ‘explain’ a frequent shear-wave anisotropy of 1.5% to 4.5%. Almost ‘all rock’ is unlikely to be pervaded by tens of millions of microcracks per hand-specimen – if it was there would certainly be a ‘critical crust’. Rather rock masses are often pervaded by one two or three joint sets – and it is these nearer-the-surface, very common structural-geological features, that may be imprinting their shear-wave splitting result on the recorded waves.

15.3.3

A critique of Crampin’s microcrack model

Because many of the observed seismic properties can be simulated by propagation through distributions of microcracks, Crampin appears to have focussed on this scale of EDA in the last decade. Others have now demonstrated dispersive effects caused by fractures of many different dimensions, using double-porosity or triple-porosity poroelastic models, with pore-microcrack-fracture-fluid interaction (see later in this chapter). The ‘problem’ is that the delayed, approximately orthogonal shear-wave arrivals are also consistent with an (occasionally) feasible, high density of aligned vertical microcracks. However, the relative stiffness of microcracks, having much higher aspect ratios than inter-locked fractures or joints, means that they cannot respond in the same way as fractures, to a given change in fluid pressure, despite Crampin’s apparent claims to the contrary. This classic aspect ratio stiffness argument, originating at least from Walsh, 1966 seems to be discounted or ignored by Crampin. He appears to overlook the ambiguity of crack density, and trust in the assumed attributes of the physically somewhat unlikely APE model reproduced in Figure 15.3, when making statements such as: ‘fluidsaturated microcracks are highly compliant’… …‘large cracks would be stiff and much less compliant’ … … ‘there is very little evidence that the splitting is caused

Figure 15.3 Schematic illustration of the Zatsepin and Crampin, 1997 APE model. The actually 3D, assumed ‘hexagonal boundary cracks’ are vertical. Note the four values of increasing maximum horizontal differential stress normalized to the critical value at which cracks first begin to close. Note the remarkable, assumed increases in normalized crack aspect ratios, with increased ‘SH’ stress. Aspect ratios were apparently chosen to give a porosity of 5%.

by larger cracks or fractures’ … … ‘the detailed geometry of fluid-saturated microcracks in almost all rocks and reservoirs’ … … ‘the underlying reason for the calculability (of APE) and predictability (1.5% to 4.5%) is that the rock mass is so heavily (micro) cracked that it can be considered as a critical system’. 15.3.4

90°-flips in polarization

Figure 15.3 illustrates the anisotropic, poro-elastic or APE model of Zatsepin and Crampin, 1997, that appears to have featured more and more in the interpretations and conclusions found in Crampin’s numerous recent articles concerning analysis of shear-wave splitting in both earthquake and reservoir scenarios. The dramatic increases in aspect ratio, the second stiffest component of rock porosity

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Rock quality, seismic velocity, attenuation and anisotropy

(after equant porosity, and before joint or fracture porosity) is supposedly able to develop in any rock, presumably because of the over-looked resistance of the intervening crystals/grains of perhaps 50 to 150 GPa Young’s modulus, that obviously will resist such assumed expansion. How could such a lateral volume increase, and therefore stress increase, from countless trillions of expanding, aligned microcracks be absorbed in a rock mass without a general reversal of the H max and h min directions? Surely an occasional mechanism such as this is the actual cause of ‘90°-flips’ in the polarization, as occasionally observed/suspected in earthquake source zones. (Crampin et al., 2002, Crampin and Peacock, 2005). The hypothesised extreme fluid pressures that supposedly can exceed h min, and even approach H max in magnitude (Figure 15.4, after Crampin et al., 2002), are surely geotechnical impossibilities? If the conceptual, hexagonal, vertical microcracks of the APE model (Figure 15.3) were miraculously present in e.g. a soft mudstone, then, and only then, could such an aspect-ratio expansion be envisaged, with or without the help of high pore pressure. They would be likely to cause a ‘90°-flip in polarization’, due to the resistance of the surrounding material.

Figure 15.4 Crampin et al., 2002 explanations for ‘90°-flips’ in polarization, as apparently observed above small earthquakes in Iceland. Their model supposes high fluid-pressures within 1 or 2 MPa of a ‘critical stress’. This figure shows modelled variations of shear-wave anisotropy with increasing fluid pressure, for five different sets of principal axes of stress. They presume that anisotropy becomes negative for pore-fluid pressures close to H max. (Inset shows five assumptions for ‘sh, sH, and sv’).

The ‘90°-flips’ explanation shown in Figure 15.4 supposes that the assumed high (actually extreme, and surely impossible?) pore pressure causes the faster split shearwaves that were previously parallel to H max to do a 90°-flip and become the slower wave parallel to h min. It is not explained, nor is it clear in any way, how a pore pressure can build up to beyond h min without dissipation due to hydraulic fracturing, nor how the pore pressure could thereafter even approach H max. A possible 90°-flip would appear to be possible on occasion with extreme H max loading, causing the usually unlikely and untenable lateral expansion of aligned microcracks, as depicted in Figure 15.3. What seems to be a geotechnically very unlikely process (the EPA model) perhaps has merit in just such earthquake-related cases of ‘axial-overload’.

15.4

Theory relating joint compliances with shear wave splitting

The geophysicists’ progression from seismic propagation in isotropic media, to anisotropic layered media to transversely isotropic layered media containing one set of vertical fractures (a joint set), later increased to two sets of perpendicular fractures, and subsequently to nonorthogonal vertical sets, and later still to non-vertical sets, has resulted in a progression of theoretical papers in the geophysics literature, containing, inevitably, an increasing content and complexity of 6  6 compliance and stiffness matrices. Here we will summarize an intermediate stage in this progression, from Schoenberg and Sayers, 1995, by way of introducing, as simply as possible, some necessary theoretical aspects. These authors addressed the problem of how the presence of a single joint or fracture set would affect the elastic moduli of the fractured rock, since it is the elastic moduli and the density that determine the behaviour of seismic waves, assuming a linear, loss-free, elastic behaviour. In simplest possible terms, appropriate to the nonmathematical treatment in this book, the effective elastic compliance tensor Sijkl of a rock containing fractures, is designed to relate the average strain ij over a representative volume V, to the average stress components ij. One therefore can write: ij  Sijkl ij

(15.2)

Shear wave splitting in fractured reservoirs and resulting from earthquakes

The compliance matrix that includes the effect of a set of vertical fractures, has to include the excess compliances caused by the additional presence of the fractures. The authors assumed that this could be simply expressed as the sum (S) of the compliance of the isotropic background rock (Sb) and the excess compliance matrix associated with the fractures (Sf ). The latter is composed of the effects of a fracture-normal compliance ZN, and of a fracture-shear compliance ZT related with linear slip deformation. Based on the assumptions made, the single set of vertical fractures produces an unusually simple compliance matrix:

 ZN  0  0 S(f)   0   1  0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 ZT 0

0 0 0 0 0 ZT

       

(15.3)

From this matrix, Schoenberg and Sayers, 1995 developed the 6  6 compliance matrix (S) for the combined transversely isotropic fractured medium, involving the various combinations of Lamé constants ( and ) shown in Chapters 1 and 14. The simple addition of the three fracture compliance terms (ZN, ZT and ZT) was made in the same (1,1 5,5 and 6,6) locations in the combined compliance matrix. They then inverted this to form the elastic stiffness matrix to represent the combined isotropic back-ground and vertically fractured medium. They noted that this stiffness matrix was of exactly the same form as that developed previously by Crampin, 1984 for the case of an isotropic medium containing a vertical array of ‘penny-shaped’ fractures, although Crampin also had second-order terms for fracture density. Of importance to the shear-wave splitting context of this chapter, are the stiffness matrix terms relating to the fast shear wave propagating parallel to the fractures, given as the C44 term, and the slow shear wave propagating perpendicular to the fractures, given by the C55 term. For the case of the vertically propagating waves through the vertical fractures, there is no fracture compliance term in C44, only the Lamé constant or b for the background rock. (This was inverted in the case of S44 in the compliance matrix, as 1/ or 1/ b). For the case of the slow shear wave, the C55 term was given as b(1-T), with T (limits: 0  T  1)

417

expressed as (ZT b)/(1  ZT b). In other words there is no ZN term, which requires dipping fractures, or non-vertical wave propagation for ZN to be mobilized. (In the compliance matrix the S55 term was simply 1/ b  ZT). 15.4.1

An unrealistic rock simulant suggests equality between ZN and ZT

Schoenberg and Sayers, 1995 followed their vertical fracture set compliance matrix treatment, by citing the results of shear compliance (ZT) and normal compliance (ZN ) interpretation from loaded, roughened Lucite (‘Plexiglas’) plates used ‘to simulate a fractured medium’, reported by Hsu and Schoenberg, 1993. Schoenberg and Sayers apparently derive their assumption that ZN
ZT for the case of dry (gas saturated) cracks from this laboratory work. (It is argued in Chapter 16 that interlocked rock joints usually have quite different magnitudes of normal and shear stiffness, with the expectation that at least some of these differences remain when considering microdisplacement and the (presumed) elastic response of joints to dynamic wave loading. However, this is at present a subject under debate and therefore controversial). Hsu and Schoenberg, 1993 interpreted the normal and shear compliances from the results of static and dynamic loading tests on numerous (60 or 200), roughened Lucite (‘Plexiglas’) plates, loaded normally. Their extremely close spacing (0.7 mm) and their continuity means that fracture densities were actually in the ‘impossible’ range of 7.5 to 25, up to three orders of magnitude too high to represent fractured (or microcracked) rock. Table 15.1 indicates that these artificial-material tests were taken to quite high normal stress levels in relation to the assumed strength of Lucite. One can imagine that under the highest loads, something approaching a Table 15.1 Shear and normal compliance differences obtained from normally-loaded Lucite plates with rough surfaces. Schoenberg and Sayers, 1995. Derived from Hsu and Schoenberg, 1993. Stress (MPa)

(ZT  ZN)/(ZT  ZN)

6 12 18 24

0.1736 0.1177 0.0332 () 0.0035

418

Rock quality, seismic velocity, attenuation and anisotropy

‘welded’ state could develop for the contacting microasperities, since the ‘roughening’ would reduce the initial contact area. If a ‘locally-welded’ state developed, this would perhaps help to explain the similar (actually almost identical) values of ZT and ZN that they obtained. It is recommended that the phenomena observed in highly stressed roughened plates of Lucite, with their extreme fracture densities, should not be used to simulate rock joint response to dynamic or static loading, because the suggested ‘equality’ of ZN and ZT has permeated some of the geophysics literature, and may be far from realistic for all but the smallest laboratory specimens. Schoenberg and Sayers, 1995 used a ‘difference/sum’ (ZT  ZN )/(ZT  ZN ) format to compare the magnitudes of ZT and ZN. They used the experimental components c11/, c33/, c44/ and c66/ from Hsu and Schoenberg, 1993, for calculating the results given in Table 15.1. One may ‘solve’ for specific examples of 1/Kn and 1/Ks, thus finding the ratios of difference/sum. Let us first assume realistic small-scale pseudo-static values of Kn  1000 MPa/mm, and Ks  10 MPa/mm, and argue (for the sake of preliminary assessment), that Kn
1/ZN, and Ks
1/ZT. Thus (ZT  ZN)/(ZT  ZN)  (0.1  0.001)/(0.1  0.001)  0.98. Clearly the low numbers for the ratio difference/sum, given in the table, imply much closer values of the two compliances. Suppose ZT  0.1 mm/MPa as before, while ZN  0.05 mm/MPa. This would suggest a difference/ sum ratio 0.05/0.15, still not close enough to the Hsu and Schoenberg 1993 highly-stressed Lucite data. Significantly, with the increased pressure, ZT and ZN were approaching equality. With assumed much closer values of ZT  0.1 mm/ MPa, and ZN  0.099 mm/MPa, one obtains a ratio of 0.001/0.199  0.0050. The ‘welded’ asperity argument for the highest stress levels would not on this basis seem unreasonable. If approximate equality to the inverse of stiffness was still tested, the relevant values of Kn and Ks would be 10.1010 MPa/mm and 10.0 MPa/mm, clearly unrealistically close in rock mechanics terms, in view of the entirely different displacement mechanism involved: the former involving ‘closure’ (in a stiffening direction), the latter involving ‘slip’ (not necessarily stiffening, possibly softening, in the absence of roughness). Viewing the obviously different mechanisms involved in mobilizing the ‘spring stiffnesses’ in the normal and shear directions in the various materials depicted in Figure 15.5, it is hard for an experimentalist to understand how equality could be expected between S and n, or ZN and ZT, since in pseudo-static testing and its

Figure 15.5 Discontinuities of different scale, between sand grains, in a microfractured or jointed rock mass, and between clay particles in shale, as depicted by geophysicists concerned with the inequality (or unlikely equality) of the shear and normal compliances. S and n, or S (r) and n (r), are depicting the shear and normal compliances (of the rth discontinuity) in the three or four different scales of media. (Sayers, 2002a, 2002b, Liu et al., 2000)

Shear wave splitting in fractured reservoirs and resulting from earthquakes

empirical modelling, the mechanisms involved in closing and shearing are entirely different, and are modelled in entirely different ways as a result. Some of this difference would seem likely to remain at the microscale of dynamic wave loading. The question is whether heavily loaded, roughened Lucite plates can be accepted as realistic models for a set of stressed rock fractures. Clearly they should not be accepted, or accepted only with great caution, in view of the non-brittle ‘plastic’ behaviour of Lucite. It is therefore urged that one should re-evaluate the relevance of the ‘ZT /ZN
1.0’ theory, and adopt, in the first instance, data from tests on actual rock joints, for example those described by Pyrak-Nolte et al., 1990 (see later), or those derived (implicitly) from Chaudry, 1995 and King et al., 1995 polyaxial tests. The latter studied principal stress-developed rock fractures in highly stressed cubes of isotropic sandstone (see Chapter 13). Even though both these data sets are likely of too small scale, with respective dimensions of 52 mm and 41 mm, they are extremely likely to be closer to relevant reservoir jointing than artificial Lucite surfaces.

15.4.2

Subsequent inequality of ZN and ZT

Later work by Sayers, 2002a, was based on elastic anisotropy expressions involving both second-rank and fourth rank tensors for describing the seismic effect of microcrack and grain boundary contact normal and shear compliances in sandstones. By matching his theoretical predictions to polyaxial loading on blocks of sandstones, it was found that even at pre-fracturing microcrack scale, the shear compliance was deduced to be greater than the normal compliance, based on mismatch of theory with measurement. We may draw some parallels between the two scales of discontinuous phenomena addressed by Sayers 2002a and 2002b, each caused by present or past stress anisotropy. As Sayers, 2002a and other authors have pointed out, grain boundaries and microcracks may cause anisotropic behaviour in the presence of stress anisotropy, in otherwise ‘isotropic’ rock materials. The sandstone depicted in Figure 15.5a, will exhibit stress-induced P-wave anisotropy and S-wave anisotropy due both to preferential stress-alignment of the microcracks, and due to the likely difference in the magnitudes of the normal (ZN) and shear (ZT) compliances between the microcrack faces and between grain contacts.

419

The same will apply to the fractured or jointed medium of much larger scale, where horizontal stress anisotropy will often have caused the alignment of the natural joints or fractures. (We have termed the natural features: rock joints in most of this book, to distinguish them from artificially induced fractures, as developed around boreholes or tunnels or mine openings, or fracturing induced by MHF stimulation of tight reservoirs. This preferred terminology is following the recommendation of ISRM, 1978 and seems logical in view of the number of artificial (man-made) fractures that have to be described in these shared, rock engineering disciplines. At the larger scale, Sayers, 2002b, deduced that ZT  ZN, when analysing the results of the Chaudry, 1995 polyaxial tests on 41  41  41 mm cubes of sandstone, which had a fracture-development cycle. (See descriptions of these interesting tests in Chapter 13). This compliance inequality is of course consistent with the experience of Ks  Kn, concerning the pseudo-static shear and normal stiffnesses of joints and fractures, where stiffness is the rough inverse of compliance. The magnitude of Kn proves to be less than, but quite close to 1/ZN in good quality (unweathered) hard rock, while in the shearing direction, Ks  1/ZT, sometimes 1/ZT (see Chapters 13 and 16).

15.4.3

Off-vertical fracture dip or incidence angle, and normal compliance

Sayers, 2002a pointed out that off-axis velocity measurements would be needed to actually quantify the mismatch ZT  ZN, so he was actually not able to determine this explicitly with the principal axes polyaxial testing of Chaudry, 1995 and King et al., 1995. Sayers, 2002b therefore went on to address the problem of vertical shear wave propagation in jointed media with off-vertical dips, using the example of two conjugate sets with oppositely oriented dip angles, as depicted in Figure 15.6. Unlike the vertical wave propagation through the vertical joints, with dependence of shear-wave splitting on only the shear compliances, as discussed earlier, the shear wave components qS1 and qS2 depend here on both the shear and normal compliances, since the incident angles are no longer parallel to the joint planes. In such cases where both shear and normal compliances are involved, normal compliance is reportedly reduced (i.e. stiffened) by fluids of non-zero bulk modulus. Gas and

420

Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.6 Two conjugate sets of fractures with dips of and – . This model was used by Sayers, 2002b to investigate shear wave splitting phenomena when incident shear waves were no longer parallel to vertical fracturing.

oil should be distinguishable by respectively greater and less shear wave anisotropy, as the stiffening effect of the oil makes the fracture normal stiffness less contrasted to the back-ground medium. For dipping joints or fractures, there proves to be a significant decrease in shear wave anisotropy if the fluid has a higher bulk modulus, making the normal stiffness of the fractures greater. The average of the two shear wave velocities is therefore also increased. Bakulin et al., 2001, also pointed out that both geophysical and geological data acquired over naturally jointed reservoirs often revealed the presence of multiple sub-vertical fracture sets, which made the effective medium monoclinic. They developed a model for handling two sets of unequal, and non-orthogonal vertical joint sets, which yielded the azimuths and compliances of both sets of joints, as well as the P- and S-wave velocities of the assumed isotropic background medium. From a second model, consisting of a single set of microcorrugated joints, they stated that monoclinic symmetry stemmed this time from coupling between the normal and tangential ‘slip’. This coupling caused shear wave splitting dependence on the fluid content of the fractures. Experience from local core logging and photography of jointed core from the Ekofisk reservoir by the writer

Figure 15.7 A cross-discipline example of unequal conjugate jointing used to represent a high-porosity section of the Ekofisk reservoir, modelled by the distinct element code UDEC-BB, with non-linear, effective stress and size-dependent shear and normal stiffnesses. Barton et al., 1986.

in 1985, and inspection of jointing in the Lagerdorf chalk quarry in German, also supports the notion of a possible dominant set when conjugate jointing is present. Figure 15.7 illustrates a specific realization of jointing that was simulated when modelling the local-scale (1  1 m, 2D) compaction mechanism principles, in this massive 30 km3 North Sea chalk reservoir. The behaviour of the joints was based on measured values of wall strength (JCS) and roughness (JRC), which give pseudo-static values of both normal and shear stiffness (the latter may be significantly lower than the dynamic values). In rock mechanics modelling the non-linearity of these parameters is also an issue, with extreme stiffening of Kn at high stress, and less stiffening of Ks with stress, which in pseudo-static loading is also scale (block-size) dependent (Barton and Bandis, 1982). Sayers 2002b, again claimed that the ratio of ZN/ZT (or BN/BT in his terminology) was approximately equal to 1.0 for the case of ‘gas-filled open fractures’. This was possibly based on Hsu and Schoenberg, 1993 results for loading tests on ‘roughened plates of Lucite’, to quite high normal stress levels in relation to the strength of the Lucite. If so, the result should be regarded with great caution, as highly-stressed, roughened Lucite plates, with

Shear wave splitting in fractured reservoirs and resulting from earthquakes

three-orders of magnitude too high crack densities, surely bear little similarity to normally-stressed, interlocked joints in brittle rock, as discussed earlier. The presence of a joint-filling fluid with non-zero bulk modulus in place of gas would, as suggested by Sayers, 2002b cause a lower value of ZN/ZT (or BN/BT), but not it is suggested, just lower in relation to the above artificially high ratio of 1.0, but rather in relation to a ratio of ZN/ZT that was already significantly lower than 1.0, as seems intuitively likely due to the different mechanisms involved (namely ‘closure’ in the case of ZN, and ‘slip’ in the case of ZT. (See Figure 15.5). Interesting supportive field data was cited by Sayers, 2002b, concerning the differences in observed velocities and shear wave splitting intensity, when in the presence of gas as opposed to oil. (This will be reviewed later in this chapter). We may recall that with non-vertical fractures and with vertically propagating waves, both the shear and normal compliances are assumed to be involved in the shear wave splitting process. The field data from Oman (Guest et al., 1998, van der Kolk et al., 2001) for a fractured (supposedly nearly vertically fractured) carbonate reservoir showed higher shear wave anisotropy (due to a lower qS2) over the gas cap volume, than where there was oil. As pointed out by van der Kolk et al., 2001, this in situ fractured media result is in disagreement with the prediction of Gassmann’s theory for porous media, in which the shear modulus should be independent of the fluid. The shear modulus of the matrix governs the fast shear wave, with no ZN or ZT influence. If the in situ fractures were actually not perfectly vertical, as seems to be implied by Sayers, 2002b, then the normal compliance would also be involved in the intensity of the shear wave splitting. Because the normal compliance is reduced in the presence of a fluid with non-zero bulk modulus (i.e. oil), the ratio of ZN/ZT (or BN/BT) would reduce. According to Sayers, this should cause a significant decrease in shear wave splitting and an increase in shear wave velocity with the increased fluid bulk modulus, and therefore stiffened fractures. Without attempting to describe complex details, it may be pointed out from recent work by Gurevich, 2003, that the compliance matrix for a fluid-saturated, porous-and-fractured medium is not equivalent to the compliance matrix of any solid medium with a single set of parallel fractures. This is due to the wave-induced (micro) flow of fluids between pores and fractures. Such attenuating (micro) flow is now being modelled with double-porosity poro-elastic models, which are reviewed later in this chapter.

15.4.4

421

Discussion of scale effects and stiffness

In Chapter 16 we will see the inequality of the pseudostatic shear and normal stiffness (Ks  Kn) of virtually all joints (and filled discontinuities), and the likelihood of changing ratios of Kn/Ks as pore pressure changes affect the effective normal stress. These joint stiffnesses have been used in rock mechanics finite element modelling since the late 1960s, (Goodman and Duncan, 1968), and finite difference distinct element (DEM) modelling since the 1970s (Cundall, 1971). The important question is whether geophysicists will be able to apply the accumulated knowledge from these macro-displacement, inversed equivalents of the geophysicists’ micro-strain compliances. If the stiffnesses and compliances of these two disciplines can be related, despite the probable different orders of magnitude of dynamic and ‘static’ deformations involved, then the more researched parameters Kn and Ks could perhaps give shear wave splitting ‘even more information’ than presently assumed, since one often sees equal normal and shear compliances assumed in papers describing shear wave splitting analyses, implying that information may be limited at present, at the less accessible dynamic micro-scale of displacements. Major stress-aligned, fluid-filled or sediment-filled inclusions, (and cracks, joints or fractures) are the diverse sources of mechanical anisotropy that can be presumed to be common to all rocks. They may be the guaranteed sources of pseudo-static normal to shear stiffness ratios considerably in excess of 1, most likely from about 5 to 50 as shown later in this chapter, and reinforced in Chapter 16. They alone actually guarantee anisotropic behaviour in the ‘static’ (macro-deformation or macrostrain) regime. The fact that the same (but inverted) units for compliance and stiffness are used by the different (‘static’ and dynamic) professions, is some guarantee that deformation, like ‘squirt’, is taking place, however small this may be. The question that remains to be answered is whether, for instance, the ratio of these compliances or inverted dynamic stiffnesses for application in situ, can be in any way based on dynamic tests on three joints of about 50 mm diameter, as tested in important work at Berkeley (Pyrak-Nolte et al., 1990), to be reviewed next, or whether there could be some hidden relation to the much more common and easier pseudo-static tests on e.g. at least 200 samples of 100 mm length (as tested by

422

Rock quality, seismic velocity, attenuation and anisotropy

Barton and Choubey, 1977 and Bandis, 1980), or whether in fact in situ block sizes of decimetres or meters in size, should be the basis for in situ dynamic estimation – by back-analysis. Strictly for the case of pseudo-static loading, the in situ block sizes were suggested by Barton and Bandis, 1982, for up-scaling (to lower in situ values), of the JRC (roughness) and JCS (wall-strength) components of strength and stiffness. The natural block size was suggested as the limit for reducing these components, based on pseudo-static biaxial loading tests on 400, 1000 and 4000 interlocked, fractured blocks, generated in brittle rock-like model materials mostly consisting of dense, weakly-cemented fine sand, as described by Barton and Hansteen, 1979. There seems no physical reason why a 50 mm diameter core containing a joint (from a disused mine in Sweden), should have a strong link to in situ reservoir scale, just because this may be a convenient sampling size also for reservoir joints. That would be fortuitous indeed. There is clearly still less intuitive reason to use tests on roughened plates of ‘Plexiglas’ in this extrapolation. However, as there is so little data in this area, we must utilise what is available, and acknowledge the following very useful experimental contribution from Berkley in the late eighties.

15.5

Dynamic and static stiffness tests on joints by Pyrak-Nolte

Several aspects of the important work of Pyrak-Nolte et al., 1990, and of other published work with contemporaries at Berkeley, were reviewed in the laboratory-scale rock physics discussions in Chapter 13. The static and dynamic normal stiffness of three natural joints, their permeability, and the effect of normal stress on velocity, attenuation and seismic Q were each addressed. In this chapter on shear wave splitting, we will consider particularly the data the authors provided on the dynamic normal and shear stiffnesses. This can be inverted to compare with joint compliance data given in this chapter, and also in Chapter 16, where more rock mechanics pseudostatic data is introduced. The load-deformation data given by Pyrak-Nolte, 1995 reproduced in Figure 15.8, shows the 52 mm diameter jointed quartz monzonite sample E 35 (from the Stripa mine in Sweden), closing by more than 25 m, compared to only about 5 m closure for sample E 32

Figure 15.8 Normally loaded stress-deformation, and specific stiffness trends for two of the three jointed samples tested by Pyrak-Nolte, as reported in Pyrak-Nolte et al., 1990. The static and dynamic stiffnesses for samples E 32 and E 35 are contrasted in Table 15.2.

when loaded to 80 MPa. The latter is remarkably stiff behaviour. The contrasting behaviour possibly indicates respectively ‘rough’ and more ‘planar’ joint surfaces, (or differences in the degree of inter-lock), causing the widely different specific stiffness trends for these two samples. (Joint roughness quantifications, and interlock descriptions seem not to have been reported). The diameter of the jointed samples E 32 and E 35 was only 52 mm, which may have influenced the relatively high values of Ks(dyn), and therefore also the relatively low values of Kn(dyn)/Ks(dyn) seen in Table 15.2. This is commonly the case in rock mechanics pseudo-static testing of rock joints too: small samples have higher shear stiffness, normal stiffness may be little influenced (if correctly sampled and interlocked). Therefore the ratio of normal/shear

Shear wave splitting in fractured reservoirs and resulting from earthquakes

423

Table 15.2 Estimates of dynamic normal and dynamic shear stiffnesses derived by fitting to recorded response spectra, selected from PyrakNolte et al., 1990 data sets. Note the stiffer water-saturated behaviour. The seismic quality Qp values for these two jointed samples are also appended. (The unit MPa/ m is suggested to aid interpretation. Note that the stiffnesses are high to very high, with 1 MPa/ m  1000 MPa/mm). STRESS n(MPa)

Sample E 32 Kn(dynamic)-dry

(1012 Pa/m) or MPa/ m Kn(dynamic)-saturated

2.9 10 20 70

15.0 – – 120.0

35.0 80.0 100.0 –

STRESS n(MPa)

Sample E 32 Ks(dynamic)-dry

(1012 Pa/m) or MPa/ m Ks(dynamic)-saturated

Sample E 35 Ks(dynamic)-dry

(1012 Pa/m) or MPa/ m Ks(dynamic)-saturated

3.5 9.5 17.0 55.0

– – – –

1.9 4.8 6.2 7.4

– – – –

2.9 10 20 70

STRESS n(MPa)

(Qp  9) (Qp  24)

Sample E 32 Kn(dyn)/Ks(dyn) (dry)

2.9 10 20 70

(Qp  17) (Qp  36)

See high stiffness behaviour in Fig. 15.8b

Sample E 35 Kn(dynamic)-dry

(1012 Pa/m) or MPa/ m Kn(dynamic)-saturated

4.0 11.5 20.0 32.0

9.5 20.0 25.0 59.0

(Qp  7) (Qp  14)

Sample E 35 Kn(dyn)/Ks(dyn) (dry)

4.3 – – 2.2

(Qp  9) (Qp  30)

See low stiffness behaviour in Fig. 15.8b

2.1 2.4 3.2 4.3

Note: Qs values were generally larger than the above Qp values: see Table 10.3, Chapter 10.

Table 15.3 Kn(dyn)/Ks(dyn) ratios for sample E 30, which was of intermediate stiffness compared to E 32 and E 35. Sample diameter was also 52 mm. Derived from Pyrak-Nolte et al., 1990 data sets. Normal stress (MPa) 1.4 2.9 6.0 10.0 20.0 33.0

stiffness tends to be low when very small sample sizes are used. There is a lot of data from near-surface rock engineering projects where sample size is 600–1000 mm, and laboratory tests tend also to be in a higher 100–300 mm range compared to the high stress tests on (inevitably) smaller samples. Some of this data is reviewed in Chapter 16. Note the lack of any tendency for Kn(dyn)  Ks(dyn), or its inverse ZN  ZT, as deduced by Schoenberg and

Ratio of Kn(dyn)/Ks(dyn) 2.2 1.6 1.6 1.3 2.0 2.7

Sayers, 1995, from dynamic tests on dry, roughened ‘Plexiglas’ plates. Dynamic stiffness ratios for a joint of intermediate stiffness (E30) were also reported by Pyrak-Nolte et al., 1990. This is given separately in Table 15.3. It may be noted from the above tables that the range of Kn(dyn)/Ks(dyn) ratios for these three small jointed samples was 1.3 to 4.3 with a mean of 2.5. This means that

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Rock quality, seismic velocity, attenuation and anisotropy

Table 15.4 Comparison of static and dynamic normal stiffness data for the Pyrak-Nolte et al., 1987a jointed sample E 35, which was the most deformable sample (possibly due to greater roughness). These dynamic stiffnesses were determined by curve matching. Normal Stress (MPa) 2.9 10.0 33.0

Dynamic stiffness Kn(dyn)

Static stiffness Kn(static) (1012 Pa/m) 1.0 2.2 3.3

MPa/mm 1000 2200 3300

the ratio of the inversed compliances ZN/ZT for these 52 mm diameter samples ranges from 0.2 to 0.8, with a mean of 0.4. The remaining question is what relevance this convenient ‘core-sized’ data has to in situ reservoirs in general, with a typical spread of jointed block sizes from perhaps 200 mm to 5,000 mm, and mostly sedimentary rock as opposed to Stripa ‘granite’, or hard quartz monzonite, which had Estatic  60 GPa, and Vp  4.9–6.1 km/s over a stress range of 84 MPa, (Pyrak-Nolte et al., 1987b). Pyrak-Nolte et al., 1987a reported an earlier set of (dry) dynamic/static normal stiffness measurements, performed on one of the same jointed samples (E 35). In view of the relative scarcity of such dynamic/static data for rock joints in the literature, this is reproduced in Table 15.4. Units of stiffness more familiar in rock mechanics (MPa/mm) are also given in this table, as this unit is easier to visualize in practical terms (e.g. 100 MPa for 0.1 mm closure) than that used in geophysics, where the inverse compliance is also typically reported in ‘complex’ units of 1012 m.Pa1 (with ‘m’ sometimes omitted altogether). It is even more ‘practical’ to consider the unit MPa/ m for the first static stiffness listed in this table. One thereby comes much closer to the elastic, presumably sub-micron, dynamic wave pulse effects on micro-closure, and on micro-fluid movement during squirt-flow attenuation. In connection with the above ratios of Kn(dyn)/Ks(dyn), it may be of interest to refer to the equivalent data for artificial surfaces in aluminium, reported by PyrakNolte et al., 1992, based on interface wave experiments. An aluminium cylinder of 293 mm diameter was sawn in two, planed smooth, and then sandblasted with 300 m grit. This artificial, planar-but-roughened interface, which can perhaps be likened to the roughened ‘Plexiglas’ surfaces studied by Hsu and Schoenberg, 1993, showed predicted (curve-fitting-based) ratios of Kn(dyn)/Ks(dyn) ranging from 0.90 at 13.2 MPa, to 0.47 at 32.9 MPa normal stress.

(1012 Pa/m) 4.5 8.0 25.0

Ratio MPa/mm

Kn(dyn)/Ks(dyn)

4500 8000 25000

4.5 3.6 7.6

The aluminium results are therefore quite different from dynamic rock joint behaviour. The actual magnitudes of dynamic normal and shear stiffness were somewhat higher than for the (obviously rougher) rock joints tested by Pyrak-Nolte, for instance 22.5 and 25.0 1012 Pa/m, in the case of the normal stress of 13.2 MPa. (In alternative units these translate to 22500 and 25000 MPa/mm, or 22.5 and 25.0 MPa/ m, i.e. very stiff behaviour, perhaps due to ‘asperity-weld’.

15.5.1

Discussion of stiffness data gaps and discipline bridging needs

In comparison with the above static and dynamics data for one joint sample in igneous rock, we will see in Chapter 16 some rock mechanics data from Bandis, 1980, with numerous static normal stiffness data for rock joints in limestone, sandstone and siltstone (and other non-sedimentary rocks). We will see Kn (static) values varying from 250 MPa/mm at 10 MPa normal stress, to 31500 MPa/mm at 40 MPa normal stress. (Priv. comm. Bandis, 2005). The lowest value was for a rough, weathered joint (JRC  15, JCS  44 MPa) in limestone, the latter a smoother joint (JRC  7.6, JCS  160 MPa) in almost unweathered limestone. Unstressed apertures, prior to standard stress-cycling to achieve an approximation to in situ (consolidated) conditions, were about 0.5 and 0.2 mm respectively. Concerning shear stiffness, which is of relevance when discussing the possible magnitude of shear compliance in shear wave splitting, we will see in Chapter 16 a whole range of possible static shear stiffnesses that are seen to be inversely related with the sample size. The extent to which dynamic shear compliances are related (much more weakly, but perhaps directly) to sample size, seems to be one of the remaining unsolved areas in this important area of seismic detection of anisotropy, and the subsequent goal of interpretation of permeability.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

Some pieces of the ‘dynamic-permeability’ jigsaw are ‘complete’, but there are missing bridges between dynamic and static testing, between high stress and low stress testing, and across the related small sample to large sample void. The ‘completed’ parts of the jigsaw are the abilities to predict both (pseudo-static) stiffnesses Kn and Ks and the less tangible physical (E) and hydraulic (e) apertures, for any size of jointed rock blocks. This ability is based on index tests or estimates of the rock strength (specifically the joint wall compressive strength JCS), and the roughness (specifically the joint roughness coefficient JRC). These parts of the ‘jigsaw’ will be illustrated in Chapter 16, in case of future use when the three missing ‘bridges’ identified above, are robust.

15.5.2

Fracture stiffness and permeability

Concerning one of the three ‘bridges’ discussed above, the three joints in Stripa ‘granite’ (quartz monzonite) that were so extensively tested and modelled by Pyrak-Nolte et al., 1990, and Pyrak-Nolte, 1996, (see also Chapter 13 review), gave interesting evidence of a strong connection between the normal stiffness (termed ‘fracture specific stiffness’ by the author), and the permeability, as recorded by flow rate per unit head, during ‘sector-to-sector’ flow across the otherwise sealed joint perimeters. Figure 15.9 shows the strong relationship between flow rate per unit head (proportional to permeability), and the joint normal stiffness, which changes due to the effect of normal stress, as illustrated in Figure 15.8. The data shows that joints that support less flow obviously have higher stiffness, due also to the effect of normal stress. The author suggested that the joint stiffness was inversely related to the cube root of the flow, and that fluid flow and the seismic response of a joint could therefore be inter-related through the normal stiffness of the joint in question. Pyrak-Nolte also found that the joints that attenuated seismic waves most at a given stress level, also supported more flow, which is logical. This implies an implicit link between the permeability and the rock quality Q-value and more specifically between the permeability and the modulus of deformation, when not reduced by clay, since Qp and the pseudo-static modulus of deformation M (or Emass), expressed in GPa, were seen to display some remarkable, empirical similarities in Chapters 10 and 13.

425

Figure 15.9 Effect of joint normal stiffness on the flow rate per unit head (which is proportional to permeability. Data for three joints in quartz monzonite, with linear (not radial), sector-to-sector flow, crossing core of 52 mm diameter. Pyrak-Nolte et al., 1987a, PyrakNolte, 1996.

15.6

Normal and shear compliance theories for resolving fluid type

Interest in fracture-induced seismic anisotropy has rapidly evolved from the earlier estimation of ‘only’ fracture orientation, (with an assumed indication of major horizontal stress), to fracture intensity, and the attempted prediction of fluid saturation and permeability anisotropy. To make this advance, the sensitivity of fracture compliance to fluids has to be understood. There are several models addressing this important question. The authors Liu et al., 2000, investigated various possible representations of fractures, for use in dynamic modelling of fractured reservoirs. These consisted of an in-plane distribution of small cracks, an in-plane distribution of contacts, and a thin layer with material infill. They were able to derive specific expressions for the fracture compliances ZN and ZT . Their different models indicated strong sensitivity of the ratio ZN/ZT to the bulk modulus of the fracture infill material, with the most rapid change in the compliance ratio (and values closer to 1.0) occurring when the infill bulk modulus approached zero, such as for gas-filled fractures. However with realistically small fracture aspect ratios (i.e.  0.001), much lower values than 1 were suggested, as shown in Figure 15.10. Liu et al., 2000, and Liu and Li, 2001 presented equations for the compliance ratio (ZN/ZT), which incorporated the aspect ratio of cracks, and the ratio of bulk moduli for fluid and matrix. One of their equations, based on earlier work by Schoenberg and Hudson,

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

Figure 15.10 Liu et al., 2000 model of in-plane small cracks, for estimation of the ratio ZN/ZT versus the normalized bulk modulus ( f) of the fracture infill, via components of Hudson’s models. The matrix was a so-called Poisson’s solid with equal Lamé constants (bulk and shear moduli  ).

suggested that ZN/ZT  1 if the fractures were dry, and ZN/ZT  0 if the fractures were filled with liquid. Their interesting theory, which however is not directly supported by the dynamic rock mechanics experience with rock joints reviewed in the previous section, is also illustrated in Figure 15.11a. Their equation, on which the figure is based, is reproduced here for reference: ZN 7 5  a c   k f  1    ZT 8 2  c c   k 

  

(b)

1

(15.4)

where ac and cc are the ‘long and short axes of the elemental cracks in the fracture planes’, which they also refer to as the aspect ratios, and kf and k are the bulk moduli of the fluid and matrix. Figure 15.11a suggests, as does the above equation, that ZN and ZT are zero (i.e. stiffnesses Kn and Ks are infinite, or very high) when a fracture is ‘closed’. Of course if the fracture is no longer present this is logical, but not if stresses are merely high and contact areas are high, but significantly less than 100%. Such might be typical for reservoir fractures in weaker materials. Perhaps for the highest-porosity chalk, showing general

Figure 15.11 (a) A fracture compliance based prediction of fluid type (brine, heavy oil or gas) based on fracture aspect ratios and on the ratio of fluid and matrix bulk moduli. Liu and Li, 2001. (b) Laboratory evidence for the importance of fluid (dry or saturated) on the ratio ZN/ZT as a function of stress, from Pyrak-Nolte et al., 1990.

compaction due to pore collapse, fractures would truly be of infinite stiffness, since effectively absorbed in the matrix collapse. Based on the different bulk moduli of gas, brine and heavy oil, Liu and Li, 2001 allocated different ZN versus ZT ‘regions’ in Figure 15.11a. As partial support for the predicted rends, Liu and Li, 2001, cite the dynamic stiffness data from Pyrak-Nolte

Shear wave splitting in fractured reservoirs and resulting from earthquakes

et al., 1990, and invert the ratios (see Tables 15.2 and 15.3) to give the ZN/ZT versus normal stress trends reproduced in Figure 15.11b. They note the increased ratio of ZN/ZT from the saturated to the dry state. Converting this figure to rock mechanics terminology, the dynamic stiffness ratios Kn/Ks are predicted to vary from about 4 to 45 with increasing stress (when saturated), and from about 2 to 4 with increasing stress (when dry). The authors also referred to the Lucite-plate samples tested by Hsu and Schoenberg, in which honeysaturated (sic) tests showed even greater sensitivity to the dry and saturated states, and surprisingly close magnitudes of ZN and ZT (ZN/ZT close to 1.0) when their samples were dry, as reviewed earlier. As we have seen, the ‘intense fracturing’ (more like thin inter-bed studies) created by the Hsu and Schoenberg, 1993 tests on either 60 or 200 (!) 0.7 mm thick, roughened (10 m) Lucite plates, created an extreme crack density (almost without its equal) of 7.5 to 25, up to three orders of magnitude greater than in situ microcracking or fracturing. Possibly this factor is partly to blame for the unrealistic ZN
ZT result, that has permeated into several geophysics publications. 15.6.1

In situ compliances in a fault zone inferred from seismic Q

The low value of seismic Q for a fault zone (or possibly several faults) encountered in a well in the North Sea (Qseis averaging 45), described by Worthington and Hudson, 2000, represented an abrupt increase in attenuation, relative to the Triassic and Lower Jurassic age sandstones, siltstones and claystones that were predominantly encountered in the well. Worthington and Hudson modelled the effects of a down-going P-wave between 1000 and 2000 m depth, by assuming that one or up to several faults, intersected the transmission path. They used a theoretical compliance model developed by Hudson et al., 1997, to demonstrate the need for a very large but (to rock mechanics thinking), realistic inequality of the shear and normal compliances, suggesting the need for ZN (or Bn)  4.4  1014 m.Pa1, and ZT (or Bt)  1.1  109 m.Pa1. The equations used to estimate these compliances are quite complicated, and are reproduced here to emphasise the geophysical ‘way of thinking’ regarding microdeformation compliances. (According to Worthington

427

and Lubbe, 2004, the following two equations each had a small error in the first and second terms in brackets. In place of the 2000 versions with (4/ )  (/%a) and (8/ )  (/%a), the equations are as follows: 1   2  2 (r w ) 2   4         Bn    1  2  1     a            +
 ( 4/3)
 

rw

2  1     1 w 2   2  2 r   ( )  8

    1  Bt  r w     2     a   2      3        2    (
)  

(15.5)

(15.6)

Here, ,  are the P-wave, S-wave velocities, is the rigidity of the rock, rw is the proportion of the fault surface area that is estimated to consist of welded contact (assumed 0.2), a is the mean radius of the contact areas,
and +
are the rigidity and bulk modulus of the fault fill, and  is the mean aperture of the fault. For purposes of comparison, one may first invert these presumed micro-deformation magnitudes of geophysics, to the much more easily understood ‘physical’ macro-deformation units of rock mechanics, namely shear and normal stiffnesses of Kn
20,000 MPa/mm (and 20 MPa/ m), and Ks
1 MPa/mm. These by chance, or due to more inter-related micro-and-macro physical processes at larger scale and at lower frequency, are similar to the values one may need to use on different occasions in rock mechanics pseudo-static modelling. Heavily stressed rock joints, perhaps equivalent to the ‘welded’ portions of the modelled fault or faults, have normal stiffnesses, as we shall see in Chapter 16, that are of this high magnitude, while clay-filled discontinuities will tend to have much lower values for obvious reasons of low frictional strength. The low values of shear stiffness that are implied by the authors’ modelling, are in fact very reasonable values for blocks within faults of large dimension, that are assumed to dominate in large scale deformation processes, such as overburden subsidence over compacting reservoirs. For example, Barton et al., 1986 and Barton, 2002b, describe (‘static’) Ks as low as 102 MPa/mm, needed to realistically model large scale discontinua in the Ekofisk reservoir subsidence, thereby obtaining a better match

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Rock quality, seismic velocity, attenuation and anisotropy

to reality than continuum models. Such low values were selected from a Barton, 1982 assembly of large-scale shear stiffness data (see Chapter 16). The extremely compliant values of pseudo-static shear stiffness were due to the assumed large effective ‘block sizes’ of the major deforming elements of a conservatively estimated 150 km3 deforming volume of overburden. (The 300 m thick pear-shape reservoir in jointed chalk, in area roughly 9  14 km, has a depth of roughly 3 km). The approx. 1.0 MPa/mm, for the dynamic shear stiffness derived by Worthington and Hudson for the subNorth Sea fault, is equivalent to a static shear stiffness under 20  25 MPa effective stress (1.5 km gives about 37  15  22 MPa effective stress) of roughly 10 m effective block sizes. (See Figure 16.14 in Chapter 16). An empirical expression for the macro-deformation, pseudo-static shear stiffness, used in rock mechanics, is given in Chapter 16, and is evaluated with various input data assumptions, including the effect of saturated or dry conditions. In principle, the simple empirical equation for shear stiffness, from Barton and Choubey, 1977, is based on the peak shear strength equation divided by the displacement to peak. In other words a constant gradient of load versus shear deformation is assumed. In the case of normal stiffness, the empirical hyperbolic equation of Bandis, 1980, also given in Bandis et al., 1983, gives the basis for normal stiffness estimation. Both these stiffness equations are components of the Barton-Bandis constitutive model, and utilise the relevant joint wall roughness coefficient JRC, and the joint wall strength JCS, as measured or estimated input data. In the case of shear stiffness, the residual friction angle r is also needed. In the case of faults, we may consider JRC
0 (zero effective roughness), and r may be as low as 10° to 20°, depending on the mineralogy of the clay or possible ‘shale-smear’. (For a comprehensive review of the sometimes very low in situ pseudo-static shear strengths of clay-filled discontinuities, often tested at large scale at dam sites, but at low to moderate stress levels, see Barton, 1973b). A return to the important themes of dynamic compliance and pseudo-static stiffness will be found in Chapter 16, to better explore the similarities and dissimilarities, as the case may be. At this stage of comparison one can assume that the pseudo-static values of stiffness are lower (in the normal direction), and much lower (in the shear direction) than the equivalent dynamic values of stiffness. In view of the extreme lack of present data for the dynamic values, and the wealth

of data for the pseudo-static values, it may well prove useful to ‘bridge-the-gap’ between the disciplines and ‘quantify’ () and (). This will be attempted. 15.7

Shear wave splitting from earthquakes

Monitoring shear waves caused by the effects of earthquakes requires a certain consideration of the geometry of the situation. There is a so-called shear wave window, which is the area on the earth’s surface above the earthquake, where ray-paths subtend angles of incidence less than about 35°. This derives from the requirement of angles of incidence less than  sin1(Vp/Vs). (Nuttli and Whitmore, 1962.) For a Poisson’s ratio of 0.25, is about 35°. Outside this window the shear-wave waveforms are severely distorted. Crampin and Peacock, 2005 mention the added distortion if recordings are made on irregular topography. They also mention the ‘helpful’ surface effect that a low velocity layer may effectively widen the shear-wave window by refracting the upcoming shear-waves towards vertical incidence. The effective window may then be as much as (2 x) 45° to 50°. The polarizations of the leading, faster, split shearwaves within the shear-wave window above many recorded earthquakes are typically observed to be scattered by 10° to 20° about a direction parallel to the direction of maximum horizontal compression. (Crampin and Booth, 1985). There can be many reasons for this scatter besides general heterogeneity with a ‘mixed’ geology along the path length. Furthermore, and unfortunately, the location of the main source of shear wave splitting is not known, which is why in-hole instrumentation at up to several kilometres depth is so attractive (see Chapter 10), to remove the attenuating near-surface layers, which perhaps could also be the source of somewhat differently oriented structure and/or major principal stress. 15.7.1

Shear-wave splitting in the New Madrid seismic zone

Rowlands et al., 1993, using a network of more than thirty three-component digitally recording seismometers in the New Madrid seismic zone in the central USA, recorded shear-wave splitting, which they attributed to EDA cracks. A compressed summary of the seismic

Shear wave splitting in fractured reservoirs and resulting from earthquakes

zone, an example of shear-wave splitting, and of the split shear-wave polarizations, together with the velocity structure through the local crust is given in Figure 15.12. The majority of the seismic events were between 3 and 15 km depth, mostly in the Precambrian basement. The shear waves propagating upwards encountered three high-to-low velocity interfaces and one low-to-high interface. The aligned polarizations lay in the ENEWSW direction (average N62°E), reportedly coincident with the direction of the regional maximum horizontal stress documented by Zoback and his colleagues. This good correlation suggested to the authors that the anisotropy causing the shear-wave splitting was likely to be caused by the presence of fluid-filled, stress-aligned vertical extensive dilation anisotropy (EDA) cracks. The time delays (120 to 180 ms) and associated shear wave travel times (3.8 to 4.6 s) suggested a shear wave anisotropy over the whole path of 3 to 4%, consistent with a Crampin, 1993a, review of these ubiquitous phenomena. Rowlands et al., 1993, found evidence that the anisotropy causing the polarization alignments may have been present only in the top 5 km, rather than evenly distributed. They also reported that the basal Palaeozoic deposits (Vp  4.83 km/s, see table in Figure 15.12) were considered to be fractured, while the thick shale formation might have introduced a thin-layer anisotropy.

15.7.2

Shear-wave splitting at Parkfield seismic monitoring array

Liu et al., 1993 also confirmed shear-wave splitting at a majority of the recording stations at the Parkfield borehole seismic network along the San Andreas fault zone, obtained during 18 months of recordings from previous campaigns by co-authors Evans, Booth and Crampin, reported in 1984 and 1985, but recorded earlier than this. At three of the stations, distant 1 to 5 km from the fault, the polarizations were consistently normal or subnormal to the fault strike and parallel to the direction of the regional maximum horizontal stress. At station MM, immediately adjacent or within the fault zone (see Figure 15.13, reproduced from Liu et al., 1993), first motion (qS1) was polarized parallel to the fault strike, i.e. in this case perpendicular to the regional maximum principal stress of about N30°E. There was some evidence of temporal variation of the shear wave time delays in connection with a magnitude

429

ML  4 San Andreas fault earthquake; time delays at Station MM (7 ms/km) were roughly twice those at station VC (4 ms/km). The authors concluded that the relatively greater shear wave splitting observed at station MM suggested that the fluid-filled fractures within the fault zone were more extensive than in the surrounding crust, which is logical. The fault parallel polarization of the leading split shear wave at station MM was taken by the authors to indicate that either the stress was highly irregular in the immediate vicinity of the fault, or that the fault-related fractures were aligned by fault shearing rather than by the regional principal stress. The Liu et al., 1993, analyses were performed with co-authors’ data, also recorded between January 1989 and July 1990. All the earthquakes during which shear waves were clearly visible above the P-wave coda, showed evidence of shear-wave splitting. In a few cases, only one of the anisotropic shear-wave polarizations was recorded, due to attenuation of the slower component. The dominant frequency was 20 Hz, yielding elliptical motion. Various different polarization alignments of some stations (Figure 15.13b) were thought to be possible due to local topography, or due to changes in angle of incidence due to refraction across hard rockto-sediment interfaces. A marginal decrease in the time delay following the Ml  4 earthquake of May 1989, followed by an irregular increase was noted from stations MM and VC. Similar decreases in time delay at the time of other larger earthquakes (M  3.5, M  6.0) were cited. The average time delay at MM on the fault zone was about twice as large as those at station VC 5 km away, on the southwest block of the SAF. A greater density of microcracks and fractures in the fault zone was cited, and change of stress affecting the geometry of these fluid-filled features was assumed as a possible cause for the temporal changes. A migration of focal depth for about 100 days after the Ml  4 event was first cited as a possible cause of the decrease in time delay. However, for earthquakes with focal depths above 7 km depth, there was a pronounced increase in time delays. So the conclusion was drawn that the anisotropy of the fault zone was concentrated above 7 km. Since the polarizations at VC, VR and ED (Figure 15.13b) were approximately perpendicular to the SAF, and parallel to the regional principal stress direction (N30°E), they were considered to be consistent with

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

Vp

Vs

(c)

(d)

Figure 15.12 A compressed summary of Rowlands et al., 1993, measurements and analyses of shear-wave splitting at the New Madrid seismic zone. (a) seismic map, (b) shear-wave polarization examples, (c) table showing velocity structure and geology, (d) a shear wave splitting example (focal depth 9.1 km, epicentral distance 5.0 km. Traces on left are the original, 3 seconds duration. Traces on right are the horizontal components rotated into the fast and slow split shear-wave polarizations.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

431

(a)

(b)

Figure 15.13 (a) San Andreas fault and associated shallow thrust faults, with Parkfield high resolution seismic network (HRSN). (b) Epicentres of local small events within the shear-wave window. (Star in SE corner was an Ml  4 event at 8.3 km depth.) Lower hemispheres show polarizations of leading split shear-waves, beneath 7 of 9 stations. Liu et al., 1993.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.14 Superimposed fault plane solutions for earthquakes close to station MM. 95% of the shear waves propagated within 15° of vertical. Nishioka and Michael, 1990, cited by Liu et al., 1993.

the extensive-dilation anisotropy (EDA) concept of stress-aligned fluid-filled cracks. Nearer the fault, where the leading shear wave is polarized parallel to the fault, the indication was of fault parallel cracks instead of the adjacent regional stress parallelism of the other stations. The internal structure of the fault gouge and transition zone was assumed to be the reason for this rotation. In the immediate location of the fault zone, fault plane solutions for 68 events close to station MM (Figure 15.14) indeed show a different, and quite narrowly defined maximum stress axis between N15°W and N10°E, i.e. rotated in relation to the regional stress along N30°E.

15.7.3

Shear-wave splitting recorded at depth in Cajon Pass borehole

Liu et al., 1997 also analysed 51 local earthquakes recorded at 2.5 km depth in the Cajon Pass scientific borehole, to assess shear-wave splitting. Time delays between the split shear-waves of up to 44 ms per km were identified for 32 of the events. Their analyses suggested

that the anisotropic structure near Cajon Pass had orthorhombic symmetry. ‘Stress-aligned’ fluid-filled microcracks and pores were assumed, i.e. the standard Crampin EDA assumption, but in fact the polarization direction of N 13° W was reportedly not consistent with the numerous stress measurements and borehole break-out analyses of the surroundings, and of the uppermost 3 km of the borehole. These had suggested N 57° E  19°. (The strike of the San Andreas Fault, 4 km distant, is N 60° W.) In the upper 1000–1820 m at Cajon Pass the polarizations of split shear waves had earlier indicated a nearly consistent N 70° E  10°. The horizontal stress from inferred focal mechanisms around Cajon Pass was reported as N 17° W, which was much closer to the polarization direction N 13° W of the authors, using ‘below 2.5 km depth’ seismic data. The authors commented that the behaviour of shearwaves in the vicinity of fault zones is complicated, with the leading shear-wave polarizations often exhibiting fault-parallel alignments near the fault, but alignments with the regional stress field away from the immediate fault zone. (This would suggest respectively fault-aligned and stress-aligned joint sets, as the possible source of shear-wave splitting.) The fact that stress directions inferred from shear-wave polarizations at 2.5 km depth were different from those inferred nearer the surface did not suggest to the authors that joint orientations could be different, but that microcrack-controlling stress directions were different. The authors concluded from their study that the San Andreas Fault was probably driven by deep, regional tectonic stresses.

15.7.4

Stress-monitoring site (SMS) anomalies from Iceland

From another seismically active region, Crampin, 2003 described the preliminary establishment of a stress-monitoring site in Iceland, using state-of-the-art borehole instrumentation to monitor shear-wave splitting between a controlled-source well and two receiver wells. Such sites were designed to identify the nearly negligible changes of stress, which in appropriate circumstances could monitor the build-up of stress (or crustal adjustments) before earthquakes and volcanic eruptions. Figure 15.15 reproduces an interesting series of observations from the SMS at Húsavik, Iceland, from 8th to 24th August, 2001, also reported in Crampin, 2003. The 12-hours (per day) histograms of seismicity

Shear wave splitting in fractured reservoirs and resulting from earthquakes

433

recorded within 100 km of Húsavik show peak activity coinciding with an anomalous 1 m water level drop at 33 m depth in a well on nearby Flatey Island, immediately above the Húsavik-Flatey Fault. There was also correspondence with GPS displacement anomalies of many millimetres magnitude around Húsavik, and with various changes in prior and subsequent P-wave and S-wave travel times and delays. The shear-wave splitting was the most sensitive parameter besides ground deformation, showing a 10% variation in time delays. Significantly, Crampin, 2003 also mentioned that with the controlled source and crossborehole seismic represented by SMS borehole equipment, one was ‘free of the 90°-flips’ that may occur in source zones, (due to extreme pore pressures according to Crampin, or due to extreme loading in the H max direction, causing an extreme ‘Poisson expansion’ due to Crampin APE-crack expansion, according to the writer: see earlier discussion).

15.7.5

SW-Iceland, station BJA shear wave anomalies

Figure 15.16 reproduces the key results of a four-year study in Iceland, reported by Volti and Crampin, 2003 for seismic recording Station BJA in south-west Iceland, during the period 1st January 1996 to 31st December, 1999. The middle and top diagrams show the variation of time-delays with time, for raypaths in Band-1 and Band-2, which separate observations making solid angles of 15°45°, and 15° to the average ‘crack’ plane. The time-delays in ms per km are normalized to a 1 km path length. The vertical lines through the time-delay points are error-bars, based on errors in hypocentral distance. The irregular curves are nine-point moving averages. The inclined lines in Band-1 (middle diagram) are leastsquares estimates starting just before the minima of the Figure 15.15 Some coordinated observations of changes brought about by presumed, seismically induced crustal adjustments, recorded at the Stress-Monitoring Site (SMS) at Húsavik from 8th to 24th August, 2001. The 12-hours (per day) histograms of seismicity recorded within 100 km of Húsavik (diagram f ), show peak activity coinciding with a variety of Pand S-wave changes (diagrams a to c), to ground movements (d), and to water-well level changes (e). Crampin, 2003.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.16 Correlation of time delay changes with timing of seismic events in Iceland. The inclined lines are least-squares estimates of time-delay increases, which end with each of the larger events. Volti and Crampin, 2003.

nine-point moving average, and ending when an earthquake or large eruption takes place. The arrows indicate the time of these events, with date and epicentral distance. The bottom diagram shows the magnitudes of earthquakes greater than M  2, within 20 km of this recording station. It was Crampin’s opinion that the changes observed in shear-wave splitting, both before the earthquakes and volcanic eruptions, were due to changes in the rock mass, rather than associated with changes in the immediate source zones. Crampin claimed that the shearwave splitting showed ‘that almost all in-situ crack distributions verge on fracture-criticality’. In the opinion of the writer, the Iceland data is of great interest because of the extreme sensitivity of quite different scales of ‘crack’, namely joints and natural fractures, to minute changes of effective stress and/or fluid pressure. As argued previously, this claim that almost all in-situ crack distributions verge on fracture-criticality does not appear valid, if one assesses that the greatly expanding microcracks in the APE model (Figure 15.3) is an improbable model for rock masses. The crack density definition is ambiguous, and as applied by Crampin in numerous

publications, implies that even hand-specimens ‘of almost all rocks’, would be pervaded by tens to hundreds of millions of microcracks, since the (radius)3 term with suitably small microcracks (e.g. 10 or 100 m) guarantees completely unrealistic numbers of microcracks to generate, for example, e  0.045 (according to Crampin a typical maximum crack density), as needed for generating the typical maximum 4.5% shear-wave anisotropy. In fact, as we shall see, there are reported crack densities and shear wave anisotropies far higher than suggested by Crampin, when measuring shear wave polarization through jointed or fractured reservoirs. When the crack density calculation is applied to the often observed scale of several meters (in wells and deep tunnels), quite reasonable numbers of larger fractures or joints are predicted, and these features with their extremely low aspect ratios are, according to fundamental principles of geophysics and rock mechanics, surely more compliant than the microcracks apparently favoured by Crampin. At great depth, as stresses are more isotropic and very high, there may be no microcracks or open fractures to speak of, as they may be completely closed. It is then

Shear wave splitting in fractured reservoirs and resulting from earthquakes

435

Figure 15.17 Left-hand diagrams: Stable sliding of several millimetres on normally loaded (6 MPa) planar-but-roughened surfaces in Stripa ‘granite’ (quartz monzonite), caused a marked reduction (up to 50%) in the shear-wave amplitude. Right-hand diagrams: Stable sliding under a normal stress of about 10 MPa, followed by stick-slip effects, showed cyclic reduction of the shear-wave amplitude in abrupt steps for each slip event. The lower diagram shows an expanded view of the ‘continuous’ sliding, showing actual (but inaudible to AE) faster-slip episodes, which also caused quite rapid reductions of shear wave amplitude. Chen et al., 1993.

that the ambiguous, undefined location of the source depth of the shear wave splitting comes into play, and one can assume with some confidence that the source of the splitting will tend to be shallower than perhaps desired, where conditions of anisotropy are more favourable for shear-wave splitting. 15.7.6

Effects of shearing on stiffness and shear wave amplitude

In relation to the possible use of shear waves in detecting earthquake precursors, it is interesting to note Chen et al., 1993 investigations of the amplitude of shear waves under the influence of stable sliding and stick-slip. There were strong indications of reduced shear wave amplitude, both under stable sliding, and during stickslip events, with build-up of amplitude when ‘stuck’ and rapid reductions in amplitude just before and during slip. Figure 15.17 shows some key results. There was reportedly no change in velocity during the stick-slip process, which could help to explain why Vp/Vs reductions prior to some earthquakes are not necessarily reliable precursors for all cases.

The authors noted that the reduced shear-wave amplitude was probably associated with reductions in (specific) shear stiffness of the joint or joints undergoing shear. As shown by Boitnott et al., 1992, and as also modelled with the ‘JRC-mobilized’ concept of the Barton-Bandis joint constitutive model (Barton, 1982: see Chapter 16), there is likely to be an ‘invisible’ shearing of micron-size, prior to measurable sliding events, which could be the reason for the precursory shearwave amplitude reduction noted by the authors. This reduction is registered before sliding is detected, and will logically occur before any dilation is registered, with the eventual mobilization of roughness in the ‘sliding-up’ phase, when peak strength is approached.

15.7.7

Shear-wave splitting at a geothermal field

Shear-wave splitting at one of the largest geothermal sites in the world, the Cerro Prieto Geothermal Field (CPGF), was described by González and Munguía, 2003. Data from both weak and strong-motion earthquakes was used, with seismic recording at about a dozen

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Rock quality, seismic velocity, attenuation and anisotropy

stations, in and surrounding the production zone of the CPGF. Eight of their seismic stations showed that the faster shear waves were polarized in a range of directions from N 14°W to N 17° E. At the four remaining stations the polarization trends were between N 25° E and N 67° E. For the entire area N-S was the best average. Surprisingly, in view of the need for joint connectivity at a geothermal site, the authors followed the EDA convention, and assumed that it was microcracking that caused most of the shear-wave splitting. So when there was variation, they assumed that variation of stress direction was responsible, rather than for instance variation of sheared conjugate joint set directions. One of the areas of deviation corresponded to the epicentre of a swarm of seismic activity, which would also have suggested shearing of larger structural features. In the production zone of the field, the widest spread of orientation (up to 90° variation according to their equal area rose diagrams), and trending to the west, was actually registered, suggesting to the writer something that might resemble conjugate joint shearing, as illustrated in Figure 15.2. Good connectivity in a production zone, satisfying a ‘constant’ N-S average maximum stress direction, can readily be provided by conjugate jointing, preferably with some non-planarity if high permeability is to be generated due to slight dilation. See the extensive discussion of this topic in Chapter 16.

15.7.8

Shear wave splitting during after-shocks of the Chi-Chi earthquake in Taiwan

Before concentrating on reservoir measurements, it is useful to record the following earthquake after-shock monitoring result from Taiwan. Seismic velocity and Qseis anisotropy were recorded in the case of near-surface monitoring of after-shocks, following the destructive Chi-Chi earthquake in Taiwan, in 1999. Seismograms recorded at a 200 m deep station gave clear indication of upgoing split shear-waves with fast and slow components, indicating 8% velocity anisotropy below the top 200 m. The authors Liu et al., 2005, estimated Qseis values in the 2–15 Hz frequency band, and found values of 61 to 68 in the fast direction, and 43–52 in the slow direction. As commented upon many times, such values closely resemble possible deformation moduli (M, expressed in GPa), which can be readily estimated by the jointproperty-based rock mass quality Q. (M
10 Qc1/3, see Figure 15.33.) If the rock quality immediately below the

200 m recording depth (that was assumed to have caused the shear wave splitting), was actually poor, resemblance to dynamic moduli of deformation (expressed in GPa) would be a more appropriate suggested approximation. The authors cited microcrack alignment and their response to in situ stress as the reason for the anisotropy. However, based on the scale-dependence of dispersion seen in recent dynamic poroelastic matrix-with-fractures modelling, reviewed later in this chapter, it would seem that the anisotropy is more likely to be caused by preferential sub-vertical joint set anisotropy, which gives anisotropy at the low seismic frequencies, as opposed to microcrack anisotropy that is dominant from 1 kHz. At higher frequencies, there is insufficient time in each cycle of wave motion to allow significant movement of fluid, giving a relatively unrelaxed state with less attenuation, as we shall see in the model of Chapman, 2003.

15.7.9

Shear-wave splitting under the Mid-Atlantic Ridge

An interesting combination of shear-wave splitting analysis from local earthquakes, and P-wave anisotropy measurement with controlled sources, was used by Barclay and Toomey, 2003, to interpret the anisotropy at a 35° N sector of the Mid-Atlantic Ridge, under an ocean depth mostly in excess of 2 km. The anisotropy was attributed to a shallow distribution of vertical, fluid-filled cracks, aligned parallel to the trend of the axial valley. (Figure 15.18a). The vertical cracks give rise to so-called hexagonal anisotropy, with a horizontal symmetry axis normal to the crack planes. Most of the shear wave delay was attributed to the shallowest 500 m (seismic layer 2A: see Chapter 11). Here the shear-wave anisotropy was from 8 to 30% in this highly fissured layer. The authors considered that isolated fluid-filled cracks at depths from 500 m to 3 km were too tight to be detected by the P-wave portion of their survey, but may have contributed to the shear-wave delays. The authors’ analyses were restricted to shearwaves arriving within the shear-wave window (0° to sin1 Vp/Vs). The average value of Vp/Vs was given as 2.9 for seismic layer 2A (the shallowest 400 m). The authors reported that the time delays ranged from 35 to 180 ms, with an average delay of 90 ms. This was reportedly similar to other studies with microearthquakes (e.g. 100–300 ms in Iceland, 100–230 ms in Hawaii, 10–125 ms at the San Andreas Fault). The axial valley floor was reportedly heavily fractured and

Shear wave splitting in fractured reservoirs and resulting from earthquakes

437

Figure 15.18 (a) Bathymetric contours along a Mid-Atlantic Ridge axial valley at 35°N, showing rose diagrams of the fast polarizations. Each rose histogram has been normalized to the size of its most populated (azimuthal) bin. Solid circles denote the 65 earthquakes. Squares denote the six OBS instruments, which were spaced 4 km apart, covering an area of approximately 18 10 km. (1830 air gun shots were recorded during the first day, followed by micro-earthquake recording for 43 days.) Fault scarp (lineations) are also shown. (b) Examples of the three-component seismograms before and after rotation to the fast and slow directions. (c) Selected examples of shear-wave splitting in horizontal particle motions, with sampling points every 7.81 ms. The open circles are the origins. Each trace is 203 ms long. Selected from Barclay and Toomey, 2003.

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Rock quality, seismic velocity, attenuation and anisotropy

fissured, and also had faults with strike in the assumed maximum stress direction. The focal depths of the micro-earthquakes were limited to 3–4 km, and the authors emphasised that resolution of depth-dependent structure was not possible, but they suspected shallow structure, based on evidence from the shallow concentration of P-wave anisotropy, which reportedly decreased from 4% at 500 m depth to zero below 1.5 km depth. (P-wave anisotropy was defined as 100  (Vp max  Vp min)/Vp average, whereas, following Crampin, 1989, S-wave anisotropy was defined as 100  (Vs max  Vs min)/Vs max). 15.8

Recent cases of shear wave splitting in petroleum reservoirs

Detection of fracturing by long wave-length seismic waves, where vertical wells have given a limited sampling of the possible vertical or sub-vertical structure, is seemingly a constantly developing field. The economic pressure for discovery of new fields, perhaps more heterogeneous than their predecessors, and with less favourable matrix permeabilities, is focussing increased attention on fracture definition and understanding. It is also assuming growing importance as so many fields are in a mature phase and need production assistance, with fracturing a key to maximizing the final recovery. Optimal early production strategies are also pressing for seismic monitoring assistance. In contrast to the above seismic studies that mostly relied on earthquakes as the natural source for their inversion to anisotropic properties, the hydrocarbonbearing regions are today, by their very nature, stable areas of commercial fluid accumulation. It may be possible to use ‘natural’ sources such as AE only later in the life of a compacting reservoir, such as Ekofisk or Valhall, where for instance, shearing has been detected. The type of dynamic source will depend on whether the reservoir is on land or off-shore. On land it may range from explosives, to arrays of heavy trucks with vibrators, which can provide repeated P-wave or S-wave sources. Offshore, sub-sea-surface air-guns or explosives provide the P-wave source, with conversion to PS-waves at the sea-floor interface, and subsequent processing as S-waves. A recent application of the suction-anchor principle for sea-floor generation of S-waves (SS for emphasis compared to converted PS) is currently being tested in Norway (Westerdahl, 2005 priv. comm.).

Figure 15.19 Conversion of a P-wave source (from a sub-surface air-gun in water), to PS (converted) S-waves, showing the different reflected and transmitted angles. The converted waves reflect at sub-surface interfaces according to Snell’s Law. An S-wave always reflects more vertically than a P-wave because of its lower propagation velocity. This asymmetry complicates the acquisition and processing of converted-wave surveys. Barkved et al., 2004.

15.8.1

Some examples of S-wave and PS-wave acquisition methods

Barkved et al., 2004 discussed the significantly different demands of recording and processing S-waves (which give a fully three-dimensional wave field), and the simpler recording, and processing of P-waves. The ‘graphics’ of conversion of P-waves generated by the typical sub-surface, or sub-sea explosive or air-gun source, to S-waves, was previously shown in Chapter 14 (Figure 14.27). In Figure 15.19, the different angles subtended at an interface by the converted, reflected S-wave, and by the converted, transmitted S-wave are emphasised. The particle motion perpendicular to the wave propagation direction for the case of the converted (PS) S-waves, means that they are constrained to the plane of reflection, and in the figure, would have particle motion in the plane of the page. Three-component sensors (one vertical, two horizontal) are required to record the fully three-dimensional S-wave field, with one horizontal component aligned in the direction of wave propagation. When combined with a hydrophone that is sensitive to fluid pressure changes, the (marine) acquisition system is referred to as four-component (4C) technology.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

439

Figure 15.21 Split shear waves S1 (or qS1) and S2 (or qS2 ) from polarization, due to stress aligned fracturing. The three-component wave fields were generated by far-offset (60° or 120°) P-waves. Stenin et al., 2002.

Figure 15.20 Schematic of walk-away VSP, showing the shear wave splitting phenomenon as polarization occurs in an anisotropic zone, caused by sub-vertical fractures. It also indicates the increased time delay between the fast and slow qS1 and qS2 split shear waves, prior to their acquisition by three-dimensional or four-component sensors in the well. Slater, 1997.

On land the shear-wave source can be a direct S-wave (termed SS-wave, for distinction from converted PS). A useful representation of the subsequent shear-wave splitting principle, when for instance performing walkaway VSP with a shear-wave source, is illustrated in Figure 15.20, from Slater, 1997, whose Caucasan reservoir analyses will be reviewed later.

Variable azimuth VSP studies were described by Stenin et al., 2002, who analysed the converted PS-wave threecomponent wavefields, in order to detect and characterize the fractured intervals in the Archangelsk region of Western Russia. They used far-offset shot points, for generating P-waves, subsequently converted to PS waves as illustrated in Figure 15.21, as a supplement to conventional VSP with variable azimuth sources. The two P-wave sources with 120° or 60° separation are shown in the figure. Converted components PS1 and PS2, and qS1 and qS2 polarized waves, caused by the assumed stress aligned fracturing are also shown. The velocity anisotropy of Vs max and Vs min caused by the oriented fracturing, and by higher compression in the interpreted stress-parallel direction, is also indicated. They reportedly confirmed their seismic anisotropy analyses with core data from offset wells that could sample the fracturing. Horne, 2003, emphasised the additional advantages of walk-around VSP, (a circular path of multiple sources at fixed offset) shown in Figure 15.22a, for improved fracture definition. In this connection he pointed out that an incident P-wave, when converted to a PS wave that passes through a plane of (horizontal) symmetry, such as that caused by a vertical set of fractures, will

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Rock quality, seismic velocity, attenuation and anisotropy

15.8.2

(a)

(b)

Figure 15.22 (a) Walkaround VSP with (b) polarity reversal for converted PS waves as they pass at different angles in relation to strike, through a plane of symmetry. Horne, 2003.

show polarity reversal when incident on ‘either side’ of the fracture strike. This is illustrated in Figure 15.22b. In all the acquisition systems, the overburden is obviously involved in wave transmission, but has tended in the past to be ‘ignored’, in the sense of assuming a vertical symmetry axis, with no aligned fracturing. Tjaaland et al., 2001 emphasised that the overburden may also display anisotropy in the form of azimuthaldependent velocity. In traditional seismic processing the overburden was assumed to be isotropic and elastic. Due to the actual anisotropy of the overburden in relation to the assumptions, errors will be introduced when the seismic data are inverted to obtain reservoir parameters. They conducted synthetic modelling with realistic overburden anisotropy to compare results with the isotropic overburden assumption, and showed that travel times, and P- and S-wave velocities were each affected. If attenuation in the overburden was ignored in the analyses, the S-wave velocity could show errors of 20% or more.

Classification of fractured reservoirs

3D seismic surveys, using compressional waves to generate shear-wave reflections (converted PS-waves), as above, have found a very important role in the identification and characterization of fractured reservoirs. With shear-wave splitting and polarization due to the presence of the (relatively) compliant fracture properties, the detection of basic structural information such as fracture density, strike and (due to symmetries) dip, can be estimated, and as we shall see, some indications of both fluid-type and permeability may also be obtained. It is naturally believed that stress variations and orientations can also be determined, though here we have seen some variations and therefore suggested possible geomechanics reasons (shearing) for occasional diversion from this assumption. These will be detailed more in Chapter 16. Such deviations from the major stress direction would be caused by prior deformation along the more conducting, larger-scale features, or by today’s (or yesterday’s) water-flood treatments. The shear-wave splitting component from two sets of fractures that lie on either side of the major stress direction is clearly another reason for apparent deviation from H max, if (or because) one of the sets dominates. Presumably we should also be open to the possibility that if the fracture or joint set stiffnesses differ, then the effect of a basic crack density difference between the sets could be compromised, i.e. altered to a degree. Nelson, 1985, 2001 suggested a fractured reservoir classification that considered the dual contribution of both the matrix and the fractures on the porosity and the permeability. The total porosity was composed of the relative amounts of matrix and fracture porosity, and the relative levels of permeability were caused by the matrix and the fracturing combined. This simple scheme is shown in Figure 15.23. Type I reservoirs are heterogeneous and anisotropic, where fractures dominate in terms of both porosity and permeability. In Types II and III more reserves are stored in the matrix, but fractures control in Type II, and assist in Type III. In Type IV reservoirs, fractures still cause anisotropy and can even create barriers, and they are assumed to provide no additional porosity or permeability. Nelson 2001 suggested that unproductive wells are often a result of not recognising the significance of fractures, or joints, early in the development of a field. When wells were drilled based on the assumption of evenly distributed, matrix-controlled production (a

Shear wave splitting in fractured reservoirs and resulting from earthquakes

441

Figure 15.23 Fractured reservoir classification of Nelson, 2001, based on the relative contributions of matrix and fracture porosity and permeability, to the overall permeability and productivity of the reservoir.

form of ‘fracture denial’), it was presumably inevitable that the term ‘bright-spot’ would be the fore-runner to full-blow fracture appreciation. Laubach et al., 2000 proposed a fractal-based solution to the remarkable fact, that despite the growing interest in fractured reservoirs, seemingly worldwide, the wells are always vertical and the target structures probably vertical too (see also Ch. 14). As a consequence, cores and well-logs often give little or no useful information about the fractures. (A fortunate exception is the conjugate fracturing found in anticlinal structures, where samples of both the oppositely-dipping joint sets can hardly be avoided.) The authors referred to the use of sidewall cores to help pin-point zones having high fracture intensity; not by reaching out to the poorly sampled fractures, but by using microfracture and diagenesis data to infer the presence of the macro-fractures. Figure 15.24 shows a comparison of the very consistent microfracture strikes (nearly EW), compared with the broader but consistent orientations of macrofractures both from the same well and from the same formation combined as one data set. One may speculate both about the probable orientation of the maximum horizontal stress, and about the possibility that the ‘symmetric’ range of strikes for the macrofractures means they are conjugate joints and possibly sheared features, perhaps with extra good conductivity as a result (see Chapter 16). Also shown in Figure 15.24 is the fractal (up-scaling similarity) trend of spacing and aperture. According to the authors: ‘Microfracture proxies for large fractures are the surrogates that can provide complete, reliable, bed-bybed evidence of fracture attributes.’ The authors found that in many rocks there was a diagenesis event contemporaneous with the fracture development. The large aperture fractures in their experience, had mineral bridges and

Figure 15.24 (a) East Texas well data for microfracture orientations, with comparison to the (symmetric) spread of macrofractures from the same well and local formation. (b) Scaling patterns for aperture and spacing of microfractures through to macrofractures. Laubach et al., 2000.

abundant preserved porosity. This meant that the cements did not fill the large fractures, but those below a certain characteristic size were completely filled. These were the target for side-wall cores due to their abundance. Intermediate size fractures (the emergent threshold) were those filled-to-partly open, and by the nature of Figure 15.24b were less frequent. They termed the original apertures kinematic apertures. Cases subsequently sealed were suffering from clogging by post-kinematic cement. Further observations on the subject of ‘open’ fracture orientations were also made by Laubach et al., 2002. They cited comparisons of measured stress directions and orientations of open, flow-controlling fractures. These showed that open fractures in the sub-surface were not necessarily parallel to maximum compressive stress

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Rock quality, seismic velocity, attenuation and anisotropy

(H max). Fractures perpendicular to this direction could also be ‘open’ if partially filled with mineral synkinematic, or post-kinematic cements. They emphasised that sealed fractures parallel to H max were numerous. It was suggested, from experiences in both compressional and extensional provinces, with production data ranging from 2,400 to 6,400 m depth, that the divergence between H max and ‘open’ fractures demonstrably contributing to flow, was ‘from a few degrees to 90 degrees’.

15.8.3

Crack density and shearing of conjugate sets at Ekofisk might enhance splitting

In earlier parts of this chapter concerning shear-wave splitting, the approximate rule-of-thumb relation between crack density and shear wave anisotropy was quoted from the paper ‘Arguments for EDA’, by Crampin, 1993a. Crampin addressed the meaning of the typical 1% to 5% differential shear-wave anisotropy, reportedly measured in a wide range of rock types. He considered that the 1% to 5% was also equivalent to the generally limited range of effective crack densities, which he assumed were usually in the range 0.01  e  0.05. Crampin noted that the percentage of differential shear wave anisotropy was usually about e  100, for a Vp/Vs ratio of about 1.7 (1.732 was quoted). One may speculate whether these apparently lower crack densities implied by many earthquake studies, are a direct reflection of the sampling of ‘average rock’ (mostly imprinted on the shear-waves closer to the surface), and logically derived from low seismic Q and seismicity-prone provinces (see Chapter 10). In contrast, crack densities interpreted in fractured reservoirs from split shear-wave data, may represent a ‘biased sample’, i.e. may be caused by a rock mass that is more jointed or fractured than the norm at this depth. In connection with near-surface crack density influences, it is of interest to note the common experience referred to by Crampin, 1993a for relatively large time delays between split shear-waves to be set up in the top tens to hundreds of meters. The variations that can occur near the surface have been termed natural directivity or ND. To an engineering geologist, this phenomenon would probably imply increased occurrence of jointing, and to a rock mechanic with some geophysics interpretation added, the larger time delays would also be expected to be related to the reducing normal and shear stiffnesses of the near-surface jointing. Neither profession, it is suggested,

would be thinking of changes in the frequency of microcracks in the top tens to hundreds of meters. A common experience is also that the near-surface joint orientations do reflect the major horizontal stress direction, and consistency with permeability tensor principal directions may also be expected, as demonstrated by 3D hydrotomography by Quadros et al., 1999. A convenient example of much higher crack densities (e  N.a3/V) than apparently detected in the earthquake studies of Crampin and others will be given here, to introduce the alternative viewpoint that crack density may be more appropriately applied to describe the frequency of jointing or fractures that typically compose the fluid-bearing, tangible, visible structure making up the fractured reservoir, as opposed to a focus on microcracks. Following Leary et al., 1990, that a given number of crack populations Ni of radii ai, will give a total crack density that is the sum of the densities ei, we can consider the crack density for producing parts of the Ekofisk reservoir in the North Sea. Phillips Petroleum geologist’s core logging (H. Farrell, pers. comm. 1985), of conjugate steeply-dipping jointing in the porous, highly productive sections of the reservoir, indicated about 10 to 12 dominant (1 m long) set no. 1 joints crossing a ‘1 m window’, with oppositely dipping set no. 2 joints showing about 4 to 6 shorter joints (30–50 cm) in this same volume. In this very real case, with obviously the desirable fluid flowing towards the producing wells, we can estimate a much larger crack density than apparently suggested by earthquake studies (reportedly 0.015–0.045, Crampin, 1993a). A mid-range (2D) representation of the above joint description could be estimated roughly as follows:

∑ e  e1  e 2




11  0.53  5  0.23
1.4 1.0

The rock mass depicted in 2D in both Figures 15.7 and 15.25, is far from ‘intact’, but it tolerated an original effective vertical stress of the order of v

62  48  14 MPa, with a lower effective horizontal stress. During the first 20 years of production this effective vertical stress had built up to about 38 MPa, due to the 24 MPa pore pressure reduction prior to large-scale waterflooding (which was followed by 6 m jack-up of all platforms, and final relocation of central platforms). In a sense the ‘fragmentation’ worries of Crampin at high crack densities was seemingly being demonstrated, but in fact it was the matrix pore-space that was collapsing in the highest porosity chalks, supplemented by a shearing mechanism.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

(a)

(b)

Figure 15.25 (a) A UDEC-BB model of a compacting, conjugately-jointed 1  1 m ‘element’ of the Ekofisk chalk, which has a depicted crack density of the order of 1.4. The modelled compaction of this idealized high-porosity ‘element’ of the reservoir was 4.8%. (b) Joint shearing (shown proportional to line thickness) was modifying the compaction in relation to that of an unjointed porous matrix. M. Christianson UDEC-BB modelling: Barton et al., 1986, 1988.

When discretely modelled (as in Figure 15.25), the pore pressure reduction (in 1985) was limited to 20 MPa. A corresponding increase of the minimum horizontal effective stress, plus deformation effects, means that the

443

highly jointed rock mass was well confined. It would be correctly described as interlocked rather than ‘fragmented’, and it is clearly an exceptionally good reservoir rock mass regarding fluid-flow, with planned production possibly to 2050, an 80-year reward to Phillips Petroleum, for not abandoning the North Sea, due to the promising result of their final drillhole, when exploratory drilling in the late 1960s. Domal carbonate or chalk reservoirs of high porosity, with steeply dipping, as opposed to flat-lying jointing, can apparently be successful producers because of a remarkable joint shearing mechanism, despite the onedimensional (vertical) strain constraint. Matrix shrinkage under the large increase of effective stress, ‘makes space’ for down-dip joint shearing. The latter helps to maintain joint aperture due to shear-induced dilation, and apparently may even provide a pseudo-confinement effect (increased ko: ratio of horizontal to vertical stress), which would make the jointed reservoir somewhat stiffer (in a vertical direction), than the unjointed rock (Barton et al., 1985, 1986). Significantly, in view of the fact that our shearing theories were not at first believed, Albright et al., 1994 mention Ekofisk exhibiting ‘shear fracture microseismicity, possibly indicating that subsidence is caused by a combination of pore collapse and shear sliding’. They state that subsidence surpassed early model estimates based on pore collapse, indicating other mechanisms at work. By implication shearing was also occurring at fault scale. (See further discussion of this shearing mechanism at joint, or fracture scale, in Chapter 16.) In this connection one should refer to possible doubt concerning the use of laboratory 1D-compaction data for modelling pore-collapse versus porosity. One should recall that the modelling of compaction applies to some 30 km3 of reservoir chalk, about twelve orders of magnitude larger than the laboratory samples. Some level of scale effect may be present in the matrix, as certainly found for the case of joint strength, though with strongly reduced scale effect at high effective stress levels. The relative contributions of the matrix and the joints (and faults) to the over-all compaction is therefore inevitably uncertain where such large volumes are involved. The operator’s core-logging geologists reportedly detected slickensides on conjugate joint sets, when drilling new holes during the 1980s for pressure maintenance, using equilibrated sea-water injection. Slickensides had reportedly not been detected in earlier characterization of the Ekofisk field in the late 1960s, where production started in 1971. The most porous chalk (n  40%) that was first modelled by the NGI team in 1985, with a modulus of only

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Rock quality, seismic velocity, attenuation and anisotropy

0.33 GPa, showed maximum shearing of 3.9 mm, with an average of approximately 0.39 mm for all the joints. Later modelling by Gutierrez, with a higher pore pressure reduction of 24 MPa, showed up to 10 mm maximum joint shear. Presumably such deforming features would be seismically visible in practice (i.e. a strong source of shear wave splitting), just as the reproduced direct shear tests on rough fractures (Barton, 1973) shown in Figure 15.26 are ‘visible’, due to the dilation that is caused. Water flooding may have stimulated this shearing mechanism due to intuitive, preferential weakening at highly stressed joint-wall contacts, prior to watersoftening of the less permeable matrix. (Barton, 2002b). However, the Ekofisk rock mass does not ‘fragment’ or suffer ‘dispersion’ of pore fluid because of high crack density, although the weakening effect of the water is tending to cause ‘rubble-isation’ of the matrixplus-joints, but this is outside the scenario envisaged by Crampin, 1993a. The oil undoubtedly flows more easily towards the producing wells in response to the compaction drive and due to the originally well-developed crack-density-determined connectivity and resulting permeability. Loss of matrix (and joint) strength due to water-saturation, gives an additional production effect. The authors Saenger and Shapiro, 2002 used an explicit finite difference scheme to model elastic waves in their variously ‘cracked’ models. Interestingly, considering the above independently estimated crack density e  1.4 for the Ekofisk conjugate jointing, derived by the writer from a geologist’s description of the jointing, is the fact that Saenger and Shapiro find a value of e  1.43 to represent the critical crack density. They liken this level of crack density to a medium with ‘only finite sized pieces of solid, and there is no continuum through which an elastic wave can propagate’. To one from a different background (rock mechanics), this would almost seem like an unintended definition of the typical near-surface jointed rock masses through which we are frequently performing seismic refraction, core drilling, and driving tunnels, with frequent need for rock support. From another chalk reservoir, in Texas, relative levels of shear-wave anisotropy detected by VSP above the Austin Chalk reportedly correlated with production (Crampin, 1993a), as one would certainly expect at Ekofisk. A tendency for near-surface layers to reflect this same anisotropy was also noted for the Austin Chalk. Dimming of the amplitudes of the slow shear-wave, (due to greater attenuation i.e. lower Qseis), correlated with fractured zones, which were verified by horizontal drilling. The detection of the fractured zones was vital for good

production, due to the low matrix permeability of the respective chalks, despite their high porosity. Leary et al., 1990 referred to exceptional 2.44 km/s and 1.83 km/s fast and slow shear-wave velocities interpreted parallel and perpendicular to the inferred alignment of fractures, in an oil-bearing stratum in the same Austin chalk. The shear-wave velocity anisotropy reported by

Figure 15.26 Reconstruction of the measured shear-dilation path from direct shear tests of rough tension fractures. n 2 and n 6 depict stress level. Barton, 1973a.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

Johnston, 1986 of about 30%, would have implied a crack density of the order of 0.3, based on the Crampin ‘100e’ relation, which presumably requires modification if there are more than one joint or fracture set contributing to the crack density. The ratio Vp/Vs , and the relative levels of compliance of the contributing joints (not directly mentioned by Crampin due to microcrack focus), will also alter this ‘100x’ relation. If the crack density is contributed to by two sets of oppositely dipping conjugate joints, then following Sayers, 2002b, we can expect both shear and normal compliance contributions (from both sets), to the slowness of the slow shear-wave, and presumably therefore a lesser need for an extreme (interpreted) crack density to ‘explain’ a high value of shear-wave anisotropy. 15.8.4

Links between shear wave anisotropy and permeability

445

Horne et al., 1997 described each anisotropic zone using three parameters: the crack density, the aspect ratio and the crack content, and a variety of advanced operations which we need not be concerned with in this simplified review. The authors’ results supported earlier studies that also concluded that the observed anisotropy at the CBTF well was likely to be due to a sub-vertical fracture set dipping approximately 18° (to the SE). They showed that the fracture dip could be obtained from the shear-wave anisotropy when using opposite-azimuth VSP. The authors’ representation of the velocity anisotropy structures of qP, qS1 and qS2 wave forms for the case of vertical cracks (or joints) and 20° dipping cracks (or joints) is shown in Figure 15.28. In this last case reviewed we saw how the use of opposed-azimuth VSP could be used to interpret the dip

Horne et al., 1997, presented what they term ‘a global optimization’ to address the problem of ray-tracing, to invert the observations of shear-wave splitting from two ‘near-offset’ VSP data sets, in which two sources were employed along diametrically opposite azimuths, about the wellhead. Their shear-wave splitting analyses were based on shallow depth VSP and logging data for the Conoco Borehole Test Facility (CBTF), where an 18-layers interpretation of velocities, densities and thicknesses was in use by researchers. This layered model was split into five anisotropic zones that corresponded to the observed discontinuities in the shear-wave splitting estimates, as obtained from the diametrically opposed VSP surveys. Figure 15.27 shows the basic elements of the velocity density model, and the five selected zones.

Figure 15.27 The velocity and density model for the CBTF well. Five anisotropic zones were identified from the shear-wave splitting analysis. Horne et al., 1997.

Figure 15.28 A comparison of anisotropic velocity components, if vertical (left) or 20° dipping cracks (right). Lower plots show time delay variations over a hemisphere of propagation directions. Horne et al., 1997.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.29 Azimuthal connection is indicated between the degree of seismic anisotropy (‘birefringence’) and the permeability. Several anisotropic domains are indicated. (Horne and MacBeth, 1996, as reproduced in MacBeth and Li, 1999.)

of fracture sets or joint sets. The more usual application of shear wave splitting is to determine the azimuth. Figure 15.29, again from the Conoco test site, shows the Horne and MacBeth, 1996, linkage between seismic anisotropy (quite often termed birefringence) and the recorded permeability. We will recall that there were five domains (or zones) of anisotropic wave-splitting at this site. MacBeth and Li, 1999 also emphasised that the relationship between the stress field and a fracture model may require investigation from case to case. It appears that the hydraulically connected fractures may be those most readily detected, which implies that the link between permeability and anisotropy is being detected also. However, the generally assumed influence of a nearly parallel major horizontal stress, and therefore minimum normal stress must be assessed carefully, as we shall see in Chapter 16. It may follow present convention in shallow wells, while a (possibly conjugate) shearing mechanism may be needed at depth, unless rock strength, or partial mineralization ‘bridging’ are sufficient to keep fractures ‘open’, despite a significant effective normal stress. For vertical joints or fractures, the most pronounced anisotropy is registered when the source-receiver propagation paths are parallel and perpendicular to the strike

of the fractures. The response will be a complicated function of aspect ratio (which includes a normal stress component), fracture fill and/or porosity. A minimum of three source-receiver lines are capable of detecting fracture strike, if the particular set of fractures gives directional velocity variations in relation to the strength of other sets. The response is strongest when fractures are gas filled, as we shall also see later from a case record from Oman. In addition, a lower normal effective stress perpendicular to the major set of fractures will give a stronger velocity contrast. The gas to oil ratio in the reservoir is therefore an important component of the interpretation. The authors pointed out that the new generation of vertical cables, seabed seismic sensors and walk-away (and/or 3D) vertical seismic profiling was leading to highresolution anisotropy estimation, specifically in the offshore environment. The common goal was to detect this commercially important azimuthal anisotropy. If the alignment of fracture sets could be deduced, this would assist in the optimal lay-out of producing wells, and perhaps subsequent injection wells for water-drive. Azimuthal anisotropy detection techniques can help resolve both the large fault-scale structures, and the expected inter-block scale fracture (or joint) set structures. The advantage of this ability to interpret structure more fully, at several scales, can be envisaged in the complex stratigraphy shown in Figure 15.30. MacBeth and Li expressed the opinion that azimuthal anisotropy determination at fracture set scale, could fill the gaps between the fracture characterization from core, from borehole logs, from outcrop analogues, and that inferred from 3D seismic above complexly faulted and fractured reservoirs. The conceptual scale-dependency of fault throw magnitudes, after Yielding et al., 1992 and MacBeth and Li, 1999, is sketched in Figure 15.31. Interesting from a rock mechanics viewpoint was the suggestion by MacBeth and Li that ‘sub-vertical wave propagation through vertical fractures could provide direct knowledge of the conditions influencing tangential movement across the fracture faces’. They suggested that this could lead to discrimination between the solid or liquid content of the fractures, evaluation of porosity, and perhaps geometric aspects of the surface topography. One may speculate if the numerically modelled joint shearing shown earlier for an element of the Ekofisk jointing (Figure 15.25) could be seismically detected, likewise the rock-to-rock (R) and fluidbearing open (O) parts of shearing joints depicted in Figure 15.2b.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

447

Figure 15.30 A seismic interpretation that shows complex stratigraphic and structural relationships (London-Brabant Massif, North Sea). Seismic azimuthal anisotropy analysis offers potential for resolving major fracture set azimuths within the faulted blocks. MacBeth and Li, 1999.

Figure 15.31 MacBeth and Li, 1999 suggested that seismic anisotropy analysis could fill a gap between the fracture characterization from core and that from borehole logs and outcrop analogues, and that inferred from 3D seismic. From Yielding et al., 1992.

15.8.5

Polarization-stress alignment from shallow shear-wave splitting

Liu et al., 1993 had previously addressed shear-wave sources from the shallow (50 m deep) multi-azimuth, reversed VSP at the Conoco Borehole Test Facility, where earlier analyses had demonstrated that fracture parameters could be estimated from cross-hole, reversed VSP, and borehole data, as we saw in Chapter 14.

The authors found that the shear wave data could be interpreted as showing both velocity anisotropy (azimuthal variation in travel times), and attenuation anisotropy (azimuthal variation of amplitudes). The common central azimuth N70°E, which was also the strike of the dominant, steeply dipping macro- and microfractures, happened also to be the direction of maximum horizontal stress at shallow depth in the area. (Figure 15.32a, b and c). At this shallow near-surface location there was clearly excellent stress-fracture alignment, as expected. The nearby surface exposures suggested two approximately perpendicular fracture sets at the CBTF. Liu et al., 1993 managed to infer the multiple fracture sets using shear-wave polarization, with sufficient azimuthal coverage, in this case 160° of data. Their equal area polar projections show two maxima in approximately orthogonal directions, which almost exactly parallel the strikes of the two fracture sets. Figure 15.32a shows the outcrop jointing and Figure 15.32b the velocity structure. The target for these analyses was a fractured limestone from 16 to 29 m depth, sealed above and below by impermeable shales. Its velocity of about 4 km/s does indeed suggest well fractured rock (but a small velocity-depth gradient across this layer is perhaps likely). Reference to Figure 15.33, which reproduces key rock mass quality Qc-Vp-depth charts, suggest a rock quality in the range 2  Qc  4, when a porosity adjustment of presumably some few per cent is made. This typical jointed rock quality, could be ‘generated’ by a logical combination of e.g. RQD
45–90, Jn
9 (3 sets of joints; two sub-vertical, plus bedding), Jr
2 (smooth but undulating joints), Ja
2 (slight weathering), Jw
0.66 (wet, some water flow), SRF
2.5 (near

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

(c)

Figure 15.32 (a) Outcrop jointing, (b) assumed velocity structure, (c) polarization of shear-wave arrivals. Arrowheads show actual dominant fracture strike. Liu et al., 1993.

surface, some looseness in relation to greater depth). (See Appendix A for full Q-system rating tables.)

Q


45  90 2 0.66  
1.3  2.6 9 2 2.5

If the uniaxial strength of the limestone was e.g. 100 MPa, then Qc (Q  c/100) would be
1 to 3, which is mutually consistent with the measured velocity of about 4 km/s. A simple approach is to check along the ‘4 km/s diagonal’ in the simplified near-surface (nominal 25 m

Shear wave splitting in fractured reservoirs and resulting from earthquakes

449

(a)

(b)

(c)

Figure 15.33 (a) Rock mass quality Qc-Vp-depth gradients, (b) Qc-Vp-depth-porosity-modulus, (c) simplified Q-Vp-c chart (nominal 25 m depth). Based on Barton, 1995 and Barton, 2002a. Note: support pressure in b) refers to tunnels.

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Rock quality, seismic velocity, attenuation and anisotropy

depth) model shown in Figure 15.33c. Note that in the area of Q
2 to 3, the implied uniaxial compressive strength is around 100 MPa, which appears realistic for a limestone. If in reality the rock was closer to say chalk, then higher matrix porosity, lower uniaxial strength, and slightly less jointing than assumed above (giving a higher rock quality Q-value, could still be invoked to derive a suitable P-wave velocity of about 4 km/s. Great azimuthal consistency is shown by this Liu et al., 1993 data set, due perhaps to the shallow depth, which allows the ‘open’ joints or fractures to indeed follow the conventional concept with likely parallelism with the H max direction. As pointed out earlier, and analysed in more detail in Chapter 16, such parallelism may be compromised at reservoir depths in less competent rock than limestone, due to effective normal stress induced joint ‘closure’. A (conjugate) shearing mechanism might then be required for sufficient ‘openness’ of the conducting joints. Alternatively, suitable amounts of mineral filling for ‘bridging’ might be needed, neither too much ( sealing), nor too little ( stress-closure). A shear wave polarization component (from e.g. two similar conjugate joint sets) that was still roughly consistent with the  h max direction, might be assumed from much deeper sets of perpendicular break-out analysis, from caliper logs. But here there would be the possibility of a lot of ‘noise’ in the data, possibly from joint-induced break-out at other angles, more consistent with the possible conjugate, partly sheared (minor-faulted) jointing. In addition to this possible ‘anomaly’ in relation to conventional thinking, there is also the possible ‘rotation effect’ caused by the joint shearing per se, giving different orientation for the fluid-bearing (O) and stress-bearing (R) parts of a non-planar, shearing joint (Figure 15.2b). The above aspects will be addressed in more detail in Chapter 16, where important supporting case records will be found for the ‘shearing anomaly’. It is possible that parallelism of one conducting set of joints to h max is in fact the anomaly, when no longer close to the surface, in view of the stress-induced joint closure phenomenon, unless the reservoir rock is rather strong, like limestone, or a hard sandstone but not chalk, or poorly cemented sands, which would have sufficient matrix flow to make shear wave splitting a less relevant mechanism.

15.8.6

Shear-wave splitting in argillaceous rocks

In a doctorate study at the University of Edinburgh, Slater, 1997, also investigated if there was a relationship

between seismic anisotropy and productivity. He used VSP walk-away data that was shot at two North Caucasus oil fields. Due to the usual low permeability of clay rocks, hydrocarbon reservoirs in argillaceous rocks are not commercially viable unless they are strongly fractured. Prior to the commercial use of shear-wave splitting, primarily since the early 1990s, argillaceous reservoirs were reportedly found almost accidentally, while drilling towards prospects in other rock units. Slater, 1997 investigated the azimuthal anisotropy to check if the strong azimuthal variation in productivity was caused by variations in fracture intensity. In one of the reservoirs, walk-away VSP at two of the wells indicated velocities increasing as the direction of propagation moved away from the vertical direction. The reservoirs were in layered clays. In Figure 15.20, introducing the topic of shear wave splitting, a schematic of the walk-away VSP was shown, from Slater 1997. Shear wave splitting and polarization was occurring in the near-surface anisotropic zone, caused by sub-vertical fractures. Also indicated is the increased time delay between the fast and slow qS1 and qS2 split shear waves. Later in this chapter, we will see many more examples of these phenomena, and also see models capable of simulating the squirt-flow causes of dispersion or frequency dependence at different fracture-size scales. Slater, 1997, examined the typical transverse isotropy of the lower strata in these clay reservoirs, which display isotropy about a vertical axis of symmetry as shown in Figure 15.34. The VSP analyses demonstrated strong increases in velocity when the direction of propagation moved away from the vertical direction. The very low velocities calculated from VSP at wells 85 and 87 at one of the Caucasan oil fields are shown in Figure 15.35. The layered sandstones, limestones and clays, and the Maicop Clay, do not follow the rock quality Qc-depth-Vp trends shown elsewhere in this book, except in the top few hundred metres where azimuthal anisotropy indicates jointing that would tend to show closure with depth as in the Qc-Vp-depth model of Figure 15.33. Perhaps below this anisotropic zone, the change to clay, and the reported high pore pressures cause under-compaction, despite depth increase. A lack of fit with the writer’s Q-Vp-depth-soft-porosity model would then be logical, unless a correction for overpressure was made, and an ‘apparent depth’ estimated. An important finding from careful analysis of much earlier multi-offset VSP in the Paris sedimentary basin, indicated non-parallel shear wave polarizations at different azimuths and offsets. Polarization by sub-parallel cracks or fractures was not sufficient to explain these

Shear wave splitting in fractured reservoirs and resulting from earthquakes

Figure 15.34 Examples of transversely isotropic layering in argillaceous/clay reservoirs, where VSP analyses demonstrated strong increases in velocity when the direction of propagation moved away from the vertical direction. See Slater et al., 1993 and Slater, 1997, for details of the ‘anisotropic cuspidal phases’ discovered in these studies.

data, and Bush, 1990, demonstrated that the anomalous behaviour could be the result of a combination of matrix anisotropy due to layering (termed ‘azimuthal isotropy’, with vertical axis of symmetry, as in Figure 15.34), and crack anisotropy. A paper by Bush and Crampin, 1991, showed the consistency of this combination of mechanisms at five of the offsets. 15.8.7

Time-lapse application of shear-wave splitting over reservoirs

Reportedly the first time-lapse survey designed to measure possible changes in shear-wave splitting above a petroleum

451

reservoir, was reported by Roche et al., 1997. The Vacuum field is a fractured dolomite reservoir in New Mexico, and the survey was a repeated 3C (converted wave) survey, i.e. 3C  3C, or 9C survey. The argument was made that because the dolomite was quite hard it should be a poor candidate for conventional time-lapse studies, (i.e. its joints probably had high JCS or joint wall compression strengths, and perhaps high joint roughness JRC: see Chapter 16 for the influence of JCS and JRC on normal stiffnesses, the approximate inverse of dynamic compliance). The joint parameters used for pseudo-static estimation of both normal and shear stiffness (i.e. JRC and JCS), are relevant here due to the pseudo-static nature of the planned CO2 flooding, and its effect on the increased pore pressure and therefore reduced effective stresses. Before the CO2 injection, the distribution of the shearwave splitting anisotropy parameter () varied between /8%, but averaged about 4%. Note: () as given by Thomsen, 1986 is defined from the elastic stiffness matrix as (c44  c55)/2c55, where qS1  (c44/), and qS2  (c55/). After the injection of CO2, the pore pressure at the injector well increased from 10.6 to 17.0 MPa, giving a maximum Pp of 6.4 MPa. This was sufficient to give a P-wave velocity decrease of only 4%. The shear-wave anisotropy parameter () on the other hand changed by up to 14% (from 4% to 10%). These changes were successfully modelled by Angerer et al., 2001. The polarized fast and slow shearwave velocities did not rotate during these time-lapse changes, they apparently exchanged places. According to a review of Winterstein et al., 2001, including 23 wells in six locations in NW USA, and not specifically related to fractured reservoirs, shearwave splitting anisotropy as defined above, was commonly in the range 0    21%. The general trend of the anisotropy data suggested a certain consistency in one layer or domain, with an abrupt transition to different values. One could argue that such could be caused by sedimentary beds of different geological ages with differently oriented joint sets, and also by local stress rotation near fault zones. Some time-lapse surveys using P-waves, with its relatively more simply processed information, were described in Chapter 14. At the Ekofisk reservoir, the gas-cloud was seen in Figure 14.29 to obscure P-waves from a large portion of the central, and most porous part of the reservoir. In the context of the newer S-wave technology, Barkved et al., 2004 referred to the world’s first time-lapse, marine, multicomponent (3D/4C) survey, as that performed in September 2002 at the Ekofisk jointed-chalk reservoir

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.35 Very low shear wave and P-wave velocities at two wells, as interpreted from VSP. The geological description of the 0.75 km of overburden is also seen. There appears to be over-pressure in the Maikop Clays. Slater, 1997. Alternatively, the reduced sensitivity to effective stress may be due to low pore compressibility for the clays. Holt et al. 2005.

in the North Sea. This baseline was subsequently compared with a monitoring survey acquired in December 2003. In each case, seabed cables were used to acquire data with a wide range of azimuths. (Van Dok et al., 2004). With ‘only’ about 3 108 m3 of oil out of a total of about 1.1 109 m3 produced by 2003, and production expected to 2050, it is clear that the ‘belated’ application of shear-wave technology still has an important role to play. From each survey, converted PS-waves were analysed to determine the principal directions of fast and slow shear-waves. At every sensor location, recorded traces were binned (collected) into 10° azimuth sectors, and then stacked, giving 36 traces of each component at every receiver location. Even this limited time-lapse of 15 months indicated some small changes in the direction of the fast shear wave, and in the difference between fast and slow shear velocities. The differences were not consistent across the field.

According to Barkved et al., 2004 (with ‘Ekofiskauthor’ Van Dok as one of the co-authors), the reasons for the small changes detected by the S-waves ‘had yet to be understood’. The small-scale joint-shearing mechanism identified in distinct element (UDEC-BB) studies for the Norwegian Petroleum Directorate (Barton et al., 1985, 1986), that was discussed earlier, was later ‘confirmed’ by slickensided conjugate joint faces, in core recovered from subsequent wells (post 1985) for waterflooding and production. According to Phillips Petroleum Co. geologists this slickensiding had not previously been noted, and nor was it noted in the older jointed cores made available to NGI for laboratory direct shear and coupled shearflow-temperature (CSFT) tests. The shear mechanism may seem surprising in view of the 1D-strain (‘rollerboundaries’) boundary condition, since a 9  14 km reservoir of 300 m thickness can hardly expand laterally

Shear wave splitting in fractured reservoirs and resulting from earthquakes

during compaction: this occurs more in the stretching, subsiding, overburden as ‘seen’ by shallow shear-wave splitting at Valhall, to be reviewed shortly. A possible explanation for the small changes of polarization direction and of shear-wave anisotropy at Ekofisk, can perhaps be found in the conjugate (or single) shear mechanism that was illustrated in Figure 15.2b. This mechanism was also invoked earlier in this chapter, as a possible explanation of a larger polarization rotation at the Cornwall hot dry rock geothermal project. With potential ‘opposite-rotation’ of fluid lenses and rock-torock contact areas (Barton, 2005), there could be subtle domination of effects from the primary relative to the secondary conjugate joint set, and if the ‘O-R’ mechanism can be detected by shear waves, and if the strike of the two conjugate sets is not equally oriented, then a small rotation could be explained. Variation about the field, with the ‘radially’ trending jointing and rotating principal stress (Figure 14.31) would easily explain variation of such trends. Others might quote EDA-(micro)-cracks and stress rotation as the possible cause. More subtle mechanisms may be at work, and additional complications in the neighbourhood of fault zones are almost inevitable. At the Valhall Field, quite close to Ekofisk, BP installed a permanent seabed cable array, covering 45 km2 area, to monitor changes using regularly repeated 3D multicomponent seismic surveys, to help determine the best reservoir drainage strategy. The plans for this installation were alluded to in Chapter 14. As is well known, and as will also be indirectly demonstrated in Chapter 16 using Barton-Bandis joint closure-permeability modelling, it is all too easy to produce too fast thereby prejudicing the permeability of the rock joints and fractures, close to producing wells, where pore pressure reduction may cause ‘too high’ effective normal stress on the producing fractures. A slower production helps to maintain the vital permeable routes through the reservoir, especially where matrix porosity is superior to its permeability. In such modelling, the joint-roughness-dependent conversion between mechanical aperture (following pore pressure-induced effective stress increase) and the conducting aperture, needs to be differentiated. Fortunately, the loss of mechanical aperture (E) occurs more rapidly than the loss of the smaller hydraulic aperture (e), as shown by Barton et al., 1985, Barton and Quadros, 1997. (See Chapter 16 for review of E  e data sets). A very interesting application of shear-wave splitting and polarization was described by Olofsson and Kommedal, 2002. They referred first to the significant

453

Figure 15.36 Shear-wave splitting and polarization results for the shallow overburden above the compacting Valhall reservoir. Lines show the qS1 direction, with their length corresponding to the qS1  qS2 time delay or ‘lag’. The ‘rotation’ presumably corresponds to the relative ‘visibility’ of sub-vertical (bedding-limited?) joints caused by ‘stretch’ in all directions. Olofsson and Kommedal, 2002, also Gaiser and Van Dok, 2003 and Barkved et al., 2004.

time delay of the slow shear wave in relation to the fast wave in the reservoir, where both the polarization directions, and the time delay correlated with the geological model of fracturing. In this particular paper they presented the first results of shear-wave splitting in the shallow overburden, indicating a remarkable, and very convincing match to the assumed ‘stretch’ of sub-vertical jointing caused by subsidence. (Mention of these mechanisms was made in Chapter 14, for the case of Ekofisk overburden velocity reduction). Figure 15.36 shows the result of their shallow overburden shear-wave polarization, with lines showing the qS1 direction, with their length corresponding to the qS2 time delay or ‘lag’. Barkved et al., 2004 also commented on the above near-surface Valhall result, and stated the following: ‘The actual mechanism causing the shallow shear-wave splitting is not known. Azimuthal anisotropy is usually associated with fracturing, stress or lithology. In this case the amount of anisotropy is small at the centre of the field, where the subsidence is largest, but the anisotropy is large on the flanks and small again farther from the centre. This strongly points to shear-wave splitting being sensitive to changes in stress or strain.’ By modelling changes of triaxial stress in (continuum) layers above similar compacting reservoirs, Herwanger and Horne, 2005 produced similar, but quite circular models of shear-wave polarization. The referred authors have not apparently focussed on intra-bed jointing as the likely source of the partial ‘squareness’ of some of the strongest anisotropy (i.e. the

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Rock quality, seismic velocity, attenuation and anisotropy

‘NNE-trending’ and longest lines). The depth giving this possible dominant ‘imprint’ to the polarization and velocity anisotropy is of course not known. Large-scale (axisymmetric, 10 km radius) distinct element modelling of the Ekofisk overburden response to modelled compaction, using numerous coarsely ‘bedded-jointedand-faulted (2D) UDEC models (Barton et al., 1985, 1986), showed distinct ‘joint’ opening and some ‘bedding’ shear in the overburden, due to the stretch caused by the subsidence. These effects worsened with increased compaction profiles, the subsidence/compaction S/C ratio exceeding 0.85 as compaction approached 10 m. A 3D version of such discontinuum modelling (with the 3DEC code, also developed by Cundall), would obviously have shown similar reactions from other perhaps perpendicular ‘joint’ sets. This ‘joint’ opening occurred most strongly where bending was strongest, and least both centrally and further out beyond the flanks. It is therefore suspected that the ‘stress or strain’ referred to by Barkved et al., 2004 could rather be termed intra-bed joint-opening effects, since the strength and location of these phenomena are likely to match the subsidence-bowl shape at Valhall. Where the polarization is ‘diagonal’, (i.e. ‘NE-SW’ or ‘NW-SE’ relative to the ‘N-S’ page), presumably the components to polarization (i.e. joint compliance) from both sets could be operating. (See also polarization at 300 m depth, in Barkved and Kristiansen, 2005.)

15.8.8

Temporal shear-wave splitting using AE from the Valhall cap-rock

An unusual petroleum reservoir case record concerning temporal variation of attenuation, was described by Carter and Kendall, 2005. This concerned the utilisation of micro-seismic events generated in the siltstone (above-shale?) caprock, above Norway’s Valhall jointed chalk reservoir, in rock at about 2 km depth. Subsidence, observable at the sea-floor (see previous review), caused this AE activity, which was recorded 300 to 500 m away, by a vertical string of six 3-component geophones, placed in an abandoned well near the crest of the anticlinal structure. Over a period of 56 days, continuous recording gave 572 events, 324 of which were located reliably (Dyer et al., 1999). Carter and Kendall performed shear-wave splitting analysis, comparing relative frequency content of the fast (qS1) and slow (qS2) shear waves. Their

Figure 15.37 (a) Temporal variation in minimum % anisotropy and b) temporal variation in differential attenuation, from shear wave splitting analysis using AE recorded in siltstone caprock, above the compacting Valhall jointed chalk reservoir. Carter and Kendall, 2005.

results were surprising in two ways: 1) that anisotropy appeared to be temporal, 2) that sometimes qS2 was richer in higher frequencies than qS1. These two unusual results are illustrated in Figures 15.37 and 15.38. The authors defined a differential attenuation, as the difference in energy loss per cycle experienced by qS1 and qS2. This approximates the 1/Qseis that a homogeneous constant Qseis material would require, in order to produce the observed difference in frequency content between qS1 and qS2. One may speculate that opening of sub-vertical, bedlimited jointing, with changing joint-wall contact character, could be responsible for such variation over time. According to Barkved and Kristiansen, 2005, sea floor subsidence at Valhall exceeds 5.4 m, approximating 0.25 m/year. The larger neighbouring Ekofisk field has suffered significantly larger subsidence, at an early rate of about 0.45 m per year when detected in the mid 1980s, and about 10 m of total compaction with large numbers of sometimes repeated casing damage, by the turn of the century. Since the shear-wave phenomena may be relying on vertical jointing, the question would be whether bed-slip could be affecting the successive opening and closing of bed-limited jointing. In the case of the Wilmington field, under Long Beach, California, a significant seismic event occurred, with a 20 cm presumed bed-slip, at one stage during more than 10 m of subsidence. Dussault, 2001 described the sand/shale interfaces above the Ekofisk reservoir as those most prone to causing casing damage, with episodic

Shear wave splitting in fractured reservoirs and resulting from earthquakes

455

Figure 15.38 Shear wave splitting analysed from AE events from siltstones in the Valhall field caprock. Event A exhibits the expected maximum attenuation of the slow wave S2. Event B exhibits maximum attenuation of the fast wave S1. Carter and Kendall, 2005.

microseismic stick-slip events close to the top of the reservoir. Perhaps these ongoing bed-slip events were influencing the steep or vertical bed-limited jointing, giving stimulus to qS1 to qS2 reversals. The phenomenon might possibly be related to the ‘90°-flips’ discussed earlier in this chapter, which were suspected by the writer as due to principal effective stress ‘flips’.

15.8.9

Shear-wave splitting and fluid identification at the Natih field

A series of interesting papers were published concerning a large scale 3D shear-wave experiment performed over the 1 km deep fractured carbonate (chalky limestones) Natih field in Oman. The structure of the field was described as ‘not very complex’ by Potters et al.,1999. The matrix permeability was a very low 1 to 30 mD. Hard shales overlie the 300 m of carbonates, and these Fiqa shales exhibited some interesting anomalies as we shall see. The fractures in the carbonates were nearly vertical (a detail that seems to be important if both shear and normal compliances are to be involved, following Sayers 2002b, reviewed earlier). However the authors of the two reports reviewed did not emphasise this aspect. Outcrop mapping included fractures too large to be generally detected by core or FMS analysis, meaning that vertical wells were the usual poor samplers of typical sub-vertical structure. The outcrop, of necessity 50 km distant, had joint character as shown in Figure 15.39a (scale not given by Van der Kolk et al., 2001), but possibly the same as the ‘1 m’ scale given for the reservoir in Figure 15.39b. The two fracture or joint sets had either

NE-SW strike (the dominant direction), or NW-SE strike. Note the consistent dip signs on both drawings, despite the ‘vertical or sub-vertical’ assumption. These dips, even if minimal, seem to be important for using shear waves to distinguish between gas and oil in the fractures, following Sayers, 2002b. Extensional and shear fractures were noted in each of the principal strike directions. The dominant NE-SW extensional set were continuous over hundreds of meters, and were responsible for the dominant permeability direction, as established by tracer tests. Along the crest of the shell-shaped 6  10 km antiform, which terminates at a major fault zone, the bed-curvature being increased, there was evidence of the NW-SE striking extensional set also participating in the fluid-flow network. The scope of the nine-component three-dimensional (9C3D) survey/experiment was impressive, with 10,800 3C geophones, up to 1000 vibrator positions per day, and 22 million traces recorded on 2,000 tapes during the 32 days, and 28 km2 of field work. The survey basic grid size was only 25  25 m. Shear-wave anisotropy exceeding 15% was registered over about half of the field. The average well flow rate in areas of large time delay was higher than that in areas with low S-wave anisotropy, but significantly the local fracture swarms giving individual wells high productivity were too small to be detected seismically. Potters et al., 1999 suggested that the absence of strong seismic anisotropy did not however preclude the presence of fractured zones. Recalling the earlier critique of fracture density in this chapter, it is encouraging to note the authors’ reference to the ‘well-known ambiguity that a given amount of shear anisotropy can be caused by an infinite number of combinations of fracture densities and sizes. Since different combinations have different rheological (and flow) properties, this

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

Figure 15.39 A partly contrasting, and partly consistent information from the surface exposure jointing (50 km distant), and from the 1 km deep reservoir jointing at the Natih chalky-limestone reservoir in Oman. This was the site of a large shear-wave experiment in 1991. Van der Kolk et al., 2001.

problem needs to be solved possibly by incorporating a theoretical or empirical fracture size distribution’. The latter sounds like a good solution, since the ubiquitous microcracks seemingly favoured by Crampin, do not seem to have utility in the face of the need (and existence) of the permeable fracture networks of interest especially to oil companies. The authors also addressed another uncertainty. ‘Flow is strongly influenced by fracture aperture, a property which is, at best, only weakly expressed in the reservoir’s mechanical properties’. Here we may interject a

possible future geomechanics-based solution, since the ‘mechanical properties’ referred to are in the case of shearwave anisotropy, a function of the dynamic shear stiffness (or compliance) for the case of vertical incident waves, and a function of both the shear and normal dynamic stiffnesses for the case of non-vertical waves (or non-vertical fractures), following e.g. Sayers, 2002b. As we shall indicate in Chapter 16, there are direct links between the rock mechanics of pseudo-static rock joint shear and normal stiffness behaviour, and their stress-aperture behaviour, both hydraulic and mechanical, with e  E. This is due to their common prediction by the Barton-Bandis constitutive laws, using joint characterization parameters JRC and JCS for wall roughness and wall strength respectively (Barton and Choubey, 1977, Bandis et al., 1981, 1983). In Chapter 16 we will indicate the common mismatch between the dynamic and static normal stiffnesses (roughly reflecting the differences between dynamic and static moduli), which are therefore roughly predictable. The dynamic shear stiffness (or compliance) sensed by the slow shear-wave in the case of vertical incidence and vertical fractures obviously also carries information of relevance to the stress-closureaperture-permeability behaviour of the dominant joints. By estimating the roughness parameter JRC from core or well-bore images, the (effective, confined) joint wall strength JCS could be estimated, which then allows estimation of the mechanical aperture at the given effective stress levels. Conversion to an estimate of hydraulic aperture is the final stage. Van der Kolk et al., 2001, concluded the series of articles by Shell and their collaborators in Oman concerning the Natih 3D shear-wave experiment, by presenting, reportedly for the first time, evidence that shear waves were sensitive to fluid type (gas or oil), in fractured or jointed media. Regions of gas were characterized by slow shear waves, and this had particular consequences for two phenomena described by the authors. Firstly, the shear-wave splitting map of the Natih reservoir exhibited much larger splitting values (i.e. anisotropy) over the gas cap on the reservoir. This increase in anisotropy was due to the decrease in the slow shearwave, which senses both the fractures and the fracture filling fluid. A second phenomenon was the shear-wave data from directly above the reservoir. The thick Fiqa shale also exhibited a low shear-wave velocity anomaly, but associated with a gas chimney. Van der Kolk et al., 2001 used a semi-dynamic effective medium model, to help to explain some of the

Shear wave splitting in fractured reservoirs and resulting from earthquakes

457

Figure 15.40 An effective medium BOSK model prediction of the shear-wave splitting magnitude for a set of 1 m long and 10 m long fractures, as a function of fracture porosity, i.e. directly related to aperture. Van der Kolk et al., 2001. Note splitting %  (Vs1  Vs2) Vs1  100.

observed phenomena at the Natih field. This model was based on a combination of the work of Budianski and O’Connell from the 1970s concerning the elastic moduli and visco-elastic properties of cracked fluidsaturated solids, together with extensions for arbitrary crack orientation statistics from Sayers and Kachanov in the 1990s. They termed the combined model the BOSK theory. With this model, ‘squirt’ losses were also accounted for between the pores and fractures. This model correctly predicted that the slow shear-waves, polarized perpendicular to the fractures, were more influenced by the fluid type occupying the fractures, than were the compressional-waves. (Classic Gassmann, 1951 theory anticipates a sharp reduction in the P-wave velocity in the presence of gas in porous media, and supposes that the S-wave velocity is relatively unaffected by the type of fluid). Figure 15.40 shows a BOSK model prediction of the degree of shear-wave splitting as a function of fracture porosity, for a fixed fracture density of 0.2 (where e  N a3/V). To avoid the ambiguity of e, discussed at length earlier in this chapter in connection with EDA, the authors specified reservoir-like fracture lengths of a) 1 m and b) 10 m in these two BOSK realizations. Note that there are subtle differences only where fracture porosity is extremely small. The fracture porosity at Natih was about 0.1%. It is noted that the BOSK model, as for many other effective medium models, (to be briefly reviewed soon), apparently makes no distinction between the mechanical (E  actual) assumed crack aperture and the hydraulic aperture (e). In jointed rock (E) actually controls stiffness and deformation moduli. In rock mechanics, we do not often use the crack aspect ratio. On the other hand, (e) controls the intrinsic permeability, given as (e)2/12, and both apertures (e and E) probably influence attenuation,

since they effectively define two different aspect ratios, therefore influencing the assumed squirt-flow losses and the assumed stiffness. The e  E inequality* is therefore a potential source of error for the case of effective medium modelling of roughwalled, tightly compressed (i.e. deeply buried) cracks, joints or fractures, when using only one aspect ratio. The crest of the Natih reservoir structure, with its higher (50% or more) shear-wave splitting had higher local fracture densities than the flanks, but this was not a sufficient reason for this higher value. Using the BOSK theory, van der Kolk et al., 2001 were able to investigate the effect of fluid viscosity (causing dispersive, frequencydependent behaviour). Figure 15.41a shows the modelled effect of gas replacing brine on the vertical P- and S-wave velocities, as a function of fracture density. The modelling results indicated that with a fracture porosity of 0.025%, the shear wave splitting was about 50% higher in gas-filled, compared to brine-filled fractures. With lower fracture densities than 0.15, the ‘classic

* The two joint apertures will frequently differ by a factor of about 2 to 5, most for higher roughness JRC, and highest normal stress level. This inequality was demonstrated at the Technical University of Trondheim. Heimli, 1972, used a pre-instrumented intact core, subsequently split axially, so that different experimentally set values of E  0.05, 0.1, 0.2 mm could be known with certainty. These were subsequently compared to the smaller hydraulic apertures (e) back-calculated from flow tests. The e  E inequality has since been confirmed many times, and is explained by wall roughness effects, eventually quantified by JRC. See Figures 16.6 and 16.7 in the next chapter. Data sets for (e) and (E) and an empirical JRC-based model are shown. (Barton, 1972, Barton et al., 1985, Barton and Quadros, 1997).

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.42 The ratio of seismic Qgas/Qbrine in modelled fractured media, using the BOSK model. Shear waves were much more attenuated than compressional waves by the introduction of gas. Van der Kolk et al., 2001.

Figure 15.41 (a) A BOSK effective medium prediction of the effect on vertical P- and S-wave velocities, of gas replacing brine. (Note Vs refers here to Vs2, the slow shear wave polarized perpendicular to the fractures.) Two sets of vertical fractures, in an isotropic, low porosity matrix were modelled, with a wide range of fracture densities. (b) P-wave and polarized S-wave surfaces for gas and brine filled fractures, showing the modelled influence of wave direction relative to two sets of vertical fractures. The fractures are oriented 45° to either side of these figure axes. Van der Kolk et al., 2001.

behaviour’ of P-waves more affected by fluid type than S-waves was seen. When P-waves crossed the fractures, rather than paralleling them, the predicted sensitivity to fluid type was found to be stronger in P-waves than S-waves, agreeing with the traditional behaviour.

The authors concluded that vertically moving P-waves, and the fast shear wave, were hardly affected by whether it was gas or brine in the fractures. It was the slow S-wave that was polarized perpendicular to the fractures that registered the fluid type, i.e. whether of low or high compressibility. The BOSK model was also used by van der Kolk et al., 2001 for studying the effect of frequency, and the relative effects on attenuation of gas or brine. The ratio of seismic Q for gas compared to the seismic Q for brine (Q gas/Q brine) indicated greater attenuation of the S-waves with the introduction of brine. This result is shown in Figure 15.42. The authors made some important and undoubtedly correct conclusions, which are nevertheless contrary to standard exploration practices, and will therefore be quoted in full: ‘Both the observations and the (BOSK) modelling suggest that the S2 shear-wave propagation depends on the fluid type in the fractures. For propagation parallel to and polarization perpendicular to the plane of the fractures, the observed effect is exactly opposite to what is predicted by Gassmann fluid substitution in a porous matrix. We can conclude therefore that Gassmann theory is not sufficient to model fluid replacement in (heavily) fractured media. (Matrix porosity effects must still be included in the calculations, of course). Many standard exploration practices are based on Gassmann substitution, e.g. direct hydrocarbon indicators (DHIs) such as bright spots, flat spots and sometimes AVO effects. The results obtained above suggest that these techniques may be invalid in fractured media and new extensions should be explored ’.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

(a)

(b)

Figure 15.43 (a) Rose diagram showing the consistent P-wave anisotropy directions in the reservoir (black) and the overburden (grey). (b) Differences in frequency between the fast and slow shear-waves, indicating a consistently lower frequency for the slow shear waves in the fractured reservoir from 5,800 to 6,200 feet. Maultzsch et al., 2005.

At the end of Chapter 14, an analysis of the Claire Field by Maultzsch et al., 2005 concerned P-wave attenuation anisotropy derived from analysis of field VSP data. In this case, with no gas cloud, the fractured reservoir displayed much stronger anisotropy than the overburden (Figure 15.43a), the authors drew attention to the advantages of using relative attenuation, rather than absolute attenuation. Their concept of relative attenuation

459

or 1/Qseis was derived from comparison of spectra recorded for different azimuths, but with identical source-receiver offsets. Absolute attenuation is typically recorded by comparison of spectra recorded along an individual ray path. The authors utilised the field measurements of travel time anisotropy, and were able to invert for fracture strike, fracture intensity (usually ambiguous), and scale length (presumably making the intensity formulation non-ambiguous). When attempting to measure the absolute values of attenuation with the traditional spectral ratio and the instant frequency method of Dasios et al., 2001, they found that the instantaneous frequencies of the events fluctuated strongly: the heterogeneous rock mass giving zones of apparent negative Qseis. The authors argued that since the fast and slow shear-waves had similar wave lengths, they therefore probably sampled the same heterogeneities. They therefore analysed the differences in the instantaneous frequencies of the two waves. Despite the scatter, the differences in the two sets of frequencies were consistent with their location in either the overburden or in the fractured reservoir. Figure 15.43b, showing these differences in instantaneous frequency, indicates increased attenuation of the slow shear wave, which had lower frequency in the reservoir layer (5,800 to 6,200 ft), but essentially the same frequencies in the overburden. One could perhaps speculate on another less dominant fracture direction in the overburden, in view of the mostly not quite zero differences in instantaneous frequencies.

15.9

Dual-porosity poro-elastic modelling of dispersion and fracture size effects

The ability to model various aspects of jointed rock behaviour has existed for many years, and is a complex and constantly expanding field. No attempt can therefore be made to give an exhaustive treatment in a single section of a single chapter. Since this section will address dual porosity poro-elastic modelling, with several examples, we will first summarize the different modelling needs and capabilities developed in rock mechanics, which is an increasingly close neighbour of geophysics, particularly in recent years when micro-deformation depending on joint stiffnesses, and micro-flow simulation depending on apertures, has become important for interpreting seismic response. It is probably fair to say that rock mechanics modelling advanced very far in the last several decades of the 20th

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Rock quality, seismic velocity, attenuation and anisotropy

century, for the dual reasons of rock engineering and civil engineering needs, and due to the relative accessibility of input data, specifically from drill core, shallow exploration adits, and extensive use of shallow refraction seismic, plus sampling from within tunnels during construction. This has been a ‘constant’ for many decades, although description (and use) of the joint properties has improved dramatically, with perhaps less isotropic continuum modelling than previously. In contrast, geophysics data acquisition abilities (and quantities of data) have exploded in just the last decade or two, with digital recording of increasingly complex 3D 4C receiver arrays, both on-land and especially off-shore. This development continues unabated. There is now an enormously increased need for realistic numerical models for geophysical interpretation, particularly in the area of structural anisotropy, fractures sizes and properties, and the frequency dependence of their seismic responses.

15.9.1

A brief survey of rock mechanics pseudo-static models of jointed rock

By way of an extremely brief history, one can mention the finite element modelling with joint elements that was developed at the end of the 1960s and promoted for rock engineering use by Goodman et al., 1968 and others. These authors, and Goodman, 1970 were perhaps the first to define the (pseudo-static) joint normal and shear stiffnesses needed for input to their 1D joint-slip elements for discontinuous finite element modelling. The deformation and stability of slopes, dam foundations and tunnels were the primary focus in rock engineering, and fluid flow and effective stress analyses were of course required too. These early 2D FEM models had deformable joint elements requiring linear estimates of normal and shear stiffness and of course frictional and eventual cohesive strength. Three dimensional FEM modelling, for example for dam-and-foundation interaction studies, with more limited numbers of (major) joint and fault planes was also performed during the 1970s and subsequently, but was obviously very time-consuming. In the early 1970s Cundall, 1971 developed a 2D finite difference distinct element model for randomly or regularly jointed rock masses, making it easier to model large assemblages of blocks, with the ability, if required, to follow large deformations by tracking edge and corner contacts. Initial rigid block calculations in DEC were

subsequently replaced by simply deformable, then fully deformable blocks in UDEC, with the ability to model dynamic loading, micro- or macro-deformations, and fluid flow within the joints, but not in the matrix, where only pore pressures were modelled. Here we see one of the limitations, which of course is no longer there when only modelling flow in (un-jointed) porous media. UDEC first had Mohr Coulomb linear joint strengths and linear stiffnesses, then a Cundall continuously yielding law, followed by non-linear shear strength and stress dependent shear and normal stiffnesses, following the block-size-sensitive Barton-Bandis constitutive model, in which most of the input data can be derived from simple index tests performed on drill-core, giving joint parameters JRC, JCS, and r. Block-size determined the scaling of these two joint roughness and compressive strength parameters, and the core-logged Q-value gave a stressdependent deformation modulus. As we have seen in Part I, (and in Figure 15.33) the P-wave velocity from shallow refraction seismic could be used to estimate the static deformation modulus, and to extrapolate or interpolate such data from borehole to borehole. This non-linear 2D model was termed UDEC-BB. Flow and fluid pressures were modelled by converting the physical joint apertures (E) developed at any time during the modelled joint deformation, into the (usually) smaller hydraulic apertures (e), using a linearlaminar flow assumption with joint permeability given by k  e2/12. The conversion between (E) and (e) was found to depend on roughness JRC (Figure 16.7). Subsequently 3DEC was developed by Cundall, together with colleagues at Itasca, giving the ability to model three-dimensional assemblages of jointed, deformable blocks, with any desired moduli and joint or fault properties. Linear strength and stiffness laws were followed for the joint sets and faults, to reduce calculation time. More recently, the pore space defined by the complex, three-dimensionally deforming, intersecting joint sets was fully defined, allowing flow modelling and dynamic effective stress modelling to be performed, also in three dimensions. Of course there are more dedicated 3D fracture flow models like FRACMAN (Dershowitz/ Golders) and NAPSAC (AEA Harwell), but these are lacking comprehensive joint deformation modelling. There are now several numerical models in use in rock mechanics for also modelling rock failure or cracking of the matrix blocks, caused by over-stress. These can accommodate a more limited number of pre-existing joints. Prominent among these are the particle flow codes

Shear wave splitting in fractured reservoirs and resulting from earthquakes

of Cundall (PFC2D and PFC3D), and the non-linear fracture mechanics code of Shen (FRACOD). The latter in particular, seems capable of realistic modelling of log-spiral type break-out around tunnels or boreholes, without recourse to ‘manual’ degradation of cohesion, and mobilization of friction, as needed when using an inappropriate ‘c  tan ’ formulation. This linear Mohr Coulomb law is acceptable, or at least much used, for particulate clays and sand modelling in soil mechanics, and is reasonable for pre-existing planar joints, though probably best for faults. It is incorrect for previously intact hard rock, where ‘c then tan ’ is a more correct formulation than ‘c  tan ’, due to the widely different strains involved in cohesive failure of a brittle material and subsequent frictional sliding along the failure surfaces. (See discussion by Barton, 2004b). 15.9.2

A very brief review of slipinterface, fracture network and poro-elastic crack models

Concerning the dynamic modelling of cracked rock in geophysics, we can quote Tod, 2002 who is a prominent new contributor to this field: ‘There are many theories available in the literature, resulting from a range of theoretical backgrounds that provide a description of an effective medium appropriate to describing the properties of a matrix material permeated with cracks on a length scale far less than the wavelength of seismic waves. While many of these theories agree qualitatively and are capable of describing a number of observed features, each has its particular shortcomings.’ For the modelling of cracks in geophysics, we will not go further back in history than to mention Schoenberg 1980, and Hudson, 1980. These classic developments assumed, for greater simplicity (there was enough mathematics without fluids), that there was no exchange of fluid, either between the fractures or cracks themselves, or between these and the rock matrix. The importance of fluid had of course been known for a long time, and was modelled within the pore space by Gassman 1951 and within the cracks by O’Connel and Budiansky, 1977, and by many others since then. Thomsen, 1995, showed how seismic anisotropy was enhanced by transfer of fluid between fractures and equant porosity, with perfect pressure equalization at very low frequency, and reduced equalization at higher frequencies, giving the ‘unrelaxed’ behaviour modes.

15.9.2.1

461

Schoenberg slip interface concept

Schoenberg 1980 modelled elastic wave behaviour using linear slip interfaces. These allow reflection, transmission, conversion, and delay to take place at the modelled interface, with the magnitudes depending on the specific stiffness, the frequency content, and the angle of incidence. The assumption is that when an elastic wave propagates across a fracture, there is a displacement discontinuity that is linearly related to the normal or shear force generated. The seismic particle displacement is discontinuous, while the seismic stresses are assumed to be continuous. In the linear slip model, the displacement discontinuity vector u was assumed to be linearly related to the traction t as follows:  ZT  u   0  0 

0 ZN 0

0 0 ZT

  t  

(15.7)

In geophysics it became customary to talk of fracture compliances, with inverted nomenclature and units (e.g. MPa/mm for stiffnesses, and m.Pa1 for compliances). Naturally, the compliances or stiffnesses used in geophysics refer to the dynamic properties of the joints or fractures, which generally have somewhat greater stiffness (or lower compliance) than the pseudo-static values commonly used in rock mechanics modelling. These differences have been mentioned many times, and will be quantified further in Chapter 16.

15.9.2.2

Hudson effective medium concept

Hudson, 1980, in contrast to Schoenberg, utilised a ‘method of smoothing’ for the effect of modelled cracks, which was capable of representing the elastic parameters of a ‘cracked’ material, in the form of an effective medium. This allowed calculation of the effect of incident dynamic waves of long wavelength. Subsequently, Hudson et al., 1996 extended the model to allow for the cracks to be connected via the porosity of a rock matrix. In this extended case, cracks could be deformed by an incident wave in a manner that depended on their aspect ratio and on their orientation with respect to the incident wave. Clearly the modelling of intrinsic attenuation mechanisms such as squirt flow, and its frequency dependence, was transformed by this extended capability.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.44 (a) Schematic of the pore space created by the misfit of (sand) particles, (b) a possible distribution of cracks that are subject to a sub-parallel stress, c) oblique cracks in a fault zone applied in a new model. Tod, 2002, and Tod et al., 2002.

15.9.2.3

Tod crack density decay model

Tod et al., 2002, extended this model further, by allowing for a continuous but independent distribution of both crack orientation and aspect ratios, and by allowing each to depend on the applied stress and on the fluid pressure. At high frequencies, the cracks behaved, as

expected, as isolated (stiff ) features, while at low frequencies they behaved as ‘poorly-drained’, since squirt losses at lower frequencies cause a ‘soft’ behaviour because of some (micro) drainage. The model developed by Tod effectively allows the crack density to decay with an increase in applied stress, from an initial value representing the unstressed state. However, the model is purely elastic, and relaxes to its original state during unloading. Crack density was designed to decrease with increasing compressive stress, from e.g. 0.1 at zero effective stress to e.g. 0.05 at 200 MPa. Only cracks with normals lying in the h minimum direction were assumed to remain open. The model is capable of capturing the changed anisotropy caused by fluid pressures and applied stresses, which impact the aspect ratios of the cracks. However the pore space, illustrated in Figure 15.44a is non-compliant. Wave speeds approach that of the matrix at high pressures. Shear waves proved to be more sensitive to pressure change than the compressional waves, as known from other studies. The non-compliant pores of the Tod model, transfer fluid to the physically unconnected cracks, therefore giving dispersive, or frequency-dependent velocities and attenuation. The theory predicts that there is a pressure at which anisotropy reaches a maximum value, before the conducting properties are reduced, by increasing stress, eventually to that of the uncracked matrix. Tod also extended his modelling to the case of faults with parallel cracks aligned at an angle to the main fault plane (Figure 15.44c). Since these authors, and also Chapman, 2002 and 2003 (see later), utilise aspect ratios that can in practice be reduced to very low values by high stress, the inequality of physical (E) and hydraulic (e) apertures will affect interpretation, since fluid volumes in actual cracks or joints are greater than hydraulic capacity, since permeability k
e2/12. In dynamic modelling seen so far, this distinction does not appear to have been treated. However, the improved model described by Tod et al., 2002, (together with Cambridge Professor ‘seismic’ Hudson: there is a prominent Professor J.A. Hudson in rock mechanics too), provides a new level of sophistication, since crack aspect ratio, crack density, crack orientation and responses to applied stress and fluid pressures, are each incorporated into the permeable, but noncompliant pore space between the matrix ‘grains’. The new formulations and the interdependencies of crack orientation, aspect ratio and applied (effective) stress gives an elastic loading and unloading behaviour, but

Shear wave splitting in fractured reservoirs and resulting from earthquakes

(a)

(b)

(c)

(a)

(b)

(c)

463

Figure 15.45 Three examples of the nucleating branching fracture networks, showing their changing attenuation and frequency dependence. Source wavelets of 30 Hz applied at centre of each model. Vlastos et al., 2003a. Reproduced by kind permission.

with no hysteresis, and no stress history, in obvious contrast to the larger-deformation modelling of the rock mechanics UDEC-BB code. 15.9.2.4

Vlastos-Narteau automaton model

Interesting new developments in modelling capabilities in geophysics were also demonstrated by Vlastos et al., 2002 and Vlastos et al., 2003a. The first authors Vlastos and Narteau, utilised the 2D finite difference method termed the multi-scale ‘cellular automaton model’ developed by Narteau, 2001 to study progressive changes of attenuation in nucleating, growing, branching and coalescing arrays of fractures. They studied the effects of scattering attenuation in what evolves, through shear fracturing, into an anisotropically fractured network, with fractures of increasing length and reduced frequency as shear localization develops. Examples of the successive stages of fracturing that can be generated are shown in Figure 15.45. These are successive ‘snapshots’ generated by a particular realization of this dynamic network model. In the seismic attenuation modelling described by the authors, only the scattering attenuation component is modelled. This is related to the structural heterogeneities (i.e., the growth and coalescence of fractures),

but does not include squirt or intrinsic attenuation losses. Nevertheless, scattering attenuation is also found to be frequency dependent, showing Qseismic values as low as 1/0.6  1.7 for case (b) in Figure 15.45. In the numerical fracture models illustrated in Figure 15.45, background values of Vp and Vs were 3.3 km/s and 2.0 km/s respectively. Density was 2.2 kg/m3. Vlastos et al., 2002 and Vlastos et al., 2003a used what are considered by the writer to be unrealistically equal normal and shear compliances (ZN  ZT  5.6  1010 GPa1: presumably GPa1.m?), which (may) correspond to rock mechanics normal and shear stiffnesses (Kn and Ks) of about 1.8 MPa/mm. In general terms, due to the higher dynamic modulus of rock masses, it is likely that the micro-deformation, dynamic compliances should be much lower (i.e. much stiffer in rock mechanics terminology) than the macro-deformation values typically measured in ‘static’ loading tests on joints, as frequently performed in rock mechanics, and the shear compliance should perhaps be higher (i.e. the shear stiffness lower). Presumably with rock mechanics experiences of e.g. Ks/Kn
1/10 or an approximated Z␶/ZN
10, even greater attenuation, and greater anisotropy would have been indicated. Clearly there is promise for future links between fracture frequency, fracture character and seismic attenuation measurements.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.46 ‘Snapshots’ of the anisotropic, elliptical, pore pressure propagation with time, in the Vlastos et al., 2003b, fractured network model. Reproduced by kind permission.

Vlastos et al., 2005 presented a more comprehensive version of the Narteau ‘stochastic-deterministic’ fracture network modelling, with a 12-stage evolution of fracturing. Application of the spectral ratio method to the scattering attenuation, resulted in increasing then declining attenuation, giving seismic Q values reducing from 100 to 7 to 2.5 (with the maximum density of fracturing), and increasing again through 6, 10 and 100 as the fractures were fewer and longer, as typified by stage c) of Figure 15.45. It is clear that the wide variety of fracture-scale lengths illustrated in the most well-connected networks were within the so-called ‘percolation threshold’, and were largely responsible for the low Q seis values in these ‘central’ models, typified by case b) in Figure 15.45. Vlastos et al., 2003b, with co-authors from BGS and the universities of Berkeley, Edinburgh and CergyPontoise in France, and Lin et al., 2004, used a 2D fluid flow model and a pre-existing, anisotropically fractured numerical network, similar to the above, to study the seismic signatures of a central (borehole) fluid injection

into a simulated 2560  2560 m model. They show interesting ‘snapshots’ of the anisotropic, elliptical pore pressure progression that develops with time. Figure 15.46 reproduced in grey-scale, shows the pore pressure development 10, 40, 70, and 100 hours after the start of injection. They explained that the ellipticity of the pore pressure field, besides being due to the presence of fracturing, was due to assuming a diffusivity along the fractures, many orders of magnitude greater than the background. As the authors pointed out, injection decreased the effective stress, thereby increasing the compliance (or reducing the stiffness) of the modelled fractures. On this occasion a Schoenberg, 2002, non-linear compliance formulation was used. An increased fracture opening and/or pore throat size, could have effectively decreased the stiffness of the rock and rock mass in terms of squirt flow, thereby reducing velocities and increasing intrinsic attenuation. The authors came to the surprising conclusion that the P-waves were not sensitive to pore pressure changes,

Shear wave splitting in fractured reservoirs and resulting from earthquakes

as opposed to the S-waves and coda waves that showed high sensitivity. Could the reasons for this be found in their assumptions for compliances, in relation to rock mechanics experiences of the approximate inverse: the stiffnesses? The authors reportedly set compliances as follows (but presumably the unit should be Pa1.m, as otherwise the stiffnesses would be many orders of magnitude too high): At zero stress:

Z(To)  5.681  109 GPa1 Z(No)  2.8409  1010 GPa1

If we assume a typing error, and intended units of Pa1.m, then rock mechanics stiffnesses, if they had been equal to the inverse, would have been: Ks
0.176 MPa/mm Kn
3.52 MPa/mm These give a recognizable ratio Kn/Ks of 20. However, the equivalent Kn value, as will be seen Chapter 16, is exceptionally low, and the shear stiffness also low. Both are representative of an effective normal stress of perhaps less than 0.1 MPa. This could be the explanation of the lack of P-wave sensitivity to pore pressure change, since the modelled rock mass was, perhaps inadvertently, given the equivalent of a high confining stress. At ‘infinite’ stress, the authors used Z(To)/5 (i.e. Ks  5) and Z(No)/2 (i.e. Kn  2), changes that would be greatly exceeded in rock mechanics terms, when the original stiffnesses were so low, due to the assumed low stress. Real rock joints display strongly non-linear pseudostatic stiffness at lower stress levels, when subjected to mechanical loading causing macro-deformation. Furthermore, near-surface rock masses clearly display a strong dependence of P-wave velocity on effective stress level (and therefore pore pressure), at least in the first several hundreds of metres, and sometimes to depths of one or even two kilometres if the rock has high modulus, or if there is over-pressure. The rock quality Qc -Vp porosity – depth relations which are empirically based (e.g. Figure 15.33 and Chapter 15), confirm the relevance of low Kn at low stress, with a strong stiffening at high stress. So the authors’ conclusion regarding Vp not sensitive to pore pressure changes, may inadvertently be a function of the ‘equivalent-to-low-stress’ input data, and the application of high (fracture-closing) stress levels.

15.9.2.5

465

Chapman triple-porosity poro-elastic model

Chapman, 2002 and 2003, developed a dual-porosity poro-elastic model, based on the following important observation that typical laboratory samples, clearly unfractured, nevertheless display dispersion, anisotropy, stress sensitivity, and dependence on fluid type and degree of saturation, as we have seen in numerous contexts in earlier chapters. Chapman’s argument for developing his new model was that, when the fractures or cracks were removed from preceding models, a linearelastic material remained, contrary to observation. Chapman et al., 2001 contrasted his more recent poro-elastic double (actually triple) -porosity model with the anisotropic poro-elastic model of Zatsepin and Crampin, 1997. Although the driving process of this earlier model was the migration of fluid along intercrack pressure gradients (and subsequent preferential crack closing), the calculation of the induced velocity changes actually relied on crack models which assumed that fluid could not move at the time scale of a seismic wave. As pointed out, this could be a good approximation for high frequency laboratory ultrasonic experiments, but not for low frequency e.g. 100 Hz field data. The restriction that fluid should not move also ruled out the (correct) modelling of attenuation. Chapman had earlier presented a poroelastic theory that modelled the effects of squirt flow at the grain scale, which gave a good match to experimental data. Chapman’s new theory combined two or more length scales explicitly: the grain scale and a set of fractures of any desired characteristic length (e.g. stress-aligned dominant jointing of many potential scales: 0.01, 0.1, 1, 10 metres). He termed the latter ‘meso-scale’ anisotropic fractures. Naturally, he also modelled the all-important interaction between this meso-scale and the grain-scale equant matrix porosity and ellipsoidal microcracks. Because there may be three or more scales involved, it has been termed a ‘triple-porosity’ model in this book. An important feature introduced by the inclusion of fractures was that dispersion occurred at lower frequency ranges than those over which the micro-structure dispersion occurred. He found that the larger the size of the fractures, the lower was the relevant frequency band. Figure 15.47 gives a clear demonstration of the ability of this model of equant porosity with elliptical microcracks (first without meso-scale fractures), to model frequency dependent velocities (dispersion) in the case of an isotropic model without fractures. Figure 15.47 a and b, show that the dispersion is predicted

466

Rock quality, seismic velocity, attenuation and anisotropy

Next, Chapman added fractures of 10 cm length, at a density of 0.05, making the model transversely isotropic. Figure 15.47c shows the dispersion of the qP-wave velocities travelling parallel and perpendicular to the model fractures. Clearly, the parallel waves are unaffected by the fractures, but squirt flow gives dispersion for the perpendicular waves. There is a significant reduction in velocity at low frequencies, but no reduction in velocity above about 1 kHz, due to the apparent stiffness of the fluid inclusions. Introduction of even small 10 cm long fractures had caused dispersion to begin at lower frequencies. Figure 15.48 shows modelled shear wave velocity anisotropy [defined as before, as 100  (qS1 – qS2)/ qS1] for the case of a mix of microcracks of 200 m size, 10% equant porosity, and meso-fractures of up to 1 m size. (See visualization of the model in Figure 15.48a). Shear wave propagation was at 20° incidence to the fractures. Anisotropy reduced with increasing frequency. In contrast, Figure 15.48b had no equant porosity (0%) and crack density is reduced from 0.1 to 0.02. A marked reduction (and smaller variation) of shear wave anisotropy can be noted. The absence of the pores, means that fluid can no longer flow out of the microcracks with the passage of the seismic waves, so anisotropy and attenuation are reduced. Note that the shear-wave anisotropy is only weakly following the ‘100e’ rule-of-thumb of Crampin, since the two examples should then show 10% and 2% respectively. When modelling the attenuation, there was a singularity (zero attenuation) in the case of the pure shear wave, when the frequency was only 40 Hz, and the angle of incidence was 90°. This was believed to be due to the perfectly aligned fractures† this aspect being avoided in the new Tod, 2003 model, which utilises a ‘nearly aligned’ crack set. When Chapman modelled with a much higher frequency (3 kHz), the qP, qS and pure shear S waves were

†

Figure 15.47 (a) (b) Chapman model of dispersion with no mesofractures. (c) dispersion and anisotropy when 10 cm fractures are added. Chapman, 2003.

over a limited frequency band, roughly between 1 kHz and 100 kHz. The particular model had moduli of 17.5 GPa, density 2300 kg/m3, a microcrack density of 0.1 and 10% porosity.

On the subject of modelling P-wave anisotropy in the case of perfectly aligned fractures, Willis and Rao, 2005 pointed out that a P-wave can be cancelled out due to the time delay of the wave, when travelling between two fractures, thus creating a significant notch (or even a null) in the spectral ratios of reflected seismic traces. This happens when the P-wave length is about twice the fracture spacing. However, they also suggest that the frequency location of the notches themselves could be used to determine the fracture spacing and losses, due to scattering attenuation from the fractures.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

467

(b)

(a)

(c)

Figure 15.48 (a) Visualization of Chapman’s model of connected equant pores, microcracks and fractures with low aspect ratios, (b) S-wave anisotropy with 10% porosity, and ellipsoidal microcracks and fractures of various sizes, giving a crack density of 0.1. (c) similar to (b) but with 0% porosity, and 0.02 crack density, which caused reduced attenuation, and reduced S-wave anisotropy. Chapman, 2003.

all attenuated, with (1000/Q) in the range 18 to 24 (approx.), i.e. QqP and QqS values in the range 42 to 56, which is typical for Qp and Qs of moderately fractured rock closer to the surface (see Chapter 10). This brings one to the interesting question of stress sensitivity. By setting smaller aspect ratios for the mesofractures compared to the microcracks, one can in some way mimic the effect of higher stress, and thereby cause less attenuation (higher Qseis), as the fluid cannot ‘squirt’ or flow so easily, in response to the passage of the seismic waves. Setting a certain aspect ratio is like creating a physical aperture (E), whereas the assumed permeability of this crack of ‘fixed’ aspect ratio is actually a function of its hydraulic aperture (e). Because of joint or fracture

roughness (JRC), the usual inequality: E  e occurs, with e
E only when roughness is absent, and JRC  1. In reality, a chosen aspect ratio will have less permeability than assumed, due to joint roughness. Because of varying degrees of roughness for most joint types, and the usual inequality of these two apertures, dispersion will likely begin at lower frequencies than might be modelled; there will be extra resistance for fluid flow (in relation to the modelled aspect ratio), as roughness increases. Yet it will contain the assumed volume of fluid. The significant inequality of E and e is demonstrated in the explanation of some rock mass ‘groutability’ terminology, in Figure 15.49, and by UDEC-BB modelling of tunnels, in Figure 15.50.

468

Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.49 Physical demonstration of joint aperture concepts (E) and (e) regarding groutability. Barton and Quadros, 2003.

15.9.2.6

Maultzsch-Chapman fracture size estimation

Maultzsch et al., 2003, with colleague Chapman from the Edinburgh BGS Anisotropy Project, broached the question that seems to represent an important ambiguity in many earlier models in geophysics, namely how best to interpret the commonly used ‘crack density’ formula: e  ga 3 or e 

Na 3 V

(15.8)

where a  crack radius, and N/V is a number per unit volume (  ‘number density’). This means, as they point out in Figure 15.51a, that the same crack density can be caused by a few large fractures or many small cracks. For instance, a fracture density of 0.05 means that N/V (where e  Na3/V) can be expressed in many different ways, such as: a) 50  1 mm cracks/1 cm cube b) 5  1 cm cracks/10 cm cube

Shear wave splitting in fractured reservoirs and resulting from earthquakes

469

Figure 15.50 The inequality of physical aperture (E) and hydraulic aperture (e), demonstrated in a distinct element UDEC-BB model of tunnels in Oslo. Makurat and Barton, 1988, NGI contract report. Makurat et al., 1990a.

Figure 15.51 The problem of the crack density definition e  Na3/V used in geophysics is that both the illustrated representations of fractures of different size can have the same numerical value of e. From Maultzsch et al., 2003.

c) 50 10 cm fractures/1 m cube d) 1  1 m fracture/2.7 m cube While the crack density can be roughly estimated from the time delay of split shear waves, since a shear wave anisotropy of approximately 100e is expected according to Crampin, the result is seemingly ambiguous, since fracture compliances will also play a role in the time delay and anisotropy estimate. This ambiguity is hardly satisfactory when trying to understand the structure of a fractured reservoir. This geophysics crack density concept is in stark contrast to what engineering geologists are expected to do ‡

The first two terms of the rock mass quality Q-estimate are one step simpler than estimating m1 for each set, as above. For RQD, one records the percentage of core pieces longer than 10 cm, dividing this by the rating (Jn), for the number of joint sets (see Appendix A). These first terms in the Q-value estimate (RQD/Jn), give a close approximation to relative block size, and the degree of freedom for block movement. This is fundamental

during field logging, namely attempt to present the spacing statistics of the different sets of joints (with a mean m1 for each set), and where possible, also present the length statistics of the joints belonging to the different sets, and whether both or only one end of the joint in question is visible in the exposure. (ISRM, 1978). Quantification as joint spacing and length and number of sets, as used by engineering geologists, would be the theoretical ideal, but with compromise necessary due to the ‘invisible’ nature of the targets in geophysics. Mixed scale fracturing obviously needs to be modelled without ambiguity concerning fracture size, since it is of fundamental importance when attempting to assess fractured reservoir structure, as also argued by van der Kolk et al., 2001 in the case of the Natih field in Oman. When an engineering geologist is logging exposed rock masses or core, he also uses one or more rock mass classification methods, such as RQD, Q, and RMR).‡ Naturally, being able to see the rock surface exposure, tunnel wall or core, is obviously of inestimable value for giving this more correct description of reality. The microcrack scale is of course excluded from general field observations. Maultzsch et al., 2003, investigated the length-scale frequency-dependence of the Chapman model, taking account of fractures up to 10 m size in Figure 15.52. for rock mass stability and inter-connectivity to fluids. It is tempered by the next pair of parameters Jr/Ja, which closely represent the coefficient of friction, with contrasting contributions from joint roughness and clay filling, in the first instance for the least favourable joint set. The combined value Q
 RQD/Jn  Jr/Ja, often termed Q-prime, clearly has strong links to seismic attenuation and anisotropy.

470

Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.52 A further example of the scale and frequency dependence of shear wave splitting anisotropy, according to the Chapman model, that connects pores, microcracks and formation-scale fractures. In this example, from Maultzsch et al., 2003, the waves are propagating at 30° to the fracture planes, and are split to give the dispersive anisotropies shown.

Here the percentage anisotropy of the polarized qS1 and qS2 shear wave velocities is shown. It is implied that shear wave splitting anisotropy can be registered from wave splitting at numerous scales of crack/fracture sizes. However it is understood that attenuation in a well fractured reservoir may prejudice the arrival of the slow qS2 wave. For any given fracture radius, the shear-wave anisotropy is seen to decrease as frequency increases. The larger the size of fractures, the lower the frequency range where velocity dispersion and frequency dependence of anisotropy occurs. This property was subsequently used by the authors for inversion to fracture size. As also in Figure 15.48, the modelled results of shear wave splitting shown in Figure 15.52 suggest that the EDA concept with focus only on microcracks as the source of shear-wave splitting, may need to be reevaluated. Microcracks, as modelled, appear to give a ‘constant’ potential source of shear-wave splitting independent of frequency. In the examples shown in the two figures, anisotropies of 7.5%, 3.5% and 4.25% are shown. The ‘meso-fractures’ of 1 m and 10 m (radius) apparently have an equally strong role in shearwave anisotropy as microcracks, but only at the seismic frequencies appropriate to earthquake studies. There is therefore no good reason for only assuming that microcracks are responsible for shear-wave splitting in seismically

Figure 15.53 Comparison of Chapman model to the physical saturated sandstone-and-fracture model of Rathore et al., 1995. From Maultzsch et al., 2003.

disturbed rock masses, such as along the instrumented sections of the San Andreas Fault, as reviewed earlier in this chapter. Maultzsch et al. 2003 demonstrated the application of the Chapman model with two examples. One was a novel physical model of known fractures and pore structure located in IKU, Trondheim, Norway, made by embedding thin metal discs into a sand-epoxy matrix, with subsequent acid leaching of the discs to create cracks of known geometry and orientation (Rathore et al., 1995). This physical model will be described in greater detail at the end of this chapter. It appears likely to have aperture characteristics satisfying E  e, (i.e. without contact or apparent stress transfer, and with limited, if any, roughness). The Maultzsch et al., 2003 match to these laboratory determined qP, qS and Sh velocity components with azimuth, was excellent, and is shown in Figure 15.53.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

15.9.3

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Applications of Chapman model to Bluebell Altamont fractured gas reservoir

Since the Chapman, 2002 and 2003 dynamic equivalent medium model handles squirt flow in a triple-porosity poroelastic medium with porosity, microcracks and a fracture set of any desired fracture length or density, it is logical that it becomes a useful tool for demonstrating both the frequency dependence and azimuthal variation of the attenuation (1/Qp) of P-waves. Maultzsch et al., 2002 used the Chapman model, and various fracture sizes to demonstrate azimuthal dependent Qseis (strictly 1/Qp) and also frequency dependence, each for four different fracture sizes. This synthetic model had a common fracture density of 0.05, and fracture sizes (radii) of 1 mm, 1 cm, 10 cm, and 1 m. Figure 15.54 shows the predicted results. Note the tendency for 10 cm and 1 m fractures to give highest attenuation at lower seismic frequencies. Maultzsch et al., 2003 applied the Chapman model to nine-component VSP field data, from the Bluebell Altamont Field in the Uinta Basin, Utah in the USA (Lynn et al., 1999a). This was a tight, fractured gas reservoir in ‘sandstones’ (or lenticular sands encased in shales and carbonates), from which production was primarily controlled by the size, orientation and concentration of natural fractures, i.e. intersecting joint sets. The near-offset VSP had the source located 550 feet west of the well, and the three components receivers were placed at depths from 2800 feet to 8650 feet, with 50 ft spacing. The Green River reservoir formation was located from 6687 to 8591 feet deep (approx. 2000 to 2600 m). A P-wave and two orthogonal S-wave sources were used, yielding a nine-component data set. Shear wave splitting had long been recognised, with the fast shear waves giving a consistent (slightly rotating with depth) N46°W to N40°W (average N43°W) polarization. This direction was identified by the authors with the fracture strike, but, actually as we shall see later it is closer to H max but nevertheless caused by fractures of large scale. Significantly, the time delay between the fast and the slow shear waves showed a sharp increase with depth at the reservoir level, indicating the presence of the fractures. Maultzsch et al., 2003 tested the Chapman model, following the Liu et al., 2003 methodology for interpreting the frequency dependent anisotropy at this fractured reservoir.

Figure 15.54 (a) Variation of P-wave attenuation with angle from the fracture normal, for different modelled fracture radii ( frequency  30 Hz in example). (b) Variation of P-wave attenuation with frequency and fracture radius. Chapman, 2002 and 2003 model, in Maultzsch et al., 2002.

The time delays between the two split shear waves, showed a systematic variation with frequency, and of course with depth. The time delay was largest (32 to 38 ms) at lowest frequencies (5–15 Hz), and smallest (30 to 34 ms) at higher frequencies (20–40 Hz). This data was used for inverting for the theoretical fracture density and fracture radius. The roughly 2000 to 2600 m deep reservoir had Vp  4877 m/s, Vs  2575 m/s, density 2.60 and porosity 9.4%. For the modelling, an aspect ratio of 0.0001 was chosen for the fractures (i.e. 100 m per 1 metre). Figure 15.55a shows the results of Maultzsch et al., 2003 modelling of the relative error between the measured and the model-computed time delays. This was for a range of fracture densities, fracture sizes and frequencies. The black section of the ‘bend’ in the figure shows minimum error, for a fracture density of 0.035 and a fracture radius of about 3 m. Reportedly, there was evidence from Lynn et al., 1995, of fracture lengths of about 2 to 3 m, based on borehole images. The

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Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

Figure 15.55 (a) Relative error between VSP measurements and Chapman model results, shows minimum at realistic fracture radius a
3 m, and fracture density of 0.035 or about one fracture/10 m cube. (b) Percentage anisotropy versus frequency match is excellent. Maultzsch et al., 2003.

consistently modelled polarization angles were 43° (the same as the average N43°W polarization that was measured), and the percentage anisotropy as a function of frequency, shown in Figure 15.55b, was a reasonably good match; and excellent at frequencies above about 13 Hz. Liu et al., 2003a, also described methods of analysis needed for interpreting multi-component VSP from the fractured gas Bluebell-Altamont reservoir in the Uinta Basin in Utah. This was the subject of the above Maultzsch et al., 2003 application of the Chapman, 2003 dynamic model of pores, ellipsoidal microcracks and aligned meso-fractures, which was used to interpret both fracture strike and fracture dimensions at this field.

Liu and co-authors emphasised the importance of frequency on the magnitude of the S-wave anisotropy, as demonstrated by the Chapman model. They also emphasised that in the Bluebell-Altamont Field VSP, the polarized fast S-waves actually showed no apparent variation with frequency (unless at very low frequency). However the time delays between the split shear waves decreased as the frequency increased, due presumably to apparent stiffening of the squirt phenomenon. At the surface there were two joint sets, one striking N22° to 32°W, and the other N60° to 77°E, within about 5° of perpendicular, on average, as described by Lynn et al., 1999. However, the maximum horizontal stress (at reservoir level), was estimated as N40° to 45°W based on perpendicular borehole elongation using four-arm calliper logs in two adjacent boreholes. Geologically recent natural hydraulic fracturing (gilsonite dikes) were oriented at a consistent N40° to 45°W as well. The extensive analyses reported by Lynn et al, 1999a, included shear wave splitting, and azimuthal P-wave response due to the fractures (the latter was reviewed in Chapter 14). Liu et al., 2003a concentrated on an analysis of the frequency dependence of the S-wave anisotropy, looking at data both above and within the 1980 to 2590 m deep reservoir. The techniques of rotation, band pass filtering, minimising off-diagonal energy and so forth, are beyond the confines of our simplified treatment. Significantly, except for the very low frequency band below 10 Hz, the polarizations were generally between 40° to 45° for the three frequency band-widths between 10 and 40 Hz, over the whole depth interval 853 to 2636 m, both above and within all the reservoir, (see Figure 15.56a). This agreed well with the average N43°W of the interpreted major stress, but did not quite agree with the dominant jointing, as actually proposed in Liu et al., 2003a and Maultzsch et al., 2003. Three distinct time-delay intervals were detected (see Figure 15.56b and Table 15.5). Within the three depth intervals there was a superimposed frequency dependence, as shown in Figure 15.56b. The steep time delay-frequency data for the reservoir (interval III) is reproduced at larger scale in Figure 15.57a, and the different gradients give corresponding estimates of frequency dependent shear-wave anisotropy percentages in Figure 15.57b. According to Liu et al., 2003a, there were at that time very few reports of frequency–dependent anisotropy in the literature, from the exploration geophysics community. However, for earthquake data, Marson-Pidgeon

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473

Table 15.5 Time delay-depth gradients for interpreting seismically isotropic and anisotropic (fractured) depths at the Bluebell-Altamont Field. Liu et al., 2003a. Interval I, 853–1219 m

Interval II, 1219–2072 m

Interval III, 2072–2636 m (reservoir interval)

Time delays linearly increase with receiver depth increase: i.e. seismically anisotropic, as shear wave splitting is occurring Time delays almost constant: i.e. seismically isotropic, as no further shear wave splitting Time delays abruptly start increasing: i.e. strong shear wave anisotropy of 3 to 4%, due to splitting. Attributed to fracturing.

(a)

(b)

(a)

Figure 15.56 (a) Except at low frequency (0–10 Hz), a reasonably constant polarization at 40° to 45° is shown. (b) Time delays show three intervals: gradient, flat, gradient, implying anisotropy, isotropy, anisotropy. Bluebell-Altamont Field anisotropy interpretation, from Liu et al., 2003a, with kind provision of files from Liu, pers.com. 2005. (see colour Plate 6).

and Savage, 1997, had reportedly shown a systematic decrease in time delay with increasing frequency, as also shown by the reservoir data in Figure 15.57. Liu and co-authors suggested that if a proper mechanism (or mechanisms) for this frequency dependence could be understood, as implicitly shown in the Chapman, 2003, dynamic model of triple-scale porosity reviewed earlier, then meso-scale fractures and their fluid flow properties could be understood. Naturally, it is logical to refer to Figure 15.52 and see again from the example of Chapman triple-porosity modelling, the

(b)

Figure 15.57 (a) Steep time delay gradient in reservoir interval, with frequency dependence. (b) Interpretation of anisotropy percentage as function of frequency. Bluebell-Altamont Field anisotropy interpretation, from Liu et al., 2003a, with kind provision of files from Liu, pers.com. 2005. (see colour Plate 7).

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.59 Time-delays estimated from synthetic data for 4 frequency bands (solid lines). The real data is shown with dashed lines, showing generally excellent fit. Liu et al., 2003b.

Figure 15.58 (a) The relative error between the predicted and measured time-delay/depth, evaluated over four frequency values for a range of possible fracture densities and sizes, for comparing with multi-component shear wave VSP data acquired in the BluebellAltamont field in Utah. (b) The rms error zoomed around the minimum, where the error is less than 5%. (Chapman model application, by Maultzsch et al., 2003 and Liu et al., 2003b). (see colour Plate 8).

tendency for an increased relevance of larger-scale fractures or joints, for explaining shear-wave anisotropy at the lower frequencies. In a companion paper Liu et al., 2003b, also gave the Maultzsch et al., 2003 prediction of fracture density (appropriately re-named, from crack density) and mean fracture radius, obtained with the Chapman model. Figure 15.58 shows the more complete result of this analysis of the Bluebell-Altamont Field anisotropy, with interpreted fracture density of 0.04 and fracture radius of 3 m. These imply, from e  Na3/V, about one of these major fractures per 9 m cube of rock.

The estimated time delays from the Chapman model (stepped) were finally compared with mean trends from the reservoir (dotted lines). (Figure 15.59). The slight discrepancy (‘a matter for future investigation’) could perhaps, among other more complex factors, be due to the inequality of physical aperture (E) and hydraulic (smooth parallel-plate) aperture (e), when modelling the aspect-ratio-dependent treatment of squirt flow losses and frequency dependence in the Chapman model. In other words a given aspect ratio assumption contains a fluid volume equivalent to thickness (E), but permeability in the ‘real world’ is governed by (e) since K  e2/12 if laminar. The effect of E/e  1 is caused by joint or fracture roughness (Barton et al., 1985). If looking for more reasons for partial lack of fit between model and one may note that Olsson and Barton, 2001, showed from coupled shear-flow experiments by Olsson, (reviewed in Chapter 16), that the E/e  1 inequality with pure normal closure is modified in a subtle way when there is joint shearing. There would then also be greater relative mobilization of shear stiffness, compared to normal stiffness, which is not of course modelled in the Chapman poro-elastic model, but could be the ‘reality’ in situ. There is also the possibility of the shear-related ‘O/R’ rotation shown in Figure 15.2b at the beginning of this chapter. Figure 15.60, which summarises the various azimuthal relationships pertaining to the Lynn et al., 1999a Bluebell-Altamont field investigations in Utah, in fact

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475

occur down to seismic frequencies, as we have seen in Figure 15.52.

15.9.4

The SeisRox model

There are an increasing number of numerical models that can represent the effect of a single set of fractures (typically vertical) on the otherwise transversely isotropic behaviour of a layered reservoir. Two contrasting reservoir idealizations were presented by Johansen et al., 2004 and are shown in Figure 15.61. A reminder of the theoretical velocity components, kindly provided by Johnsen (pers. comm., 2005) is shown in Figure 15.62. a) an isotropic medium without fractures (Figure 15.61a) b) an transversely isotropic material with one set of fractures giving a horizontal symmetry axis (Figure 15.61b)

Figure 15.60 Azimuthal fracture orientations from outcrop and core, compared to interpreted stress and interpreted seismic data, for the Bluebell-Altamont field. Based on Lynn et al., 1995 and Lynn et al., 1999a.

indicates a 15° discrepancy between reflection seismic interpretation of S1, and the polarized shear-wave interpretation of S1. This actual small discrepancy of the polarization directions for the supposed 3 m fractures, in relation to the oriented fractures in the core (a possible 15° to 25° discrepancy) could be due to experimental/acquisition errors (Lynn, 2005 pers. comm.), but might also be due to a phenomenon such as illustrated in Figure 15.2b. Liu and co-authors emphasised that the Chapman model reverted to a grain-size squirt flow model when without fractures. But with the introduction of a fracture set, two characteristic frequencies then existed: the traditional lab-scale squirt frequency and a lower frequency that depended on fracture sizes. This meant that dispersion (frequency dependent velocity) could

Johansen et al., 2004, coupled a rock physics model with a finite difference scheme for visco-elastic seismic modelling (termed SeisRox), to represent the coupling between fluid-filled fractures and pores. They demonstrated a stiffening behaviour (increased velocities), as frequency was increased. The contrasting effects of their models of pores only (Model A) and communicating pores and fractures (Model B), are shown in Figure 15.61. The properties assumed for their fractured reservoir layer (Table 15.6), gives insight into the level of modelling detail. Note the rather large aspect ratios for the assumed cracks, which fall short of actual fracture (or joint set) simulation in this particular case. To emphasise the links between stiffness, velocity and attenuation, we may refer to the published article (Johansen et al., 2004) in which the vertical axes of Figures 15.61a and b were given the alternative nomenclature ‘real part of stiffness’ in place of velocity, and ‘imaginary part of stiffness’ in place of attenuation. The four sets of curves of behaviour for the six ‘V’ and ‘Q’ components were unchanged, in this alternative nomenclature, yet in place of a velocity scale of 2.0 to 4.5 km/s, they gave a stiffness scale of 5 to 50 GPa, and in place of an attenuation scale (1/Q) of 0 to 0.20 (or minimum Q  5) they gave a stiffness scale of 0 to 6 GPa (the ‘imaginary part of the stiffness’). It is of interest at this juncture, to refer to Figure 15.33b, for the purpose of cross-discipline connections, suitably tempered by the dynamic situation. This diagram

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 15.61 Modelled wave speeds and attenuation as a function of frequency, using the SeisRox model, for (a) an isotropic medium with random pores, (b) communicating pores and oriented vertical cracks in a transversely isotropic medium with horizontal symmetry axis. Johansen, pers. comm., 2005.

shows the empirical link between P-wave velocity from refraction seismic, and the static deformation modulus M (as opposed to the dynamic value obviously just referred). The relationship has ‘common ground’, namely, the rock quality Q or Qc value, which can however be dispensed with, when the proposed direct link from seismic Vp and static modulus (M) is used (Barton, 2002a). It may be noted, for purpose of comparison, that the above 2.0 to 4.5 km/s range of velocities, with their equivalent (dynamic) ‘real part of stiffness’ of 5 to 50 GPa, have a predicted static moduli (M) range of 3 GPa to 22 GPa, respectively. The maximum attenuation (1/Q) scale value of 0.20, giving the particularly low Qseis value of 5, and an

equivalent (dynamic) ‘imaginary part of stiffness’ of 6 GPa, following Johansen et al., 2004, would (falsely) give a low Qc estimate of about 0.2 (‘very poor rock quality’) if one temporarily ignored the Edynamic  Mstatic norm, and used the empirical link M  10 Qc1/3 shown in Figure 15.33b.

15.9.5

Numerical modelling of dynamic joint stiffness effects

In the foregoing double-porosity models we have witnessed the use of crack representation by aspect ratios.

Shear wave splitting in fractured reservoirs and resulting from earthquakes

477

(a)

(b)

Figure 15.62 The stiffness matrices showing the velocity components modelled in Figure 15.61. Johansen, pers. comm., 2005.

Important insight into the influence of (dynamic) joint stiffness and joint spacing effects on seismic dispersion is provided by the modelling of Monsen, 2001. The motivation for his study was the interpretation of high frequency investigations of rock masses, in which the wave length may be less than the joint spacing, for instance in

cross-hole seismic at frequencies of several kHz. Monsen first explored the influence of single fractures, and assumed dynamic normal stiffness values (100, 1,000 and 10,000 MPa/mm) equivalent to widely different normal stress levels, from e.g. close to surface to kilometre depths, as this range indicates (see Chapter 16).

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Rock quality, seismic velocity, attenuation and anisotropy

Table 15.6 Parameters used to compute effective visco-elastic properties of reservoir rock. (Johansen et al., 2004). Porosity (%) Permeability (mDa) Clay content (%) Viscosity (cP) Fluid density (kg/m3) Fluid velocity (m/s) Aspect ratio quartz-related pores Aspect ratio clay-related pores Aspect ratio cracks Crack density Effective density (kg/m3)

15 50 15 1 1000 1500 0.15 0.027 0.01 0.1 2383 (a)

The soft-fracture near-surface simulation, showed the single fracture to be a good reflector, with a wide range of low to medium transmission coefficients (T) until frequencies were lower than 1 kHz, when T became unity. The stiffest, deepest simulation, showed transmission coefficients of mostly 1.0, except at frequencies higher than 100 kHz. In effect the time delay here was close to zero except at the highest frequencies. There was naturally more delay and attenuation as the dynamic fracture normal stiffness was reduced. The effect of multiple parallel fractures on the group velocity, as compared to a ‘sedimentary rock’ matrix velocity of just below 2490 m/s is illustrated in Figure 15.63. The same range of dynamic normal stiffness as above was used (i.e. from near-surface to several kilometres equivalent depths), and three alternative spacings of 0.1, 1.0 and 10 m were used. The reduced velocity with small fracture spacing is of course a familiar trend in near-surface rock mass quality (Q) relations to Vp, with limited effect on velocity (and rock quality), when the spacing is as high as 1 or particularly 10 meters. However, as also suggested by the results in Figure 15.63, when equivalent depth is of kilometre to several kilometres magnitude, a fracture spacing as small as 0.1 m has small, or negligible effect on the perceived velocities with dynamic stiffnesses of Kn  1,000 and 10,000 MPa/mm, unless at frequencies beyond 10 kHz. This is a good illustration of the benefit of high frequency cross-well measurements, in particular in view of the long transmission distances of high frequency waves at depth, when joints and fractures are stiff, as also referred to in Chapter 14. When modelling wave propagation through jointed or fractured rock with distinct element codes like

(b)

Figure 15.63 (a) Group velocity versus frequency for three fracture spacings, at a constant (near-surface, and very low) dynamic normal fracture stiffness of 100 MPa/mm. This behaviour corresponds quite accurately with near-surface rock quality (Q) versus seismic velocity expectations. (b) Group velocity versus frequency with a constant fracture spacing of only 0.1 m, and the full range of dynamic normal stiffnesses of 100, 1,000 and 10,000 MPa/mm. The benefit of cross-well, high frequency surveys is demonstrated quite well by these scoping studies. After Monsen, 2001.

UDEC, the provision of realistic input data concerning joint or fracture dynamic stiffnesses is fundamental for a representative result. In Figure 15.64, we see the effect of a more realistic ‘jointed rock’ (in 2D), on the attenuation of wave amplitude, on velocity reduction, and on frequency change. The centre of each model (intact or jointed) is the source location, with a measurement point at the boundary in each case. (Non-reflecting/ absorbing boundaries are of course used). In the cases

Shear wave splitting in fractured reservoirs and resulting from earthquakes

479

Figure 15.64 An illustration of wave propagation differences between intact and realistically jointed (but 2D) models, with dynamic normal and shear stiffness input estimates appropriate to the dynamic wave form. Note the multiple effects of (vertical) wave transmission through the layered and jointed medium: i.e. the delay, the amplitude reduction (i.e. attenuation), the velocity reduction and the frequency reduction. (Monsen, 2005 priv. comm).

illustrated, the dynamic stiffnesses assumed were within the range studied by Monsen, 2001. There is at present no matrix flow modelling in UDEC.

15.9.6

A ‘sugar cube’ model representation

A practical ‘sugar-cube’ model with three orthogonal joint or fracture sets was proposed by Brown et al., 2002, as a means of integrating seismic data to production data. The authors combined the ideas of Oda, Kachanov, Schoenberg and Sayers to produce the rather obvious representation of a multiply-jointed rock mass, where three, more or less mutually perpendicular joint sets is almost a rule rather than an exception. Such a representation for the permeability of rock masses at dam sites was used by

Snow, 1968, and is utilised for grouting predictions in rock engineering (e.g. Figure 15.49). Brown et al., 2002 assumed that both the fracture permeability tensor and the fracture compliance tensor would ‘diagonalise’ in the same principal coordinate system. The model predictions for P-wave and S-wave phase velocities, contrasting the matrix velocity with the effect of either a drained or brine-filled fracture network is shown in Figure 15.65. The authors noted that when the compliance of the fractures was large, as in the field, where fractures tend to be weaker, the effect of fluid changes on the velocity would tend to be dominated by effective stiffness increases due to e.g. brine saturation compared to drained or gas filled. The authors drew parallels to the Natih field experiences described by van der Kolk et al., 2001, which were reviewed earlier in this chapter.

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Rock quality, seismic velocity, attenuation and anisotropy

15.10

Figure 15.65 A ‘sugar-cube’ model of compliance and permeability, for integrating seismic and flow measurements. Brown et al., 2002.

A porous and fractured physical model as a numerical model validation

The technique for constructing synthetic, fractured sandstones by Rathore et al., 1995, was referred to earlier, as a means of basic validation of numerical models. The (future) cracks are placed as metallic discs in a porous sand-epoxy mixture, and subsequently leached out, leaving empty voids. They thus have a known aspect ratio, size, position and orientation and are a close approximation to basic aspects of dual-porosity theoretical models. (Both however have the potential weakness in relation to reality, that stress and displacement is not transferred across the crack faces, so E  e, since roughness may be absent). The crack geometry studied by Skjærstein and Fjær, 2000, consisted of 1425 circular parallel cracks per dm3, with all cracks of 8.25 mm diameter and 20 m aperture. The crack density (number of cracks per unit volume  crack radius cubed) was 0.1. A representation of the crack-modelling principles is shown in Figure 15.66a. The authors pointed out that the (Rayleigh wave) scattering was strongly dependent on the wavelengthto-crack size ratio, and therefore on the frequency for a given crack size. Since the velocity anisotropy was not equally dependent on frequency at high ratios of wavelength-to-crack-size, the big discrepancy between Vmin/Vmax and Amin/Amax should decrease with decreasing frequency. With the crack size studied by Skjærstein and Fjær, 2000, the P-wave velocity anisotropy was greatly reduced by saturation, while in earlier models studied by Rathmore et al., 1995, there was significantly less reduction in velocity anisotropy with saturation, due probably to the smaller size of cracks that were used, giving different conditions of pore pressure equilibration. Skjærstein and Fjær, 2000, testing first dry then saturated cracks, found that the attenuation was strongly dependent on the incidence angle, as indicated in Figure 15.66b and in Figure 15.67. The attenuation, which was caused by scattering, distorted the wave forms and changed their frequency content. The angular dependence of attenuation was affected by the frequency (e.g. 100, 250 or 500 kHz). In the case of the 100 kHz excitation pulse applied across the 16-sided prismatic, fracture-filled sample, the wavelength-to-crack diameter ratio was in the range of 1.7 to 3.0. Under the experimental conditions investigated by Skjærstein and Fjær, 2000, the attenuation anisotropy was

Shear wave splitting in fractured reservoirs and resulting from earthquakes

Figure 15.66 (a) The prismatic, sixteen-sided, crack-bearing synthetic sandstone used by Skjærstein and Fjær, 2000. (b) A comparison of P-wave and polarized S-wave (qS1 and qS2) results using variable angle of incidence, for the two cases of i) through-going spotwelded fractures: open symbols, and ii) small parallel cracks: closed symbols. Squares are P-waves, circles/triangles are S-waves polarized parallel/quasinormal to the cracks. Fjær, 1997.

much more visible than the velocity anisotropy. Also at higher frequencies, where the P-wave velocity anisotropy vanished, the attenuation anisotropy remained high and clearly visible. Likewise, when saturated, causing a significant reduction in the P-wave velocity anisotropy, the attenuation anisotropy remained high. The authors recorded Vmin/Vmax  0.80, and Amin/Amax  0.01 for the same wave frequency. In Figure 15.66b, we may note one of the ‘complicating’ factors concerning the diagnostic use of P- and Swave polarization. Fjær, 1997, presented the P-wave and polarized S-wave results in parallel for i) through-going but spot-welded cracks, and ii) small parallel cracks. The

481

Figure 15.67 (a) Recorded P-wave signals propagating parallel or normal to dry cracks in a synthetic, crack-bearing porous sandstone (D/t  8.25/0.02 mm/mm) from Fjær, 1998. (b) Recorded P-wave signals when using three different excitation frequencies, in a dry crackbearing synthetic, porous sandstone. A five-cycle pulse was used at 500 kHz. These samples had 1425 circular parallel cracks/dm3 with the same D/t measurement as above. Skjærstein and Fjær, 2000

closed symbols in this figure represent 5.5 mm diameter cracks of 20 m aperture, while the open symbols represent the through-going but spot-welded cracks, where the contact spot diameters were 1.4 mm and the open parts the same 20 m. Each case studied was dry. These two special (and rather theoretical) geometries were chosen to represent a Hudson, 1981, type of crack distribution, and a White, 1983, model with spot-contact points on the larger fracture planes. When the wave-length was many times larger than the crack diameters, the cracked material effectively appeared as a homogeneous medium with reduced stiffness, while at higher frequencies, the smaller wave length-to-crack diameter ratio effectively made the medium appear more heterogeneous. Shear wave splitting with fast and slow components then showed greater contrast.

16

Joint stiffness and compliance and the joint shearing mechanism

This final chapter is designed to act as a cross-discipline reference point between rock mechanics and engineering geological behaviour in the ‘static’ world of slow-andmacro deformation processes, and the geophysicists ‘dynamic’ world of fast-and-micro deformation and attenuation processes. That there are important links between the two in terms of joint or fracture compliance and its inversion: stiffness, and in terms of rock quality, deformation modulus, and seismic quality, has been established in various contexts in the chapters of Part II. In particular, this last chapter attempts to extend current thinking regarding fractured reservoirs, ‘open’ joints, and assumed H max parallelism, to also embrace the possibility, even probability, that multiple-joint-sets and shear-dilationconductivity coupling are needed, due to the inevitable tendency for joints in less competent rocks to close at reservoir depths, even when under the influence of ‘only’ h min. Shear wave splitting and polarization from two sets of conjugate (or H max straddling) joints can also appear to satisfy ‘open joints were parallel to H max’ assumptions. The important improvement would be that rock mechanics theory is not violated, when assuming that unsheared joints in weaker reservoir rocks can be conductors, when actually under high levels of effective stress. Shearing to great depth has been verified in other areas of the earthsciences, and the need for adoption in the geophysical interpretation of petroleum reservoirs is discussed, with simple joint-model illustrations. The ‘critical shearing crust’ is interpreted here in terms of the non-linear BartonBandis shear strength and coupled behaviour constitutive model. An evaluation of the importance of joint roughness at several scales, and the need for dilation-corrected stress transformation in the earth sciences is also treated.

16.1

Some important non-linear joint and fracture behaviour modes

In the Chapter 15 review of some of the recent dynamic, poroelastic, multiple-porosity modelling, mostly only one

set of ‘perfectly’ aligned, or partially aligned, sets of cracks, fractures (or rock joint analogues) was seen. The mathematical complexity of multiple sets clearly presents numerical problems, but no doubt such will be solved in due time, as it was, with simpler boundary conditions, in rock mechanics, due to the need for modelling hydraulically communicating, deforming, multiple joint sets, but without the dynamic interaction with grain-size pore space. The deliberate addition in Figure 16.1, of a secondary ‘crack set’ to the Tod, 2002 conceptual model of a variably oriented single set of cracks, fractures or joints, is to emphasise the obvious: that fractured (or jointed) reservoirs often have at least two sets of joints or fractures, that can assist in the drainage of the matrix towards the wells. Primary drainage pathways are usually considered

Figure 16.1 A secondary set of joints (i.e. natural fractures) have been added to the Tod, 2002 schematic, to emphasise that in many cases there will be additional intersecting sets of joints in fractured reservoirs. Joints may also be under a state of shear stress, rather than the implied normal-stress-only.

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Rock quality, seismic velocity, attenuation and anisotropy

to be along the set that approximates the H maximum direction, as we have seen, with some variations, in the shear wave splitting analyses reviewed in the last chapter. This conventional assumption may be modified however, if the rock is weak and porous, since conducting joints might be too tightly closed, or not exist, at depths of kilometres, unless there was shearing. This aspect has dominated the selection of material for this chapter. In case of significant non-alignment of the present-day H maximum direction with the dominant set (or sets) of joints, then shear-dilation-conductivity coupling becomes a potential mechanism for effective reservoir drainage from matrix-to-joints-to-producing well. The range of effective block sizes illustrated in Figure 14.1 (1, 2 and 3 are examples) will then also come into consideration, since block size will determine how much shear-dilationpermeability coupling has been possible, especially with elevated pore pressure. Scaling of the small-scale roughness JRCo to effective roughness JRCn for the appropriate block size, following the Barton-Bandis constitutive model, suggests that case 3 with the largest block size, can have presented the lowest shear stiffness (and shear strength) to the historic anisotropic stress that may have caused shearing in the past. A sheared-joint situation would presumably tend to enhance the velocity anisotropy (both for azimuthal P-waves, and for split shear-waves). A cross-disciplinary reference to the (macrodeformation) hyperbolic normal-closure behaviour of rock joints, and to the scale effect on shear strength caused by relative block-size, are key items in this ‘sheared-earth’ thinking. These macro-deformation aspects of jointed rock behaviour are shown at the top of Figure 16.2, taken from Bandis et al., 1983, and 1981. This macro-deformation behaviour is shown here, in view of the influence it could have on the micro-deformation compliances of joints that were ‘lying close’ to the respective rock mass stiffness curves. Of course their will be differences between the inverted magnitudes of dynamic compliance and ‘static’ stiffness, but differences may be minor when rock quality is reasonably high. The assumed stress-deformation behaviour of three categories of rock mass, as visualised by Barton, 1986, are shown below the normal-closure (N) and sheardisplacement (S) components, in Figure 16.2c, and in Table 16.1. There is large scale, up to 8 m3 biaxial flat-jack loading, and uniaxial plate-loading verification of these three categories of non-linear and hysteretic behaviour. (The linear load-deformation line in case B appears to be due to two partly opposed non-linear mechanisms).

Numerical discrete element modelling of these three categories of jointed structures, was performed by Chryssanthakis et al., 1991, with UDEC-BB, incorporating the Barton-Bandis non-linear and scale-dependent joint behaviour laws, to confirm this type of rock mass stress-deformation behaviour. Type A and Type C can be considered typical of many reservoir jointing scenarios (greatly simplified), with sedimentary bedlimited jointing in Type A, often with a vertical major principal stress, but with an intermediate horizontal principal stress that could cause fracture-set alignment. Type C, representing conjugate jointing, is of tectonic origin, as for instance in the anticlinal Ekofisk reservoir in jointed chalk. The deformation, joint-shear and principal-stress plots from this numerical modelling are shown in Figure 16.3. The one-dimensional application of the Barton-Bandis normal closure modelling, shown in Figure 16.4, from Barton et al., 1985, follows the multiple load-unload consolidation cycles performed on numerous natural rock joints by Bandis, 1980. In the discrete element UDECBB modelling performed in rock mechanics analyses of e.g. slopes, tunnels and caverns for civil engineering use, we automatically follow the ‘fourth cycle’ which is assumed to approximate the ‘undisturbed’ in situ condition. There is naturally an exaggerated hysteresis (and closure) in the first cycle of a stress-closure test on a sampled ( disturbed) joint. In the context of the microdisplacements experienced by joints with the passage of seismic waves, it is clearly the consolidated state one is concerned with. Hatchell and Bourne 2005, have recently highlighted the importance of hysteresis in the interpretation of timelapse time shifts surrounding depleting, compacting reservoirs. Depletion induced time shifts have opposite sign inside and outside the reservoir. Laboratory testing of velocity-effective pressure needs to also be focussed on unloading and on strain behaviour. Models that use linear slip theory, following earlier Schoenberg work, and therefore require fracture compliances rather than aspect ratios, are gaining ground in geophysics, as we have seen from some of the modelling reviewed in Chapter 15. Here we will consider a remark by Gurevich, 2002, who describes the theoretical construction of a poro-elastic model with aligned fractures that obey linear-slip theory, and are characterized by ‘excess’ normal and tangential fracture compliances, following Schoenberg and Sayers, 1995. Gurevich commented on the fact that several authors had expressed, intuitively, the likelihood of a link between normal and

Joint stiffness and compliance and the joint shearing mechanism

485

Figure 16.2 a) Non-linear, hysteretic normal-closure behaviour of rock joints. b) Shear strength dependency on block size, also showing strong non-linearity and two reasons for strong shear stiffness scale effects. c) Conceptual pressure-deformation curves due to N and S components, or their combination. From top left: Bandis et al., 1983, Bandis et al., 1981, and Barton, 1986. Table 16.1

Three characteristic load-deformation behaviour-modes for rock masses.

Type

Dominant mode

Shape

Hysteresis

Lateral expansion*

Poisson 

A B C

normal normal  shear shear

concave linear convex

small moderate large

small moderate large

low medium high

* Under conditions of one-dimensional strain the relative magnitudes of these differences in behaviour will be reduced. Reduction in pore pressure, and compaction of the matrix, would allow a Type C mechanism in a compacting reservoir to develop further, as for instance in the Ekofisk reservoir.

tangential fracture compliances and the porosity of the host medium. From the rock mechanics world of inverted compliance, i.e. stiffness (where Kn and Ks stand for normal and shear stiffness in units of MPa/mm), there is also an

implied linkage to porosity, since the term JCS, the joint wall compressive strength, and its ratio with effective normal stress (JCS/n
) is an important component of the equation for shear stiffness and peak shear strength (Barton and Choubey, 1977), and of the hyperbolic

486

Rock quality, seismic velocity, attenuation and anisotropy

equation for normal stiffness (Bandis, 1980). The value of JCS is obtained from rock mechanics index testing, using a Schmidt (L-) impact hammer, the rebound of which (10 to 95% approx.) can be linked to uniaxial compression strength c (or UCS), also using rock density, following Miller, 1965. Clearly porosity will therefore affect this conversion of rebound to JCS (or to matrix UCS). Hence the connection to stiffness, and therefore perhaps compliance. The Schmidt hammer is used as this is almost the only way to record the reduced strength of the few millimetres of (eventually weathered, or altered) joint walls. In other words JCS  c, unless there has

been mineralization at some time, as shown in the photographs (Figure 16.5, a and b) of a wave-cut platform in dolomite, from Kimmeridge Bay in Southern England. Note the complete cementation of all joint sets in Figure 16.5c, which probably removes the need for a roughness and wall-strength based classification method.

16.2

Aspects of fluid flow in deforming rock joints

Several recent workshops have focussed strongly on seismic anisotropy, suggesting an active recognition of the

Figure 16.3 Distinct element modelling with UDEC-BB code, with the Barton-Bandis joint behaviour sub-routine, demonstrates the relative magnitudes of the shear and normal deformation components. Top: deformation, Centre: joint shearing, Bottom: principal stresses. Chryssanthakis et al., 1991.

Joint stiffness and compliance and the joint shearing mechanism

over-riding importance of dominant fracture sets (or joint sets in engineering geology terms) for drainage of reservoirs. This is particularly important where matrix permeabilities are low, yet storage in the form of porosity, obviously high enough for commercial development, sometimes to an exceptional degree. The Ekofisk field in the North Sea, is expected to have at least 80 years of production from this well jointed reservoir.

16.2.1

Coupled stress-flow behaviour under normal closure

Coupled stress-flow-deformation joint behaviour has long been of concern in rock mechanics, where there is a ‘standard’ test called the coupled shear flow test (CSFT), developed by Makurat at NGI, in Norway,

(Makurat et al., 1990), and first used for extensive studies of the conjugate joints (or fractures) in the Ekofisk chalk, to investigate oil and brine flow under normal and shear deformation, also with the effect of elevated temperature. Various aspects of this work with laboratory-scale testing of reservoir joints and reservoir-scale deformation modelling in the chalk were described by Barton et al., 1986. Although dispersive (frequency-dependent) attenuation and velocity are dynamic concepts, involving microresponses in the interior of any rock joint, it seems intuitively likely that the macro-responses of joints to coupled deformation and flow can represent ‘end-members’ for the dynamic loading and squirt attenuation concepts of geophysicists. The normal and shear compliances (units of m.GPa1) presently utilised in geophysics, have their rock mechanics inverse values, termed normal and shear stiffness (units of GPa/m). Their (inverted) magnitudes are remarkably similar, especially in the case of Kn, suggesting some yet to be determined relationship, albeit perhaps in an ‘end-member’ role. Under normal closure (i.e. the perpendicular incident wave case), the hydraulic aperture (e) of a rock joint, as measured in a (macro) flow test, is related to the larger (mean) physical aperture (E) by the roughness-related empirical equation (Barton et al., 1985):

e ≈

Figure 16.4 Normal closure and conductivity cycles and hysteresis from the BB model. An imaginary injection-production cycle is highlighted in gray. Barton et al., 1985. (The importance of hysteresis in time-lapse interpretation both inside and outside a compacting reservoir was recently emphasised by Hatchell and Bourne, 2005.)

487

E2 JRC 2.5

(16.1)

(where E  e. The joint roughness coefficient JRC, varies from 1.0 for smooth joints: giving, implicitly e  E, to about 20 for extremely rough tension fractures). There seems every reason for these ‘macro-roughness’ and ‘macro-flow’ concepts to apply as boundary conditions, in the case of intrinsic attenuation, at least in broad terms. The fundamental importance of joint or fracture (macro) roughness is demonstrated by empirical data in Figure 16.6, and Figure 16.7 shows the form of this empirical relation. An illustrative example of the physical mismatch of E and e, and the practical effect this can have on e.g. the groutability of a near-surface rock mass is illustrated in Figure 16.8. This ‘cubic’ model of Snow, 1968, with additions by Barton, 1986 is a convenient vehicle for planning the choice of suitable grout particle sizes (d95), with the rule-of-thumb E  4 d95. When there is insignificant mismatch of these quantities E and d95 due to high stress or due to the low permeability of tight joints, then

488

Rock quality, seismic velocity, attenuation and anisotropy

(a)

(b)

higher (locally deforming) injection pressures are used e.g. Barton, 2003. Note the interpreted increase of the spacing of water-conducting joints or fractures with depth, based on a statistical analysis of the Lugeon water injection test, which was depicted diagramatically in Figure 15.49, in Chapter 15. The above very simple single-parameter approach to characterizing the mismatch of the mechanical or physical aperture (E) and the usually smaller hydraulic aperture (E), does not seem to be known in the geophysics literature reviewed. There is of course data from an increasing number of research projects that has supported, and continues to support, the fundamental mismatch of these quantities, with early sources of such data listed in Figure 16.6. Key experimental research in this area includes Witherspoon et al., 1979, Barton et al., 1985, Gale, 1987, Gentier 1986, Pyrak-Nolte et al., 1990, Makurat et al., 1990, and Cook, 1992. A more recent review by Renshaw, 1995, and aperture modelling contributions from Sisavath et al., 2003 and Liu, 2005 emphasise the interest in this ‘detail’, which in fact is fundamental in controlling the world’s supply of oil, gas and water. Liu also considered that naturally fractured formations under reservoir conditions would have very small apertures (0.1–10 m), very rough fracture surfaces, and a large proportion of the fracture surfaces in contact with each other. This opinion, which is shared if only normal closure (i.e. interlock) is considered, turns out to be the least productive condition, exceeded only by more planar joints in weaker rock, which would hardly conduct fluids if tightly closed. With somewhat lesser roughness and slight shear, a fundamental enhancement to these (too) limited apertures is possible, as we shall see below.

16.2.2

(c)

Figure 16.5 A wave-cut platform in a jointed dolomite bed. These beds occur at intervals in the Kimmeridge shale, outcropping in Kimmeridge Bay, Dorset, England. The joints show a) implied JCS  c due to weathering and preferential wave erosion, and b) implied (local) JCS  c, due to subsequent mineralization of dominant conducting joints. c) A fine example of joint cementation which may prevent the use of normal joint characterization techniques. Widemouth Bay, near Bude, Devon, England. (See Plate 9).

Coupled stress-flow behaviour under shear deformation

When there is shear displacement (i.e. a discontinuity in the shear stress-load behaviour), experiments show that the roughness ‘iso-curves’ of Figure 16.7, are cut nearly at right angles in the E/e versus e space. Some of these trends are seen in Figure 16.6, from a slightly sheared, heated block test (see ‘N–S’, ‘E–W’ etc.). Esaki et al. 1995, confirmed these ‘perpendicular’ trends, and Olsson and Barton, 2001, formalised the results, following further CSFT testing by Olsson (Figure 16.9) for the case of the mismatch of (e) and (E) that occurs when there is shear

Joint stiffness and compliance and the joint shearing mechanism

489

Figure 16.6 Mismatch of (e) and (E) due to joint or fracture roughness. Barton and Quadros, 1997, (updated from Barton et al., 1985)

Figure 16.7 An empirical model for the mismatch of E and e, from Barton et al., 1985.

(and some gouge production). The following empirical relation was found to apply: 1

e  E 2  JRCmob

(16.2)

The JRCmobilized concept of joint or fracture shear strength mobilization is explained with a low stress example in Figure 16.10. The early mobilization of friction, followed later by dilation and roughness mobilization and

490

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.8 A cubic-network approach to near-surface permeability at dam sites (after Snow, 1968), with the addition of aperture differentiation and roughness discrimination by Barton, 1986.

final roughness degradation, was quantified by Barton, 1982, and forms an important basis for the shear-part of the Barton-Bandis constitutive model. Note the location of ‘dilation begins’, corresponding to the initial mobilization of roughness. In the ‘roughness destroyed’ post-peak area there is a physical reduction in JRC, in other words retesting would show a reduced peak strength for the joint in question. The early mobilization of friction (prior to dilation), can be envisaged as a potential contributor to the intrinsic frictional attenuation mechanism, but would presumably involve (almost) recoverable micro-slip. The other part of intrinsic attenuation involving fluid flow: potential viscous shearing, or ‘squirt’, will

Figure 16.9 Data points are from CSFT (coupled shear-flow tests) by Olsson, in Olsson and Barton, 2001, showing ‘perpendicular’ trends in relation to the E-e-JRC model, due to shearing and gouge formation. The ‘sloping-to-theright’ curves are relevant to shear behaviour, and are similar to trends shown by Esaki et al., 1995. In other words shearing, dilation, and possible gouge formation causes data to climb the curves (for JRCmob), shown to the left.

clearly be affected by minor (or larger) amounts of (pre-) shearing. Figure 16.11 shows a set of experimental data (solid black points), from a self-weight, very low stress ‘CSFT’ from Maini and Hocking, 1977. The ‘twin’ curves in the other three diagrams were obtained using the shear, dilation and flow coupling given by the BartonBandis model, based on the JRCmob concept shown in Figure 16.10. Note the large change of measured and modelled permeability due to slight dilation, for the case of these very planar (low JRC) cleavage joints. A more recent coupled shear-flow test performed at higher stress by Olsson, using controlled normal stiffness loading in a large direct shear box apparatus (see Olsson and Barton, 2001), is shown in Figure 16.12. The term ‘krm’ in the individual figures stands for applied normal stiffness, with ‘krm  0 kN/mm’ representing a conventional, constant normal load, zero-stiffness test.

Joint stiffness and compliance and the joint shearing mechanism

491

Figure 16.10 The JRCmobilized concept of Barton, 1982. This shows shear strength development for rock joints expressed as a dimensionless JRCmob/JRCpeak, and reduction of this ratio with dimensionless (/peak) displacement. Peak shear strength is given by ␶  n tan [JRC log (JCS/n)  r], from Barton and Choubey, 1977. This diagram also gives a direct method for predicting the theoretical (maximum) permeability development with displacement and dilation. For this one uses the JRC-based E  e inequality, and the initial-apertureenhancing dilation. (For gouge-reduced permeability estimation, one uses the JRCmobilized relation, as shown in Figure 16.9).

A CSFT test by Makurat (Makurat et al., 1990) is shown in Figure 16.13. This was selected as it shows that with gouge production caused by shearing damage, there will be a discrepancy between the dilation-based permeability modelling (assuming full application of the dilation-enhanced aperture), and the experimental result. The measured permeability increase with shearing was less than expected from the measured dilation, due to gouge production compromising the effect of the increased aperture. In two of the above cases, the theoretical effect of the modelled dilation on permeability is shown. In the low stress case (Figure 16.11), a reasonably good match to the dramatic, two-orders-of-magnitude increase in permeability with less than 0.6 mm of shear is suggested. The tests by Olsson (Figure 16.12) show a smaller, but significant increase (e.g. one order of magnitude increase with

Figure 16.11 An early coupled shear flow test by Maini (in Maini and Hocking, 1977), and an attempt to match this by estimating the shear-induced increase in joint aperture due to full application of the dilation effect, using the Barton-Bandis model. (Barton, 1982).

2 mm of shear) but with reduced rate at larger shear deformation. From the point of view of attenuation potential in the reservoir situation, the presence of ‘open’ fractures caused by limited shear, may be an important additional effect for dynamically induced (micro) fluid flow, and squirt losses, during the passage of a wave front. Sheared fractures may represent some of the ‘open’ fractures

492

Rock quality, seismic velocity, attenuation and anisotropy

16.3

Figure 16.12 CSFT tests by Olsson using controlled normal stiffness during the shearing. One order of magnitude increase in permeability with 2 mm of shear is indicated. (Olsson and Barton, 2001).

Figure 16.13 CSFT test by Makurat, showing the experimentally measured increase in permeability during 2.5 mm of shearing on a joint in weathered gneiss, compared to the modelled, much larger permeability increase, if one assumes no blockage to flow by gouge production. Makurat et al., 1990b and Bandis et al., 1985.

often referred to, and they could be an important source of in situ anisotropy, as described in Chapters 14 and 15. However, with higher effective normal stresses, and with the likely presence of some gouge, making for a tortuous flow path and generally tighter apertures (i.e. smaller aspect ratios, despite shearing), flow resistance is likely to be significant.

Some important details concerning rock joint stiffnesses Kn and Ks

Normal stiffness Kn is defined as the normal stress increment required for a small closure of a (usually very tight) joint or fracture, at a given level of effective stress. It is therefore clear that it is usually of significantly larger value than the shear stiffness Ks which is the stiffness in shear, usually taken as the average slope up to the shear strength-displacement peak. Since compliance in both normal and shear directions is becoming of such importance in recent geophysics modelling, some of the parallel, but macro-displacement aspects of the inversed parameters, Kn and Ks will be further explored in this section. It is believed that when rock quality is good, and joints are hard, there will be great similarity in magnitude between Kn and its dynamic ‘inverse’ 1/ZN, where ZN is the dynamic normal compliance. This is probably because of the similarity, in good rock conditions, between E dynamic and E static, as investigated in Part I. Between Ks and its dynamic ‘inverse’ 1/ZT, where ZT is the dynamic shear compliance, there is likely to be a significant difference, due to the lesser likelihood that block size will be the determinant factor, as it is for the magnitude of the pseudo-static shear stiffness Ks. When rock is of poor quality, and joints are altered or clay-bearing, there will be greater discrepancies between each of the above three pairs of parameters, but Kn and 1/ZN should remain within an order of magnitude of each other. These aspects have been discussed in slightly different context, in a number of chapters in Part II. Barton, 1972, Barton and Hansteen, 1979, Bandis, 1980, Bandis et al., 1981 and Barton, 1982 have each emphasised the scale-dependent nature of shear stiffness Ks. An assembly of various sets of data is reproduced in Figure 16.14, from Barton, 1982. By means of characterizing joint samples recovered in core, using the JRC (joint roughness coefficient) and JCS (joint wall compressive strength) parameters, it is possible with Barton-Bandis joint modelling to simply estimate the above scale-dependent shear stiffnesses. An example, using two different laboratory (core) sized samples, is shown in Figure 16.15 for an assumed block-size range of 100 mm to 10 m. The three diagonal pairs of curves, represent shear stiffnesses at three effective normal stress levels. Techniques for estimating the joint characteristics JRC and JCS, developed by Barton and Choubey, 1977, are illustrated in graphical format later in this chapter,

Joint stiffness and compliance and the joint shearing mechanism

Figure 16.14 Experimental ‘large strain’ data for the shear stiffness (Ks) of rock joints, clay-bearing discontinuities, and model tension fractures. A very strong scale dependence, and a strong (effective normal) stress dependence are each implied. These are fundamental properties of rock masses in ‘macro-deformation’ processes. Barton, 1982.

when exploring the effects of stress on modelled joint apertures. Normal stiffness (Kn), by comparison to Ks, may not be scale-dependent, although it is undoubtedly

493

Figure 16.15 Estimation of peak shear stiffness based on extrapolation of two different joint characters (as observed at core-scale) using Barton-Bandis scaling, from Barton, 1982. The extent of direct relevance of these ‘macro-displacement’ stiffnesses to seismic ‘microdisplacements’, using the stiffness-compliance inversion, with adjustment for the Edynamic # ,static inequality, is presently more uncertain, when moving in the direction of larger block sizes.

‘sample-dependent’, i.e. if a larger, more continuous, water-bearing, feature is sampled, it will likely have lower normal (and shear) stiffness than a less continuous, probably unweathered and usually rougher joint surface (Barton, 1990b). As shown in extensive studies by Bandis, 1980, and Bandis et al., 1983, the normal stiffness of joints Kn is especially sensitive to sample disturbance (i.e. inevitable unloading when recovering samples), and the first load

494

Rock quality, seismic velocity, attenuation and anisotropy

cycle as depicted in Figure 16.16, shows much lower initial stiffness and much larger hysteresis. Lower normal stiffness is also seen following shearing, due to a certain mismatch of the previously interlocking roughness. The reduced contact area causes the reduced stiffness, with typically 1⁄2 to 1⁄8 reduction, depending on stress level (Bandis et al. 1983). Adverse effects on the dynamic compliances ZN and ZT are likely too. The contrasting normal stiffnesses from first, second and third cycles of loading for fresh joints in hard rock are shown in Figure 16.17. Corresponding curves for joints in weaker rocks or weathered rocks are markedly less steep, and show much more hysteresis on the first cycle. The relative effects of different rock types on normal stiffness including the weaker sandstones, siltstones and limestones are illustrated in Figure 16.18, from Bandis, 1980. Here we see the total (rock  joint) deformation Vt. 16.3.1

It is clear from inspection of data in Figure 16.17, and elsewhere, that these average third cycle, initial normal stiffness values of roughly 30 to 120 MPa/mm, correspond to effective normal stresses in the lowest

Initial normal stiffness measured at low stress

A major tabulation of initial normal stiffness (Kni), normal stiffness and maximum closure ranges for first, second and third load cycles for numerous rock joint samples with widely different JRC and JCS values was assembled by Bandis, 1980. In Table 16.2, just the average values have been reproduced. As will be noted for moderately weathered and fresh sandstones, siltstones and limestones, the third cycle, have Kni values in the respective ranges as follows: Sandstone 27 to 37 MPa/mm Siltstone 23 to 54 MPa/mm Limestone 99 to 118 MPa/mm

Figure 16.16 Normal stiffness testing of rock joints Vt  total deformation VJ  net joint closure. First cycle of load-unload. Bandis, 1980; Bandis et al., 1983.

Figure 16.17 Three load-unload (VJ) cycles for joints in hard unweathered rock. Bandis et al., 1983. These will be used for estimating normal stiffness dependence on normal stress, at the highest stress levels.

Joint stiffness and compliance and the joint shearing mechanism

possible range of perhaps 0 to 1 MPa, and at the same time correspond to the pre-consolidated condition, since measured after three load-unload cycles.

Figure 16.18 Comparative total deformation (Vt  rock  joint) for different rock types, based on the most deforming first cycle of loading. Bandis, 1980. Table 16.2

16.3.2

495

Normal stiffness at elevated normal stress levels

From 0 to 5 MPa, there is a rapid rise of the average (pseudo-static) normal stiffnesses to between 250 and 500 MPa/mm, and between 0 and 10 MPa, 400 to 800 MPa/mm is more common for the average normal stiffness of the fresher joints, and about 200 MPa/mm for the (JCS  40–50 MPa) joints in weaker rock. The average normal stiffnesses between 0 and 50 MPa are of the order of 2,000 to 3,000 MPa/mm for the hardest joints. However, considering local or incremental stiffnesses, at tens of MPa stress levels (such as 10 to 40 MPa), normal stiffnesses for these unweathered hard joints with high JCS may rise to tens of thousands, but may only rise to about 1,000–2,000 MPa/mm in the case of the weaker rocks (e.g. with JCS  40–50 MPa). Before proceeding to a detailed treatment of possible stiffness ratios, we will present normal stiffness data kindly prepared by Bandis from his 1980 doctoral studies in the University of Leeds. This can be compared, where

Bandis, 1980 data for Kni (3 cycles) and maximum closure Vm (3 cycles). Vm and Kni data 1st cycle

Rock type and weathering state of joints

JCS (MPa)

SLATE Fresh Mod. weathered Weathered

175 142 77

DOLERITE Fresh Weathered

2nd cycle

3rd cycle

Kni MPa/mm

Vm mm

Kni MPa/mm

Vm mm

Kni MPa/mm

Vm mm

3 1 3

35.0 13.1 12.7

.039 .106 .331

181.1 69.0 32.6

.027 .046 .146

266.2 235.5 63.6

.027 .039 .118

167–182 60–76

2 3

24.2 10.8

.101 .484

67.1 50.0

.053 .150

111.2 80.4

.067 .109

No. of joints

LIMESTONE Fresh to slightly weathered Mod. weathered Weathered

152–170

11

18.8

.091

85.3

.042

117.9

.030

94–120 35–53

5 5

30.1 8.5

.116 .373

51.7 44.2

.060 .115

98.9 56.9

.040 .079

SILTSTONE Fresh Mod. weathered Weathered

105 67 44

5 2 3

18.9 10.8 10.4

.135 .310 .514

43.9 20.8 27.8

.072 .205 .104

53.5 22.9 35.0

.063 .184 .113

68–95

8

12.8

.170

23.4

.075

37.2

.054

64–58 22

9 4

9.3 3.1

.240 .469

17.9 11.3

.101 .131

26.7 15.6

.089 .080

SANDSTONE Fresh to slightly weathered Mod. weathered Weathered

496

Rock quality, seismic velocity, attenuation and anisotropy

possible with data in Table 16.4 from Pyrak-Nolte et al., 1990 that was reviewed in Chapter 15. To conserve space in Table 16.3 normal stiffness values for weathered joints are excluded, in view of their lesser relevance for reservoir conditions. A rough (JRC  15), weathered (JCS  44 MPa) joint in limestone showed Kn values of 250, 1,275 and 2,550 MPa/mm at normal stress levels of 10, 25 and 40 MPa. More planar (JRC  6), weathered joints (JCS  25–45 MPa) in

sandstone and siltstone displayed normal stiffnesses of between 200 and 900 MPa/mm at normal stress levels of 10 and 25 MPa. Several of the pseudo-static values of normal stiffness from the tests of Bandis, 1980 shown in Table 16.3 had higher values of pseudo-static normal stiffness than the dynamic normal stiffnesses of this more deformable joint in quartz monzonite. Another series of tests by PyrakNolte and co-workers, using a stiffer (E 32) sample, and

Table 16.3 Normal stiffnesses in (MPa/mm) measured by Bandis, 1980 in pseudo-static loading. Aperture (a) represents the approximate unstressed aperture prior to testing. (Bandis, 2005 pers. comm.)

Normal Stress

(MPa) 10 25 40

Limestone

Limestone

Sandstone

Sandstone

Siltstone

F JRC  10 JCS  160 MPa a  0.25 mm (MPa/mm) 1,200 6,300 15,750

SW JRC  7.6 JCS  160 MPa a  0.2 mm (MPa/mm) 850 10,500 31,500

F JRC  12 JCS  68 MPa a  0.25 mm (MPa/mm) 470 12,750 –

MW JRC  7.5 JCS  44 MPa a  0.25 mm (MPa/mm) 350 12,750 –

F JRC  9 JCS  105 MPa a  0.15 mm (MPa/mm) 350 3,100 –

Table 16.4 Comparison of static and dynamic normal stiffness data for the Pyrak-Nolte et al., 1987b jointed sample E 35, of 52 mm diameter, which was the most deformable of three joint samples, possibly due to greater roughness. Normal Stress

Static stiffness Kn(static)

Dynamic stiffness Kn(dyn)

Ratio

MPa

MPa/mm

MPa/mm

Kn(dyn)/Kn(static)

2.9 10.0 33.0

1,000 2,200 3,300

4,500 8,000 25,000

4.5 3.6 7.6

Table 16.5

Selected dynamic normal and dynamic shear stiffnesses from tests on two joints in quartz monzonite. Pyrak-Nolte et al., 1990.

STRESS

Sample E 32

(all stiffnesses in MPa/mm)

Sample E 35

(all stiffnesses in MPa/mm)

n (MPa)

Kn(dynamic)-dry

Kn(dynamic)-saturated

Kn(dynamic)-dry

Kn(dynamic)-saturated

2.9 10 20 70

15,000 – – 120,000

35,000 80,000 100,000 –

4,000 11,500 20,000 32,000

9,500 20,000 25,000 59,000

n (MPa)

Ks(dynamic)-dry

Ks(dynamic)-saturated

Ks(dynamic)-dry

Ks(dynamic)-saturated

2.9 10 20 70

3,500 9,500 17,000 55,000

– – – –

1,900 4,800 6,200 7,400

– – – –

Joint stiffness and compliance and the joint shearing mechanism

the same E 35 sample as above, provided both dry and saturated results. These are repeated in Table 16.5 in compatible (MPa/mm) units, for ready comparison.

16.4

Ratios of Kn over Ks under static and dynamic conditions

Due to equipment capacity limitations, when Bandis, 1980 tested both the normal and shear stiffnesses of the same joint sample, involving tests in a shear box rather than in a high-capacity loading frame, significantly lower levels of normal stress than any of the above were applied. Values of Ks ranging from 1 to 7 MPa/mm were obtained, where normal stress values were in the range of approx. 1 to 5 MPa, for the 100 mm long samples. It seems reasonably certain that Ks static is likely to be some orders of magnitude lower than Ks dynamic at comparable normal stress levels. Future testing to develop an improved data base is obviously required. Significantly we do not yet seem to know the effect of in situ block sizes on Ks dynamic. Block size has a dramatic, and well documented reducing effect on Ks static (e.g. Barton, 1972, Bandis et al., 1981, Barton, 1982), as also seen in Figures 16.14 and 16.15. When the ratio of Kn/Ks (both static) could be compared directly on the same 100 mm long samples, mostly at the low normal stress of 1 MPa, Bandis found that the ratio varied from extremes of 5.7 (dolerite) to 132 (slate), but with most ratios of Kn/Ks in the narrow range of 11 to 15. Table 16.6 gives the ratios of Kn(dyn)/Ks(dyn) for the dry samples listed in the Table 16.5. Note that the ratios of dynamic stiffness are for 52 mm diameter specimens. Under pseudo-static testing, the size of sample plays a significant role in reducing the shear stiffness, thereby increasing the ratio Kn/Ks to much larger values than the range given in Table 16.6. Under dynamic testing this appears not to be the case. It may be noted from the above tables that the range of Kn(dyn)/Ks(dyn) ratios for these three, 52 mm diameter jointed samples in quartz monzonite was only from 1.3 to 4.3 with a mean of 2.5. This means that the ratio of the inverted compliances ZN/ZT for these small samples ranges from 0.2 to 0.8, with a mean of 0.4. The remaining question is what relevance this convenient ‘coresized’ data has to in situ reservoirs in general, with a typical spread of jointed block sizes from perhaps 200 mm to 5,000 mm, and mostly sedimentary rock as opposed to Stripa ‘granite’, or hard quartz monzonite.

497

Table 16.6 Ratio of dynamic Kn/dynamic Ks for the three PyrakNolte et al., 1990 joint samples in quartz monzonite. The authors’ data set is partially incomplete. All samples were of 52 mm diameter. STRESS

Sample E 30

Sample E 32

Sample E 35

n (MPa)

Kn(dyn)/Ks(dyn) (dry)

Kn(dyn)/Ks(dyn) (dry)

Kn(dyn)/Ks(dyn) (dry)

2.9 10 20 33 70

1.6 1.3 2.0 2.7 –

4.3 – – – 2.2

2.1 2.4 3.2 – 4.3

16.4.1

Frequency dependence of fracture normal stiffness

The dynamic stiffness data for the three joints reported by Pyrak-Nolte et al., 1990, were acquired over a limited ultrasonic frequency range (mostly 0.1 to 1 MHz). Different aspects of these tests were reviewed in Chapters 10 and 15, and have been summarised in part in this chapter, for comparison with static data. An important ‘detail’ is the fact that the dynamic stiffness, showing roughly four to eight times greater magnitude than the static values for the ‘soft’ joint in Table 16.4, is actually dependent on the frequency. Pyrak-Nolte and Nolte, 1992 addressed this important aspect, suggesting that the frequency-dependence may be a simple consequence of the fracture or jointwall geometry. They referred to a ratio of dynamic/static normal stiffness ‘of typically three’, and likened this ratio to the difference of the dynamic to static moduli. As we have seen in Part I, the ratio is rock quality dependent, and the Table 16.4 result for the more deformable joint (E 35), is consistent with this picture: the ‘softer’ the joints, the greater will be the difference. This applies to an even greater extent if the shear stiffness of the joints is also involved in the respective static and dynamic loading directions. Pyrak-Nolte and Nolte 1992 applied the displacementdiscontinuity theory of Schoenberg, involving assumptions of discontinuous displacement, but continuous stress across the fractures. An assumption of inverse proportionality between the discontinuity displacement and the specific stiffness of the fracture is also involved. The authors assumed that the different parts of any given fracture in intimate interlock due to normal stress, will

498

Rock quality, seismic velocity, attenuation and anisotropy

earlier frequency-independent values of 11,000 and 24,000 MPa/mm (shown by black dots). For the sake of completeness, Figure 16.19a shows one of the experimental data sets for the static normal stiffness of the three joints, which was reviewed in Chapter 10. Pyrak-Nolte and Nolte, 1992 observed that the dynamic stiffness is equal to the static stiffness at low frequencies. This is clearly an important ‘end-member’ when considering the interpretation of fracture stiffnesses at much lower seismic exploration frequencies. It suggests that fracture properties, as defined in detail in Bandis 1980 static data (i.e. JCS and JRC, and resultant behavioural trends) will have more to say when comparing static and dynamic behaviour at seismic frequencies, than when comparing static and dynamic behaviour at laboratory ultrasonic frequencies. The in situ scale of fracturing and block sizes, and the use of lower frequencies, suggest that one should remain open to the possibility that static behaviour can be a useful guide to possible joint-parameter influences at seismic exploration frequencies. Note from Figure 16.19 that laboratory ultrasonic frequencies ‘automatically’ cause Kn (dynamic)  Kn (static). At frequencies below 0.1 MHz, somewhat closer dynamic to static magnitudes are suggested.

16.4.2 Figure 16.19 a) Static normal stiffness trends for three joints in quartz monzonite (Pyrak-Nolte et al., 1987a). b) Dynamic stiffness as a function of frequency, for normal stress levels of 10 and 20 MPa. Pyrak-Nolte and Nolte, 1992.

have different characteristic frequencies, due to the distribution of voids and highly stressed rock-to-rock contacts. This will mean that different parts of the fracture will pass lower frequencies, while other parts will pass higher frequencies. They therefore assumed that the local transmission coefficients would depend on the local static stiffnesses. The authors used a so-called stratification percolation model to simulate fracture aperture distributions and to match (with excellent precision) experimental amplitudefrequency curves from the tests by Pyrak-Nolte et al., 1990 referred to earlier. The result of their dynamic stiffness-frequency modelling is shown in Figure 16.19b: the two curves apply to normal stress levels of 10 MPa and 20 MPa, and were considered an improvement on the

Ratios of static Kn to static Ks for different block sizes

Since there are several variables involved in joint stiffness, beside the influence of wall strength JCS and roughness JRC, we will in the following simplify by assuming either small or moderate in situ block dimensions of 100 mm (i.e. bed-limited blocks) or 1 m (i.e. moderately jointed reservoirs). Block volumes might well rise to 10’s, 100’s or 1000’s of m3, in sparsely jointed rock masses. Since Kn is not believed to be scaledependent (but sample-dependent), while Ks is clearly very scale dependent, it can be expected that static ratios of Kn/Ks will tend to rise strongly with increasing block size. Ks is very scale dependent because both peak shear strength and displacement to peak are scale dependent. It could be described as doubly-dependent on scale. Comparison of the reviewed Kn trends, with the Ks ranges seen at (effective) normal stresses from 1 to 10 MPa in Figure 16.14 (usually about 1 to 10 MPa/mm for 100 mm samples, and 0.2 to 2 MPa/mm for 1 m block sizes), indicates that ratios of Kn/Ks are

Joint stiffness and compliance and the joint shearing mechanism

most likely to be in the following very approximate ranges, based on data reviewed earlier: 1) 1 to 10 MPa: 100 mm size: Kn/Ks  (200–800)/ (10)  20–80 2) 1 to 10 MPa: 1 m size: Kn/Ks  (200–800)/ (2)  100–400 3) 10 to 40 MPa: 100 mm size: Kn/Ks  (1000– 20000)/(10–25)  100–800 4) 10 to 40 MPa: 1 m size: Kn/Ks  (1000–20000)/ (2–4)  500–5000 (Italics implies uncertainty in incremental, high stress, normal stiffnesses) This means that the pseudo-static Kn/Ks ratios may be in the low hundreds to low thousands at typical reservoir effective stresses, in the case of weaker or harder rocks, respectively. Here we assume that Ks remains between about 2 and 20 MPa/mm, at large (1 m block-size), and small-scale (0.1 m block-size) respectively, as suggested at stress levels of about 10–20 MPa in Figure 16.14. At the higher (effective) normal stress levels, Kn is seen to rise much faster than Ks, so it is therefore that ratios of Kn/Ks may climb to a range of about 500 to 5,000, in the context of in situ block sizes, as opposed to joints in small, highly stressed laboratory samples. It goes without saying that the reasons for the ‘mismatch’ of these macrodeformation stiffnesses, is because they are defining such different processes: Kn approaches the stiffness (and stability) of the intact rock, while Ks approaches the failure direction. (This is emphasised in Figure 15.5). These two different stiffnesses are truly the hard and the soft stiffnesses of a rock mass, just as the matrix pore space, and the joints, are respectively the hard and the soft porosities of a rock mass. However, we have seen that ultrasonic, laboratory-scale measurements suggest less softness, since the ratios of dynamic Kn/Ks are much lower than the static ratios just listed. The most important question that remains to be solved is whether seismic exploration frequencies, combined with much larger in situ fracture sizes and block sizes, will cause larger dynamic Kn/Ks ratios than those listed in Table 16.6. If the significantly ‘anisotropic’ or unequal static joint stiffnesses are in any way responsible for an (inverted) ‘anisotropy’ or non-equality of ZN/ZT, then they are surely a strong reason for the potential ‘visibility’ of water/oil/gas conducting joints to shear waves, as their potential weakness in shear and their anisotropy of stiffness (Kn/Ks) may be so marked compared to the more isotropic intact rock.

499

One could suggest, based on the above, that joints (or ‘meso-scale’ fractures) should be more seismically visible than stress-aligned microcracks, or the ‘extensive dilatancy anisotropy’ (EDA), if visibility depended on compliance contrasts, unless for some reason macro-deformation stiffness ratios (Kn/Ks) have no influence as ‘starting points’ for the micro-deformation dynamic compliance ratios (ZN/ZT). In good quality rock when Estatic is close to Edynamic, there should in fact be close correspondence of Kn(static) and 1/ZN (dynamic), but apparently from what we have seen thus far, there may not be good correspondence of Ks(static) and 1/ZT (dynamic), unless block size and frequency have influence.

16.4.3

Field measurements of compliance ZN

Important recent contributions to the problem of determining field-scale joint or fracture compliances were made by Lubbe and Worthington, 2005 and Lubbe, 2005. These were not reviewed in earlier chapters as they are most directly comparable with the foregoing rock mechanics work concerning in situ joint stiffnesses, and the scale effect known to act on the (static) shear stiffness Ks. These topics belong here in Chapter 16. Lubbe and Worthington utilised three 40 m deep boreholes drilled in the floor of a Carboniferous limestone quarry near Bristol, in southwest England. Core analysis, wire-line logging, and local fracture mapping provided the important characterization data, for future comparison to other sites. Although using much lower frequency sources than in the laboratory (2000 Hz from a sparker), these cross-hole investigations were of course at significantly higher frequency than that of seismic exploration. The stiffness-frequency trends shown in Figure 16.19 should therefore be remembered. The authors found that the rock mass had a P-wave anisotropy of 10% which they attributed to the predominantly horizontal, partly open fractures. P-wave velocities were often in the range of 5 to 6 km/s. An average of 5250 m/s for the fractured regions was quoted. The average density was 2,600 kg/m3. For a near-surface location, this velocity suggests a rock mass quality Qc value of about 55, and a deformation modulus of about 38 GPa, assuming a UCS of a nominal 100 MPa. Lubbe et al., reported an intact seismic Q as high as 60, and an in situ value as low as 25 – the implied minimum. Again the similarity of Qseis to the potential

500

Rock quality, seismic velocity, attenuation and anisotropy

static E-modulus or rock mass deformation modulus, expressed as GPa is striking: see Figure 13.60. By using the upgoing or downgoing waves between borehole source and receivers, Lubbe and Worthington were able to estimate (dynamic) fracture normal compliances within the range of 2.5  1013 to 3.5  10 12 m/Pa. These we can invert to dynamic normal stiffnesses in the range 4000 to 286 MPa/mm, or reversing the order and adopting a more ‘friendly’ unit, between 0,3 to 4 MPa/ m. Assuming an average of two continuous fractures per meter from 5 to 20 m depth, between all three boreholes, they estimated a mean fracture compliance of 1.25  1012, which converts to 800 MPa/mm in more easily understood rock engineering units. Later in the paper a ‘reasonably robust average’ of 1000 MPa/mm was suggested, following some numerical scoping. As they pointed out, their compliances were an order of magnitude higher (therefore the stiffnesses lower) than obtained from laboratory experiments at higher stress and on smaller and stiffer samples. However, they referred to other field data showing low Kn(dynamic) values of only 500 MPa/mm (dynamic compliance  2  10 12 m/Pa), for columnar joints in basalt, as interpreted by Myer et al., 1995 from Hanford Basalt cross-hole tests performed by King et al., 1986. (In Chapter 13 we also noted a very low seismic Q in the same horizontal measurement direction at this

site, i.e. crossing the basalt columns, which was probably related to low levels of horizontal stress at this shallow test tunnel site: see Figure 13.61). Examination of Figure 16.19 and Tables 16.4 and 16.5 in fact shows the stiffer end of the above range of in situ data to be the same as the ‘softer’ E 35 sample of Pyrak-Nolte, when tested at only 2.9 MPa normal stress, while the least stiff in situ result of 286 MPa/mm, is obviously closer to Bandis, 1980 static Kn data shown in Table 16.3. Lubbe and Worthington considered that the vertical fractures at the quarry (Figure 16.20) appeared to be stiffer than the measured bedding planes, resulting in horizontal velocities that were close to those for the unfractured rock. There appears to the writer the possibility that the quite high horizontal P-wave velocities of typically 5.3 to 6.2 km/s could be due a horizontal stress concentration beneath the floor of the quarry. If so, this would give an ‘equivalent depth’ correction to the empirical Qc – M – Vp relationships shown in Figure 13.59, thereby ‘not requiring’ so high Qc values. This would actually be more in line with the quite jointed appearance of the quarry seen in Figure 16.20, where a rock mass Q-value of about the following magnitude would normally be expected (see Appendix A for ratings): Q 

90 2 0.66    13 9 1 1

(E Mass
24 Gpa)

Figure 16.20 Oxford University Earth Sciences Department website photograph of the Carboniferous limestone quarry near Bristol that was used for careful in situ investigations of normal compliance. (Lubbe et al., 2005). Note dipping bedding planes and subvertical joints, presumably seldom sampled by the vertical boreholes in the floor of the quarry. The cross-hole seismic was performed between three vertical holes spaced at 7 m. These are in the foreground. (www.earth.ox.ac.uk)

Joint stiffness and compliance and the joint shearing mechanism

The authors also discussed shear compliances at the end of their paper, referring to Worthington and Hudson, 2000, fault studies. ‘Values of shear compliance of the order of 1010 to 10 9 m/Pa can be predicted and tentatively compared to field observations’. These can be inverted to in situ fault-related dynamic normal stiffnesses of only 10 and 1 MPa/mm, giving a somewhat closer match to the scale-dependent static shear stiffnesses plotted in Figure 16.14 and calculated in Figure 16.15. Such in situ, modelling-based estimates would be about one order of magnitude stiffer in relation to the static stiffness values for in situ block sizes of say 10 m, assuming ‘in situ’ effective stress levels above and below a nominal 10 MPa. If on the other hand, in situ block sizes were only 0.5 m, as feasible in the neighbourhood of a fault, such ‘soft’ dynamic values (also obtained at lower seismic exploration frequencies), would match static values very closely.

16.4.4

Investigation of normal and shear compliances on artificial surfaces in limestones

Lubbe and Worthington, 2005 also referred to Lubbe, 2005 laboratory data for artificial fractures machined from Jurassic and Carboniferous limestones, tested dry under 5 to 60 MPa normal stress, at ultrasonic frequencies between 0.6 and 1.0 MHz. Using the displacement

501

discontinuity theory of Schoenberg, 1980, values of Kn (dynamic) ranging from 22,220 to 200,000 MPa/mm were derived, when inverted from the reported 4.5  1014 to 0.5  10 14 m/Pa compliance units. These dynamic stiffnesses are similar, to somewhat stiffer, than the Pyrak-Nolte data for natural joints of 52 mm size reviewed earlier. Lubbe, 2005 found that the ratio of normal to tangential compliance for the 50 mm diameter ‘fractured’ samples, was approximately 0.4 in the case of smoother surfaces, and increased from 0.3 to 0.8 in the case of corrugated surfaces that experienced ‘asperity-crushing’ beyond 30 to 40 MPa normal stress. The ratio of 0.4 for the smoother surfaces is the same as the mean value reported by Pyrak-Nolte et al., 1990 from their tests on 52 mm joint samples, as reviewed in Chapter 15. Lubbe et al., 2005 reported details concerning the type of artificial fractures that were prepared for these tests. Samples were either cut with a ‘fine-toothed’ diamond saw and then polished, or, in the case of just the Jurassic limestone, samples were cut and grooved to produce a ‘corrugated fracture interface’ with specific voids and contact areas. The two ‘fracture’ types, which were all tested dry, are shown in Figures 16.21 and 16.22, together with the respective, and contrasting, compliance-normal stress behaviour. In these figures we have added stiffness scales on the right-hand axes, to aid comparison with the laboratory stiffness data reviewed earlier in this chapter. The Jurassic limestone samples had porosities of approximately 13%, while the Carboniferous limestone

Figure 16.21 a) Samples of Jurassic (J) and Carboniferous (C) limestone, with ‘fractures’ prepared with a fine-toothed diamond saw. b) Shear and normal compliance versus normal stress, with inversion to dynamic stiffnesses shown on the right-hand axis. Lubbe et al., 2006.

502

Rock quality, seismic velocity, attenuation and anisotropy

samples had porosities of only 2.4%. Densities were 2710 and 2660 kg/m3 respectively. The lower stiffnesses seen in the case of the corrugated fracture surface, giving artificial (initial) limits to contact areas, has some resemblance to the reduced (static) normal stiffnesses recorded by Bandis, 1980 for slightly sheared joints, shown in Figure 16.16 (see ‘mismatch’ result). A marked acceleration in the axial shortening of the sample was noted by the authors between stress levels of 30 and 40 MPa, which also corresponded with the increment of dynamic normal stiffness seen in Figure 16.22. It is also consistent that a decrement of dynamic shear stiffness should also occur at this same stress level, resembling a ‘roughness-destroyed’ portion of pseudo-static shearing simulation (the JRCmobilized concept), shown in Figure 16.10. The authors discussed the marked difference of compliance behaviour exhibited by their two types of artificial fracture. The ‘grooved’ sample showed a steady reduction in both normal and shear stiffness up to 30 or 40 MPa, exactly the reverse of the stiffening behaviour of the sample that actually had a more ‘natural’ contact area development. They proposed, very reasonably, that a gradual weakening (of the asperities) was occurring in the grooved case. They also reported a layer of powdered rock development beyond 40 MPa. Finally they doubted that the theoretical use of the ZN/ZT compliance ratio was justified, as an indicator of potential fluid saturation (and fluid type), as reviewed and also doubted in Chapter 15 (see Figure 15.11).

It seems, also from earlier review of the Perspex plates model of Hsu and Schoenberg, 1993, and of a cut ‘fracture’ in aluminium, that the less ‘rock-joint-like’ the sample, the more likely it is that the ratio of ZN/ZT will approach 1.0. In the case of the above grooved limestone interfaces, the ratio rose markedly, towards 0.8, beyond a stress level of 40 MPa. In the rock mechanics world of pseudo-static testing, including laboratory and field scales of blocks, the more ‘rock-mass-like’ the sample becomes (i.e. when moving into the in situ environment), the higher the ratio of Kn/Ks. If this behaviour has a certain influence, even only minor, on exploration seismic behaviour, (at orders of magnitude lower frequency than all the laboratory compliance testing reviewed in this book), then a lower ratio of ZN/ZT would be expected, far from the neighbourhood of 1.0, as seen in many laboratory-based or modelling-based geophysics publications. Concerning the actual effect of water saturation compared to the dry state, which we could tentatively extrapolate to the hydrocarbon equivalent of ‘brinesaturated compared to gas’, we will see later in this chapter that both the pseudo-static Kn and Ks magnitudes will reduce somewhat when water saturated. Devoid of any attenuation in the form of fluid-changed scattering or squirt losses, these reductions can simply be explained (and quantified) by reduced JCS (joint wall strength) with moisture for the case of a reduced Kn, and reduced JCS and r (residual friction angle), for the case of a reduced Ks.

Figure 16.22 a) Samples of Jurassic (J) limestone, with ‘fractures’ prepared by cutting and grooving, to produce a ‘corrugated fracture interface’. b) Shear and normal compliance versus normal stress, with inversion to dynamic stiffnesses shown on the right-hand axis. Lubbe et al., 2006.

Joint stiffness and compliance and the joint shearing mechanism

Although the micro-displacement phenomena mobilized by dynamic waves may not be fully affected by such pseudo-static reductions in stiffness, there is of course increasing evidence and logic, in reduced dynamic stiffnesses in the case of weakened joint or fracture surfaces. After all, such reductions will also tend to reduce Estatic (or M), and Edynamic, assuming that frequencies are not too high to prevent micro-flows of fluid.

16.4.5

The Worthington-LubbeHudson range of compliances

10-9

6

1

10

10-10

100 10

Kn (dyn) (MPa/mm)

Normal or tangential fracture compliance (m/Pa)

Lubbe, 2005 considered that the main conclusion from his research on compliance, could be summarised in Figure 16.23. This was kindly provided for reproduction in this book. The careful three-author title to this sub-section is due to the joint contribution of these researchers, and is also based on the figure’s earlier appearance in Worthington and Lubbe, 2004. The data

5

-11 4

2

1000

3 1.4 MPa

10-12

10,000

1 5 MPa 60 MPa

10-14 10-2

85 MPa

10-1 CORE

100 LOG

101 XHOLE

102

100,000 103 SEISMIC

Log fracture dimension scale (m)

Figure 16.23 Scaling of fracture compliance from laboratory and field data. The data numbered 1, 3 and 5 was produced by Lubbe from compliance measurements on artificial fracture surfaces in limestone, reviewed above, from the limestone quarry data reviewed earlier, and from a highly fractured shale-rich field site. The latter two included sonic logging and cross-hole interpretations, assuming a given mean beddingplane fracture spacing. The other data are explained in the numbered text that follows. The horizontal axis of the figure was diagrammatic, since ‘it is not possible to measure any parameter that accurately represents the size of the fracture’. (Worthington and Lubbe, 2004, Lubbe, 2005, Figure 7.1 and Lubbe, 2005 pers. comm.).

503

numbered 1, 3 and 5 extending from ultrasonic to sonic to cross-hole frequencies, represented Lubbe’s D.Phil. contribution to this important compliance-size trend. We will summarise the differently numbered data sets, and also convert compliance units to dynamic stiffness units, for easier reference to both pseudo-static and dynamic test data, where the ‘Pa/m’ format (or MPa/mm) is used, instead of the geophysicists’ somewhat cumbersome ‘m/Pa’, with the need of multiplication by a very small number like 1012. 1. Laboratory compliance tests, using artificial 50 mm diameter surfaces in Jurassic and Carboniferous limestone. The vertical bar bounds the 5 to 60 MPa normal stress range. The complete range of both normal and shear compliances was 0.5  1014 to 4.5  10 14 m/Pa, or 200,000 to 22,220 MPa/mm (equivalent to a very stiff-sounding 200 to 22.2 MPa/ m). See Figures 16.21 for the differentiation of ZN and ZT results. (Data from the ‘grooved’ samples: Figure 16.22, are not incorporated in Figure 16.23). 2. The compliance interpretations of Pyrak-Nolte et al., 1990 for dynamic tests on three natural joints in quartz monzonite, of 52 mm diameter. Normal stress levels ranged from 1.4 to 85 MPa. Compliances ranged from 5.3  1013 (the lowest ZT value) to 10 14 m/Pa (the highest ZN value). In stiffness units, these correspond to 1,900 MPa/mm to 100,000 MPa/mm (or 1.9 to 100 MPa/ m). 3. This sonic-log based field data was from the Carboniferous limestone quarry at Tytherington, depicted in Figure 16.20. The approx. 23 kHz compressional wireline measurements were analysed by Lubbe, first using a ZN  ZT assumption and the theories of Schoenberg, 1980 and Pyrak-Nolte et al., 1987b. Allowance for a 20° variation in fracture dips resulted in an estimate of ZN  4.8 (2.6)  1013 m/Pa, or 2,080 MPa/mm (range 4,405 to 1,350 MPa/mm). Lubbe also used the Schoenberg and Sayers, 1995 excess compliance theory, using the vertical velocity reduction accorded to fracturing (500 m/s) to give a 2.5  1013  ZN  5.0  1013 m/Pa estimate of normal compliance. This range converts to a Kn (dynamic) range of 4,000 to 2,000 MPa/m respectively. Lubbe used a third calculation method, dispensing with the ZN  ZT assumption, and basing his estimates on Hudson and Crampin theories to interpret the 10% P-wave anisotropy as an assumed 0.035

504

Rock quality, seismic velocity, attenuation and anisotropy

fracture density for the horizontal ‘open’ joints. This resulted in a similar 2.6  1013  ZN  5.2  1013 m/Pa, or 3,850 to 1,920 MPa/mm dynamic normal stiffness. As one may note from the location of these larger scale, lower frequency data in Figure 16.23, only the low stress laboratory ultrasonic data lies in the same magnitude bracket. 4. The data point labelled ‘4’ in Figure 16.23 was the Myer et al., 1995 normal compliance estimate for Hanford Basalt columnar jointing, derived from cross-hole measurements. The normal compliance estimate was 2  1012 m/Pa, or a dynamic normal stiffness of 500 MPa/mm. (In Worthington et al., 2001, the respective values are 5  10 12 m/Pa, or 200 MPa/mm). Both are of similar magnitude to the laboratory (100 mm) scale pseudo-static Kn data obtained at higher (10 MPa) stress, as measured by Bandis, 1980 (see Table 16.3). 5. The vertical bar labelled ‘5’ in Figure 16.23 is from a highly fractured shale-rich field site called Reskajeage, where Lubbe, 2005 again used Hudson and Crampin theories to relate a 22% P-wave anisotropy to a 0.07 fracture density. Normal compliance estimated for single fractures were as follows: 6.6  1013  ZN  8.3  1013 m/Pa, which converts to a dynamic normal stiffness range of 1,510 to 1,208 MPa/mm. A second method of estimation, again involving the ZN  ZT assumption and Schoenberg and Pyrak-Nolte theories, resulted in the following range of compliances: 1.9  1012  ZN  2.4  10 12 m/Pa, meaning dynamic normal stiffnesses ranging from 525 to 410 MPa/m. Thirdly, Lubbe, 2005 followed the methodology of Pyrak-Nolte et al., 1990 and Myer et al., 1995, modelling the observed attenuation from the P-wave transmission amplitudes in a highly anisotropic ‘open’ fractured zone, deriving a normal compliance of 4.5  1013 m/Pa, or a dynamic normal stiffness of 2,230 MPa/mm, both reportedly consistent with cross-hole travel time data. Lubbe remarked that the Reskajeage compliances were higher (and stiffnesses therefore lower) than at the limestone quarry site, due to the greater continuity of hydraulically conducting ‘open’ fractures. 6. The data point labelled ‘6’ in Figure 16.23 was from Worthington and Hudson, 2000 and related to a computed shear compliance estimated for a major fault zone from 1 to 2 km depth, intersecting a North Sea well at an angle of 50°. (see Figure

10.67). The shear compliance estimate was 1.1  109 m/Pa, or a dynamic shear stiffness of 0.9 MPa/mm. The theories of Hudson and Schoenberg were used to derive a range of possible low stiffnesses, as reviewed in Chapters 10 and 15. The frequency band was 10 to 150 Hz. 7. Finally, the dotted black line in Figure 16.23 was based on the theoretical prediction by Hudson et al., 1997 for tangential compliance. For fault-like features it also applied to normal compliance if the ‘fracture’ was filled with weak material, assuming a 10% area in ‘welded contact’. Lubbe, 2005 therefore considered that the internal consistency of this spread of data demonstrated that compliance increased with the assumed scale of the fractures, dynamic stiffness thereby reducing with size. The experience from pseudo-static testing, and also from structural-geological logic, obviously supports such a thesis, and has long been a part of shear stiffness prediction in relation to block size, since Barton, 1972. Lubbe, 2005, perhaps incorrectly, felt that the very low interpreted shear compliance for the North Sea fault zone might be highlighting ‘the theoretical possibility of ZN/ZT being close to zero’, since he considered that the normal compliance of a fracture at 2 km depth ‘would be vanishingly small’. Clearly this is an exaggeration, as the effective stress at 2 km depth in a petroleum reservoir may be ‘only’ 20–25 MPa. However, the important point was emphasised that the ratio ZN/ZT could be very small, thereby indirectly linking the dynamic behaviour to the pseudo-static behaviour. In subsection 16.4.2, potential pseudo-static ratios of Kn/Ks for typical 1 m in situ block sizes were derived, ranging from 100–5000. These are large ratios, but they are finite. ZN/ZT never vanishes, as perhaps implied in Figure 15.10, at very small aspect ratios. That ZN/ZT becomes very small at large scale is however easy to understand. Worthington and Lubbe, 2004 presented a slightly different version of Figure 16.23, describing their analysis of a cross-hole tomography investigation in Cornwall, which was published by Herwanger et al., 2004. They estimated the compliance contribution of a dominant, dipping fractures zone, which showed velocities with a range of about 3.0 to 4.5 km/s, and an estimated fracture density of 0.07. Using the Schoenberg and Sayers, 1995 excess compliance concept, they estimated total values of ZN and ZT for the fracture zone of 6.5  1012 and 7.0  1012 m/Pa. Due to a heterogeneous distribution of fracture frequency in the zone,

Joint stiffness and compliance and the joint shearing mechanism

505

Table 16.7 An assembly of (macro-deformation, pseudo-static) normal and shear stiffnesses from laboratory and in situ tests on clay-filled discontinuities, from Brazilian dam foundations. After Infanti and Kanji, 1978. Clay-filling Thickness (mm)

Ks MPa/mm

Kn MPa/mm

Ratio Kn/Ks

50–100 12–20 1 mm

0.01–0.1 0.1–0.6 1.0

0.1–0.5 0.5 – 2.0 5.0

6 (5 to 10) 3.6 (3.3 to 5) 5

they estimated a possible range of 7.0  1013 m/Pa if 10 fractures/m, and 7.0  1012 m/Pa if only 1 fracture/m. These invert to dynamic stiffnesses of 1,430 and 143 MPa/m respectively. Their estimated range could be added as a ‘5b’ set of data in Figure 16.23 (immediately to the right-side of line ‘5’, thereby slightly extending the trends for lower stiffness at larger assumed size, as sampled by ‘lower’ frequency. 16.4.6

Pseudo-static stiffness data for clay filled discontinuities and major shear zones

While addressing the subject of likely large-scale compliances and dynamic stiffnesses, civil engineering contributions to the subject of pseudo-static stiffnesses of clay-filled (i.e. major) discontinuities can be cited, from Brazilian dam foundation testing. Table 16.7 shows macro-deformation normal and shear loading tests from the 1970s, reported by Infanti and Kanji, 1978. The applied effective normal stress levels were from only 0.5 to 2.5 MPa, representing ‘near-surface’ conditions in a geophysics perspective. A much more comprehensive assembly of shear stiffness data from in situ testing at Brazilian, and other dam sites was subsequently reported by the same authors, in Infanti and Kanji, 1990. The general trends for their extensive shear stiffness data are summarised in Figure 16.24. Note the dominance of values of shear stiffness of less than 1 MPa/mm, but at stress levels that are an order of magnitude less than reservoir effective stresses. Much of the data range corresponds to the black-discs shown at 0.7 m size in Figure 16.14. An interesting coupled-process investigation of large scale fracture zones at the Underground Research Laboratory (URL) in Manitoba, based on extensive borehole-based measurements, was reported by Martin et al., 1990. Hydraulic pressure changes caused by

Figure 16.24 General trends from in situ tests at dam sites, concerning the (pseudo-static) shear stiffness of normal-andshear loaded rock joints and clay-filled discontinuities, as a function of effective normal stresses in the nearsurface range of 0.1 to about 4 MPa. I) Rough unfilled joints, or with thin clay film, peak  1 mm. II) Joints without filling, or with thin clay film, peak 1.0–2.5 mm. III) Filled joints (thickness up to 12 mm) with peak 2.5–5.0 mm. IV) Smooth joints with fillings 20 mm, and peak  20 mm. Infanti and Kanji, 1990.

injection or pumping could be monitored by so-called ‘Pac-ex’ combined double-packer-extensometer units installed in boreholes intersecting the fracture zones. Interpretation of the normal-deformation effective-stress change allowed estimation of large scale pseudo-static normal stiffness from measurements in a total of ten boreholes, with numerous measurements concentrated in ‘Fracture zone 2’, which was a major dipping feature intersected over hundreds of meters extent at the URL. The data sets describing the in situ normal stiffnesses were extensive, due to the range of normal stress levels measured in different locations adjacent to and within the fracture zone, and due to the fact that the pore pressure

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could be altered at will. In a so-called cataclastic and very permeable section of FZ 2, where the effective stress was determined to be as low as 0.2 to 2 MPa, the measured normal stiffnesses ranged from only 2 to 6 MPa/mm. Elsewhere, where effective normal stresses were as high as 20 MPa, the normal stiffness ranged between about 20 and 500 MPa/mm. Flow-rate interpreted hydraulic apertures were as large as 400 m in the cataclastic zone, and as small as approx 20, 40 and 60 m where normal stiffnesses and stresses were an order of magnitude, or more, higher. Reasonably good correspondence to Barton-Bandis coupled modelling was reported by the authors. The low values of normal and shear stiffness reviewed here, represent very attenuating, heavily fractured, and sometimes clay-bearing rock masses. In terms of attenuation (1/Q) they would represent cases of complete energy loss, not per cycle, but in just part of a cycle, i.e. below the traditionally defined Qseis  2 ‘limit’. As shown earlier in this chapter, ratios of pseudo-static Kn/Ks perhaps of several hundred to several thousand, are suggested if clay-free fracturing or jointing is to be represented. But with a dominance of clay-filling due to faulting as above, ratios of Kn/Ks perhaps as low as about 5, and therefore ratios of ZN/ZT as high as about 0.2, would be suggested. (Refer also to the discussion on faultscale stiffnesses given in Chapter 15, section 15.6.1). Of course it is not known whether the existing ‘static’ stress-deformation conditions acting on the joints or fractures in question, could be considered to have significant influence on the stiffer dynamic micro-displacement ‘excursions’. Such cyclic excursions presumably will tend to occur with suitably increased gradient, above the existing in situ stress-deformation gradient (or loading path). When this is already ‘soft’ due to clay-filling, higher (dynamic) compliances seem reasonable to expect. Interestingly, Lubbe, 2005 refers to Japanese work concerning faults under high stress that were assumed to potentially suffer inelastic behaviour in the solid wall-rock material, during transmission of elastic waves within the shallow sub-surface. ‘Reverse’ stiffening, as in the grooved sample of Lubbe (Figure 16.22) could then affect the compliance/stiffness response.

16.4.7

Shear stress application may apparently affect compliance

Nakagawa performed an interesting laboratory test which demonstrated that the application of static shear stress

on a planar fracture actually caused normal incidence P:S conversion. This led Schoenberg and Nakagawa, 2002 to demonstrate that linear slip theory and offdiagonal terms in the Schoenberg fracture compliance matrix, could be used to relate the dynamic traction on the experimental fracture with the dynamic displacement discontinuity across the fracture. They found that due to an applied shear stress, a fracture compliance matrix had a single off-diagonal term that coupled the normal component of dynamic stress with the tangential component of displacement, and vice versa. The off-diagonal component (ZN V) appeared from their laboratory tests to be linearly related to the shear stress component. In a partly related field, where joint stiffnesses are of concern for the modelling of deformation in rock masses as a result of, for example, tunnel or slope excavation, we generally assume a linear initial shear stressdisplacement relation. If the joints are displaced in shear (as depicted in Figure 16.16 – see ‘mismatch’), there will tend to be a linear relation between normal stiffness and normal stress, following Bandis, 1980 and Bandis et al., 1983. Perhaps from these physical results we can approximate the off-diagonal response referred to above. An example of the Barton-Bandis shear strengthdisplacement-dilation modelling of joints or fractures of different sizes, is shown in Figure 16.25. One may note the modelling of a delayed dilation as block size increases. Each of the responses to shear stress are scale-defined. The likelihood of minor cross-jointing in situ, to thereby define blocks of a certain size, will be found to give different macro-shear stiffnesses, due to the ‘double-effect’ of scale on both peak shear strength and displacement to peak; the latter also tending to determine the initial slope. The extent to which this ‘macro-deformation’ behaviour will ‘steer’ dynamic micro-deformation behaviour is of course uncertain, but the scale effect seems unlikely to be totally ignored. As a corollary, why should small laboratory samples give more ‘correct’ values of compliance and stiffness than in situ block sizes? Possibly the Worthington-Lubbe-Hudson data shown in Figure 16.23 is tending to resolve this dilemma. In view of the Nakagawa laboratory observation that application of shear stress causes P:S conversion on a fracture, one may speculate whether the ‘open’ fractures that are the dream of well production, are also under sufficient shear stress through limited mis-alignment with major principal stress, that the shear wave splitting phenomenon is also affected in an equivalent manner to the above wave conversion.

Joint stiffness and compliance and the joint shearing mechanism

507

excursions in this area, it is surely justified to continue the classic assumption that ‘friction’ is indeed one of the sources of seismic attenuation (Q1) in a rock mass.

16.5

Figure 16.25 Example of manually calculated shear stressdisplacement-dilation curves for different block sizes, using the JRCmobilized concept of Barton, 1982. Scaling of parameters JRC and JCS shown in the table, follows developments described by Bandis et al., 1981.

Figure 16.10 showed the dimensionless JRC mobilized concept that is used to predict the various ‘macrodeformation’ shear strength-displacement-dilation behaviours depicted in Figure 16.25. In the initial part of the curve where ‘mobilization of friction’ is written (i.e. a reservoir joint under limited shear, or differential stress), one may imagine an impinging dynamic wave causing very slight, cyclic, m-magnitude (?) shear displacements. Since such shear waves are known to ‘mobilize’ a shear compliance of recognisable magnitude with recognisable units (m.Pa1) during dynamic

Effect of dry or saturated conditions on shear and normal stiffnesses

The effect of the environmental conditions (gas, brine, or oil) on the anisotropy-causing compliances of rock joints or fractures, at levels of effective normal stress relevant to reservoir conditions, have obviously not yet been investigated to the level required, now that shear wave splitting and fracture diagnostics are becoming more common, and more important in hydrocarbon exploration and time-lapse monitoring. There is the added complication that the application of high, reservoir-related stress levels has demanded the use of rather small (roughly 40 to 50 mm) sample sizes in the very few laboratories who have investigated (dynamic) joint compliances. We have reviewed readily available data, under various contexts, in Chapters 10, 13 and just now in this chapter. With the exception of temperature and oil-saturation effects, there is a large body of relevant test data from earlier rock mechanics investigation that can be used to deduce the approximate normal and shear stiffness magnitudes for rock joints. Joints and fractures developed in different rocks obviously have different rock strength, wall-alteration and roughness (UCS, JCS and JRC) characteristics. Although not direct models for compliance, the different characteristics can perhaps be of value in guiding the extrapolation of the presently very small, and very small-scale compliance data set. The variable shear strength and shear and normal stiffnesses of rock joints have been of concern for a long time (for almost 40 years, at publication time), due to the need for basic rock stability calculations, and for subsequent coupled flow-deformation analyses. It is therefore logical to look at this earlier evidence for the effect of dry (assume equal to gas-saturated) or water-saturated conditions on joint or fracture properties. This line of investigation is followed here, under full recognition that the ‘macro-deformation’ behaviour of rock joints has to be applied with caution to the tentative extrapolation of micro-deformation dynamic/ seismic wave loading effects, being mindful of the usual Edynamic  Estatic inequality. Before referring back to ‘environmental’ test data from the 1960s and 1970s, it is helpful to address the

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components used in the most comprehensive-yet-simpleto-apply joint model. The Barton-Bandis criterion is widely used and referenced outside geophysics literature, where it is unknown, and is part of a well established rock mechanics numerical modelling procedure (UDEC-BB). A useful feature of the model is the ease with which input data can be acquired from index tests on drill-core. The shear-related components JRC, JCS and b were introduced by Barton, 1973a, and were refined by the addition of r and simple index test methods by Barton and Choubey, 1977. This development was based on numerous tilt-shear and direct shear tests on 130 fresh and partly weathered joint samples. The just developed JRC-JCS-r joint strength parameters were subsequently utilised by Bandis, 1980 in very extensive studies of both shear and normal stiffness and scale effects on shear strength. These three strength parameters, and the scaling of the first two, have been referred to elsewhere in this chapter. Here we will provide some details of the parameters themselves.

16.5.1

Joint roughness coefficient (JRC)

It is reasonable to believe that the joint roughness coefficient (JRC), which varies from 0 to about 20 (for completely plane to extremely rough joints) is not significantly affected by the dry or wet condition, since it is essentially ‘geometry’. Examples of laboratory-scale (100 mm) profiles and their JRC values (now termed JRCo) are shown in Figure 16.26. Examples of JRCn profiles of longer joints, as may be used in larger-scale shear strength estimation, are shown in Figure 16.27. In softer, younger rocks, JRC may perhaps reduce slightly during the process of compaction caused by pore pressure reduction when producing from a reservoir. This effect, which can hardly be evaluated, is a function of the changing effective stress/strength ratio: specifically 
/JCS. n The idea behind JRC is that it is extremely easily determined, as indicated by several index test methods, shown diagrammatically in Figure 16.28. These include self-weight tilt tests which can be performed on joints recovered from core, as for instance performed on joints from the Ekofisk chalk reservoir in the mideighties. Also shown is the roughness-profile gauge ‘comb’ method, which one enterprising manufacturer,

Figure 16.26 Laboratory-scale joint roughness profiles with their measured JRC values, from Barton and Choubey, 1977. Note that the roughness is defined by one parameter for simplicity. The lab-scale JRCo value is reduced when larger block sizes are involved, using a JRCo to JRCn scaling equation, for block sizes of length Ln in place of Lo. Scaling equations are given later in the text.

without the writers knowledge, has called ‘the Barton comb’. The amplitude (a) of asperities per measurement length (L) can also be used, with a/L scaling to JRCn (Barton and Bandis, 1990). In practice, the index tests illustrated in Figure 16.28 are performed on several samples of each joint set that is to be modelled (e.g. in a UDEC-BB distinct element model). Makurat et al., 1990 gave examples of such applications, from one of the earlier tunnel modelling exercises with UDEC. An extract from this modelling, concerning the different apertures (e and E), their distribution with depth, and effects of tunnel excavation, was illustrated in Figure 15.50.

Joint stiffness and compliance and the joint shearing mechanism

16.5.3

509

Basic friction angle Fb and residual friction angle Fr

The third and fourth components of the shear strength criterion are the basic friction angle (b) of unweathered artificial, planar, dry rock surfaces, and the residual friction angle (r) applying to flat, non-dilatant, saturated, well-sheared surfaces that may be weathered, i.e. r  b. Since it is very difficult to reach this minimum strength value in standard direct shear tests, an ultrasimple empirical equation was developed to enable estimation of r from the easily measured b (often close to 30°), using Schmidt hammer rebound (r) on the saturated joint walls to compare to the rebound (R) on the dry artificially cut rock surfaces. With r  R, the residual strength is estimated as follows: r  ( b 20) )  20(r/R ) Figure 16.27 Large-scale (1 m) laboratory-determined roughness profiles, and their JRCn values as determined from self-weight tilt testing, from Bakhtar and Barton, 1984.

16.5.2

Joint wall compression strength (JCS)

The joint wall compression strength (JCS) is known to generally reduce with water saturation compared to the dry state. This is because of the much researched effect of moisture on the uniaxial compressive strength (c), and on the Point load tensile strength (I50), which emanates from the late 1960s. When correctly performed, JCS measurement by Schmidt hammer is performed on clamped, water saturated joint samples, specifically to record eventual moisture-reduced wall strength, with JCS  c in general, as illustrated in Figure 16.5a. It will be noted from the peak shear strength criterion of Barton-Choubey (for laboratory scale estimation), and from the Barton-Bandis (larger scale) version, to be given as equation 16.5, that when JRCo or JRCn are zero, due to complete planarity and smoothness (but without complications of work-hardened polishing), the ratio JCS/n
no longer influences the shear strength. This assumes of course that the remaining value of shear strength (n
tan r) correctly captures the essence of r for the rock concerned. This is the function of the following ratio r/R.

(16.3)

The back-calculation of JRC from tilt tests or direct shear test, and the JRC-labelled profiles in Figure 16.26 are based on this method of estimating r . Since moisture generally reduces both JCS and r, there are inevitable consequences of saturation both on the shear stiffness (which is given by JRC, JCS and r), and on the normal stiffness (which is given by JRC and JCS). Barton, 1973a and Barton and Choubey, 1977, gave extensive reviews of the effects of saturation on b, r, and c. One of the first sources of data for these reviews was Horn and Deere, 1962, who showed that massive crystal structures such as quartz and calcite may cause the ‘coefficient of friction’ (flat, artificial surfaces, i.e. b in the context of these tests) to increase with saturation, while layer-lattice structures such as mica and chlorite caused the ‘coefficient of friction’ (b) to reduce. Barton, 1973a, tabulated numerous test results from the dry and saturated states for the three categories 1) b (or r) 2) c (or t: the tensile strength), and 3) the overall shear strength (which incorporates effects on b, r and JCS). Rock types included sandstones, siltstones, limestones, chalk, and shale, and several igneous rocks such as granites, basalts, dolerites, porphyries, metamorphic gneisses and slates. This review showed that: 1. b may typically range from 26° to 34°, while r can be several degrees less, depending on the degree of weathering (since r  R). In general terms, moisture (‘wet’ compared to ‘dry’) caused from 0° to 4° (generally 1° to 3°) reduction in b and r, since pure crystal structures (massive/layer-lattice)

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.28 Diagrammatic illustration of joint characterization methods, from Barton, 1999a. a) The left column illustrates direct shear box testing, where shear force T is designed to act ‘in-line’ in practice, to avoid over-turning moments. Note shear strength-displacement-dilation and shear strength envelope results for three hypothetical joint samples. b) The second column illustrates self-weight tilt tests, performed on the joints for back-analysis of JRC, and performed on (un-polished) core sticks or sandblasted flat-sawn surfaces (both unweathered) for input of b to the empirical equation for estimating r. c) The third column shows Schmidt hammer tests for estimating JCS and c, and for input of the degree-of-weathering ratio r5/R5 (see worked example showing use of highest 50% in each case) for input to the r estimation. d) The fourth and final column illustrates amplitude/length (a/L) measurement, and ‘comb’ roughness profiling, with respective application in the a/L diagram for JRCn estimation, or for JRCo profile-matching at laboratory scale, using Figure 16.26. e) At the bottom of three of the columns, the statistical distribution of each of the key joint strength-and-stiffness parameters is illustrated, together with a reminder of the likely scale-effects on JRC, JCS and the uniaxial compressive strength c. The core photograph is a fine example of contrasting JRC values from an inter-locked joint and a minor fault in welded tuff, with respective JRCo values of about 15 and 1.

Joint stiffness and compliance and the joint shearing mechanism Table 16.8 Examples of the effect of water saturation compared to dry conditions, on the basic friction angles of flat, unweathered rock surfaces. From review by Barton, 1973a. Rock type (flat, smooth, non-polished surface)

b dry (degrees)

b wet (degrees)

sandstone siltstone limestone

26–35 31–33 31–37

25–33 27–31 27–35

are seldom the only component of rock joint samples as opposed to mineral samples. However, an exceptional 9° reduction for slate (dominant layerlattice) was noted due to water saturation. Three examples are given in the Table 16.8 extract from Barton, 1973a. 2. In general terms moisture (‘wet’ compared to ‘dry’) caused from 10% to 50% (generally 20 to 40%) reduction in uniaxial strength (c or UCS), and a similar reduction in point load or tensile strength (t). (Water injection into a reservoir like chalk can therefore have serious consequences – which may be overridingly positive especially if planned for). Water saturation causes reduced UCS, reduced JCS, reduced b and reduced r, therefore reduced joint normal stiffness, reduced joint shear stiffness and reduced peak and residual shear strength. As shown in Figure 16.28, the value of JCS can be estimated from Schmidt hammer tests on saturated, fresh or weathered joint surfaces, using a density-uniaxial compression strength conversion, from Miller, 1965. See also ISRM, 1978. It is logical to expect that JCS will also be adversely affected by moisture, as is the case for UCS, since JCS specifically involves asperity failure/ stiffness when contributing to either the shear or normal stiffness in the Barton-Bandis models for these two components. Most likely JCS will be more sensitive to weakening by water than the rock matrix, if there is any trace of weathering, and because of the increased surface area and microcracking associated with jointing. 16.5.4

Empirical equations for the shear behaviour of rock joints

We can illustrate the above effects of the dry or saturated state on shear stiffness, by evaluating examples. (See

511

Barton, 1982 for derivation of the following empirical equations, two of which were derived in Bandis et al., 1981 from Bandis, 1980 scale-effect experiments). A ) Shear stiffness

Ks 

peak

(16.4)

peak

B ) Shear strength

   JCSn    r  (16.5)

peak  ′n tan  JRCn log    ′  n  

C ) Displacement to peak strength 1 3 L n  JRCn   peak ≈  500  L n 

(16.6)

(peak, Ln in metres) D ) Large -scale joint roughness  L 0.02 JRCo JRCn ≈ JRCo  n   L o  E) Large -scale joint wall strength  L 0.03 JRCo JCSn ≈ JCSo  n   L o  F ) Initial unstressed aperture   JRCo  Eo ≈  0.2 c  0.1  5  JCSo

(16.7)

(16.8)

(16.9)

where Lo  lab-scale sample length (usually 100 mm) Ln  in situ block size (generated by the intersecting joint set) Eo  millimetres We will assume the following input data: r dry  30° (e.g. gas) JCSo dry  70 MPa JRCo  8 Lo  100 mm

r wet  27° (e.g. brine) JCSo wet  50 MPa Ln  500 mm

n
 10 MPa, 20 MPa

Thus according to the expected effects of moisture on two of the three strength components, there is a

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Rock quality, seismic velocity, attenuation and anisotropy

Table 16.9

Barton-Bandis modelling of the possible effects of water saturation on the shear stiffness of joints sampled at two different scales.

A. Dry cases

B. Wet cases 0.028

 500    100 

1. JRC n ≈ 8 

 6.2

1. JRC n (assume unchanged)

0.038

 500  2. JCSn ≈ 70    100  3.  peak

 6.2  ≈ 0.001    0.5 

 47.6 MPa 1

≈ 2 . 3 mm (0. 0 023 m)

 

  47.6    30)   6.8 MPa  10  

 

  47.6    30)   12.7 MPa  20  

ii) peak  20 tan  6.2 log 

ii) K s ≈

6.8 2.3 12.7 2.3

≈ 3.0 MPa/mm at 
n  10 MPa ≈ 5.5 MPa/mm at 
n  20 MPa

Table 16.10 Barton-Bandis modelling of the adverse effect of water saturation on the conducting apertures of a joint at two different normal stresses.

1. JCSo dry  70 MPa 2. JCSo wet  50 MPa

 34.0 MPa

3

4. i) peak  10 tan  6.2 log 

5. i) K s ≈

0.038

 500    100 

2. JCSn ≈ 50 

n
 10 MPa

n
 20 MPa

e  5.1 m E  30.3 m e  3.9 m E  26.5 m

e  1.6 m E  16.8 m e  1.2 m E  14.4 m

moderate 13 to 15% reduction in shear stiffness from the dry to saturated cases, in the examples in Table 16.9, in which moderate assumptions for effects of saturation have been made. A similar exercise for normal stiffness is more easily performed using the BB numerical model. A cursory application shows that the initial normal stiffnesses (where Kni is the stress-closure gradient at very low stress), are in the region of 28 to 32 MPa/mm with the above input data. Normal stiffness rises by a factor of at least thirty at 20 MPa normal stress, on cycle #1. With the foregoing assumptions for input data (JCSo dry  70 MPa, JCSo wet  50 MPa, it is found from BB modelling that the initial (first load cycle) normal stiffnesses are relatively little affected by the dry: wet condition. However, the final apertures, being so small, are

3.  peak (assume unchanged)

 

  34.0   10   27 )  5.8 MPa

 

  34.0   20   27 )  10.8 MPa

4. i) peak  10 tan 6.2 log 

ii) peak  20 tan 6.2 log 

5. i) K s ≈ ii) K s ≈

5.8 2.3 10.8 2.3

≈ 2.5 MPa/mm at 
n  10 MPa ≈ 4.7 MPa/mm at 
n  20 MPa

significantly affected as a result of the assumed reduction in wall strength JCS due to moisture. The incremental normal stiffnesses can easily rise by a factor of 10 to 100 when joints in weaker rock are ‘imaged’ at an effective normal stress of 10 or 20 MPa, as may apply in a reservoir. As we also saw earlier, from Bandis normal stiffness testing, Kn can rise to 103 or 104 MPa/mm if effective stresses become close in magnitude to the saturationreduced JCS values. This is logical, since the joints in question will be almost closed. Thus, fluid saturated joints in weaker rocks may have very high ratios of Kn/Ks. We will return to this theme of ‘almost closed’ joints in greater detail later. Concerning the anisotropic shear wave splitting and polarization into the fast qS1 and slower qS2 wave speeds, the former parallel and the latter perpendicular to the dominant joint or fracture sets, one may assume that it is the relative low value of KS (or the high value of shear compliance ZT), rather than the high value of Kn, that is most responsible for shear wave splitting. It would also appear reasonable to assume that very tight (low-permeability) joints, with high normal stiffness, will tend to give faster qS2 wave speeds. Shear-wave anisotropy, and attenuation anisotropy might therefore tend to be increased. Theoretical treatment in this area of ‘compliance-anisotropy’ was given in Chapter 15.

Joint stiffness and compliance and the joint shearing mechanism

16.6

513

Mechanical over-closure, thermal-closure, and joint stiffness modification

Unfortunately, when joint samples are recovered from a borehole for laboratory testing, or exposed in a tunnel or mine adit for in situ testing, the object of our investigations is ‘cold’, in relation to its likely formation temperature. The laboratory may also be ‘cold’ in relation to the sample’s recent environment. Several pieces of experimental evidence from heated lab-tests, from heated block tests and from heated ‘mine-by’ tunnelling experiments, suggest that the rock joint normal stiffness, and therefore the apparent rock mass deformation modulus changes, when the rock is heated in the presumed direction of higher joint formation temperatures. What appears as a measured reduction in stiffness and modulus, is actually producing a stiffer medium. Clearly this process is also going to affect normal compliances, particularly when rock quality is high, and Estatic is closer to Edynamic. Both indirect circumstantial evidence, and directly measured evidence for these phenomena, were reviewed by Barton and Makurat, 2000, in an NGI contract report (‘Hydro-Thermal and Mechanical Hysteresis and Over-Closure Effects in Joints and Rock Masses caused by Mechanical and Thermal Loading and Unloading’). Some published results of such tests were given by Barton et al., 1985, discussed in Barton, 2004b, and reported by Barton and Makurat, 2006. One of the best documented cases, and also the first of very few hydro-thermo-mechanical in situ tests in rock mechanics, was described by Hardin et al., 1981, and further analysed by Barton, 1982. The 8 m3 in situ test set-up, allowed biaxial (normal) loading, or uniaxial loading in ‘N–S’ and ‘E–W’ directions, i.e. shearing. Flat-jack loading on four (or two) sides of the sawn-inplace block of quartz monzonite provided the desired stress levels. There was also a line of borehole heaters to raise the temperature by some 60°C. A simplified schematic is shown in Figure 16.29. The mean joint spacing in the area of the block test is indicated. The aspect of the test to be described here is the permeability test holes, drilled parallel to the long diagonal, foliation joint. Jointed core extracted from these holes is drawn in Figure 16.30, and shows the measured joint roughness traces, and the tilt-test failure angles, giving JRCn estimates of 8.0, 8.3 and 7.9 due to the 200 to 300 mm long samples, while the mean JRCo was 13.

Figure 16.29 Idealisation of average local jointing in the 2  2  2 m TerraTek/CSM heated block test in quartz monzonite. This test gave the first well instrumented in situ data on MHT coupling, suggesting that joint apertures closed under the effect of increased temperature, despite carefully controlled normal stresses. Note the flat-jack loading of four vertical boundaries, and the line of borehole heaters. Hardin et al., 1981.

The flat-jack loading test cycles are shown in Figure 16.31. Maximum stress was generally 1000 psi, or 6.9 MPa. The very first unload-load-unload-load cycles are shown in Figure 16.32, plotted in terms of normal stress versus hydraulic aperture (e), where permeability during low-pressure-gradient laminar flow was assumed to be given by K  e2/12. The vertical axis of the figure shows the e  38 m hydraulic aperture before the block was line-drilled to make space for the boundary flat-jacks. This unloading caused the hydraulic aperture to increase to e  61 m. Following a minor

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.30 Three of the axially jointed core from the block test permeability test holes, with as-recorded roughness profiles, correct tilt angles at shear failure (70.1°, 72.1° and 69.8°) and back-calculated JRCn roughness coefficients of 8.0, 8.3 and 7.9 at the given length scales. Barton, 1982.

Figure 16.32 Hydraulic aperture (e) versus normal (applied) stress for the first ambient temperature, biaxial load-unload cycle. Note apertures before and after drilling of the flat-jack slots. Hardin et al., 1981. (See normal stiffness calculation, and possible normal compliance interpretation, in text.)

Figure 16.31 The main boundary-stress-temperature test paths, for the HMT heated block test. Hardin et al., 1981.

Joint stiffness and compliance and the joint shearing mechanism

0–3.5–0 MPa ‘dress-rehearsal’ test cycle, the first ambient 0 to 6.9 to 0 MPa biaxial test is shown, with 1  2, n  6.9 MPa and  0 MPa. 16.6.1

515

end of the roughness and strength scales for petroleum reservoir rocks, and perhaps relate best to the stronger carbonates. The uniaxial strength of the present igneous rock was however, ‘too high’. The JCS  c mismatch was due to slight alteration of the rough joint walls.

Normal stiffness estimation

The typical increasing normal stiffness seen from n  3.45 to 6.9 MPa, mirrors laboratory testing. If one had assumed e  E, then the normal stiffness in this increment would have been 3.45/(34.4 – 30.0)  103 MPa/mm  784 MPa/mm. However, the physical apertures can be estimated to have reduced from 144.8 m to 135.2 m, making E
9.6 m. This estimate is based on JRCo  13 and application of the empirical model e  E2/JRCo2.5, shown in Figure 16.7. The interpreted normal stiffness is then about 360 MPa/mm, which is exactly in line with Kn laboratory test results reviewed earlier in this chapter. If we make the assumption that the rock quality was sufficiently high for Estatic
Edynamic, this Kn value of 360 MPa/mm would imply, by inversion, a normal compliance ZN of about 0.0028 m/GPa, or 2.8  1012 m/Pa. In fact the rock mass quality was very good, as the following estimation of Q-parameters shows (see Appendix A for ratings).

16.6.2

Thermal over-closure of joints and some implications

When temperature was applied in the above block test, unexpected over-closure of the diagonal test joint was experienced. Figure 16.33 shows a three-parameter (coupled-process) plot of (e) versus (n) versus temperature (°C), and the following result. The added joint closure means that this cooled (sampled), unloaded joint is displaying an apparent reduction in normal stiffness. This will be estimated shortly. In the reality of e.g. a warm-shallow, or hot-deep petroleum reservoir, joints are likely to be better interlocked than when we unload and cool them for (initial) laboratory testing. In fact it would be better to keep them hot

 100 3 1   ≈ 67 Q c  Q  c 9 1 0.5 100 200 Q c ≈ 67  ≈ 130 (‘very good’) 100 Q 

Chapter 13, Figure 13.59 relating Qc – Vp – M – depth – porosity, suggests a static modulus of deformation as high as 70 GPa, when taking into consideration the favourable mine-adit-based (and applied) stress level, equivalent to 300 m depth, and a nominal (hard rock) 1% porosity. This figure also suggests a seismic refraction Vp close to 6 km/s for such good rock, located next to the cross-hatched ‘hard-jointed’, ‘hard-massive’ boundary. One could then reasonably assume that the measured normal stiffness Kn
360 MPa/mm derived from the permeability test ( under a 3.45 to 6.9 MPa increment of normal stress), was almost equivalent, in this case, to a normal compliance ZN
2.8  1012 m/Pa. The roughly 1 m size result would ‘plot’ immediately above the (Hudson) diagonal line in Figure 16.23. The joint characterization of the permeability test hole cores, gave JRCo  13 and JCSo  90 MPa. One could estimate that these values would both be at the upper

Figure 16.33 Hydraulic aperture (e), versus normal stress (n), versus average rock temperature (T°C) in the permeability test volume of the TerraTek heated block test, CSM mine, Colorado. Note aperture (e) reductions from 30.0 m to 18.3 m, to 12.9 m and finally to 9.1 m as a result of temperature rise, despite constant applied stress. This gives an apparent reduction in the normal stiffness in this test, but in the warmth of a deep petroleum reservoir, would have allowed joints to remain stiffer since their formation. Barton, 1982. see Plate 11.

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Table 16.11 Effect of temperature on joint (hydraulic) apertures at the heated block test. Test No.

11

12

13

16

n (MPa) e ( m) Temp°C

6.9 30.0 12°

6.9 18.3 41°

6.9 12.9 55°

6.9 9.1 74°

Note: water viscosities corrected for T°C, before calculating (e).

before testing, and test them hot too, to get the most relevant response, whether for simulating in situ normal stiffness, or dynamic compliance. The key parameter affected by thermal-closure is the thermal expansion coefficient. Joints must be included, and tested hot. The explanation for this phenomenon was assumed to be quite simple (Barton, 1982). Namely that the joint in question, and perhaps the huge majority of joints developed in the crust, were formed at variously elevated temperatures. They were thereby given a primeval ‘fingerprint’ of 3D-roughness, which was influenced by all the minerals (or grains) forming the joint walls. When cooled, various subtle changes would occur, causing reduced fit. In the case of igneous rocks, many of the earliest jointing episodes would be at the cool side of the brittleductile transition. When such a joint, any joint, is encountered today, (e.g. at shallow depth in a mine, or if drilled at depth and bought to the surface causing unloading and further cooling?), the 3D roughness finger-print, though very recognisable, would be subtly altered in its finer details. These details (very important at the micron-scale) would be a combination of: a) a slight expansion from (anisotropic?) stress relief when sampled from depth b) a sampling damage, but neglected for sake of simplicity c) a general thermal contraction effect, but this might allow the equally altered finger-prints from each wall to still fit perfectly d) locally inhomogeneous contraction superimposed on c), due to non-equality of the thermal contraction coefficients of the constituent minerals and grains along the joint walls Factors a) and d) are good reasons for less than ‘perfect fit’ of the primeval joint walls in a testing situation, when initially testing at ambient temperature. Factors a) and b) alone, without temperature considerations, are

enough to explain the need for several load-unload-load cycles to move beyond the strong hysteresis ‘always’ experienced on the first load cycle, as emphasised by Barton, 1971, Bandis, 1980 and Bandis et al., 1983, and demonstrated in Figures 16.17. To illustrate the order of magnitude involved, from the above coupled HMT block test, one may utilise the ambient Kn value of approximately 360 MPa/mm as a starting point. This value was established under ambient conditions, with a final stress increment of 3.5 to 6.9 MPa, therefore reaching the same stress level as applied in the heated part of the test. The constant 6.9 MPa was carefully monitored during heating of the block, to avoid thermal expansion-caused increases in flat-jack pressure. The successive reductions of conducting aperture were from 30 m to 18.3 m to 12.9 m to 9.1 m, for temperature increases from 12°C to 41°C to 55°C and finally to 74°C. The process took about 1 month: in geophysics terminology about 107 Hz. As shown earlier, if one had assumed e  E, then the normal stiffness in the previous ambient increment would have been equal to 3.45 MPa/(34.4 – 30.0) m  103
780 MPa/mm. But since E
14.0 m, based on JRCo  13 and the empirical model E2
e2. JRCo2.5, the interpreted ambient normal stiffness was about 360 MPa/mm, which was in line with (ambient) Kn test results reviewed earlier in this chapter. The estimations of thermally-changed (static) normal stiffnesses (and therefore potentially changed dynamic compliances) are set out in Table 16.12, for transparency. The assumption is made, for purposes of calculation, that each thermally-induced reduction in aperture occurred at the end of the last load increment. The successive closures are therefore allowed to have an accumulative effect on normal stiffness, as if each test started at 12°C and 3.45 MPa normal stress. In fact, since a strict definition of stiffness is stress increase divided by aperture reduction, one could claim that the joint had ‘zero’ stiffness, since no stress increment (rather a thermal increment) was applied. If this (almost reversible) thermal over-closure phenomenon is of general application in the case of the less planar jointing, it implies that when the joint in question is ‘sampled at depth’ by seismic anisotropy determination, in the familiar warmth of a petroleum reservoir, the elevated stress and temperature will likely result in lower compliance, due to its previously imprinted greater stiffness. However, the present temperature at depth is unlikely to be the same as the temperature when the joint was formed.

Joint stiffness and compliance and the joint shearing mechanism

517

Table 16.12 Estimation of thermally-induced, apparent reductions of (static) normal stiffness, from the heated block test. For Kn estimation assume each test starts at 12°C and 3.45 MPa, and ends at the specific elevated temperature. Temperature increment

Hydraulic aperture (e) m

12 to 12°C (ambient) 12 to 41°C 41 to 55°C 55 to 74°C

34.4 to 30.0

4.4

144.8 to 135.2

9.6

360

30.0 to 18.3 18.3 to 12.9 12.9 to 9.1

11.7 5.4 3.8

135.2 to 105.6 105.6 to 88.6 88.6 to 74.5

29.6 17.0 14.1

88 61 49

e ( m)

The joint will also be open to changes bought about by the partial cooling caused by e.g. water flooding. The above mechanisms suggest a ‘better than expected’ aperture and permeability enhancement as a result of water flooding. Efforts to reduce the natural warming of this water on the way down the injection well, could be beneficial too, but avoidance of matrix contraction and oil-bypass (unstable fingering) might be a contrary requirement. This hydrothermomechanical HTM coupling ‘detail’ (in fact a quite important experimental detail), has not yet been absorbed into numerical modelling. It has not even been coded in the Barton-Bandis joint model, mainly because data is presently limited, as the phenomenon is little known, researched, or acknowledged in the rock mechanics (modelling) community. Barton and Makurat, 2006 have addressed the problem once more, in an attempt to bring over-closure (in rock mechanics) into focus, as it has been in soil mechanics for decades, but regarding a somewhat different mechanism (i.e. hard, over-consolidated clays, with their altered matrix properties due to unloading from higher historic effective stress levels.). 16.6.3

Mechanical over-closure

There is another unresearched aspect, which may have application to shear wave splitting phenomena (and assumed anisotropy), and that is mechanical over-closure. Rough joints or fractures that are historically loaded to a higher effective normal stress, and later sheared (or shear-wave loaded) under today’s lower effective normal stress, (due for example to an episode of over-pressure), will have a higher shear strength, a higher shear stiffness, and a higher normal stiffness, than if conventionally tested at 1:1 n levels. Over-consolidation ratios of 4:1 and 8:1 were shown by Barton, 1973, to cause several degrees higher frictional

Physical aperture E ( m) estimated

E ( m)

Kn (MPa/mm)

strength in relation to 1:1 control samples, in the case of rough tension fractures which remained ‘over-closed’ following removal of the pre-stress. This caused difficulties with over-stable modelled rock slopes, in 40,000block tension fracture models. Barton, 2004b, discussed this phenomenon as being due to ‘JRC at right angles’, (i.e. an effective JRC in a perpendicular sense relative to the joint plane). This causes effective locking of asperities, if roughness is sufficient, and the stress reduction significant. When JRC is sufficiently low, such as less than 10, possibly only less than 6, the phenomenon is not expected (refer to Figure 16.26 100 mm roughness profiles in this context). The writer has experience of a very rough tension fracture, generated to make a sample for demonstrating tilt testing, actually tolerating a tilt angle of 180°, i.e. going from horizontal (no shear, pure normal stress from the self weight of a carefully placed upper half of the block) to 90° (vertical) to 180° (upside-down). In other words even the small pre-stress from self weight loading, amounting to about 0.02 MPa, was sufficient to give an apparent tensile strength to the fracture, due to asperity inter-lock. Barton, 1973, discussed similar experiences reported by a colleague at Imperial College, who registered an error when preparing a direct shear test. An over-closure episode prior to shear testing (M. de Freitas, pers. com. 1970) caused a jointed sample to be too strong to shear, even though the normal stress was already reduced to the correct level. The sample required mechanical wedging to open it, when extracted from the over-loaded DST apparatus. 16.7

Consequences of shear stress on polarization and permeability

In Chapters 14 and 15, when addressing P-wave and S-wave anisotropy in reservoirs, several case records were

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Rock quality, seismic velocity, attenuation and anisotropy

reviewed that showed some angular discrepancy between the various indicators of predominant joint strike (FMS, oriented core), the assumed H max direction (90° from borehole calliper-log long axis), and the principal axes of either (or both) P-wave and S-wave anisotropy. The latter is obtained from shear-wave polarization when splitting into fast and slow qS1 and qS2 components. Figures 14.16, 14.35 and 15.60 are three of the cases. In this section of Chapter 16, we will explore in much greater detail, some of the reasons for believing that shearing (as well as mineralization ‘bridging’) may be a necessary mechanism for explaining hydrocarbon (especially oil) production, from highly stressed joints or fractures. Vertical, dominant fractures perpendicular to the minimum horizontal stress direction, as often sought and sometimes ‘confirmed’, may be a more complex aspect of geomechanics than usually assumed. Contrary to the assumption of joints or fractures loaded by 20 to 40 MPa ‘minimum’ stress actually being ‘open’, there may be: 1. insufficient strength (specifically JCSconfined) for conducting joints in the assumed direction 2. there may be two sets of joints contributing their seismic ‘components’ on either side of the assumed H max direction 3. there may be conjugate shearing on one or more joint set and therefore permeability enhancement (or maintenance).

16.7.1

Stress distribution caused by shearing joints, and possible consequences for shear wave splitting

The in situ heated block test of 8 m3 volume, described in the previous sub-section, was subsequently the object of distinct element modelling by numerical modelling colleagues at NGI in Oslo. Some of this work is reported in Chryssanthakis et al., 1991. The modelling was a form of validation of the distinct element code UDEC, with the Barton-Bandis joint model as a subroutine, termed UDEC-BB in this non-linear form, or UDEC-MC when with simpler linear Mohr Coulomb joint modelling. An example of the complex stress distribution in even just a four-block (simplified) model is shown in Figure 16.34. The flat-jacks were simulated as fluid-filled boundaries. Note the complex stress distribution, even with equal (biaxial) 1  2  5.4 MPa

Figure 16.34 A UDEC-BB model of the Terra Tek/CSM heated block test. Note the complex stress distribution even in an ‘equal-biaxial’ loading situation, with only four (assumed) interlocking blocks. Input data for the different joints were: JRC  10 or 13, JCS  90 or 120 MPa, r  25° or 28°. Chryssanthakis et al., 1991.

(approx.) loading. Normal stresses across the joints are clearly in equilibrium, but the stress in the perpendicular direction can be dramatically different, with at least 10 MPa difference, from one side of a joint to the other side. One may visualise that the passage of shear waves through such a jointed (fractured reservoir) medium could perceive the joints as both displacement discontinuities and stress discontinuities, even though the classic Schoenberg 1980 assumption is for stress continuity across the displacement discontinuity. If this stress discontinuity complication (in the jointparallel direction) was generally in operation, there could then be four potential contributors to shear wave splitting, needing acceptance or rejection by the theoreticians who debate, conclude and publish such things: 1. the possible stress discontinuity (even when joints were under no shear stress) 2. the potential stiffness anisotropy (Kn dyn  Ks dyn, ZN - ZT) 3. the excess compliances/stiffnesses (the presumed source of (qS1 – qS2/qS1 anisotropy) with different contributions according to incident angle

Joint stiffness and compliance and the joint shearing mechanism

519

Figure 16.36 Multi-linear modelling of joint roughness with UDEC, showing shear-displacement vectors of upper sample, and the asperity-controlled principal stresses caused by the simulated shearing. Gutierrez and Barton, 1994.

Figure 16.35 Equal biaxial (1  5.4 MPa, 2  5.4 MPa) loading effect on the maximum values of the physical (E) and hydraulic (e) apertures. Top: 142 m, 35 m, Bottom: with dilation-limited shearing, E  169 m, e  49 m. Chryssanthakis et al. 1991.

4. the presence of a variable thickness film of water between the opposed, contacting sides of nonplanar slightly sheared joints. If there has been pre-shear (in a ‘critical crust’ scenario), then presumably the parts of the joints that were dilated and fluid filled would have changed local stiffness in relation to the rock-to-rock stress-transferring parts, thereby contributing differently to attenuation, P-, and S-wave anisotropy. In Figure 16.35, the modelling of physical (E) and hydraulic (e) apertures is shown, based on the assumed JRC  10 or 13, JCS  90 or 120 MPa, r  25° or 28° input data. The upper pair of (E) and (e) models are under equal biaxial stress, while the lower pair are under N–S (1 only) loading. Slight non-uniformity of aperture is shown, though shearing was very limited, for important reasons which will be discussed below, and treated later. The maximum joint apertures shown in Figure 16.35 were as follows: 1  2  5.4 MPa e  35 m E  142 m 1  5.4 MPa, 2  0 e  49 m E  169 m

The limited shearing corresponds also to the reality of this in situ test. There was no more than 0.25 mm shear, despite exceeding the shear strength according to conventional (Mohr) stress transformation of stresses. This is because the conventional stress transformation equations, for converting principal stresses into shear and normal stress components, fail to take account of the contribution of dilation to what are actually noncoaxial stresses and displacements. The mobilized dilation angle needs to be added into the cos 2  , sin 2  terms of the classic transformation equations. Barton, 1986. If we move now to a more direct simulation of joint shearing, in a simulated DST direct shear test, as opposed to a uniaxial/biaxial test, we avoid the problem of the stress transformation error, as the principal stresses are applied parallel and perpendicular to the joint plane. Gutierrez in Gutierrez and Barton, 1994, used the discrete element code UDEC to simulate the roughness of rock joints in a direct, unusually realistic manner, by constructing multi-linear sectors to represent some of the measured 100 mm long roughness profiles of Barton and Choubey, 1977 (from Figure 16.26). One of the UDEC models is shown in Figure 16.36. Note the dilation-related inclination of the deformation vectors for the ‘upper’ sample, the bottom being fixed. The principal stresses applied were parallel and perpendicular and there was simultaneous flow of fluid simulated from left to right, along the joint void. This particular joint simulation had JRCo  5. The constant normal stress was only 1 MPa. It is very easy to note the entirely different principal stress vectors above and below the shearing joint. The only locations where there are more similarities in magnitudes, but not directions, are the concentrated regions of stress transfer at the two major asperities, which resemble the more exaggerated case of a sheared undulating

520

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.37 Interlocked and sheared joints in ‘wavy’ columnar basalt, demonstrating the role of asperities and dilation on aperture distribution. Columbia River Basalts, Washington State, USA. See Plate 12.

joint in basalt, from the Columbia River basalt sequence in the Western USA, shown in Figure 16.37. On the basis of such rock stress related phenomena, one may then pose the following questions to geophysics theoreticians. In the case illustrated by the shearing joint model of Gutierrez, will shear wave splitting occur more readily where the principal stresses ‘plunge’ into another direction (as at the stress-transferring asperities), or will shear wave splitting be able to occur across the ␴1 stress discontinuity, as generally seen in Figure 16.36, due to the general presence of a ‘fluid-filled’ lense between these same locations? A painstaking ‘diagnostic’ of the simulated shearing joint was performed by Gutierrez. This is shown in Figure 16.38. In the diagrams we see the following distributed phenomena, along the 100 mm long simulated rock joint: a) individual contact lengths (mm) for 0, 1 and 2 mm shear b) individual contact angles for 0, 1 and 2 mm shear c) stress to strength (n/JCS) ratios for 0, 1 and 2 mm shear d) contact apertures for 0, 1 an)d 2 mm shear There is probably a correlation of high stress to strength ratios where there are small contact lengths and high contact angles. The highest (compressive) stress concentration was 38 times the applied (average) normal

stress (n), and the maximum tensile stress was 13 times higher than n. Apertures were mostly ‘closed’, or ‘opened’ to about 2 mm. (There appears to be a ‘mm for m’ misprint in diagram d, where 103 m and 106 m should be the two approximate extremes). Finally, to round off this present discussion of the possible consequences of an actual local stress-discontinuity at joint surfaces, especially when under shear stress, one may consider the inter-bedded bituminous shale and dolomite ‘Kimmeridge clay’ source rocks depicted in Figure 16.39a and b. The views are taken looking upwards from the base of the 10 m high cliffs at Kimmeridge Bay in Dorset. Although a certain consistency can be noted in the orientation of the two (actually up to three) sub-vertical joint sets in the harder dolomite beds, it is easy to imagine the relative complexity of the joint stress distributions, in view of the stress discontinuity trend discussed above. Interpretation of shear wave splitting in such a fractured reservoir environment, perhaps with nonaligned horizontal stress anisotropy, can be imagined as somewhat demanding. 16.7.2

The strength-deformation components of jointed rock masses

The potential for shear-wave splitting as a means of monitoring temporal changes in the geometry of the aligned,

Joint stiffness and compliance and the joint shearing mechanism

521

Figure 16.38 Numerical diagnostic of the sheared UDEC joint, showing contact lengths, contact angles, contact apertures and stress ratios, with 0 or 0.5 mm, 1.0 mm and 2 mm of shearing. Gutierrez and Barton, 1994.

Figure 16.39 Vertical view through the inter-bedded bituminous shales and dolomite bed, in Kimmeridge Bay, showing a) complex, b) ordered sub-vertical joint patterns. Dorset coast, S. England. See Plate 13.

522

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.40 Depiction of the effect of block size on the shear strength components of joints, from Bandis 1980, and Bandis et al., 1981.

fluid-filled features responsible for the splitting, can be further visualised by reference to cases where shear deformation occurs in the course of production from a petroleum reservoir. Due to the usual non-planarity of joints (despite their obvious depiction as straight lines or planes in the literature), there will usually be nonlinear normal stress-closure-opening behaviour, and nonlinear shear-dilation behaviour, Some of the details of joint behaviour need to be explored further, if stress anisotropy causes shearing during production, and if seismic monitoring is to be used for diagnosing the effects of new production measures. There is the potential for shearing when producing from conjugately jointed reservoirs when a vertical principal stress roughly intersects the two steeply dipping sets of conjugate joints in the reservoir (cf. Ekofisk, as described in Barton et al., 1986). This case will be discussed later in this chapter. The potential for shear also exists when water flooding into a jointed reservoir with non-aligned, anisotropic principal stress, for enhancing production. A related case is the injection of cold water into a geothermal reservoir, to establish hydraulic connection to wells on the far side of the reservoir. In the first case a gradual but major reduction in pore pressure (at least 20 to 24 MPa, prior to water-flooding) had caused an equivalent effective stress increase, following some 15 years of production. The porous chalk matrix apparently contracted sufficiently to make space for down-dip shearing, despite one-dimensional compaction, (see Figure 15.25). In the second case the injection caused an increase in pore pressure, and sufficient reduction in effective normal stress for the unequal principal stresses (70 and 30 MPa, Pine and Bachelor, 1984) to cause slight shearing.

Evidence for this was obtained from acoustic emission monitoring, which showed migration of micro-shearing to successively greater depths, when attempting to establish hydraulic connection between wells, for extraction of thermal energy. A schematic of such a case was illustrated in Chapter 15, Figure 15.2a, and temporal effects on shear-wave anisotropy were documented. The representative block size, given by the number of joint sets and their spacing and orientation, plus the surface character and length of the joints, combined with the effective normal stress levels acting on each set, collectively contribute to the possible response of a rock mass to shearing, when under the influence of an anisotropic, and non-aligned principal stress field. Figure 16.40, from Bandis, 1980, shows the dramatic potential effect of the individual block size, on shear strength, and displacement to peak, especially when joint roughness is significant. Barton and Choubey, 1977, had anticipated the effect of block size on displacement to peak (peak), as shown conceptually in Figure 16.41. Despite identical JRCn for joints AA and BB, the altered block size was expected to reduce peak. Clearly the bulk modulus of the second case would nevertheless be lower than for the massive rock mass, as there are so many more joints involved in the deformation process. Confusingly perhaps, it may be the ‘better quality’ rock masses, with wider joint spacing, and with greater joint continuity, that could be most prone to (previous) shearing deformation along the joint sets, when under the influence of a non-aligned, anisotropic, (differential) stress field, caused by some historic tectonic adjustments, of which there is no shortage. A heavily fractured rock mass, though obviously with lower (bulk) modulus, may resist significant shearing

Joint stiffness and compliance and the joint shearing mechanism

523

for their first (photogrammetry-measured) shearing events of 21.6, 25.1 and 26.7 when tested in biaxial shear, i.e. shear strength rising as block size reduced. The mass ‘Poisson ratios’ estimated from these ‘static’ biaxial shear tests are seen to rise dramatically as differential stress rises. Values exceed the continuum ‘limit’ of 0.5, due to the influence of micro-shearing along numerous fracture surfaces. Presumably, in the context of a sheared reservoir situation, such could be detected by the seismic anisotropy response. Shear wave anisotropy would be enhanced most by the more easily shearing (and therefore more conducting) primary set of fractures. (Note that these would not be parallel to the customary H max direction). In these physical tension fracture models, the first parallel set of fractures developed on the double-guillotine table, were continuous, and remained continuous, following the development of the secondary, intersecting set, which due to up-stepping and down-stepping when crossing the pre-existing fractures, would impart an anisotropic strength and stiffness to the assembly. It is reasonable to believe that in the context of conjugate joint sets, this dominance of a primary set is common. It was certainly the case in the jointed chalk of the Ekofisk field, as reviewed in Chapter 15, Figure 15.7. Figure 16.41 Scale effect on  (peak) caused by increasing block size. Barton and Choubey, 1977. The scaling of peak is one of the components of Ks that causes low stiffness as block size increases.

along individual joints, due to the higher collective shear resistance of smaller block sizes. When the block sizes are small, blocks can rotate slightly, thereby sampling the steeper joint-surface asperities that contribute to higher strength. (Barton and Bandis, 1982). Some physical modelling evidence of the influence of block size is shown schematically in Figure 16.42a, from Barton and Hansteen, 1979, as also analysed further by Bandis et al., 1981. The (differential) stressdeformation behaviour of the three different models is shown in Figure 16.42b. Back-analysis showed that the elemental tension fractures, common to each model, whether forming 250, 1000, or 4000 interlocked blocks, had a ‘JRCn’ value averaging 20, from numerous ‘large-scale’ direct shear tests. The tension-fractured assemblies, made with a dynamic ‘double-guillotine’ device (Barton, 1972), each fabricated of identical rocklike, brittle material, had back-calculated JRC values

16.7.3

Permeability linked to joint shearing

In a deep petroleum reservoir, and strictly from a geomechanics viewpoint, one can hardly imagine that ‘open’ joints can be found at typical 2 to 4 km reservoir depths, unless there are one or more of the following conditions: mineral ‘bridging’ holding parts of fractures open, high-strength rock and rough-surfaced joints, or joint shearing (possibly where there is less roughness). This viewpoint is held because of a probably too high effective minimum stress (h min) of perhaps 20 to 40 MPa magnitude, in relation to probable similar magnitudes of JCSn in the case of the common weaker reservoir rocks. Shearing, as in weak Ekofisk chalk, and perhaps at a larger number of reservoirs than the petroleum industry suspects, is linked of course to the potential for dilation, and therefore potential permeability maintenance (in the face of the high normal stresses), and perhaps even permeability enhancement. Example values of the three basic components of joint or fracture shear strength and stiffness (JRC  roughness, JCS  joint wall compressive strength, r  residual

524

Rock quality, seismic velocity, attenuation and anisotropy

Peak strength of jointed mass

(a)

(b)

Figure 16.42 a) A comparison of the shear strength of interlocked assemblies of tension-fractured, idealised, model rock masses, with 250, 1000 or 4000 blocks. b) The respective differential stress-versus-strain curves in the 1 and 2 directions for the same models. Note entirely different behaviour of the most heavily fractured model with 4000 blocks, due to greater freedom for (micro) block-rotation. Barton and Hansteen, 1979.

friction angle) are shown contributing to peak shear strength in Figure 16.43. Estimated peak dilation angles are also shown on each strength envelope, at appropriate normal stress levels. Clearly as shearing continues beyond peak, rates and angles of dilation will steadily reduce. However the joint (minor fault?) aperture has probably accumulated some vital void space for fluid conduction, minus areas of contact with crushed material and finer gouge causing local blockage, as we saw in Figure 16.13. Barton-Bandis modelling of individual joint responses as either block size or normal stress changes are shown in Figure 16.44, from Barton et al., 1985. The relative

amounts of predicted dilation, with the given input data assumptions, are shown in the middle diagrams. In the lowest of the three sets of predicted behaviour curves, the theoretical maximum change in permeability with the shear-induced dilation is shown. Here, gouge production (and partial joint blocking) is ignored. Note the assumption of an initial hydraulic aperture (eo) of 25 m in each case. The dilation curves show how the initial physical aperture (Eo) changes. The sum of Eo  E (E1) is converted to eo  e (e1) to estimate permeability from the assumed cubic law K  e2/12.

Joint stiffness and compliance and the joint shearing mechanism

Figure 16.43 The peak shear strength equation for in situ scale rock joints, and example strength envelopes. The subscripts on JRC: (JRCn) and on JCS: (JCSn) imply large scale, block-size-dependent values in general. In the two uppermost strength envelopes shown, input values are more typical of laboratory samples, where roughness tends to dominate behaviour. The lower envelope might apply to a minor fault, or to a weak, or weathered rock joint.

16.7.4

Reservoir seismic case records with possible shearing

Seeking more detail about the fracture directions and stress direction at the Bluebell-Altamont Field, one may note from Lynn et al., 1999, that the borehole elongation data indicated a range of possible major stress orientations from N20° to 50°W. Fracturing could presumably have influenced this result. Three methods of fracture orientation (outcrops, FMS log and core samples) indicated a spread between N20° to 35°W, with the second set less well delineated at about N60° to 80°E. The Maultzsch et al., 2003, Liu et al., 2003a and Liu et al., 2003b analyses of shear wave anisotropy, reviewed in Chapter 15, actually suggest polarization more related to the major stress direction than the dominant fracture direction. However, the variation of anisotropy at lower frequencies suggests that their results must be

525

fracture related rather than stress-aligned microcrack related (EDA). In Figure 15.60, we could see the various sources of orientation data from Lynn et al., 1999. There was clearly great consistency in the direction of the N20° to 35°W joint set, which was presumed by Maultzsch et al., 2003, Liu et al., 2003a and Liu et al., 2003b to be the source of the qS1 polarization. Yet diagram b) in Figure 15.60 showed ‘VSP S1’ at about N43° to 45°W, some 10° to 20° different from the fracture orientation obtained from core data, yet almost parallel to the gilsonite dykes. One may speculate that a possible explanation for the potential discrepancy between qS1 polarization and the fracture orientation could be due to non-planarity of the fractures combined with slight shearing. It could also be due to unavoidable, minor sources of error, in data acquisition, as suggested by Lynn (pers. comm. 2005). The Chapman modelling reviewed in Chapter 15, had suggested 6 m diameter fractures at a frequency of only one per 9 to 10 m cube of rock mass, i.e. implying quite large block sizes, but this would be dependent on the spacing of the N60° to 80°E set. With large block size and non-coaxial major principal stress one could have a situation in the reservoir (especially if fluid pressures had been high) that, in principle, could resemble the shear-dilation mechanism shown in Figure 16.45. These are rough tension fractures that have a prototype scale of many metres length (due to up-scaling of a weak brittle model material). The measured profiles of roughness have been sheared following the shear-dilation (X, Y coordinates) measured during direct shear tests at a) low normal stress (top: n 2) and b) at high normal stress (bottom: n 6). Two different degrees of pre-peak and post-peak shear and dilation are shown. The black (overlapped) contacting areas that transfer shear and normal stress have, on average, a significantly different orientation to those (white) areas that are dilated, and which in a ‘slightly-sheared’ reservoir situation would contain most fluid. Could it be that the rotated mean direction of these ‘fluid lenses’, obviously distributed in three dimensions, could be more responsible for the shear wave polarization than the average joint plane, or would it be the rock contact areas? These large, rougher than normal tension fractures show a 10° to 20° effective rotation of the lenticular apertures in relation to the mean fracture planes. They might represent the areas where squirt attenuation was least active, due to higher permeability.

526

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.44 Barton-Bandis models of shear strength-displacement-dilation-permeability coupling. Curves generated by Bakhtar with a programmable calculator. (Barton et al., 1985.) The permeability estimate is the theoretical, dilation-produced maximum, devoid of considerations of gouge production. The latter requires a modified treatment of roughness for (E) to (e) conversion, using JRCmobilized, as shown by Olsson and Barton, 2001. (See Figure 16.9).

The oppositely rotated rock-to-rock contact areas with their extremely high stress, are less likely planes for reflection. So if the lenses were fluid-filled, an apparent rotation between the reflectiveness to S-wave and the squirt attenuation source areas might be the result, in relation to the mean plane of reference, some 10°–20° between the two. Previous figures in this chapter showed that shear strengths, shear displacements, dilations and shear stiffnesses, were each affected adversely by increasing block size. (Barton and Bandis, 1982). Due to reductions of effective roughness JRC and wall strength JCS, and increased displacement to peak, each caused by larger block size, the in situ (pseudo-static) joint shear stiffness even at 10 to 20 MPa effective normal stress, may be close to 1 MPa/mm for the case of say 2 m in situ block sizes. Such a low pseudo-static stiffness is two or more orders of magnitude softer than the ‘Hudson compliance’ diagonal (Figure 16.23). Is this also significant?

16.7.5

The apertures expected of highly stressed ‘open’ joints

As introduction to the question of ‘open’ fractures and their orientation, we refer to another case record of reservoir seismic anisotropy investigation, this time involving a large (43 square mile) 3D full-azimuth, full-offset P-wave survey in a fractured carbonate gas field in Texas, as described by Lynn et al., 2000. The deep target formations were carbonate and chalk formations at 14,000 to 15,500 ft (about 4,280 to 4,730 m). The faster P-wave velocity direction was parallel to the strike of the local structure, and interpreted as also parallel to the local maximum horizontal stress direction. As the authors state: ‘The interpreted open fractures are those approximately parallel to the local maximum horizontal stress, and are considered to be the fluid-flow pathways or permeable conduits’. Clearly, at four-and-a-half km depth, one is far removed from the near-surface, where H max oriented

Joint stiffness and compliance and the joint shearing mechanism

527

Figure 16.46 A collection of large scale stress-permeability tests on joints in hard crystalline rocks, both at ambient and elevated temperature, showing ‘linear’ log-logpermeability-stress trends, with various gradients. Barton, 1982. (Pratt et al., 1977, Witherspoon et al., 1977, Iwai, 1976)

Figure 16.45 Reconstructed shear-and-dilation events for model tension fractures with the illustrated roughness profiles, cut out as plastic ‘replicas’. Note the ‘opposite’ rotations of the (potentially) fluid-bearing lenses, which are down-dipping to the right, and the up-slope to the right rock-to-rock contact areas which are of ‘double’ thickness therefore signifying the production of crushed particles. The lenses will therefore have debris/gouge at their extremities. Barton, 1973a.

joints are certainly very typical. Such cases were reviewed in Part I of this book, and were the source of marked azimuthal P-wave anisotropy. In contrast to the near-surface, the adverse effect of many tens of MPa minimum effective stress would have suggested to a rock mechanic that the more ‘open’ joints should be at an

angle to the major stress. Such a scenario for the ‘open’ joints has been emphasised and convincingly demonstrated in deep well analysis, by Colleen Barton, Zoback and Moos, 1995, and this and later studies by Zoback and his colleagues will be reviewed later in this chapter. Before considering some convincing evidence for the possible/probable non-alignment of ‘open’ sub-vertical fractures with the major principal stress direction (H max), from these and other authors, one must consider the case of fractures that are orientated in this classically assumed ‘mode 1’ direction. In such cases, the minimum effective stresses may tend to keep the ‘open’ fractures actually more closed than open, unless the rock is rather strong, and/or the fractures are ‘bridged’ by mineral cementation. Even for joints in hard crystalline rocks, coupled (MH) stress-permeability tests of joints at mostly in situ scale (1 m diameter jointed cylinders, and 2 to 8 m3 jointed in situ blocks), demonstrate a marked reduction in permeability with normal stress. Figure 16.46 from Barton, 1982, shows ‘linearity’ on a log-log plot of permeability versus normal stress. One earlier ambient

528

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.47 Log-linear relation showing the effect of normal stress on the closure of physical aperture for various rock joints, in mostly sedimentary rocks, as tested by Bandis, 1980.

temperature and one heated block test (described in Figure 16.29 to 16.33), constitute the main body of data assembled in this figure. There was experimental evidence from these tests of even smaller conducting apertures when temperature was elevated. This would add to the downward trend of permeability, with increased depth. Hydraulic apertures in the lower right corner of the figure are down to a few microns in size. It seems unlikely that such would be considered ‘open’ in the context of oil producing reservoirs. The physical closures of joint apertures in (mostly) sedimentary rocks, as a result of applied normal stress, were shown by Bandis, 1980 to decline linearly against the log of normal stress. This relevant result is shown in Figure 16.47. The large closures seen in the weaker rocks like siltstone, would be expected to nearly ‘close’ such joints, and with conversion from physical aperture (E) to hydraulic aperture (e), small residual permeabilities would be expected.

The laboratory normal stress-conducting aperture data shown in Figure 16.48 was assembled by Makurat (pers. comm. 2006), from numerous tests performed in the CSFT apparatus developed by Makurat at NGI (Makurat et al., 1990, Makurat, 1996, Makurat 2006). As is readily observed, there are a large number of test data showing extremely small apertures, often well below 10 m, when even moderate normal stress levels in relation to JCS values were applied. The data for tuff and ignimbrite joints from the UK Nirex Ltd planned Sellafield Rock Characterization Facility, were derived from tests at up to 30 MPa normal stress. Although this is equivalent to effective stress levels at about 1.5 km depth in a petroleum reservoir, the ratio of applied n/JCS was less than 0.15, due to the high strength of the tuff. The fact that the joints were quite planar, with JRCo mostly from 3 to 6, was an important contributor to their small conducting (and mechanical) apertures under stress. It was noted by Makurat that tests on weak reservoir rocks like chalk and shale, often showed higher conducting apertures than expected, in relation to quite high ratios of n/JCS, such as 0.7, 1.4 and even 2.0. This was interpreted as due to sampling damage, as it is easy to ‘lose’ material (prior to reaching the laboratory environment), due to recovery by drilling and subsequent transport. Loose grains and cracked pieces can be more easily lost when strength is in the 2 to 5 MPa range, as for several of the JCS values of joints in the chalk, sandstone and shale. The hoped for ‘open’ joints in a fractured reservoir can hardly be expected to be significantly open, unless the joints or fractures are rather rough, or are ‘bridged’ (but not sealed) by hard minerals, thereby resisting complete closure during hydrocarbon production. Of course if the fluid is over-pressured and is very close to the minimum total rock stress, so that the effective stress (h min – Pf ) is small, then closure again would be limited until much later in production. If we consider 3 km depth, and a fairly typical minimum total stress (h min) magnitude of 40 to 50 MPa (compared to an assumed density-based total vertical stress (v) of 60 to 70 MPa), there may be a hydrostaticbased pressure of about 30 MPa for the 3 km deep reservoir. It is then clear that the effective normal stress of 10 to 20 MPa will be holding joints parallel to H max nearly closed, since they are undisturbed, and have no way of losing material, as above. We can deviate briefly to the micro-world of elliptical cracks and consider that the theoretical closure pressure

Joint stiffness and compliance and the joint shearing mechanism

529

(a)

(b)

Figure 16.48 a) Normal stress-conducting aperture behaviour from CSFT tests in natural joints in tuff, ignimbrite, granite, sandstones, shale and chalk. b) Mean behaviour for each rock type, using power-law extrapolation. Makurat, 1996, Makurat pers. comm. 2006.

P, for the case of a stiffer elliptical crack of aspect ratio (), under hydrostatic stress (Walsh, 1965) is:

P  3K s  

1  2 2 (1   2 )

(16.10)

in which Ks  bulk modulus of solid material (e.g. about 40 GPa for clean sandstones), and   Poisson’s ratio of solid material (0.17 for clean sandstones). The closure pressure for a microcrack of aspect ratio 103 is then approximately 40 MPa. Using this theory, King and Marsden, 2002, had assumed that microcracks with

530

Rock quality, seismic velocity, attenuation and anisotropy

(c)

(d)

Figure 16.48 c) Normalised stress-to-strength ratio (
n/JCS) versus conducting aperture plots, which emphasises the different rock strength magnitudes. d) Power-law fit to mean data for a given rock type, with extrapolation to higher stress-to-strength levels. Makurat, 1996, Makurat pers. comm. 2006.

smaller aspect ratios would not be open at applied effective stresses greater than 40 MPa. If up-scaling is performed to much longer cracks and discontinuous joints, with aspect ratios of e.g. 105 or less, the above theory for ‘elliptical’ cracks will presumably

break down, as rock joints with some wall roughness appear not to close completely (Bandis et al., 1983). The normal stiffness merely becomes extremely high, but complete closure is virtually prevented by asperity roughness, like a joint roughness coefficient JRCo that

Joint stiffness and compliance and the joint shearing mechanism

531

Figure 16.49 BB normal closure-permeability and shear dilation-permeability modelling. Case A ‘sandstone’ with JRC  5, JCS  25 MPa, r  27° and c  30 MPa. Note extremely small apertures and low permeability in the left-side plots ( normal closure) and the marked dilation and rapid permeability enhancement in the right-side plots ( shear).

is acting at right-angles. However, we would be reaching micron size (e.g. 1 to 5 m or less) in such cases, unless previous shearing had occurred. It would appear that the ‘conventional wisdom’ of the most conducting joints being parallel or sub-parallel to the major stress direction, which is clearly proved in the near-surface, by means of three-dimensional permeability testing (e.g. Quadros et al., 1999), needs to be re-assessed in the context of petroleum reservoirs, in weaker sedimentary rocks at great depth. Will a joint set with apertures of a few microns or less, really satisfy the description ‘open joints’, and will they cause shear wave splitting when they have such a high area in contact as is necessary for h minimum of 10, 20 or 30 MPa to be transferred across their relatively weak joint walls? If the ‘open’ apertures are actually mainly ‘tape-worm-like’ channels, within ‘closed’ joint planes,

would shear wave splitting and recognisable fast and slow wave speed anisotropy have been registered by the geophysicists?

16.7.6

Modelling apertures with the BB model

In order to investigate this further, the stress-closure (n – E) and stress-permeability (n – K) cycles resulting from Barton-Bandis modelling of three hypothetical, but realistic joint characteristics were investigated. The input data assumptions are listed in Table 16.13, and Figures 16.49 to 16.51 and Table 16.14 show selected results of this parameter study. The first two of these BB modelling figures shows that the modelling of both cases originates from an initial

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.50 BB normal closure-permeability and shear dilation-permeability modelling. Case B ‘carbonate’ (low roughness) with JRC  5, JCS  50 MPa, r  33° and c  60 MPa. Note extremely small apertures and low permeability in the left-side plots ( normal closure) and the marked dilation and rapid permeability enhancement in the right-side plots ( shear).

Table 16.13 Input data assumptions for investigating the physical and conducting apertures likely to be available with an ‘open joints parallel to H max assumption’. Unless joints are rough, and the rock is hard, this orientation proves unlikely to give the assumed ‘open’ joints at reservoir effective stress levels. Note subscripts JRCo and JCSo representing lab-scale parameters, which are assumed to be most representative for normal closure modelling. Case A

Case B

Case C

JRCo  5 (medium rough, slightly undulating) JCSo  25 MPa (medium weak rock e.g. sandstone) c  30 MPa r  27° JRCo  5 (medium rough, slightly undulating) JCSo  50 MPa (medium strength carbonate rock) c  60 MPa r  33° JRCo  10 (rough, slightly undulating) JCSo  50 MPa (medium strength carbonate rock) c  60 MPa r  33°

unstressed aperture (Eo) of 0.14 mm (or 140 m). This was estimated from the following empirical equation (Barton, 1982) based on Bandis, 1980, tests of numerous natural joints. E o (mm) ≈

JRCo 5

   0.2 c  0.1   JCSo 

(16.11)

This equation makes allowance for the experimental result that initial apertures are larger when the small scale joint roughness coefficient (JRCo) is greater than about 5, as in Figure 16.51 which has JRCo  10. The ratio of c/JCSo allows for the increased aperture when there is weathering when JCSo  c. Clay-fillings or clay-coatings, as tackled in the rock quality Q-system, are not considered in Barton-Bandis modelling.

Joint stiffness and compliance and the joint shearing mechanism

533

Figure 16.51 BB normal closure-permeability and shear dilation-permeability modelling. Case C ‘carbonate’ (high roughness) with JRC  10, JCS  50 MPa, r  33° and c  60 MPa. Note improved apertures and permeability in the left-side plots ( normal closure) and the stronger dilation and rapid permeability enhancement in the right-side plots ( shear). Table 16.14 Estimates of physical (E) and conducting (e) apertures, for two assumed reservoir rock joint scenarios, with low and moderate strength rock, and low roughness. Predicted apertures are too small to be considered ‘open’, with this limited roughness. 3  3rd cycle, 4  4th cycle of loading.

Input data At n
 10 MPa n
 20 MPa At n
 10 MPa n
 20 MPa

Case A

Case B

JRCo  5 JCSo  25 MPa E3  0.90 m E4  0.37 m e3  0.01 m e4  0.01 m

JRCo  5 JCSo  50 MPa E3  2.26 m E4  1.03 m e3  0.09 m e4  0.02 m

Both models with the least rough joints were consolidated three times to 20 MPa, then to 10 MPa on the 4th cycle, as if there was a certain overpressure. They show extremely small minimum apertures (E3, E4) on

the third and fourth cycles of consolidation (actually ‘reloading’, as in the Bandis experiments, to reach an almost stable assumed ‘in situ’ aperture). The effective normal stresses applied were to simulate H min with an ‘open joints parallel to H max assumption’, as referred to by many geophysicists with presumably the agreement of the field reservoir engineers. Hard rock and rough joints (or ‘bridging’ with hard minerals) seem to be needed for this orientation to satisfy the ‘open’ joints requirement, judging by the very small apertures predicted for these two least-rough-joints cases. One set of conducting fractures will give the rock mass an (anisotropic) mass permeability equal to Km (following Louis, 1967): Km  Kr  K j

e L

(16.12)

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Rock quality, seismic velocity, attenuation and anisotropy

where Kr  permeability of rock matrix Kj  joint permeability e  average hydraulic aperture L  average spacing of conducting joints Since in the highly stressed (n
 20 or 10 MPa) examples (cases A and B), e3 and e4 are in the range 0.01 to 0.07 m, it is clear that both the Kj  e2/12 term, and the e/L term will give minute contributions to the bulk permeability Km, and one will depend on the matrix permeability Kr (and porosity), in each of these two cases. On the other hand when JRC  10 (as in Figure 16.51, the apertures and permeabilities are considerably larger, and ‘open’ joints in the direction of H maximum can then be imagined. There is however, a dilemma exposed by the JCSo assumptions in Tables 16.13 and 16.14, concerning which magnitude of the confined joint wall strength JCSo one should actually select for reservoir joint modelling. Clearly a positive effect of confinement on strength (represented by the expanding Mohr circle diameter 1 – 3), should help to increase apertures somewhat, but would likely be insufficient to give ‘open’ character in the case of the less rough joints in the weaker, porous reservoir rocks. The problem for a weak reservoir rock, like porous sandstone or chalk, is that very high confinement, as when at several kilometres depth, may no longer be positive for strength development, due to the onset of plastic deformation and eventual pore-collapse trends. The Mohr strength envelopes tend to curve rapidly towards a maximum shear strength with increased confinement (i.e. have strongly non-linear internal friction angles), and therefore reach a maximum value of 1 – 3 at the point where the Mohr envelope becomes horizontal, usually corresponding to a ‘critical state’ line defined by a gradient 1  33 suggested by Barton, 1976. This will be shown later. At higher confinement a ‘cap’ or declining trend occurs. Loss of porosity or reduction in void ratio for a rock like porous chalk, plus a reducing rate of gain in strength, occurs at successively lower effective mean stresses as the porosity rises from e.g. 20 to 30 to 40% and more. In contrast, hard rocks, and especially very hard rocks, show great benefit of confining stresses equivalent to many kilometres depth, by not crossing the ‘critical state’ line until hundreds of MPa confinement, or up to tens of kilometres of equivalent depth in exceptional cases. These aspects will be discussed further in the next section.

16.7.7

Open joints caused by anisotropic stress, low shear strength, dilation

In contrast to the normal closure modelling of apertures discussed above, the shear-dilation modelling that is also shown in Figures 16.49 to 16.51, indicates that significant apertures will be developed after some few mm of shearing in all three cases, even with the weaker of the ‘reservoir’ rocks. So repeated shearing in a ‘critical crust’ scenario (as interpreted by Townend and Zoback, 2000, and others who support the ‘geomechanical’ school of thought), could easily develop the apertures needed to make the above case A, and case B ‘hydrocarbon reservoirs’ productive, with truly ‘open’ sheared joints and less need for a permeable matrix, than seen in the normal stress-closure examples. In the case of shearing under an arbitrary effective normal stress level, the peak shear strengths ( ) can be estimated from the following equations, which were presented earlier. Block-size induced scale effects, reducing JRCo and JCSo, are seen to reduce peak shear strength. They will also affect the subsequent shear resistance reductions, towards residual strength, the latter taking perhaps 1 meter, or more, of shear displacement.   JCS  

 
n JRCn  log 
n   r    n    L 0.02 JRCo JRCn ≈ JRCo  n   L o   L 0.03 JRCo JCSn ≈ JCSo  n   L o  It will be noted that in contrast to the normal closure modelling of the three cases A, B and C in the previous section, there is here a necessity for r estimation, since shearing is to be modelled. In Table 16.13, r  27° was assumed for the case A, weak ‘sandstone’, and r  33° for cases B and C, representing stronger ‘carbonates’ with two different joint roughness magnitudes. In situ block sizes Ln of 1.0 m were assumed here in each case, in order to demonstrate the orders of magnitude of possible strength reduction, due to reductions of JRCo and JCSo according to the scaling equations of Bandis et al., 1981. The experimental form of the JRCo and JCSo reduction with block size is illustrated in Figure 16.52. Note that the dilation curves shown in Figures 16.49 to 16.51, were non-conservatively linked directly to

Joint stiffness and compliance and the joint shearing mechanism

535

Table 16.15 Estimation of shear strength reduction due to block size, for the three reservoir rock scenarios. Assumed mean block size  1.0 m. (Note the friction coefficient format: useful for comparison with data from the ‘critical shearing crust’ section that follows).

Figure 16.52 Experimentally determined reductions in JRC and JCS, based on analysis of the extensive scale-effect investigations of Bandis 1980. Note the use, and important influence, of small-scale roughness JRCo in this scaling. Bandis et al., 1981.

aperture increase, following Barton et al., 1985. The reality from case to case is difficult to estimate, without using the Olsson and Barton, 2001, JRC : JRCmob modified, E to e conversion (Figure 16.9), for roughly

Case A (assume n
 10 MPa)

Case B (assume n
 10 MPa)

Case C (assume n
 10 MPa)

JRCo  5 JRCn  4.0

JRCo  5 JRCn  4.0

JRCo  10 JRCn  6.3

JCSo  25 MPa JCSn  18 MPa

JCSo  50 MPa JCSn  35 MPa

JCSo  50 MPa JCSn  25 MPa

r  27°

r  33°

r  33°

o  5.5 MPa

o  0.55

n  5.3 MPa

n  0.53

o  7.4 MPa

o  0.74

n  7.0 MPa

n  0.70

o  8.4 MPa

o  0.84

n  7.1 MPa

n  0.71

estimating gouge-production effects on reduced permeability enhancement with shear and dilation. This will result in less extreme increases in permeability with shear unless the rock is hard, and/or the roughness low and the rock hard enough to resist ‘wear’. There may be an approximately 50% reduced conducting aperture caused by gouge, according to Makurat’s CSFT (coupled shear flow test) results. (Makurat et al., 1990). This will be depend partly on the n
/JCS ratio which describes one of the important components of damage. Damage during shear will also depend on JRC, as steeper asperities tend to get more damaged, though also cause more dilation. (Barton and Choubey, 1977 developed a damage coefficient on the basis of the above). These opposed tendencies obviously have complex consequences on the permeability development with shear. As discussed before, both smaller scale and larger scale joint or fracture non-planarity, will cause several possible interpretations of ‘fracture orientation’, in relation to shear wave splitting and polarization. Interpreted anisotropy results that are actually non-parallel to H max but not greatly different, might sometimes mislead analysts into thinking that the productive fractured reservoirs they are interpreting, have ‘open’ fractures approximately ‘parallel’ to H max, when an alternative interpretation is possibly more realistic in geomechanics terms. (Here we recall from Chapter 15 that two conjugate sets can provide components suggesting H max parallelism.). As demonstrated in the above BB-modelling exercises, that parallelism of ‘open’ fractures to the H max direction is unlikely in weaker rock unless joints are quite rough, or production very poor, despite the fracturing (i.e. if the

536

Rock quality, seismic velocity, attenuation and anisotropy

joints were nearly closed they would satisfy the geomechanics criterion, but not the production requirement). In stronger (e.g. carbonate) rock, with greater roughness, there may be naturally larger apertures, which would give ‘open’ fractures also without the benefit of historic or recent tectonic shear deformations.

16.8

Non-linear shear strength and the critical shearing crust

Hydraulic fracturing based stress measurements performed for a pressure tunnel design in 1980 in Georgia, USA while working in the USA, and acoustic emission events recorded by others when injecting water into the Cornwall Geothermal Project (Pine and Batchelor, 1984), were the stimulation for the sheared-fracture/ sheared-joint sketches given in Figures 16.53a and 16.53b, which we will use to introduce the ‘critical shearing crust’ concept. These are ‘forced’ events, caused by pore-pressure increase. Nature appears capable of something similar without human intervention. When there is a significant mismatch of horizontal stress magnitudes, and pre-existing joints that are not parallel to H, there is a good statistical chance for joint shearing, when attempting hydraulic break-down in a minifrac stress measurement (Barton, 1981). In a leaking pressure tunnel-liner situation, the same event is possible at much larger scale. In this section, the important findings of Colleen Barton and Zoback and co-workers will be reviewed regarding the convincing evidence for the existence of significant shear stress on joints or fractures that were hydraulically conducting in a deep boreholes in crystalline rock. Data from several wells are now available, thanks to the analyses of the Zoback team. By careful analysis of fracture orientation and inflow logging, they also showed that insignificant shear stresses were acting on joints that were not conducting. In this work, they compared their stress estimates with the ‘standard’ 0.6   1.0 joint friction model that has been popular in the USA since Byerlee, 1978. (The ‘Byerlee law’ suggested a generally applicable


0.85 for the coefficient of friction). Before reviewing their flow or no-flow data, we will look at the actual non-linearity of shear strength, in all its forms. Their data on conducting joints and fractures fits the Byerlee ‘band’ of shear strength, but the fit can be improved by considering non-linear friction.

(a)

(b)

Figure 16.53 a) The nature of conducting ‘open’ joints or hydraulic fractures caused by pore pressure and shear stress induced shearing. Barton, 1986. b) The suggested mechanism of hydraulic fracture ‘breakdown’ by shear mobilization, given by Barton, 1981, for the case of pre-existing joints where stress measurements (or leaking pressure tunnels) are involved.

16.8.1

Non-linear strength envelopes and scale effects

In an attempt to understand the actual non-linearity of shear strength envelopes, both for rock joints, for fractured triaxial samples at high stress, and for intact rock itself, Barton, 1976 assembled and analysed a large number of test data from the literature. The following contrasting sets of (non-linear) shear strength data, consist of high pressure triaxial shearing of (small)

Joint stiffness and compliance and the joint shearing mechanism

(a)

Returning to these and further data sets in 1990, at the First International Workshop on Scale Effects in Rock Masses in Loen, Norway, and armed with some important scale-effect research by Bandis, 1980, as summarised in Bandis et al., 1981, the writer (Barton, 1990b) sketched approximate ‘scale effect’ bounds on the significantly updated data sets. Figure 16.55 shows the assumed ‘shifts’ in the data boundaries. It was estimated that in case a) due to the intensely high stresses to 800 MPa, there would be a very limited scale effect (assuming faults were excluded). The engineering data at stress levels mostly below 4 MPa shown in Figure 16.55b, were known to display a severe scale effect. In other words tests on 100 mm samples of a given joint were always of higher strength than 1000 mm samples, unless roughness was virtually absent. Subsequently, the generally expected non-linearity of the shear strength envelopes for rocks, rock joints and crushed rock were assembled by Barton, 1999a, to compare the various empirical strength criteria that have the form:

 n tan(X log10 Y  .)

(b)

Figure 16.54 a) Shear strength of induced fractures in small, extremely high pressure triaxial tests following failure of the centimetre-size intact samples. (Data from Byerlee, 1978 and others). b) Shear strength from direct shear tests on natural rock joints (one test per sample), at low rock engineering stress levels. Typical sample lengths of 100 mm to 1000 mm. Barton, 1976.

‘faulted’ samples, shown in Figure 16.54a, and a low pressure set of data shown in Figure 16.54b. The latter were obtained from direct shear tests on natural rock joints, and included the test results for the 130 fresh and slightly weathered joint samples tested by Barton and Choubey, 1977.

537

(16.13)

where X represents the effect of roughness, e.g. JRC, and Y represents the strength/stress ratio, i.e. joint wall strength JCS/n
in the case of engineering stress levels, which will need the confined strength (1  3)  JCS, i.e. the strength/stress ratio (1  3)/n
, in the case of shearing at high stress levels (Barton, 1976). The schematic arrangement of the different strength envelopes is shown in Figure 16.56. Two of the sources for the schematic envelope for intact rock in this figure, are reproduced in Figure 16.57. These show the tendency of the numerous, mostly ultra highstress data to cross the ‘critical state’ line (defined by Barton, 1976), in a more-or less horizontal orientation, i.e. beyond the brittle-ductile transition, in the advancing ‘plastic’ state. Note that Z  c  26.6° in this model, as indicated by the expanding and then declining Mohr circles in Figure 16.58. The general non-linearity of the Barton-Choubey (small-scale) and Barton-Bandis (general scale) constitutive equations for the shear strength of rock joints, can be reduced to the traditional, but actually less geotechnically representative Mohr Coulomb parameters c and , by the simple equations shown in Figure 16.59. The particular case shows how to derive c and  between arbitrary effective normal stress levels of n3 and n4.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.55 a) Triaxial, high stress and b) direct shear (low stress) data for induced fractures and joints respectively. Scale effect curves are estimates only. Barton, 1990b. Adapted from Barton, 1976 with additional data from Byerlee, 1978.

The general strengthening-by-confinement that we have seen in the above shear strength envelopes, will obviously apply strongly in the case of deep wells in hard crystalline rock, both for the intact rock, and for the faulted discontinuities or sheared joints. We will address this aspect again when reviewing deep permeability data. Strengthening-by-confinement is likely to be of only moderate strength in the case of hydrocarbon reservoirs

in weaker sedimentary rock, due to their limited tolerance of very high confinement, before ‘state change’, such as pore collapse (in chalks), or general porosity reduction. (Refer to Figures 12.22 and 12.23 for the case of sandstones). These medium weak rocks would obviously not support 20 to 50 MPa effective stresses, and mostly maintain porosity, without some strengthening due to confinement.

Figure 16.56 Schematic representation of the non-linearity of strength envelopes for various ‘earthscience’ materials, showing a comparison of the empirically derived roughness (X) and strength/stress (Y) ratios. Barton, 1999a.

Joint stiffness and compliance and the joint shearing mechanism

539

3

Figure 16.58 A general model for representing the shear strength of intact rock, showing the succession of key Mohr circles that also span the brittle-ductile transition and reach the ‘critical state line’, defined by Barton, 1976 as 1
33. From this point, strength envelopes may have a tendency to show reduced strength with increasing confinement, in the ‘cap’ region.

(a)

24

2000

1800

23

12

DIFFERENTIAL STRESS σ1σ3 MN/m2

1600

1400

14

21

1200 20

1000

16

22

17 19

800

15

AL IC IT TE R C STA

13

600

9

8

400

3σ 3  σ1

7

11 6 4

200

5 10 1

3 2

100

(b)

200

300

400

CONFINING PRESSURE σ3 MN/m

500 2

Figure 16.57 Shear strength data for intact rock at a variety of mostly high confining pressures, from the numerous sources reviewed by Barton, 1976.

Figure 16.59 Conversion of the non-linear Barton-Bandis shear strength equation to Mohr Coulomb parameters c and  at a specific range of stress. Note use of largescale rock joint characteristics, i.e. in situ block size Ln with JRCn and JCSn, compared to Lo with JRCo and JCSo for lab tests.

540

Rock quality, seismic velocity, attenuation and anisotropy

That there are limits to the strengthening-byconfinement in the case of weaker rock, can be seen from the ‘weakest’ strength envelopes in Figure 16.57, which are seen in diagram b) to cross the ‘critical state line’ at comparatively low confinement. There might also be the occasional ‘adverse’ effect of water flooding on e.g. the Ekofisk chalk, where the confined strength was indeed exceeded in the most porous sections, due to draw-down causing pore collapse, but with excellent compaction drive production as a result of the subsequent further weakening by water. Before leaving the failure of intact rock it is of interest to see the dilation and brittle fracturing that occurs when rock is highly stressed. This was found by Rummel et al., 1978, to be a significant source of P-wave anisotropy. They utilised a biaxial loading arrangement with fastreacting servo-control, to study the development of dilation adjacent to the shear failure surfaces. They found that the P-wave velocity increased continuously in the direction of maximum compression in the pre-peak region. In the post-failure region, the P-wave velocity decreased almost reversibly with reducing compression. By comparison, the minimum and intermediate principal stress directions suffered a marked reduction of P-wave velocity (recorded as travel time increases), after fracturing was initiated. (Enhanced permeability would be a related phenomenon of such dilation: this would presumably occur mostly in the 1 direction). The authors mention the need to be aware of the possibility for increasing velocity anisotropy, when interpreting field seismic data in crustal regions where large tectonic stresses are assumed to be operating. Figure 16.60 shows the complete stress-strain curves for their granite specimens, which were tested in a 1.0 GPa pressure vessel. These triaxial tests were on cylindrical samples. The markedly non-linear shear strength envelope resulting from these highly confined samples is shown in the same figure, together with the frictional strength of the resulting fractures, which are also nonlinear, just as they were in Byerlee, 1978. The frictional strength of the resulting fractures, follows the non-linear shear strength model of Barton, 1976 closely, with an equivalent JRC of 20, and the use of confined strength (1 – 3) in place of JCS, as indicated in Figure 16.56. This was also the case when matching equivalent sets of data for various rock types, given by Byerlee, 1978. The friction coefficient (approx. 0.7) for the Rummel et al., ‘fractures’ compares well with the ‘critical shearing crust’ well data of Zoback and coworkers, as we shall see shortly, although  0.7 is

Figure 16.60 Shear stress – axial strain data for high pressure triaxial testing of intact granite, showing strength envelopes for subsequent sliding on the ‘minor faults’, and stick-slip using some artificial saw cut surfaces of the granite. Note the reducing non-linearity of the strength envelopes for these three categories. Rummel et al., 1978.

Joint stiffness and compliance and the joint shearing mechanism

(a)

541

(b)

Figure 16.61 Distinctive pole populations of joints or fractures that were conductive, and those that were not, from analysis of Cajon Pass Scientific Drillhole results. Colleen Barton et al., 1995.

lower than some of their data. Note the lower friction coefficients of the saw-cut surfaces, which resemble minor faults at residual strength.

16.9

Critically stressed open fractures that indicate conductivity

A significant contribution to our understanding of the geomechanics acting at deeper levels below the earth’s surface, was made by Zoback and Colleen Barton and coworkers, regarding the delineation of fracture directions that appear to be conducting directions, and those that do not. The ‘simple’ yes or no concerning conducting directions is fundamental evidence, also for geophysicists and petroleum engineers. Here we will review several cases that support the philosophy of ‘open’ joints actually often being those that are under a significant state of shear stress, rather than being parallel or sub-parallel to H max and without shear stress. Authors in geophysics and even those working in the petroleum industry, who are each dependent on ‘open’ joints: both for shear wave anisotropy, and for petroleum production, appear to have favoured the ‘parallel to H max’ model. Figure 16.61 shows the differentiation of fracture orientations a) for those that were hydraulically conductive, and b) for those that were hydraulically non-conductive. These different populations were recorded by Colleen Barton et al., 1995 in the Cajon Pass Scientific Drillhole, which was drilled to 3.5 km depth into granites and granodiorites, 4 km from the San Andreas Fault

near San Bernadino in California. The hydraulically active fractures were located by temperature anomalies, and mapped by televiewer, to an accuracy of 1.0 m from each temperature anomaly. The above authors had noted break-out direction anomalies over large depth intervals, in relation to the perpendicular-to-H max direction norm. These proved to be associated with slip on joints (or minor faults). Their plots of normalised mobilization of friction: ( /v) versus (n – Pp)/v shown in Figure 16.62 are a convincing demonstration of the importance of shear stress (rather than just minimum normal stress) for explaining the ‘openness’ of joints, and therefore their conductive capacity. One may speculate that in such granites and granodiorites, the values of JRC and JCS that one might typically estimate, would probably be high enough even for joints that were under h min normal stress, to be marginally conductive. However, shearing-enhanced permeability would obviously greatly dominate in signal strength, as apertures would be very small in the case of the ‘closed’ joints. Such a proposition can be tested. A quick 1-D Barton-Bandis modelling, starting with equation 16.11, with JRCn  5 or 10, JCSn  100 MPa, and an effective normal stress of 75 MPa suggests conducting apertures as small as 2.5 and 15 m. Apertures appear to reach such ‘residual’ levels after a few tens of MPa, due to the combined effect (in this crystalline rock case), of high wall strength and significant joint wall roughness. Comprehensive supplemental data to the above deep borehole interpretation was more recently reported by Townend and Zoback, 2000, and Zoback and Townend, 2001. These very extensive data sets are reproduced in

542

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.62 Mohr stress representation of the shear and normal stress components, acting on the Cajon Pass fractures, (i.e. sheared joints or minor clay-free faults?), according to their conductive or non-conductive characteristics. Note authors’ friction coefficient limits, as per Byerlee, 1978, (  0.6 to 1.0). These could apparently be extended/modified to 0.4 to 0.9 in practice. Colleen Barton et al., 1995.

Figure 16.63 Normal and shear stresses for fractures identified as hydraulically conducting (closed symbols) or non-conducting (open symbols). Cajon Pass (triangles), Long Valley (circles), Nevada Test Site (squares). Townend and Zoback, 2000, with data also from Colleen Barton et al., 1995. (Zoback, 2006 pers. comm., by kind permission.) See Plates 14, and 15.

Figure 16.64 Normal and shear stresses for fractures identified as hydraulically conducting or non-conducting, using borehole imaging. Cajon Pass (red diamonds and dots), Nevada Test Site (green circles and dots), Long Valley (yellow triangles and dots), KTB (Germany – blue squares and dots). Inset shows  /n for combined data set. Zoback and Townend, 2001, with data from Ito and Zoback, 2000, and from Colleen Barton et al., 1995. (Zoback, 2006 pers. comm., by kind permission.)

Joint stiffness and compliance and the joint shearing mechanism

Figures 16.63 and 16.64 by kind permission. Note the widely different stress magnitudes in these two figures. Figure 16.63 shows conductive (closed symbols) and non-conductive (open symbols or dots) from Cajon Pass (triangles), Long Valley (circles) and Nevada Test site (squares). It is clear from this data that either due to joint character or due to stress level, or a combination of both, the interpreted friction coefficients can range from (at least)  0.4–1.0 (Yucca Mountain: at normal stresses below 16 MPa), to  0.5–0.8 (Long Valley: 10 to 40 MPa), to  0.5 to 0.9 (Cajon Pass: 14 to 70 MPa). The quite wide range of for Nevada Test Site (i.e. Yucca Mountain) can be due both to the lower stress levels (i.e. shallower depth), and to the wide range of joint roughnesses. Joint roughnesses have been interpreted to be from about 1 to 15 for JRCo, when assuming, for simplicity, a representative JCS of 100 MPa, and r of 30°. These estimates are based on in situ roughness recordings in the exploratory TBM tunnels, and on a series of medium scale direct shear tests. Values as low as  0.4, shown in Figure 16.63, implying a 22° angle of friction, suggest some clayfillings. In fact even lower values are indicated in the Nevada Test Site data set, but these are non-conducting, as expected for clay-filled discontinuities. A clearer picture of the frictional content of the stress data from these six deep boreholes, is reproduced in Figure 16.65a and 16.65b, from Townend and Zoback, 2000, and Zoback and Townend, 2001. The crosses shown in the figures are the error bars for the different sets of data. The three dotted lines representing  1.0, 0.6 and 0.2 were derived by these authors from the Jaeger and Cook, 1979, equation: S1  Pf  S3  Pf

(

2  1 

)

2

543

(a)

(16.14) (b)

The authors Townend and Zoback, 2000, and Zoback and Townend 2001, do not give specific explanations for the likely reasons for the above ranges of friction coefficient (notably 0.6 and 1.0). As interpreted, these are the levels of mobilized friction tolerated by the analysed joint planes, at the time of analysis. A manmade change of pore pressure would not change the differential stress, but would change the effective mean stress or the effective normal stress, thereby altering the shear resistance of the joint planes in question, and their friction coefficients, in view of non-linearity with stress.

Figure 16.65 a) Differential stress versus effective mean stress and b) maximum effective stress versus minimum effective stress, for six sets of deep borehole data. See Townend and Zoback, 2000, and Zoback and Townend, 2001, and other referred authors who are the sources for the various data sets.

It is notable that the Cajon Pass rocks showed consistently high values of (resistance to)
1. As shown earlier in this chapter, it is likely, in the case of joints and fractures, that this is due to the interaction of a moderate to high roughness JRCn, medium to high r

544

Rock quality, seismic velocity, attenuation and anisotropy

(say 30° approx.), and tolerable stress/strength ratios n
/JCSn. The high strength rock will give high values of JCSn, or more specifically: high confined strengths (1 – 3), if joint walls had minimal alteration. We can ‘assemble’ estimates of input data for application in the high-stress, large block-size, version of the Barton-Bandis criterion (Barton and Bandis, 1990):    ( 1  3 )   n  (16.15)

 
n tan  JRCn log     r     
n   where (1 – 3)n is an estimate of the confined strength of the rock, with assumed absence of alteration along the joint or fracture walls. If there was alteration and reduced wall strength, one would expect a less ‘confined’ estimate of JCSn, i.e. of magnitude  (1 – 3)n for the triaxially confined intact rock. Of course in situ, the rock is poly-axially confined. The following assumptions will be made to explore if the toleration of transformed shear and normal stress in a ratio as high as 1, i.e.
1, can be ‘explained’ with a representative range of parameter values, as follows: JRCn  8 or 10 JCSn  200 MPa or (1 – 3)n  400 MPa

r  29°–31° n
 30–60 MPa

This is an effective stress range similar to the easily estimated vertical effective stress at (hydrostatically saturated) depths of 2 and 4 km, assuming a simple average crystalline rock density of 2500 kg/m3 (i.e. 2  2.5 – 2 : 30 MPa, 4  2.5 – 4 : 60 MPa). As will be demonstrated, unless in situ block sizes around the analysed wells are quite small, in fact significantly less than 0.5 m, then impossibly high, lab-scale JRCo values would be needed to generate mobilized friction as high as  1. One would need to greatly exceed the ‘JRCo limit’ (about 20), illustrated in Figure 16.26. As one may note from the estimates in Table 16.16, a range of  0.65 to 0.9 (approx.) can be reasonably ‘explained’, but specifically from peak shear strength estimation. If we engage in further analysis of maximum possible confined strengths (1 – 3)n by looking at more of the available triaxial strength data (Figure 16.57), we see the possibility of even higher strengths than 400 MPa at appropriate depths to our example, if the rock is very strong under triaxial conditions. (Unfortunately for the ‘parallel to H max model’ weaker reservoir rocks do not have such benefits from confining stress.).

Table 16.16 Estimates of potential tolerance of mobilized frictional strength, to explore the meaning of  1 for e.g. Cajon Pass data from Zoback and Townend, 2001. Case A (minor alteration of joint walls)

Case B (hard unaltered joint walls)

JRCn  8, JCSn  200 MPa, r  29° n
 30 MPa
0.72 n
 60 MPa
0.65

JRCn  10, (1 – 3)n  400 MPa, r  31° n
 30 MPa
0.91 n
 60 MPa
0.82

Substitution of 500 MPa or 600 MPa for (1 – 3)n in the Case B example in Table 16.16, again at effective stresses of 30 and 60 MPa respectively, would raise the Case B estimates of peak from 0.91 to 0.94 (with 600 MPa), or from 0.82 to 0.87 (with 500 MPa). Here we have ignored the inevitable small size of the samples used to generate the Figure 16.57 data (down to approx. 10 mm size cylinders), and have therefore assumed limited scale effects at these intensely high pressures. 16.9.1

The JRC contribution at different scales and deformations

The only other conceivable contributor to higher shear strength values might appear to be roughness JRCn. However, with block sizes of 0.5, 1.0, or even 5.0 m, the empirical scaling laws would demand quite exceptional JRCo values for the small-scale roughness, and frankly, little possibility that ‘the critical shearing crust’ was ever mobilized. The optimistic value of JRCn  10, applied in Case B in Table 16.16, is already actually ‘too high’, since it implies JRCo values (for nominal 100 mm scale), as high as 20 or 21, even when the assumed in situ block size round the analysed wells is limited to 0.5 m. This is shown, by regression, from the inverse application of the previously described block-size scaling of roughness:  L 0.02 JRCo JRCo ≈ JRCn  n   L o 

(16.16)

The standard set of ten JRCo values and their roughness profiles, from Barton and Choubey, 1977 were reproduced in Figure 16.26. The ten selected samples were mostly granite, aplite and gneiss, plus basalt, hornfels, slate and calcareous shale. The roughest sample no. 10 was an artificial tension fracture in a weak soapstone.

Joint stiffness and compliance and the joint shearing mechanism

The exceptional roughness needed to explain a tolerance of as high as 0.94, namely: JRCo  20 if Ln is 0.5 m, therefore JRCn  10, together with the highest defensible confined strength of 600 MPa (JCSn  (1 – 3)n), is still below the interpreted values of transformed in situ principal stress anisotropy, of mostly

/n
  1. This was for the Cajon Pass research borehole data of Zoback and Townend, who had interpreted effective mean stresses up to almost 60 MPa, at 3.5 km depth. The only possible explanation seems to be that there was a small average block size, even at several kilometres depth, in this tectonically disturbed area. Two additional perspectives concerning roughness are provided here, in view of the important potential contribution of large-scale roughness in explaining high values of interpreted, transformed anisotropic stresses. The even larger-scale roughness profiles shown together with appropriate JRCn values, in Figure 16.27, were obtained from extensive characterization of fractures developed in sandstone, tuff, concrete and hydrostone samples, with sheared areas of about 1.0 m  1.10 m. Characterization included roughness profiling at different scales, Schmidt hammer testing, tilt testing of the diagonally ‘jointed’ samples (weighing some 2.5 tons), and final biaxial shear testing in a 1 m3 loading frame at TerraTek, in Salt Lake City, as reported by Bakhtar and Barton, 1984. As will be discussed at the end of this chapter, great difficulty was experienced in shearing some of the rougher samples. This difficulty may have parallels to the Zoback and Townend deep borehole interpretations. Bandis, 1980, performed a remarkable series of scaleeffect tests, using repeatedly cast replicas of natural joints, which were tested at different sampling lengths, that could then be compared with each other since the material strengths and compositions were identical. He presented a set of eleven roughness profiles, with equivalent lengths of between 5 and 15 m, together with back-calculated JRCn values. These are shown in Figure 16.66. The various profile lengths in this up-scaled format, represent typical medium to hard rock strengths. Inspection of the major undulations on some of these long profiles, and on some of the 1 m profiles shown in Figure 16.27, suggest that significant shearing of joints involved in the ‘critical shearing crust’ scenario, would likely be limited to JRCn values somewhat below 10. Otherwise there would be a combination of too much volume increase, developing too much increase in normal stress and stiffness, thereby causing too high shear strength for the mechanism to be viable.

545

Figure 16.66 Profiles and interpreted large-scale roughness coefficients (JRCn), from Bandis, 1980 scale-effect investigations with model materials cast as joint replicas. Details are also given by Bandis et al., 1981.

16.9.2

Does pre-peak or post-peak strength resist the assumed crustal shear stress?

A further factor to be considered when evaluating and attempting to geomechanically ‘explain’ the interpreted

-mobilized values close to 1.0, is that it is clearly not logical that the conducting joints identified in these deep borehole studies by Zoback and his colleagues, should be exactly at peak strength. This point or eventual plateau on the shear strength–displacement curve is in many ways a singularity, involving some few millimetres of shear in the case of in situ block sizes, and perhaps a millimetre or less in typical lab samples. A wide-ranging review of such displacement data, from Barton, 1982 is reproduced in Figure 16.67. The data is divided into three size categories (roughly 5 to 30 cm  lab-scale, 0.3 to 3 m  in situ test scale, 3 m  exotic tests and up-scaled models). Even for small samples there is a wide range of ‘strains-to-peak’, when expressed as a displacement-to-peak divided by sample length, and expressed as a percentage. A very interesting point arises when considering whether the shear-stressed joints involved in the ‘critical shearing crust’ are at their peak, pre-peak, or postpeak shear strength. Reference to the JRCmob concept, which was shown in Figure 16.10, and to the shear strength-displacement-dilation worked examples shown in Figure 16.25, reveals that the ‘necessary’ permeability enhancement due to the beginning of dilation, actually occurs when roughness starts to be mobilized, and may already be active after a few millimetres of shearing.

546

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.67 Extensive test data review of displacement-to-peak (peak), from a wide variety of sample/block sizes, from laboratory and in situ direct shear tests. Barton, 1982.

As can be seen, the larger the modelled block size the ‘later’ this dilation and assumed permeability enhancement occurs. In view of the need for combined shear stress and permeability, to qualify for registration in the mobilized-friction-with-flow diagrams (Figures 16.61 to 16.65), the joints need to be sheared, but they actually do not need to be sheared very far. If they are rough and

undulating, too much dilation would prevent further shear, due to a massive build-up of normal stress. When there is faulting, or hydrothermal alteration, with clay-filled or clay-coated discontinuities present in the immediate vicinity, the relevance of the parameters JRCn and JCSn in the Barton-Bandis joint constitutive equation appear, at least at first sight, to be limited. The reality may be no remaining roughness of note

Joint stiffness and compliance and the joint shearing mechanism

547

(JRCn : 0), but with the possibility of a residual (i) value, to account for the added shear resistance given by any remaining undulation, with effective inclination angle (i) in relation to the mean plane. This could be simply accounted for by applying the Patton, 1966 equation, possibly with a cohesion intercept (c) added for the case of (obviously cohesive) clay-fillings:

 
n tan ( r  i )  c

(16.17)

As was shown by a wide review of the shear strength of clay-filled discontinuities, the residual friction angles (r), and therefore overall frictional strength relevant to such features ranges, from below 10° to about 25°, depending on mineralogy and degree of over-consolidation (Barton, 1973b). If one attempts to use the Barton-Choubey strength criterion:  n tan [JRC log (JCS/n)  r] to see if it fits clay-related experimental data, it will be noticed that when n (strictly n
for effective stress) exceeds JCS, (e.g. an over-consolidated fault gouge of 5 MPa strength with a local effective normal stress of 20 MPa), the log (JCS/n
) term becomes negative. Contractionwith-shearing, in place of dilation is then actually predicted by the model, (as for normally consolidated clay, or heavily loaded over-consolidated clay), but not if JRC  0. Clearly it would be relevant to also apply a suitably reduced value of r relevant to clay-smeared surfaces, to obtain a meaningful fit to data. Predictions of fault strength with this ‘rock joint and rock fracture’ constitutive equation are of course of limited reliability, and there is little option besides testing or back-analysis. In further relation to the interpreted mobilized friction coefficients of 0.6 to 1.0 shown in Figures 16.61 to 16.65, one may refer to direct shear test results on tension fractures developed in weak, brittle model materials, as reported by Barton and Hansteen, 1979. (These materials could be formulated to give various frictional and cohesive strengths, and consisted of fine sand, fine Ballotini glass spheres, Pb304 red lead, and small proportions of gypsum and water, with curing at high enough temperatures to cause disassociation of some of the water: Ca.CO3.2H2O : Ca.CO3.1⁄2H2O thereby reducing the compressive strength: Barton, 1971). It may be noted from the normal stress magnitudes given in Figure 16.68 that there is a model/prototype (M/P) stress and strength scaling of 400, assuming a strong 175 MPa prototype rock. The length scale from Buckingham’s -theorem for dimensionless products,

Figure 16.68 Shear strength envelopes (peak, h  1%L, and h  2%L) and assumed residual strength for direct shear tests on model tension fractures of 100 mm length. Barton and Hansteen, 1979. The material was a brittle, very fine-grained, sandstone-like material. The stress and strength scale:   400, and the length scale:  320, was due to lower model density of 2.0 gm/cm3. Note that  0.6 and  1.0 correspond to the ‘residual’ strength envelope (0.58  tan 30°) and to the mean of the h  1 mm and 2 mm strength envelopes, representing the shear strength remaining (at different stress levels), following a mean 0.45 m of shearing at full scale, for these simulated 30 m long fractures. However these samples were free to dilate, with constant normal stress applied.

is then    m/r, where m and r are the respective densities of model material and rock. With respective values of 2.0 gm/cm3 and 2.5 gm/cm3 (and   400), one can estimate a length scale  320. The samples therefore represent approximately 30 m long, rough undulating major fractures. Due to this scaling, the given shear displacement magnitudes of 1 and 2 mm as recorded in the 100 mm long direct shear tests correspond to about 0.3 m and 0.6 m at full scale. The larger of these two shear displacements has reduced the shear strength of these rough, high strength simulated fractures (JRCo  20,

548

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.69 a) A dimensionless representation of the complete shear stress-displacement behaviour of model tension fractures shown in conventional format, in Figure 16.70. The shear test data has been normalised using the JRCmobilized concept (Barton, 1980, 1982).

JCSo  0.44  400  176 MPa) to a minor fault character of
1.0 at a simulated, medium normal stress of 8 MPa, and to  0.8 at a simulated maximum normal stress of 16 MPa, but each free to dilate. The various data sets from Zoback and Townend, reproduced in Figures 16.64 and 16.65, are obviously composed of variable rock strengths and variable joint/ fracture/minor fault roughnesses, since the different data belong, obviously, to a wide variety of rock types, joint characters, and minor fault types. These will inevitably have suffered various deformation magnitudes, controlled by a variety of non-linear shear strength envelopes, representing different degrees of pre-peak, close-to-peak and post-peak shearing, as suggested by the model tension fracture envelopes, shown in Figure 16.68. In relation to post-peak shearing, it is helpful to invoke the JRCmobilized concept again. (See Figure 16.10). Figure 16.69 shows a dimensionless set of shear strength displacement data, representing the whole range of behaviour shown in conventional stress-displacement format in Figure 16.70. JRCmob can be estimated at any desired location along shear stress-displacement curves, by evaluating the mobilized shear strength ( mob) at the point of interest. It is estimated by a simple re-arrangement of the Barton-Choubey peak shear strength equation:

JRCmob

  tan1  mob   r    n  JCS log
n

(16.18)

Figure 16.70 Direct shear and dilation data for model tension fractures representing 30 m long, rough-undulating fractures in hard rock. This is the source of DST data for the dimensionless representation in Figure 16.69. Barton, 1993.

It will be noted that the ‘ultimate’ strength, after some 1 m of simulated shearing (or 3% of the length of the fractures) is still well above the true residual behaviour, as indicated in Figure 16.69. This is also found when testing rock joints. It is not possible to reach true residual strength in the normal confines of a (linear) direct shear device. It is likely that Zoback and coworkers’ frictional interpretation of deep borehole ‘critical crust’ behaviour is showing  0.4 to 1.0 coefficients due not only to different JRCn/JCSn/r and n
/JCSn ratios, but also due to different degrees of shearing, both pre- and post-peak.

16.10

Rotation of joint attributes and unequal conjugate jointing may explain azimuthal deviation of S-wave polarization

We have previously investigated hypothetical joints in typical reservoir ‘sandstone’ and reservoir ‘carbonate’

Joint stiffness and compliance and the joint shearing mechanism

(JCS  25 MPa and 50 MPa), and seen the dramatic closure of aperture that was predicted to occur if these joints were consolidated/closed by 10 or 20 MPa or higher effective normal stress, representing an assumed range of (effective) h min, acting on sub-vertical joints or fractures in the reservoir. Although down to a certain depth, an increased JCSn could be assumed, by utilising a confined compressive strength (1 – 3)n for the joint walls, it has been demonstrated with triaxial test data that this increase is limited in the case of weaker porous rocks. It may not be sufficient to explain ‘normal-closure’ apertures more than a few microns, according to modelling predictions. This is especially so if roughness is limited. With the advent of improved digital data acquisition, and strong interest in the use of shear waves for interpreting reservoir fracturing, it has become increasingly important to correctly interpret what a certain level of anisotropy and attenuation at a certain frequency means, when analysing the fast and slow shear waves qS1 and qS2. How far the industry has come in accepting the need for a shearing mechanism interpretation on some occasions, or a non-aligned set of fractures, or that two intersecting fracture sets are actually the source of the measured components, is difficult to judge, even from most recent publications. We should probably consider five possibilities: ●

●

●

●

●

H max-aligned ‘open’ joints due to sufficient wall strength and roughness H max-aligned ‘open’ joints due to hard-mineral ‘bridging-but-not-blocking’ ‘open’ joints at some angular deviation from the H max direction apparently ‘H max-aligned-open-joint-set’ that actually is two conjugate sets a generally non-planar joint wall topography in all cases

The third and fourth of these cases will be addressed here. In the handful of cases reviewed in earlier chapters, the anisotropic P-waves, or the polarized, split qS-waves do indeed orient themselves in approximately the ‘correct’ (conventional) direction in relation to the calliper-logged-perpendicular-to-break-out assumption for the H max orientation. However, we noted, e.g. from Lynn et al., 1999, and Maultzsch et al., 2003 data, that the line-up of assumed fracturing and assumed major stress directions was not ‘perfect’. In fact there could be 10° to 20° discrepancies, if one can rely on the

549

data acquisition accuracy of each set of measurements. There are many possible sources of error (Lynn, 2005, pers. comm.), so this is uncertain. The logic and data of Zoback and Colleen Barton and Townend and their colleagues regarding the probability of shearing is surely incontrovertible. Although we perceived certain difficulties with as high as 1.0 at several kilometres depth, the ‘critical-shearing crust’ phenomenon was easy to verify on a local scale, using for instance non-linear shear strength and BartonBandis coupled behaviour modelling. Although presented by these authors in the context of mostly multiple-kilometre deep boreholes in predominantly crystalline rock, it is the opinion of the writer that it is the petroleum industry that will have the greatest benefit of recognising the possibility (and sometimes the necessity), of a shearing mechanism, often conjugate in form. At Ekofisk in the North Sea, a model-predicted, and subsequently core-sampled confirmation of a conjugate shearing mechanism (causing slickensided joints), was probably fundamental for the two sets of 60° dipping joints to be able to continue to drain the porous, low permeability chalk matrix. (Nowadays there is an additional component of compaction drive, due to water weakening of the matrix and joints) There would probably have been no development at Ekofisk if there had been just one set of joints parallel to H max. They would have been closed before discovery (i.e. therefore never discovered), and ‘further closed’ by a 20 to 24 MPa increase in effective normal stress, (prior to water flooding), if an obstinate owner had decided for development. Of course other solutions (MHF and proppants) would perhaps have been found effective. So the details of fracturing, in terms of number of joint or fracture sets, may be important for production, and therefore ideally should be detectable by seismic interpretation. In addition, there is the simultaneous importance of the non-planarity of most joints and fractures. At one extreme, one has the cleavage joints in slates that give ‘billiard-table’ planarity and smoothness, and clearly have no place in explaining petroleum production. They would ‘fail to produce’ on two counts: their apertures would be too minute when acted on by reservoir levels of effective normal stress, and in a ‘shearing earth’ scenario, where they would have difficulty tolerating  0.4 when wet, they would nevertheless not dilate when sheared. So permeability would be unlikely on both counts. At the other extreme there could be marked non-planarity of the one or two key joint sets, as illustrated in the next figures.

550

Rock quality, seismic velocity, attenuation and anisotropy

Intermediate between these extremes of planarity or non-planarity are all the other numerous cases, which are vitally necessary for petroleum production because a compromise between the extremes is needed for productivity, if shearing is to be possible historically. There will be no shearing (or only pre-peak shearing), if nonplanarity is too great, as suggested earlier when reviewing the two sets of JRCn profiles. Figure 16.71 shows several features that can explain an interpreted ‘open fracture set’ orientation that differs somewhat from the calliper assumed direction. The undulating (non-planar) nature of conjugate joints that have become slightly sheared, or even conjugate minor faults, through successive shearing in response to H – h (or S1 – S3) and perhaps fluctuating pore pressure, has been exaggerated for clarity. As has been noted previously in both Chapters 15 and 16, from the reconstructed shearing of model fractures by Barton, 1973a, there is in Figure 16.71 an opposite ‘rotation’ of the fluid filled parts of the joints/minor faults, shown with open O-symbol, in relation to the rock-to-rock shear and normal stress transfer sections of the asperities, which lie on the opposite ‘slopes’, and are denoted by the R-symbol. Open (O) and contacting (R) sectors, lie on either side of the assumed mean plane of the joint (J). Note that shearing of one of the conjugate sets has been assumed to take ‘priority’, thereby displacing the secondary set, which may also shear, but to a lesser degree. This is a frequent and almost inevitable consequence of ‘conjugate shear’. Considering the potential for shear wave splitting; if we can make the assumption that the average orientation of the fluid-filled sections (O) of the joints or minor faults have a different influence on the splitting/polarization mechanism of shear waves, than the average orientations of the rock-to-rock sections of the joints (R), then we have immediately come 10° or more, further away from the H (or S1) direction. The ‘contrary’ fluid rotations can be visualised from the ‘frozen’ evidence of quartz injections into a shear stress field, causing actual shearing, as illustrated in Figure 16.72. As indicated in the extensive caption to Figure. 16.71, the influence of a second set of potentially shearing fractures/minor faults may be of importance in the eventual polarization directions of the split qS-waves. If the dominant joint or fracture set physically displaces the secondary set (as noted in the UDEC-BB modelling of Ekofisk joints, Barton et al., 1986), then we have the possible influence of higher shear resistance and therefore higher shear stiffness for the secondary

(a)

(b)

Figure 16.71 Idealised and exaggerated joint/fracture/minor fault undulations, for a conjugate pair of ‘joints’, with one dominant and displacing the secondary set. Note contrary ‘rotations’ of ‘R’ and ‘O’ in relation to mean plane ‘J’. Shear wave splitting is assumed to occur with different strength from the slip-prone ‘R’ sections, with their finite shear and normal stiffnesses (and Kn  Ks), compared to that from the more fluid-bearing ‘O’ direction. (Theoretical opinion is sought here!) Reflection may occur more strongly from the more fluid-bearing ‘O’ direction. Rotation of the polarization of the qS1 and qS2 waves towards the H max direction would require the partial help of an opposite component of polarization from the secondary set of joints, which might be less conducting and thereby have reduced lengths of fluid lenses. It may be assumed that the pseudo-static shear stiffness KS2 of the minor, displaced set would be increased in relation to KS1 by the ‘off-set’ mechanism. This results in an actual cohesive intercept in the sense of shear resistance of the secondary set, further stimulating shear in the dominant set.

Joint stiffness and compliance and the joint shearing mechanism

551

Figure 16.72 a) Reconstructed shearing of a rough fracture at low stress, showing the effective contrary rotation of fluid-filled and rock-to-rock sections. b) A ‘frozen’ quartz filling of a minor fault showing the same contrary rotation of ‘fluid lenses’ and rock-to-rock contacts. Høvik, Norway.

set. Presumably this could influence (reduce) shear compliance in the secondary direction to some degree, even though compliance is a dynamic micro-displacement parameter. Figure 16.73 shows a double-bladed guillotine method for creating primary parallel fracture sets, and intersecting sets of secondary parallel fractures in 25 mm thick slabs of weak brittle model materials. These types of interlocking ‘fractured’ models were used in pseudo-static biaxial shear testing, as illustrated previously in Figure 16.42. They were also used to create ‘two-dimensional’ physical models of steep, ‘jointed’ rock slopes (Barton, 1971) with up to 40,000 blocks, and also to physically model the excavation of large span, ‘near-surface’ caverns, in various anisotropic stress fields, and with various intersecting ‘jointing’ patterns (Barton and Hansteen, 1979). In each case the progressive deformation fields were monitored by photogrammetry. Figure 16.74 shows the results of direct shear tests of three classes of model joint that have parallels in nature. Peak and ultimate (larger deformation) strength envelopes are shown for a) primary (set no. 1), b) primary cross-cut set no. 1 (PCJ ), and c) secondary (stepped, castellated) set No. 2. Clearly the secondary set has a true cohesion intercept, and in a real situation at reservoir depth, would lie somewhere between the shear strength envelopes for the intact material and the dotted ‘J’ curve in the Mohr circle-based strength envelope diagram (Figure 16.58).

Figure 16.73 a) Double-bladed guillotine for developing parallel sets of tension fractures, and for creating intersecting sets by azimuthal rotation of the whole sample. b) Continuous joints of set no. 1, and stepped/offset joints of set no. 2, as often observed in nature. c) Roughness profiles of the rough model tension fractures, as measured by photogrammetry. Barton, 1972a.

552

Rock quality, seismic velocity, attenuation and anisotropy

1968) that preceded the modelling of jointing in UDEC and UDEC-BB, that started with the developments of Cundall, 1971.

16.11

Figure 16.74 Direct shear test strength envelopes for primary, primary but cross-jointed and secondary joints, indicate that there will be higher shear stiffnesses, and therefore potentially lower compliance for the less dominant directions. Barton, 1972a.

The offset joints have shear strengths that are 1.5 to 3 times higher than the primary joints, with greatest difference at lowest stress. This offset-by-shear mechanism will obviously cause the shear stiffness of this secondary set to be higher than that of the primary set, and perhaps cause the dynamic compliance of the secondary set to be lower than that of the primary set. In the case of conjugate sets of vertical reservoir jointing, this could be another potential source of azimuthal deviation of the shear-wave polarization, away from the likely intersecting H max direction. The modelled (30 m long prototype) primary joints gave measured ratios of Kn/Ks at prototype, scaled-up stress levels as follows (Barton, 1972a). n Kn/Ks

3 250

7 75

11 73

MPa

At that time, in the late sixties, there was not the incentive to further investigate stiffnesses, apart from the interesting problem that large anisotropy (or inequality) of these two fundamentally different (pseudo-static) stiffnesses reportedly caused numerical stability problems in the FEM joint element modelling (Goodman et al.,

Classic stress transformation equations ignore the noncoaxiality of stress and displacement

In Figure 16.71a, there is discrepancy between the applied shear stress orientation (S) parallel to the mean plane (J), compared to the subsequent direction of shear displacement when roughness is mobilized, and a non-co-axial dilation begins. The resolved shear and effective normal stresses ( and n
) acting on the rock-to-rock contacting parts (R) of the non-planar dominant joint, emphasise this non-coaxiality. The non-planarity of most joints, perhaps many minor faults, (and sections of major faults), actually causes non-coaxial stress-and-displacement (i.e. violation of the coaxial stress and strain principle of St. Venant). This means that the ‘global’ application of the Mohr Coulomb equation and following classic stress transformation equations is actually erroneous to some varying degree.



1 ( 1  3 ) sin 2 2

n 

1 1 ( 1  3 )  ( 1  3 ) cos 2 2 2

(16.19)

(16.20)

( is the acute angle between 1 and the plane in question. Note that equation 16.20 is sometimes quoted erroneously in literature, with a () sign between the two parts of this equation. A joint at 30° to the 1 direction cannot have n  as implied in this particular case: clearly  n). In theory the plane should be imaginary (thereby not rotating the local principal stress directions), it should also not shear, and it should certainly not dilate, causing another error. The problem with the classic stress transformation equations was experienced first hand by Bakhtar and Barton, 1984, who were attempting to biaxially shear 1.0–1.1 m long diagonal fractures developed in 1 m3 blocks in a large test frame at TerraTek, Salt Lake City, as referred to earlier in this chapter. (See large-scale roughness profiles in Figure 16.27). In fact the same problem

Joint stiffness and compliance and the joint shearing mechanism

553

The discrepancy between the carefully estimated full scale strength envelope, and the assumed loading path (no. 1) is shown in Figure 16.75b. Correction for sidefriction and use of modified stress transformation equations, finally explained the ‘inexplicable’ high stresses needed to achieve shearing. In fact most of the ten samples could not be significantly sheared, due to the classic neglect of the problem of dilation. The following equations were needed to explain these experimental difficulties: (a)



1 ( 1  3 ) sin 2 (  d n mob ) 2

n 

(16.21)

1 1 ( 1  3 )  ( 1  3 ) cos 2 (  d n mob ) 2 2

(16.22) where d n mob 

(b)

Figure 16.75 a) Large scale biaxial shear tests of 1 m3 blocks with diagonal, well characterized joints or fractures. Note non co-axial ‘stress and strain’ due to dilation angle dn. b) Calculated, scale-adjusted shear strength envelope and 1) theoretical, 2) dilation corrected and 3) fully corrected loading paths that explain the difficulty of shearing due to a break-down of the classic stress transformation equations, when not modified to account for the mobilized dilation angle. Bakhtar and Barton, 1984; Barton, 1986; Barton, 1999a.

was experienced earlier, but not recognised, in the in situ block test depicted in Figure 16.29. The limited (0.25 mm) shear on this occasion was naturally assumed to be due to the ‘attached’ base of the block. Ten 1 m3 samples with varying degrees of fracture roughness had been prepared and thoroughly characterized, including the performance of large scale tilttesting, following Barton and Choubey, 1977. The experimental setup is schematised in Figure 16.75a. Great care was taken in minimising side friction (S1 and S2 symbols in the figure), using double flatjacks and a thin Teflon sandwich separated by a fluid film of molybdenum disulphide grease.

 JCS  1 JRCmob log 
n   n  2

(16.23)

(The mobilized roughness concept of Barton, 1982 was illustrated in Figure 16.10. The conventional equation for peak dilation angle, uses JRCo or JRC n and not JRCmob.) Example: Close to shear failure of the diagonally fractured block (Fig. 16.75): 1) 1 had been increased to 28 MPa, 2 was reduced to 0 MPa 2)   45° 3) Assume dn mobilized  10° With the ‘classic’ assumption of no dilation, equations 16.19 and 16.20 give:  n  14.0 MPa. (since sin 90°  1.0, cos 90°  0). Shear failure of the fracture had been expected/predicted even before ␮  1 was reached, as assumed here. With modified ‘dilating’ equations 16.21 and 16.22, the sin 110° and cos 110° terms (0.939, 0.342) indicate the actual difficulty in shearing, since  13.16 MPa (lower than assumed), and n  18.79 MPa (higher than assumed), dilation causing an effect similar to an increasing angle . The new calculation of the actually applied ratio of shear and normal stress (with an assumed mobilized dilation angle of 10°, was too low. With applied

only  13.16/18.79  0.70, the strength of the joint was too high for shearing more than a fraction of a millimetre, i.e. pre-peak. Both these changes ( p, nq) in the ‘actual’ compared to the ‘assumed’ boundary stresses

554

Rock quality, seismic velocity, attenuation and anisotropy

are also illustrated by the contrasting stress paths shown in Figure 16.75b. They help to explain the dangerous burst of one of the real-life flat-jacks at 28 MPa pressure, nearly causing injury, and displacing pictures around the laboratory walls due to the high pressure oil burst. Only two of the surfaces illustrated in Figure 16.27 could be sheared easily. Since these experimental difficulties, further descriptions and analysis of the problem have been given by Barton, 1986, and Barton, 1999a, including convincing evidence from the analysis of a large series of biaxial hydraulic-jack based shear box tests, where the applied loads S1 and S2 had to be resolved into the assumed components and n acting on the 45°/45° oriented joint planes in the centre of the shear box. (This is not required in a standard shear box, with perpendicular and parallel application of forces in the principal planes). The main author of these biaxial shear box tests was convinced that the JRC-JCS criterion of Barton and Choubey, 1977 needed to be modified. In fact the consistent ‘error’ in relation to a 1:1 gradient between ‘predicted’ and ‘measured’ (as compared to an almost perfect 1:1 relation in standard shear boxes), was caused by unintended neglect of a dilation adjustment in the classic transformation equations, as described above. On the basis of the above, Barton, 1999a argued that ‘classic’ stress transformation in all potentially dilating geotechnical materials (e.g. rock joints, rock-fill, dense sand, over-consolidated clay), may need to be considered as violation of the St. Venant principle of co-axial stress and strain. One may speculate that the earlier referred Cajon Pass analysis of Zoback and Townend, indicating in this case, a tolerance of  1, could also be subject to the possible need of a mobilized dilation correction, since this research borehole is located in the tectonically active San Andreas fault area, with the possibility of a more tectonized ‘broken’ rock mass with smaller blocksizes and perhaps rougher joints. As demonstrated earlier in this chapter, it was extremely difficult to justify such high tolerance of shear stress, using all known means of maximizing shear strength. The dn mobilized equation 16.23, means that one must consider roughness (and therefore block-size), and the magnitude of shear displacement. This is because the magnitude of JRCmobilized depends numerically, upon the degree of shear displacement. So the mobilized dilation angle will depend on the present displacement, in relation to the initial, usually interlocked condition of the joint.

A long way beyond the peak singularity (where the strength and dilation angle are maxima), there will be little need of a correction for dilation. So for mature sections of faults one can apply the standard transformation with almost no error, whereas in newer regions of faulting, a roughness/dilation estimate may well be required for more correct interpretation. Research in this area, starting in the laboratory, is urgently needed.

16.12

Estimating shallow crustal permeability from a modified rock quality Q-water

Townend and Zoback, 2000, and Zoback and Townend, 2001, argued convincingly for acceptance of a ‘critical crust’ concept, with hydrostatic rather than lithostaticrelated pore pressure throughout the brittle depth of the crust. Their analyses of deep well data were reviewed earlier in connection with the importance of the mobilized ratio of shear and normal effective stress, as a strong indicator of water-conducting fractures. From the JRCmobilized concept we argued that permeability enhancement could even be with pre-peak shear displacements of just millimetre size. However the sometimes high ratios of resisted ( /n
) of up to 1.0 obviously suggests a close-to-peak condition, since we showed that it is difficult to construct such high in situ full-scale shear strengths. Post-peak seems unlikely in the case of the highest values of resisted , while the values below 0.6 to 0.7, implying mobilized friction angles less than 31°–35°, could well be representing post-peak strengths, or minor faulting. Clearly even lower values of of 0.4 to 0.5 (i.e. mobilized friction angles of only 22° to 27°), as seen in Figures 16.62 to 16.65, have to be minor faulting, but without the ‘complication’ of sealing gouge, since they were also recorded as conducting features, by the relevant authors. Zoback and Townend also assembled the deep borehole permeability measurements that are reproduced in Figure 16.76. In the case of the KTB hole in Germany, permeability test intervals varied between a few tens of metres to 3.5 km, with bulk permeabilities between about 5  1015 to 1017 m2, or approximately 5  108 to 1010 m/s if the water was close to 20°C. In a shallower series of tests (1 km depth) at the Monticello reservoir, Zoback and Hickman, 1982, (with data also shown in Figure 16.76), reported permeabilities ranging from 1015 to 1016 m2, or 108 to 109 m/s. Thermal models of borehole temperature suggested

Joint stiffness and compliance and the joint shearing mechanism

555

As we have seen earlier, nearer the surface, the degree of potential connectivity in a rock mass may be reflected in the relative block-size ratio of RQD/Jn, because of the great importance of the number of joint sets Jn. However when clay was responsible for low RQD values, this relation would likely be compromised. One began to speculate whether the second pair of shearstrength related parameters, Jr/Ja could also have a role in ‘explaining’ relative magnitudes of permeability for individual joint sets? We will start by describing the actual limitation of what was proposed in Barton, 2002a, where an extremely simple approximation between rock quality and the Lugeon value was proposed for central ‘jointed rock’ qualities in the integrated Q-diagram, reproduced here for easier reference, as Figure 16.77. L ≈ 1 Qc

Figure 16.76 Zoback and Townend, 2001, assembly of deep crustal permeability from well-known deep borehole projects such as Cajon Pass, KTB, Kola. Intact samples (with K 1018 m2) are given on the left. See original paper for references to other projects.

1014 (107 m/s) for the 0 to 2 km depth interval at Kola, and 1017 m2 (1010 m/s) for the 6 to 8 km depth interval. The above, and similar data, led Zoback and Townend, 2001, to conclude that the upper crust had permeabilities of
1017 m2 (1010 m/s) to 1016 m2 (109 m/s) over 1 km and 10 km (depth) scales.

16.12.1

The problem of clay-sealed discontinuities

With this interesting evidence for the maintenance of some significant permeability to great depth, presumably related with even deeper operation of the ‘critical shearing crust’ mechanism, it was of interest to know if there was a possibility that a rock mass description scheme like the Q-system, could ‘explain’ such diverse ranges of permeability, and the partial maintenance to greater depth.

(16.24)

where L  Lugeon (1 Lugeon
107 m/s
1014 m2 at 20°C), and where Q c  Q  c/100, where c  uniaxial compression strength of the rock. As preliminary examples we see K
1014 m2 (
107 m/s) when Q c  1 (a quite heavily jointed rock mass, e.g. 3 to 4 joints sets, near-surface), and we see K
1016 m2 (
109 m/s) when Q c  100 (sparsely jointed, quite massive rock, typical at hundreds of metres depth and beyond). So far the approximation is reasonable, but as hinted earlier in this book, the relation L
1/Qc inevitably breaks down when there is clayfilling along the joints or fault zones. As may be noted from Figures 16.76 and 16.77, the above deep well data (often
109 to 1010 m/s, or 0.01–0.001 L), lies in a partly ‘consistent’ position on the Q (or Q c) – Vp – L chart concerning the high quality end of the diagram, showing ‘hard jointed’ and ‘hard massive’ black-and-white curves. However, extrapolation of the diagram to much greater depth would be needed, by extending the ‘1000 m’ depth diagonal upwards, into higher velocity and higher modulus territory. Recent compilations of permeability data from the Äspö site in Sweden, which is a quite well-jointed site in diorite and granites, shows a range of K  104 to 1010 m/s based on analysis of numerous tunnel probe holes from 50 to 400 m depth. There was also a recorded 260:1 permeability anisotropy around the spiral access tunnel (Vidstrand, 2003). An interesting scale effects analysis by the same author showed K varying from about 105 m/s to 108 m/s at the 100 m scale, and K varying from about 104 m/s to 1010 m/s at the 10 m

556

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.77 The jointed rock mass quality Q-diagram, showing potential integration of the UCS-normalised Q c value, Vp, Emass and Lugeon value. (1 Lugeon
107 m/s). (See Chapter 9).

scale, Below the 1 m scale, values reduced to intact matrix values of 1012 m/s as a minimum. The above six orders of magnitude corresponds to the full range of permeabilities shown in Figure 16.77. The simple (too simple) correlations between rock quality, velocity and permeability, presently represented in Figure 16.77, are reproduced in Table 16.17. In Figure 16.78 two sets of equations are shown in the table above the figure. The uppermost set of equations correspond to the L
1/Q c inverse relation discussed above, and show the standard ‘definition’ of rock mass quality Q, here normalised by the UCS of the rock. The lower part of the table shows recent work by the writer for rationalizing the permeability – Q-value linkage, which has inconsistencies where clay-filled joints or discontinuities are concerned. One may note from the following: Q water 

J J RQD  a  w Jn Jr SRF

(16.25)

Table 16.17 Some suggested inter-relations between rock mass quality, P-wave seismic velocity, and permeability. Note that ‘faulted rock’ qualities, with Q  0.1, implying clay-filled (and probably sealed) discontinuities, have been excluded. Extremely/ very poor

Poor

Good

Very good

Qc Lugeon K (m/s)

0.1 10 106

1 1 107

10 0.1 108

100 0.01 109

(approx.)

Vp

2.5

3.5

4.5

5.5

(km/s)

that the friction-based Jr/Ja ratio has been inverted to Ja/Jr to allow improved consistency where clay-filling is concerned. With clay-filling on dominant jointing, Qwater now increases, and the inverse permeability reduces. A further step to enable general stress or depth dependent permeability to be modelled, is normalization by 100/JCS; i.e. when the joint wall compression strength is less than 100 MPa, there will be an increase

Joint stiffness and compliance and the joint shearing mechanism

557

Figure 16.78 The permeability-depth trends that are predicted by the QH2O modification of the rock quality Q formula. The trends are preliminary, but show the potential for a comprehensive rock mass description method to give a first estimate of possible permeability values.

in ‘quality’, and the inverse, giving permeability, will reduce further: Q H2 O 

J J RQD 100  a  w  Jn Jr SRF JCS

(16.26)

Finally, there is a preliminary depth-permeabilityQH2O relation, based on analysis of shallow-borehole Lugeon testing at a rail tunnel project in the Oslo area, and at a metro tunnel project in São Paulo. K ≈

2 5 1000  Q H2 O  D 3

(16.27)

The inclined lines in Figure 16.78 show this relation in graphic form, with an extended permeability range 101 to 1011 m/s. It is relatively easy (perhaps too easy), with the above formulations, to ‘construct’ realistic permeability estimates at depth, with any desired jointed or faulted rock mass quality/character (see Appendix A for details of the Q-parameter ratings). So far, the method is appropriate to ‘jointed and faulted’ rock problems, and application in highly porous rock types, with significant matrix permeability must be avoided.

Example 1. Clay-bearing, well-jointed rock at 100 m depth, with a low UCS of 10 MPa.    regular Q-value  50  1.5  0.66   9 4 1    1.4, i.e. ‘poor’  50 4 0.66 100     98 Q H2 O  9 1.5 1 10   2 K ≈    9  109 m/s  1000  98  100 5 3  (Quite low permeability due to clay coatings, and compressible joint walls). Example 2. Sparsely jointed, rough undulating joints, quite massive rock, with high UCS  200 MPa, with high water pressure at 1000 m depth.    regular Q-value  100  3  0.5   3 1 0.5    100, i.e. ‘very good’  100 1 0.5 100     5.5 Q H2 O  3 3 0.5 200   2 K ≈   4  109 m/s 5   1000  5.5  1000 3 

558

Rock quality, seismic velocity, attenuation and anisotropy

Figure 16.79 a) An example of a massive rock mass with rock quality Q
1000 and a deformation modulus in excess of 100 GPa. A very low attenuation is implied. b) The fault-collapse blocking the tunnel on the right would give almost the lowest rock quality Q
0.001, and a modulus of deformation lower than 1 GPa. It is perhaps ‘off-the-scale’ regarding the conventional definition of Qseis, and would need to be under stress to allow spectral analysis of measurable amplitudes. Its Q-value would then be higher too. See Plate 16.

(Quite low permeability due to limited jointing and high stress level, which cancels out the conducting effect of hard, rough joint walls. Near-surface, significant permeability). Example 3. Negligibly jointed, low permeability, massive rock at 5 km depth (here we extrapolate beyond the curves of Figure 16.78, and base the estimate on the equations).    regular Q-value  100  4  1   1 1 0.5    800, i.e ‘extremely good quality’  100 1 1 100 Q H2 O      25 1 4 0.5 200   2 K ≈   5.5  1011 m/s 5   1000  25  5000 3  (extremely low permeability due to lack of jointing and high stress level) By way of illustrating rock mass Q-values and their extreme range, and also rounding off this wide review of ‘the rock beneath our feet’, a pair of contrasting rock conditions are illustrated in Figure 16.79. By chance both are from Brazil, one a famous landmark, the other

a particularly difficult tunnelling project. The different qualities are typified rather well by the need for a cable car to reach the top of ‘Q  1000’ rock, while a boat was needed for hazardous tunnel inspections of several similar ‘Q  0.001’ fault zones, due to the flooded state of the tunnel between each fault blockage. As we have seen in several chapters the seismic Q values, the inverse of attenuation, might have similar numbers, remarkably, as these pseudo-static moduli (when expressed in GPa) namely 100 and 1. While permeability might be even lower than 0.001 Lugeon in the Sugar Loaf (i.e. 1010 m/s, or 1017 m2), roughly corresponding to the Figure 16.77 prediction, the fault zone quality of 0.001 would be very unlikely to give 104 m/s or 1011 m2 close to the surface, as implied in Figure 16.77, because a lot of sealing clay is obviously present. If devoid of clay, Q could remain quite low, and permeability quite high. Application of ‘QH2O’ from Figure 16.78 to this faulted case, with an assumed 0.1 MPa strength-of-clay JCS estimate near-surface, and 1 MPa at 1000 m, would give a predicted range of permeability of about 106 m/s at the surface – i.e. wet conditions, while at 1000 m depth, a value closer to 109 m/s would be suggested. These estimates appear reasonable.

17

Conclusions

Introduction

PART I

In a great range of applications stretching from tectonophysicists’ interest in microcracks, frequency dependent attenuation and earthquake source mechanisms, civil engineers’ concerns with low modulus dam foundations, petroleum engineers’ interest in shear-wave anisotropy and the permeability of fractured reservoirs, or tunnelling engineers’ concerns with the approaching difficulties of a low velocity regional fault zone, the common use of seismic measurements unites many fields of earth science. The richly illustrated material in this book has been assembled as a result of an interest in a variety of civil, mining, petroleum, geophysics and earth science fields. The common denominator has been rock mass and rock joint behaviour and their impact on the seismic interpretation of the sub-surface. The geophysics of the sub-surface and the rock mechanics of jointed media often focus on related aspects of the same infinitely variable material. Yet different scales and different frequencies have caused these disciplines to have a mostly separate development, with limited crossreferencing in the multitude of journals. Bridging this void in some strategic locations is the major objective of this book. Two of the strongest bridges will be seismic quality and rock quality, and fracture compliance and stiffness, as applying in particular to fractured reservoirs. Part I of this book is mostly focussed on civil engineering, and the links between seismic interpretation of rock conditions at laboratory and field-scale, and their impact on rock quality interpretations for tunnels, deep foundations, dams, planned nuclear waste repositories, and mines. Part II of this book focuses on greater depths, greater scales, and more subtle geophysical detail, as befits this rapidly developing field. The chapters of Part II treat attenuation and anisotropy in detail, and topics range from the use of shear wave splitting to interpret anisotropic fractured hydrocarbon reservoirs, to the interpretation of mid-ocean spreading-ridges, and crustal conditions as interpreted between earthquake source zones and the near-surface.

Chapter 1

Shallow seismic refraction and importance of rock type

1.1 Many geophysicists insist that obtaining high-resolution images from ground level to just 50 m depth is still one of the major challenges of modern geophysics. This happens to be the layer of the subsurface closest to most of our civil engineering endeavours, from tunnels, to dams, to the foundations for high buildings.

1.2 Shallow refraction seismic measurements – using first arrival, compressional P-wave velocities close to the surface can give a remarkable picture of near surface conditions due to some fortuitous interactions of physical phenomena. Weathering and the usual lack of significant stress near the surface has allowed joint systems, shear zones and faults to be exaggerated in both their extent and severity. Stress levels are low enough to allow joints and discontinuities to be seismically visible due to their measurable apertures. Acoustic closure occurs at greater depths than those usually penetrated by conventional hammer seismic, unless rock strengths are rather low.

1.3 Micro-fractures and rock joints are sensitive to stress levels. The more closed state of the discontinuities that are perpendicular to the major stress, and the more open state of those that are parallel will give the rock mass anisotropic stiffness. The rock mass will therefore frequently display anisotropic seismic velocities. Hydraulic conductivities and deformation moduli that show anisotropic

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distributions should therefore be easily detected by near-surface seismic refraction measurements.

1.4 The intimate interaction of the dynamic Poisson’s ratio and the compressional P-waves and transverse S-waves, gives strong correlation with the physical condition of sediments, due to the propagation of P-waves in fluids and the lack of propagation of S-waves due to the absence of shear strength in fluids. Soft, saturated sediments that display Poisson’s ratios of almost 0.5 have negligible Swave velocities and large ratios of Vp/Vs as a result. This ratio eventually falls to below 2.0 as Poisson’s ratio falls and lithification occurs, as seen at greater depth. Shear zones or faults display high values of Poisson’s ratio and higher ratios of Vp/Vs for similar reasons, despite the relatively low value of Vp in such zones.

1.5 Shear-waves offer better vertical resolution than compressional-waves in shallow, unconsolidated sediments. Shear-wave velocities in such cases are only a fraction of the compressional-wave velocities. This results in very small wavelengths, despite the fact that the dominant frequency of shear wave data is generally lower than for compressional waves. To obtain the same level of resolution with P-waves, energy of very high dominant frequency has to be generated, and this is correspondingly more attenuated in the low seismic Q sub-surface.

1.6 Shear-waves are not attenuated at the water table, and are little affected by changes in fluid saturation. They may therefore more easily detect lithological changes with correspondingly less ambiguous velocity contrasts. Under conditions of full water saturation, P-wave velocity contrasts between similar lithologies may be small, whereas shear-wave velocities may reflect true lithological changes.

1.7 Rock mass quality can be described by the Q-value (here frequently termed Qrock), which is a logarithmic

scale of quality from about 0.001 (for major, clay-filled fault zones) through 1.0 (for well-jointed rock) to 1000 (for massive, unjointed bodies of rock). Static rock mass deformation moduli might vary from 0.1 GPa, through 10 GPa to 100 GPa for the same range of qualities, more exact values depending on the strength and porosity of the rock material, and on the level of stress or depth. Qrock also has relationship to the seismic-frequency based magnitude of Vp, with 0.5, 3.5 and 6.5 km/s corresponding, roughly, to the above rock mass qualities, when measured near-surface.

1.8 The Q symbol is also used by geophysicists as a measure of the attenuation or energy loss when seismic waves propagate through a medium. Low energy storage and high energy loss per cycle, signifying low Qseismic values and high attenuation (equal to the inverse Q1 seis ), will obviously correspond to low rock quality Q-values, and vice versa, suggesting potential correlation between these two Q symbols. As will be shown in Part II, correlation may be most valid through a ‘shared earth’ parameter: the stress-dependent rock mass deformation modulus.

1.9 The seismic refraction method has some important limitations. Horizontal or sub-horizontal ray paths record only the upper part of each seismic layer. A thin high-speed layer can mask underlying material, while a low-velocity intermediate layer will not be recognised for similar reasons. Depth calculations to underlying refractors will then be erroneous. Hidden low velocity zones can be detected by up-hole shooting from a borehole to the seismic spread (i.e. reversed VSP), and of course by inspection and index testing of core, if boreholes are available.

1.10 The overburden at typical shallow refraction sites for civil engineering projects may not present uniform conditions. Even a simple site may contain velocity anomalies, which reduce the image quality. The time horizons suffer push-down beneath slow-velocity anomalies, and pull-up beneath fast velocity anomalies.

Conclusions

Chapter 2

Environmental effects on velocity

2.1 Numerous factors influence seismic velocity. Joint frequency, porosity, rock (and joint wall) strength, density, depth, stress, stress anisotropy, degree of saturation, and type of saturating fluid are among the primary influences. Velocity generally increases with depth and with rock stress increase, due to increased joint normal stiffness, joint aperture reduction, joint frequency reduction, and reduction of clay content in the joints. The increased depth also causes deformation modulus to increase, and in general, the permeability reduces due to the increase in effective stress. There may also be changes of lithology with increased depth. Seismic interpretation must therefore be neither separated from the geology, nor from the structural geology.

2.2 Surface weathering effects alter numerous properties of both the rock material and the rock mass. Reduced density, reduced compression strength and increased porosity correlate both separately and collectively with strongly reduced matrix P-wave velocity. Because of the increased void space in weathered materials, there is a marked reduction in velocity as the degree of water saturation reduces below 100%. There is a less pronounced reduction in velocity with reduced saturation, when rocks are unweathered. Dry rock shows the greatest range of P-wave velocities.

2.3 Linear trends for Vp versus the inverse of porosity (1/n%), and linear Vp versus density () relationships, may conceal a non-linear Vp–uniaxial compressive strength (c) trend for the matrix. Weathering reduces all three parameters, and therefore also the velocity. The approximately inverse proportionality between velocity and porosity is influenced by many subtle variations bought about by such factors as clay-content in sandstones. Where joint or crack porosity increases due to weathering, and the matrix porosity increases too, the reduction of velocity may be several km/s, causing very steep velocity-depth gradients near the surface.

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2.4 A large majority of matrix velocity-strength data lies between the trend lines c
V p3 and c
0.25 3p , with Vp expressed in km/s. However, this 4:1 range is still insufficient to encompass some high porosity, low strength data, and is also insufficient to encompass some high strength igneous rock data. c
2 V p3 may be needed as an upper limit. A doubling of rock strength for each 1 km/s increase in Vp is also a good mean trend at intermediate velocities. The effectively concave velocitystrength trend implied by the above, is replaced by a linear Vp – Schmidt (N) hammer rebound trend, with Vp
0.1 N as a first approximation.

2.5 At the low end of the Vp-c spectrum (c  1 MPa to 10 MPa), laboratory data for intact samples of Tertiary mudstones and sandstones show roughly an order of magnitude increase in strength (1 MPa to 10 MPa) for 1 km/s increase in velocity (i.e., 1.5 km/s to 2.5 km/s). Concerning the rock mass, another general trend is that rock mass quality Q-values increase 10-fold for each 1 km/s increase in Vp for the case of hard, low porosity rocks at shallow depth.

2.6 In the case of shale, with its mixed content of similar density minerals (quartz   2.66 gm/cm3, illite and montmorillonite   2.61 gm/cm3 ), the correlation of compressive strength and density is inevitably poorer than for most rocks. P-wave velocity is therefore not a sensitive indicator of compressive strength for shales.

2.7 When slopes or foundations are excavated, there is usually a change of stress (mostly unloading) and a reduction in pore pressure. Improved drainage and increased permeability are also likely. Monitoring of Vp in such zones usually shows significant reductions in velocity, especially when the rock mass is significantly jointed or damaged by the excavation process. Depending on the type of excavation, there may also be shear stress development due to the excavation, which may accentuate

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such effects. Weathering, and frost damage near the surface, may accentuate these velocity reductions in susceptible materials, if left unprotected or insufficiently supported. Velocity will then tend to decrease over time, signifying reduced resistance to shear stress. Chapter 3

Effects of anisotropy on Vp

3.1 Even in the unstressed state, and even if stresses are isotropic, the presence of microcracks, fabric, bedding or jointing will give anisotropic distributions of seismic velocity if these features are themselves anisotropically distributed, as is obviously the case for fabric and sedimentary structures. 3.2 Intact specimens of rock that exhibit strongly anisotropic or orthotropic tendencies such as slate, show significant velocity differences when measured parallel to foliation (e.g., 5 km/s) and perpendicular to foliation (e.g., 4 km/s). This anisotropy varies smoothly as the angle of incidence to the foliation is varied from 0° to 90°. Intact samples of quartzite, amphibolite, hornfels, gneiss, phyllite, schist, and slate exhibit ‘weak’, ‘moderate’ and ‘strong’ degrees of foliation. They can be expected to show matrix velocity anisotropies of 2–6%, 6–20% and 20–40% respectively. 3.3 Micro-cracks that are closed by stress give higher velocity in the direction of the applied stress. Fabric such as schistocity will also give velocities that are strongly dependent on stress levels, when the loading is normal to fabric and the rock is dry. The same reasoning applies to joint sets that are closed by the stress or depth effect. When however loading is parallel to predominant microcracks, fabric or jointing, velocities are higher and there is less sensitivity to stress level, either in the dry or saturated states.

may be mainly a result of coring damage caused by the release of anisotropic stresses. Stress dependent behaviour is particularly pronounced at low stresses compared to the higher virgin stress. Above the previous stress state, the sensitivity to stress change is less. There is little or no stress dependence when no cracks are formed in the recovery process, or when the rock is loaded or unloaded near the original stress state. In a limited stress regime around the original stress state, the rock matrix may behave as a linear elastic material. 3.5 Vertical or sub-vertical joint sets showing dominant strike and continuity of the primary set, cause anisotropic Pwave velocities. The degree of velocity anisotropy may range from 10% for high velocity rock masses to as much as 40% for lower velocity rock masses. The magnitude of anisotropy is accentuated if the dominant set is also parallel or sub-parallel to an anisotropic distribution of the principal horizontal stress magnitudes H max and the perpendicular h min. Near-surface jointed chalk has shown velocity contrast in perpendicular directions as extreme as Vmax. of 2.85 km/s and Vmin. of 1.75 km/s, giving a total velocity anisotropy (Vmax.-Vmin.)/Vmax.  0.38 or 38%. 3.6 The commonly occurring interbedding of sedimentary strata, such as sandstone, shale and mudstone, represent layers that also have different porosity, density, modulus and uniaxial strength. These contrasts of the major mechanical parameters cause variable velocity anisotropy for perpendicular and parallel wave propagation. The fine layering of sedimentary strata means that the dominant wavelength of a seismic pulse is long compared to the thickness of individual layers. The medium will exhibit a vertical symmetry axis in the case of horizontal layering. (For detailed treatment of anisotropy, see Part II). Chapter 4

Cross-hole velocity and cross-hole velocity tomography

3.4

4.1

It has been suggested that stress dependent velocity caused by microcracks seen in cores taken from great depth,

Traditional cross-hole or between-adit velocity measurements at dam sites gives only average velocities for

Conclusions

use in extrapolation of deformation measurements. Crosshole seismic tomography allows both the width and location of low velocity zones to be estimated, and has revolutionized sub-surface seismic measurements for tunnels, caverns, deep foundations (and petroleum reservoir monitoring: see Part II). 4.2 Severe topographic changes and gradational weathering in mountainous terrain, make the use of conventional traveltime refraction seismic hard to use, as long geophone arrays may receive shortest path direct waves earlier than the refracted head waves. Gradational, progressive weathering, rather than distinct layering, causes less clear development of head waves. The use of tomographic inversion techniques for tunnels through steep terrain, is therefore an attractive alternative, and may include tunnel to surface imaging, where fault zones are expected. 4.3 There is an apparent decrease in the velocity of high velocity layers with increasing separation of boreholes. The high frequency direct first arrival received at small borehole separations may be replaced by a long dispersed wave-form at the largest separations. Attenuation of the higher frequency, higher velocity part of the wave at increasing distance may occur in strongly attenuating rock masses. 4.4 When comparing cross-hole and downhole velocity measurements, the downhole sonic probe is considered to give a smaller-scale, and usually higher velocity magnitudes than the averaged cross-hole result. However, the smallscale excavation damage zone (EDZ) that may accompany a borehole in incompetent rock, may be the reason for sometimes measuring lower local velocities at the small scale. Cross-hole measurement generally shows a smoothed, average behaviour. While general trends are similar, the details between the cross-hole and sonic logs differ, due to the change of scale and sampling location. 4.5 When seismic velocity tomography is performed at different scales around loaded rock samples, across loaded

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mine pillars, or through rock masses under high in situ stresses, a clear effect of rock stress on seismic velocity is demonstrated. In hard jointed rocks near the surface, the P-wave velocity may increase by 1 or even 2 km/s as a result of a stress increase of only 5 MPa, and this may occur where there is no rock mass quality improvement. In soft jointed rock, acoustic closure may mask the subsequent effects of a stress increase, unless higher stress causes compaction of the pore space. Care needs to be taken in the interpretation of higher velocities measured at depth. These may or may not be associated with improved rock quality at depth. 4.6 When the cross-hole tomography method is used to image highly stressed and burst prone areas in mining, steep velocity gradients may be found associated with such zones. Attenuation tomograms that change with time as mining advances, may be due to high stress anomalies, stress release phenomena, changes of joint aperture and stress induced fracturing. High shear stresses may be present where steep velocity gradients occur. Seismic velocity tomography can also be used to follow the effects of loosening and void formation caused by blasting. 4.7 P-wave amplitude and S-wave frequency measurements in the laboratory have shown superior sensitivity to stress change and to the effects of joint frequency change, as compared to P-wave velocity. Amplitude attenuation tomography and pulse broadening tomography may therefore correlate better with variable geology or variable structure when in situ stresses are very high, or where deep mining is involved. Chapter 5

Relationships between rock quality, depth and seismic velocity

5.1 The simplicity of first arrival P-wave velocities from shallow refraction seismic, and the easy access for core drilling have stimulated various correlations between Vp, RQD, joint frequency and the rock mass quality Q-value. For hard, low porosity rock a useful rule-of-thumb

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Conclusions

is that Vp  3.5  log Q km/s, where Q is the rock mass quality (range of Q  0.001 to 1000). 5.2 When rock has a uniaxial strength (c) significantly lower (or higher) than the nominal 100 MPa for hard rocks, the Q-value needs to be modified to Qc  Q  c/100 in the above Vp–Q relationship. When rock matrix porosity (n) is significantly more than the nominal 1% for hard rocks, Vp must be corrected by a porosityrelated reduction in velocity. When depth is significantly greater than the nominal 25 m for shallow refraction seismic, a depth or stress related increase in velocity occurs, which can also be estimated in the case of rock masses dominated by ‘soft’ porosity, or jointing. A non-linear correlation of Vp with static deformation modulus has also been developed, which can be utilised both with, or without, knowledge of the rock mass quality Q. 5.3 Data from sites in chalk, chalk marl, sandstones, mudstones, shales and tuff have been used to develop empirical Qc – velocity – depth corrections, which are non-linear in the case of depth or stress level, but nearly linear in the case of porosity. 5.4 For near-surface measurements in harder rocks, the ratio of P-wave velocities Vfield/Vlab., when squared, has often proved to be numerically close to the value of RQD (with RQD expressed as a ratio rather than a percentage). RQD is defined as the % of core that has core sticks 10 cm long. It applies to a given core run, or to selected structural domains, or to specific rock types, or to cycles of rock types, where there is some continuity. Since stress can ‘acoustically close’ joints in weaker rock, joint frequency as reflected in RQD may then prove to have little correlation with the velocity. This is where other seismic attributes than P-wave velocity become important. 5.5 Increasing depth will usually cause both the vertical and horizontal stress to increase. Besides stress increase,

both RQD and Qrock typically increase rapidly in the first tens of meters, making a reliable depth correction problematic, since the three variables quality, depth, and velocity are often all changing at once. Sensitivity of velocity to stress is greatest in these first few MPa of stress increase. The velocity-depth relation is non-linear, and has a steep gradient. Velocity increase with depth can occur in harder rock masses, even when rock mass quality (Q-value, RQD, or joint spacing) remains constant.

5.6 A measured 20 metres deep profile of weathered granites, showing improvement with depth of all the indices of quality (hardness, RQD, density, etc.), demonstrated a very large increase in Vp from 1.0 to 4.5 km/s. The associated velocity-depth gradient of 175 s1 emphasises the potential value of rock quality description. Velocity-depth gradients as high as 80 s1 in the upper 20 m, and as high as 40 s1 over the first 50 m were recorded at a cavern site in jointed gneiss with only slight weathering. Unusually, the rock quality parameters: RQD, F m1 and Q, did not improve at this site between 5 m and 60 m depth. A maximum velocity rise of some 2 km/s (3.5 to 5.5 km/s) occurred in the depth range 10 to 60 metres, in which horizontal stresses were interpreted from stress measurements to have increased by 2 MPa to 4 MPa, depending on direction relative to h min and H max. 5.7 Fracture zone widths in the upper tens of meters tend to be larger if the velocity outside the fracture zone is also low. Narrowest zones tend to have lowest internal velocities, and highest external velocities. There is commonly a reduction of the widths of low velocity zones with increased depth.

5.8 When apertures are less than approx. 0.04 mm (or 40 m), the frequency of such fractures appears to have little influence on the P-wave velocity. This is implied by experiments with ‘line-samples’ in the form of multiple-jointed columns of carefully machined rock cylinders. Seismic surveys underground also suggest that apertures need to be considerably wider than 40 m, for fracture

Conclusions

or joint frequency (F m1) to influence the velocity ratio Vjointed/Vintact.

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to about 1 to 10 m, typical of the weathered zone. At 0.25 MPa normal stress, equivalent to about 10 m depth, conditions varying from no gouge to 2 mm of gouge, may give S-wave velocity reductions of as much as 50%.

5.9 No reduction in P-wave velocity is predicted with as little as 1 joint per meter. However, with 5, 10 or 20 joints per meter, a hard crystalline rock with Vintact of 5.5 km/s, is predicted to show reductions to 4,100, 3,300 and 2,500 km/s respectively. Strong sensitivity of Vp to stress level in the range 0.3 to 3 MPa is implied for the case of filled discontinuities, including sensitivity to the total cumulative joint aperture and moisture condition. Vp is found to be proportional to n in the stress range 3–20 MPa, but drops rapidly when n  3 MPa. These experimental findings are similar to the empirical, fielddata based Qrock – VP – depth model. 5.10 Compressive wave amplitude gives a more sensitive measurement of the density of jointing than P-wave velocity. The amplitude ratio A/A0 (A0 for intact rock) shows excellent sensitivity to the density of jointing. Apertures less than 0.01 mm (10 m) apparently do not have influence on the wave propagation, even when the normal stress is as low as 1–2 MPa. Physical apertures (E) of this size, in contrast to hydraulic apertures (e) which are smaller due to roughness effects, are probably rare in the upper 20–30 metres of rock masses where refraction seismic is carried out, so this result is probably consistent with experience in the field. 5.11 Hydraulic apertures of about 10, 1.8 and 0.3 m are implied with E 10 m, if joint roughnesses are respectively 2.5 (quite smooth and nearly planar), 5 (nearplanar but some small undulations) and 10 (non-planar with marked inclined asperities. The smallest of these apertures would hardly be considered as ‘open’ joints. 5.12 Shear-wave velocity gives a very sensitive indication of the effect of gouge thickness at low stress levels, equivalent

5.13 Careful experiments have demonstrated that shallow seismic refraction measurements that operate at low stress levels are likely to be successful in distinguishing joint frequency and aperture. Amplitude measurements appear to be much more desirable than velocity measurements at high stress levels, if joint frequencies and character are to be distinguished. This emphasises the value of attenuation measurement, or of seismic Q. Reduced amplitude and increased attenuation occurs as joint roughness increases, which fits with the picture of joint closure difficulties when joints are rough. Shearing and dilation similarly reduces amplitude and increases attenuation.

Chapter 6

Deformation moduli and seismic velocities

6.1 It is well known from dam site investigations that the dynamic modulus of elasticity (Edyn) that is calculated from Vp, Vs and density exceeds the pseudo-static modulus of elasticity (Ee) obtained from plate-load tests. The latter is itself usually several times larger than the static modulus of deformation Ed, i.e. Edyn  Ee  Ed. In poor quality rock masses, ratios of Edyn/Ed may be as high as 10 to 20, due to the fundamentally different levels of strain involved, but in massive hard rocks under high stress the ratio will be quite close to unity. Ed is variously termed Estatic, D and M in the diverse literature.

6.2 The differences between static and dynamic moduli are attributed to the different strain amplitudes involved (perhaps 103 and 106 respectively). The different magnitudes of these moduli are also caused by the presence of pores, cracks and joints, which are measurably deformed in pseudo-static tests, but only very slightly deformed by dynamic waves. When stresses are very

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high and the pores, cracks and joints are almost closed, the static and dynamic moduli are likely to be of almost equal magnitude in the common direction of loading.

6.3 The modulus of elasticity (Ee) is traditionally obtained from the gradient of the unloading curves, which tend to have elastic character due to the frequently nearly closed state of the stress-deformation loops. When unloading from higher stress levels, as when back-analysing shaft or cavern deformation, higher values of both Ed and Ee are indicated. The rock mass becomes stiffer both in loading and unloading, due to the increased degree of joint closure as depth or stress increases.

6.4 The total deformation measured at the highest load level, after several load-unload cycles, is the usual basis for the calculation of Ed. The applied stress level is usually based on the size and type of dam, or other structure to be located on the particular rock foundation. Clearly, this limits the range of stress over which these parameters have typically been investigated. However, back-analysis of tunnels and caverns and deeper shaft deformations, and higher pressure testing for large bridge foundations, has extended the near-surface range of stress.

6.6 Since seismic velocity also senses the effects of higher joint stiffnesses, modulus can apparently be estimated from the empirical relation M 10(Vp0.5)/3 GPa, even without reference to the rock mass quality Q c which is common to both. Where seismic ‘closure’ in relation to Vp measurement occurs at shallower depth in weak rock, the above relation may cease to track the assumed, continued increase in moduli. One may then revert to the Qc value and apply the appropriate porosity () and depth () adjustments, in order to predict the continued, assumed modulus increase.

6.7 Deformability data have been measured at dam sites in weathered or soft rocks with uniaxial strengths ranging as low as 2 MPa, and at sites with extremely hard rocks with uniaxial strengths as high as 300 MPa. These relatively shallow civil engineering sites may have in situ P-wave velocities ranging from about 0.5 up to 5.5 km/s. Corresponding ranges of Ee may be from about 0.5 to 80 GPa, and ranges of Ed may be from about 0.1 to 50 GPa. At intermediate rock strengths and intermediate velocities of 3 to 4 km/s, Ed and Ee values tend to be from about 5 to 10 GPa and 10 to 20 GPa respectively. Porous rock, such as weaker limestones, results both in lower velocities and in lower moduli.

6.8 6.5 Static deformation moduli (also termed Estatic, and M), can be estimated from the non-linear relationship with Vp, or from the rock quality Q-value, c, n% and depth correlations developed in this book. In the undisturbed state, the consolidated state of the rock mass ensures a depthdependent deformation modulus, due to the tighter interlock and higher stiffnesses of the rock joints. One should be aware that most rock masses observed or tested, are actually on part of a major unloading curve due to erosion, or due to the rock excavation involved in preparing for the test. In the case of rock masses with rougher, interlocked joints, lower joint stiffnesses may be registered, than if the jointed rock mass was loaded up without this prior unloading.

The inequality Ee  Ed applies to the two rock engineering parameters that are actually in the ‘static’ loading, ultra-low-frequency sphere of geophysics. The inequality of the moduli is due to mechanical hysteresis, and is not related to another key inequality in geophysics, namely that the (static) joint stiffnesses become less than the inverse of the (dynamic) joint compliances, as rock mass quality deteriorates.

6.9 Plate loading tests taken to such high stress that rock mass failure occurs are unfortunately extremely rare. The measurement of P-wave velocity at such sites may allow tentative extrapolation to other sites through a common rock

Conclusions

mass quality estimate. Such data are then the source of tentative rock mass strength (c mass) estimation. The following selected sets of (smoothed) data reflect the potential linkages: Vp  2.3, 3.7, 4.0 km/s, Ed (or D)  1, 3, 15 GPa, c mass (uniaxial-loading)  4, 20, 50 MPa.

6.10 It has been recognised in soil engineering that strain levels associated with normal foundation designs are rather small, for example, 0.01 to 0.1%, and therefore stiffnesses may be successfully described by the correlations obtained from in situ seismic measurements. Such measurements have the advantage of registering the stiffness of the ground at in situ stress levels and in the undisturbed condition. When a tunnel or test adit is constructed at considerable depth in rock, the excavation disturbed zone (EDZ) effect will alter the above conditions in a complex way, to a degree that depends on rock quality and the care with which the excavation of the access adit and block test site has been performed.

6.11 The three dynamic moduli (Young’s, shear, bulk), can theoretically be estimated from Vp measurement alone, if the dynamic Poisson’s ratio is estimated, rather than derived from Vp and Vs. This however can cause significant inaccuracies, and such values given in the literature should be treated with caution. It is normal to register lower dynamic Poisson’s ratios in the case of higher velocity laboratory data, and the opposite trend for the lower velocity field data. High dynamic Poisson’s ratios are a sign of the influence of jointing. In shear zones and faulted rock, very high values (0.4) of dynamic Poisson’s ratio are common. Static values of ‘Poisson’s ratio’ (mass-expansioncoefficient) 0.5 may be measured when loading jointed rock towards shear failure. At hard rock sites, typical in situ values of the three dynamic moduli Edyn, k and

might be 65, 50 and 25 GPa when the average P-wave velocity is as high as 5.5 km/s.

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moduli Ed values as low as 5 to 10 GPa. The most likely explanation is that the large scale deformation modulus test, as practised at dam sites (plate load, flatjack or occasionally pressure chamber) is nearly always registering an excavation disturbed zone (EDZ) in a loading direction parallel to the (unloaded) radial stress (r) direction. In contrast, the velocity measurement may be averaging velocities over a larger volume, and may be recording velocities parallel to the  (tangential stress) direction, or perhaps axially along the test adit wall. The tangential stress is a much higher, maximum local principal stress, compared to the minimum radial stress, which approaches zero, due to the effect of excavating the test adit. The axial direction would have intermediate stress levels, and presumably intermediate velocities as a result. Chapter 7

Excavation disturbed zones and their seismic properties

7.1 Excavation disturbed zones (EDZ) caused by tunnel, slope or open excavation may show up to several km/s reduction in P-wave velocity due to the combined effects of radial stress relief, blasting or excavation damage causing fracturing. Improved drainage and drying-out of the near-field rock mass will also contribute to the reduction in velocity. Time effects, reducing Vp even more, may result from deformation or deterioration caused by inadequate rock mass reinforcement or surface protection. 7.2 Cross-hole seismic monitoring of a ship lock excavation, which reached a depth of more than 20 metres, caused a 200–300% reduction in velocity, a 75 to 85% reduction in deformation modulus, and a 1 to 20 times increase in (back-calculated) ‘joint voids’. The combined effect of loosening caused by blasting, stress relief, presumed inadequate slope reinforcement, and a one-year delay between two of the monitoring stages, were responsible for the easily monitored degradation in properties.

6.12

7.3

Quite high P-wave velocities, such as 4.5 to 5.5 km/s are sometimes reported together with static deformation

A larger scale version of stress relief at a gorge, which cuts through massive, bedded limestones, had an outer

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Conclusions

layer of 5 m thickness with a velocity of 2.9 km/s, while deeper into the walls of the gorge, the velocity was 5.5 km/s. The potentially greater effect of weathering in nature may be thwarted by lack of multiple joint directions and permeability enhancement. Slope ‘EDZ’ may exceed the EDZ associated with tunnelling, due to the longer and more effective influence of surface weathering, including frost damage.

background stresses are more isotropic. Illustrative mean results for the three zones may be Vp  3.5, 5.5 and 4.5 km/s respectively. Least effects on Vp tend to be seen when tunnelling in saturated massive rock at greater (but pre stress-fracturing) depths, and greatest effects on Vp are seen in drained or dry jointed rock at shallower depth. The hazardous stress fractured zones of tangentiallystrained and radially-loosened or dynamically loosening rock, would show lowest velocities if measurements could be achieved.

7.4 Seismic attenuation can be used to evaluate the efficiency of rock excavation by blasting, by quantifying the degree of brokenness of the rock before and after blasting. Certain frequencies may be attenuated more than others due to the effect of fracture size and fracture-induced voids. Attenuation will tend to be larger and more irregular at shallow depths, where existing joints and new fractures open more easily. Attenuation is more regular and more limited at greater depths, where confinement limits fracture and joint opening. Such EDZ effects may be accompanied by rotations of both the attenuation anisotropy axes and the velocity anisotropy axes, as a result both of disturbance to pre-existing joint patterns and dissipation of prior stress anisotropy.

7.5 The removal of stressed rock and its usual replacement by air at atmospheric pressure when tunnelling, results in a radial stress (r) that approaches zero at the excavation walls. The tangential stress ( ) usually increases in diametrically opposite sectors, but may also incorporate diametrically opposite sectors of negative  min if the far-field stress anisotropy is 1 : 3. Joint set orientations relative to an anisotropic stress, adverse rock strength/ stress ratios, and the disturbance caused by the excavation method (blasting, boring, or line-drilling), may each have strong influence on the physical EDZ, and on the resulting seismic EDZ.

7.6 Three velocity zones may be visualized around a tunnel: a 1 m or less loosened zone with lowest velocities, a stress bearing ring with highest tangential stresses and velocities, and an uninfluenced zone with reduced velocity where the

7.7 Mining of excavations in bedded salt has shown greatest effect on the attenuation of P-waves. Mining induced radial stress relief and increased tangential stress tend to cause under-saturation due to dilation of the salt. A reduction in P-wave amplitude, which may increase with time after excavation, may give a stronger indicator of the EDZ than a minor reduction in P-wave velocity.

7.8 The effect of radial stress release close to a tunnel excavation in jointed rock, generally increases the joint apertures, which can actually be expressed as a void ratio. A time-average equation utilising the P-wave velocity through air or water-filled joint voids, together with the P-wave velocity of intact rock, can be utilised to interpret depth-dependent downhole or up-hole P-wave velocities. The result is explained in terms of an increased jointaperture related void-ratio, with reduced depth of measurement from the excavation walls.

7.9 Cross-hole seismic measurements performed in a columnar-jointed basaltic rock mass at BWIP, Washington, USA were made between four horizontal boreholes drilled 12 metres into the wall of a drill-and-blasted underground opening at 46 m depth. The basalt columns were regular but sinuous, 0.15 to 0.36 m in thickness, dipping 70 to 90°, with frequent low angle, discontinuous cross-jointing. The horizontal and (to a lesser extent) the diagonal seismic measurement paths crossed the more open columnar joints, and these features clearly opened most as a

Conclusions

result of excavation, giving the strongest reductions in velocity of 55% to 65%. The seismic quality factor Qseis increased in the vertical direction, in the same direction as the highest velocities recorded where there was least EDZ effect. Qseis in the horizontal direction remained low (5 to 8), in the same direction that showed the maximum EDZ-reduced velocity, with VP declining from 5.5 or 6.0 km/s to 3.5 km/s at the tunnel wall.

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AE events clustered both where tangential stresses were highest and where seismic velocity (Vp) gradients were steepest. The acoustic emission results confirmed that rock failure was initiating just inside the tunnel wall, orthogonal to the 1 direction. Relatively decreased velocities were seen in the two regions that were under tensile tangential stress. Calculated P-wave velocities showed quite strong anisotropy in the massive granite, caused by the principal stress anisotropy given in the previous paragraph.

7.10 The underground research laboratory (URL) in Manitoba, Canada was the site of numerous geophysical studies. The dominance of massive, unjointed, highly stressed granite resulted in particular focus on stressrelated EDZ, with down-hole sonic logging and acoustic emission monitoring, together with parallel laboratory tests and numerical modelling studies. At the smallest scale, the state of micro-cracking in selected core samples from radial boreholes drilled in the walls of a drift where excavation was either by normal blasting or by smooth blasting, indicated Vp reductions of about 1 to 1.5 km/s in the outer 0.8 m of the normally blasted tunnel, and reductions of about 0.5 km/s in the outer 0.5 m of the smooth blasted excavation.

7.13

7.11

7.14

The effects of highly anisotropic, sub-horizontal stresses at URL were studied in a unique test tunnel excavated by line drilling and reaming, followed by mechanical breakout to avoid blast damage. Principal stresses of approximately 60, 45 and 15 MPa, caused classic ‘break-out’ resembling that in a borehole. The isotropic-elastic theoretical tangential stresses of 165 MPa (31  3) at 11 o’clock in the roof and 5 o’clock in the floor (with 33 – 1  15 MPa in the side walls), caused prominent V-shaped notches of rock failure. The stress-related disturbance was measured directly in 1 m deep boreholes using a micro-velocity probe with 10 cm separation of the transducers.

At the Äspö hard rock laboratory (HRL) in Sweden, seismic tomography investigations were performed to compare the depth of excavation damage zones in immediately adjacent drill-and-blast and TBM sections of tunnel. Principal stresses at the ZEDEX (zone of excavation disturbance experiment) were approximately 32, 17 and 10 MPa. There was only a small EDZ effect on Vp and Vs, due to the high stresses and the partly discontinuous jointing. P-wave velocities were mostly in the region of 6.0 to 6.3 km/s, with small reductions of velocity in a thin ‘skin’ next to the walls. The reductions of velocity were recorded in the first 0.25 m into the TBM tunnel walls, and up to 1 metre into the walls of the drill-and-blasted tunnels.

7.12

7.15

Acoustic emission (AE) was recorded during careful (mine-by) extension of the 420 m deep test tunnel. The

EDZ effects around the tunnel were only just detectable by seismic velocity, due to the good quality of the rock

An experimental tunnel sealing experiment at the URL utilised AE for interpreting reductions in average Pwave and S-wave velocities, in the highly stressed zones that were caused by post-excavation of larger diameter ‘dog-collars’ or bulkheads for concrete and bentonite sealing. 3D coverage of an outer volume surrounding this tunnel sealing experiment, and two higher resolution AE arrays for recording in a 10 m  10 m  10 m volume around the collars, allowed AE-based monitoring of temporal changes in Vp and Vs. These were used to estimate the theoretical change in crack density (c) and saturation (s) along any particular ray path.

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Conclusions

(Q-value
22–24), and due to stresses that were high enough to have acoustically closed the joints, but not high enough to have caused excavation induced microcracking, as at the URL in Canada. The rock quality QcVp-M model predicted a P-wave velocity range from 5.8 to 6.2 km/s, using an equivalent depth range of 400 to 1200 metres, relevant to the principal stress range. The intact rock laboratory E-modulus was 69 GPa. The equation relating mean deformation modulus M with Vp, suggested deformation moduli ranging from 58 to 79 GPa, for the predicted velocity range of 5.8 to 6.2 km/s. Calculated dynamic moduli around the drilland-blast drift ranged from 76 to 79 GPa. The particular M
Edyn situation at this site implies ‘acoustically closed’ jointing.

7.18

7.16

8.1

A drift in the Stripa mine in Sweden, used for borehole heater tests, showed increased seismic velocities between drained monitoring holes in the jointed quartz monzonite, during heating of the rock mass. The initial increase in velocity with temperature was linear and varied from 2 to 4 m/s/°C. This was the presumed result of thermally induced joint and micro-crack closure. Increased P-wave velocities were recorded in directions consistent with a thermally-induced stress increase. An initial stress anisotropy giving low stress in the same direction as the subsequent thermal stress increase tended to enhance the Vp response. Greatest response was seen when degrees of saturation were also low.

Seismic velocity measurements performed from the surface prior to tunnelling need careful interpretation due to the common experiences of enhanced weathering, enhanced fault width and more open jointing experienced near the surface. Anisotropic stresses, and anisotropic fabric or structure or bedding, plus hidden lower velocity layers, add to the potential pitfalls when attempting to anticipate rock mass conditions at tunnel depth. The degree of saturation where measurements were made, compared to tunnel depth conditions is also important.

7.17 A long period of cooling (350 days) generally returned seismic velocities to values lower than before the heating, suggesting permanent changes, probably connected with the hysteresis effect of joint closure and opening. Upon cooling, the less rough, interlocked joints may have ‘sprung-open’ more than their closed neighbours, to avoid tensile stress development. This would cause a reduction in seismic velocity if the open joint or joints crossed the path of the seismic array. A velocity anomaly at about 3 m depth was smoothed-out by the heating but returned when the rock was cooled. A significant quantity of water expelled during the heating signified a general closing of the joints.

The average joint frequency in the test area, analysed from 224 m of core, was 8.3/m. An elastic continuum analysis conducted prior to the test had suggested larger stresses and local displacements than were actually measured, presumably due to the thermal compliance of the joints, as noted in Part II concerning a fully coupled HTM heated block test. This thermal compliance effect was also experienced in a heated-mine-by experiment in the Climax Mine, in the USA, where deformation monitoring also failed to match predictions, since no thermal joint compliance was modelled. Chapter 8

Seismic measurements for tunnelling

8.2 Seismic refraction profiles with appropriate azimuth, and borehole dip and dip-directions that also take due regard of structure and stress anisotropy can improve the quality of the sub-surface investigation. The use of only vertical boreholes drilled where there is predominantly vertical structure is a guaranteed way to obtain poor sub-surface information, if this is only to be based on core and borehole wall inspection. The application of geophysics helps to recover some of the lost information from representative core samples, especially if highfrequency cross-hole surveys are performed. 8.3 The common experience of improved rock quality and increased Vp at depth may be checked at intervals by

Conclusions

appropriate core-drilling. In the local absence of core, a sensible interpretation of the usual effect of depth on Vp values can be made using QVp correlation, where Q is the rock mass quality. In very general terms at hard rock sites, a ten-fold improvement of Q-value, combined with a 1 km/s additional depth effect on VP might be expected at a 50 m deep tunnel. So a near-surface Q-value of 1.0 interpreted from shallow seismic refraction, where VP was 3.5 km/s, might see VP increased to 5.5 km/s at 50 m depth, but with the Q-value equal to 10 at tunnel depth, rather than Q 100 as implied by a nearer-the-surface VP of 5.5 km/s. 8.4 There is evidence to suggest that not only rock overburden depth, but also water depths are important, in the case of undrained sub-aqueous tunnels that prove to be completely dry, due to low permeability over-lying rock masses such as phyllites. In such cases the total stress caused by rock load and water load may give a false impression of rock quality at tunnel depth, to the extent of 1 to 2 km/s. 8.5 Seismic velocity measurements performed while tunnelling have been shown to correlate in approximate terms with speed of tunnelling, support needs, and tunnel cost. Probe drilling and sonic logging of the holes can be utilised for ahead-of-the-event information on rock and hydrogeological conditions. If multiple probe holes are drilled, then cross-hole tomography can be performed to add to the tunnel contractor’s preparedness for difficult zones. This has resulted in the choice of ground-freezing for safer penetration of dangerous and/or environmentally sensitive sub-urban fault zones. 8.6 Velocity measurements should be made sufficiently far ahead of the tunnel face, at least two to three diameters, such that additional stress concentration effects are avoided. Interpretation of local effective stress conditions will be needed when evaluating results of the velocity measurements, using VpQ correlation. A ‘false’ rock quality, due to a higher P-wave velocity may be interpreted, if depth of measurement is not accounted

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for. This may mask the actual presence of a serious fault that could better be identified by shear waves or attenuation measurement. 8.7 An early example of the use of geophysical surveys in tunnels was the Straight Creek pilot bore of 4.0 m diameter, driven in the 1960’s at 200–500 m depth through granite, diorite, gneiss, migmatite and schist, under the continental divide in Colorado, USA. Deep layer velocities were measured at five seismic spreads: 5.18 km/s, 5.1 km/s, 4.8–6.1 km/s, 4.2 km/s and 6.0 km/s. Much lower shallow layer velocities, representing loosening effects were respectively 3.0 km/s, 2.3–2.7 km/s, 2.3–3.1 km/s, 1.3–1.6 km/s (worst case, class 5) and 2.3 km/s. These extremely low EDZ velocities proved, in retrospect, to be more related to the insurmountable problems in the 12 m main bore, which took several year to complete. There was possibly insufficient appreciation of the effect of stress on the seismic velocities at that time. There is also the possibility of adverse interaction when there are twin tunnel tubes, with ‘plastic zone’ overlap (or log-spiral shear-zone overlap) in faulted or weak rock zones, a problem of relevance when assessing risk in too-close twin-bore TBM tunnelling, where conditions are unfavourable. 8.8 Comprehensive geological and velocity classification of rock conditions at numerous rail tunnels in Japan from the 1970’s demonstrate the value of velocity-tunnelsupport correlation. Recommendations were based on 70 case records from 30 m2 and 60 m2 tunnels. For rocktype and geological Classes 1 to 6, with their associated high to low P-wave velocities, tunnel support loads ranged from 1 to 30 tons/m2, the spacing of the steel arch support ranged from 1.5 to 0.75 m, and the final concrete thickness ranged from 0.3 to 0.9 m. Today, we could place an equivalent velocity scale below the rock mass Qvalue, which is used for recommending shotcrete thickness and bolt spacing. 8.9 When attempting to add a rock mass Q-value scale to such velocity-rock-support recommendations, the geological part of the classification is particularly

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Conclusions

important, in view of the porosity, strength and depth corrections to the VP  Qc empirical model. Young, weak, porous rocks may have RQD  0, and incur unfavourable SRF values due to adverse strength to stress ratios in the tunnelling situation. These two factors may alter the correlation of support-type-and-degree with the velocity, unless the velocity is EDZ-based, rather than that obtained from the fully confined (pre-tunnel) situation.

8.10 Sub-sea tunnelling experiences, with velocity-rock support correlation, have revealed several cases of medium and low-velocity zones actually creating greater tunnelling difficulties than the velocities would suggest, implying an artificially elevated velocity in relation to rock quality. The tunnelling situation changes the stress level in relation to the pre-tunnelling confining stress. Based on sub-sea tunnelling experiences, Norwegian studies have shown support costs rising from 50% to at least 75% of total costs, when the P-wave velocity reduces from 5.5 to 4.5 km/s. It is likely that these are ‘depth-enhanced’ velocities, since uncritically applied Q-values would be 100 (no support) and 10 (light support) respectively, which are unrealistic when referring to significant support costs.

8.11 High velocities of typically 5 to 6 km/s may dominate in refraction seismic studies at relatively unweathered hard rock sites. The much smaller number of tectonic zones (shear zones, faults), dykes and joint swarms with velocities from about 2.5 to 3.5 km/s are what cause the construction problems, especially when high inflows of water occur. In weaker, porous rock, velocities in the range 2.5 to 3.5 km/s may signify excellent stability. The contrast from back-ground velocities is clearly the measure of the stability problem, not the velocity per se. The hard rock velocities may signify rock quality Q-values of 30–300 (very/extremely good), and 0.1–1.0 (very poor) respectively, clearly reflecting the reduction of quality, and need for local, heavy tunnel support. The weak, porous rock velocities could signify Q-values as high as 10–100 at nominal 25 m depth, if corrections for 10% matrix porosity and UCS of 10 MPa were included in the assessment. The VP  Qc

empirical model can be applied to make these assessments, where Qc  Q  c/100. 8.12 Despite the above pitfalls concerning the meaning of velocity when different porosities and rock strengths are involved, tunnel refraction seismic and tunnel boring machine (TBM) progress indicate a quite linear inverse relationship between the penetration rate (PR in m/hr, with uninterrupted boring), and P-wave velocity. This is also partly matched by an inverse PR and Schmidthammer rebound trend. Respective values might be as follows: VP  4 km/s, 2 km/s: PR  2 m/hr, 4 m/hr: Schmidt-hammer rebound  40, 20. (Inverse correlation to possible Q-values of 30 and 0.3 are also implied, as in the QTBM model). Harder, higher velocity rock signifies tougher boring (i.e. lower PR), but the weekly mean advance rates (AR) might be 1 m/hr and 0.5 m/hr respectively, due to the reduced tunnel support needs. While tunnel support quantities are roughly proportional to log10 Q, PR may be inversely proportional to log10 Q. 8.13 Sonic logging of probe holes, made by fast percussion drilling at from 2 to even 5 m per minute, can give advance information on seismic velocity if the holes are sonically logged. This can be used for subsequent rock quality class and tunnel support class estimation. The chosen excavation mode, and support components such as bolted steel arches, rock bolts and mesh, or shotcrete, can then be immediately available, and applied with appropriate timing, behind the advancing TBM tunnel face.

8.14 A seismic velocity probe ahead of a tunnel will not see the difference between a TBM tunnel and the drilland-blast tunnel. However, if refraction seismic measurements are performed along the wall of a TBM tunnel, the values of Vp obtained may tend to be higher than in the equivalent drill-and-blasted tunnel for at least three reasons. There is a reduced level and depth of damage in the wall of a TBM tunnel. Higher tangential stresses are acting closer to the TBM tunnel wall. There

Conclusions

will be a tendency for lower permeability and less drainage around the TBM tunnel, which, for reasons of more complete saturation might also increase the seismic velocity. On the other hand, there may be a reduced value of effective stress as a result of the same reduction in permeability.

8.15 The reflection method of HSP or TSP (horizontal or tunnel seismic profiling) with both source and receiver in the tunnel, is capable of locating seismic reflectors ahead of a tunnel face. However, reflector images are not related to rock quality directly, but to implied change of quality. It is difficult to determine if the rock quality will get better or worse at a given reflector, and there may be inaccuracies of reflector location due to the unknown actual velocity field.

Chapter 9

573

Relationships between Vp, Lugeon value, permeability, and grouting in jointed rock

9.1 Rock masses containing voids in the form of porosity, joints or damage zones will generally have enhanced permeability and reduced seismic velocity. Measurements at dam sites and at tunnels have indicated inverse correlation between P-wave velocity and permeability, in particular with the relatively high pressure Lugeon injection test, which may locally deform the void space created by joints or fractures. Because the rock mass quality or Q-value also correlates with the deformability, a very simple lower bound inverse relation between the Lugeonvalue (L
107 m/s) and the Q-value is indicated. (Q
1/L). This is not relevant however, when joint-sealing clay is present, causing both Q and permeability to reduce together, instead of inversely.

8.16 A logical extension of conventional high-resolution surface refraction seismic, is the application of sources and receivers at, and close behind the tunnel face, with receivers at the surface, if this is not too distant. GPS clocks are needed to synchronise the sources within the tunnel and the receivers at the surface. The use of intunnel refraction-based estimates of velocity distributions ahead of the face, can improve the accuracy of reflector positions. With the necessary velocity distribution ahead of the face, the rock mass quality can be characterized both up to and beyond the now better-located reflectors.

8.17 Velocities measured at depths of hundreds of meters or more, using in-tunnel refraction or cross-hole tomography, may bear little resemblance to the major tunnelling difficulties sometimes experienced when tunnelling. Face collapse in a Vp  4 km/s rock mass is ‘illogical’, without allowing for the depth or stress effect that may mask, in velocity terms, the true low quality. A 300 m overburden at such a collapse location, suggests a near-surface Vp of about 2.5 km/s, using the Q-Vp-depth model. This would be relevant to a serious fault zone, or extremely poor rock, and therefore more consistent with eventual collapse.

9.2 Lower Q-values and higher Lugeon values will tend to be measured when holes are oriented to cross major structure. The opposite occurs when paralleling major structure, and failing to cross the dominant jointing. The latter is typical for vertical wells prior to deviation through seismically identified oriented structure. Holes should be drilled in the ‘slow’ direction for registering highest permeability. Clay sealing of joints may compromise these simplified assumptions. 9.3 Since sub-vertical jointing may dominate in the same way that horizontal stress anisotropy may dominate, the permeability anisotropy will tend to be related to azimuth. At great depth, this model may be compromised by joint closure, and a shear mechanism may be needed to explain the maintenance of (anisotropic) permeability. 9.4 The void space in a rock mass that is responsible for greatest permeability, specifically the joints and any outwash

574

Conclusions

channels caused by weathering or soluble minerals, can usually be injected with cement, micro-cements, or ultrafine cements. Seismic measurements, principally in dam foundations, show remarkable increases in P-wave velocities as a result of successful grouting, when permeabilities are also favourably reduced. Part of the increase in velocity and resulting reduction in deformability may be due to the post-stressing effect of high pressure grouting, which also may set in a stressed state.

9.5 Most effective grouting can be expected in the joint set having greatest permeability and least magnitude of the effective normal stress. This set will thereby show greatest increase in seismic velocity as a result of the grouting. A rotation of the permeability tensor to a lesser magnitude can also be expected as a result of the grouting, and velocity anisotropy is likely to be reduced. Several of these aspects have been demonstrated using multiple borehole 3D permeability testing in Brazil.

showed a very broad transmissivity range of 102 to 1014 m2/s. Corresponding P-wave velocities ranged from 3.2 to 5.5 km/s, Vp/Vs from 2.45 to 1.72, dynamic E-modulus from 0 to 60 GPa, and dynamic Poisson’s ratio from 0.41 to 0.28.

9.8 At the Chinnor Tunnel in chalk marl in southern England, very low seismic velocities in the range 0.6 to 1.0 km/s were registered for badly fractured/jointed areas of the chalk marl. Quoted permeabilities were 104 to 106 m/s in these areas. Assuming that 1 Lugeon
107 m/s then the very high Lugeon values of 1000 to 10 imply Qc values of 0.001 to 0.1. These low Qc values can be converted to ‘tunnel support’ Q values of 0.02 to 2 (‘extremely poor’ to ‘fair’), by assuming a mean c value of 5 MPa for the chalk marl. This range of Q-values is in line with expectations for the heavily jointed rock mass at Chinnor.

9.9 9.6 The inter-related physical nature of rock mass quality (Q), deformation modulus (M), seismic velocity (Vp) and permeability (L) means that rock masses can be represented by type curves in nomograms linking these parameters. Although only approximate, such type curves serve to distinguish typical properties of massive rock, jointed rock, porous jointed rock, and fault zones. The mass properties of each will also be affected by depth and by matrix properties such as uniaxial compressive strength and porosity.

It has been confirmed from comparison with data from carefully documented block tests performed in the USA, that the parameters Q, Vp, M and L are inter-related, and that the inclusion of the Lugeon value in this inter-relation is justified, if care is taken to eliminate irrelevant non-deforming, channel flow cases, and to eliminate cases where clay sealing of the joints is occurring. Depth or stress level, also plays an important role in these mutual inter-relationships.

9.10 9.7 Extensive work in marl formations in Switzerland, indicated quite strong relations between selected seismic parameters and transmissivity measurements in five deep boreholes at Wellenberg, a potential nuclear waste repository site. Good correlations with transmissivity were obtained with Vp, Vs, Vp/Vs, dynamic shear ( ) and E-moduli, and dynamic Poisson’s ratio. The borehole depths ranged from about 400 m to 1800 m, and included faulted and brecciated rock. The measurements

Using an analogue material for heavily jointed rock, namely coal, one can see great sensitivity between velocity, stress level and permeability, which will also be present in jointed rock masses at large scale, when in situ effective stress states are altered by large scale pumping or injection experiments. Extensive data sets for numerous coal samples show the three key behaviour modes: permeability reduction with increased stress, permeability reduction with increased velocity, and velocity increase with increased stress. Greatest changes in Vp and permeability occur at the lowest stress levels and at the lowest velocities,

Conclusions

just as found in rock masses, due to the greater sensitivity to acoustic coupling across the cleats in the coal.

9.11 Researchers working at nuclear waste related rock laboratories such as Stripa, Äspö, and Grimsel have utilised seismic and radar tomography to characterise fractured zones and fault zones. Their studies have generally helped to explain why these relatively small volumes of fractured or heavily jointed rock are responsible for such large percentages of the total flow of water. Radar attenuation difference tomograms have been found more reliable in locating brine in tracer tests, than slowness tomograms.

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9.14 Dam foundation damage in the form of shearing on foliation planes, with resultant P-wave velocities as low as 0.5 km/s, was a starting point for systematic cement grouting, that saw Vp locally increased to between 2 and 6 km/s. The remaining low velocities of only 2 to 3 km/s correlated with residual permeability, which was eliminated with further grouting, and consequently increased velocities. A strong velocity-depth effect was noted, related both to rock quality improvement at depth, and to a post-stressing effect from the increasingly confined grout at greater depth. New rounds of grouting at old dams has also demonstrated increased Vp and reduced permeability. Largest grout take correspond to the locations where the largest increases in Vp are registered, following the grouting.

9.12 Radar and seismic signals are sensitive to different physical parameters (electro-magnetic wave conductivity, and mechanical stiffness respectively). The respective tomograms therefore highlight different features of the rock mass. Radar may delineate permeable zones caused by pore space or by joint apertures, in slightly different locations to the low seismic velocity zones associated with the clay-filled sections. The one will usually lie parallel to the other, since higher permeability may be associated with the heavily jointed zones that are often found in the walls of faults. 9.13 Low resistivity generally correlates with zones of increased water content and frequently with higher permeability. At a site in South Korea, a series of boreholes in weathered granites were Q-logged and later compared with resistivity tomograms in a ‘blind’ test. Sections of the core with increased joint frequency (low RQD, high Jn) did not always correlate with low resistivity and vice versa. The two parameters that did show a consistent correlation with low resistivity were low values of Jw estimated from iron staining or apparent aperture, and the high values of Ja due to sand or silt fillings, and due to clay-fillings. The latter gives ‘anomalously’ low resistivity due to the ionic effects of the clay. Water content and permeability are clearly lower in such discontinuities than in those that are sand or silt filled. This represents a potential source of error in judging the meaning of low resistivity zones.

9.15 It was noted in the 1970’s, in the 220 m high Mratinje dam foundation, that effective consolidation grouting could be performed when Vp was in the range 2.5 to 3.5 km/s. According to the Q-Vp-L correlations, this may correspond to Q
0.1 to 1.0 and 10 to 1.0 Lugeon. Velocities above 4.0 km/s (implying Q
3 and K
0.3 Lugeon) could not be improved upon by the grouting done at that time. Such results emphasise the reasons for combined use of high injection pressures of 5 to 10 MPa, and use of micro or ultrafine cements and microsilica, in today’s pre-grouting ahead of tunnels. Systematic pre-injection where average Lugeon values are as low as 0.1 (implying VP of 4.5 km/s), may not be successful without resort to high pressure and/or use of the finest cement types.

9.16 A general, approximate relationship between Lugeon value, Q-value, and measured velocity, has been compared with case records showing reduced Lugeon values and monitored velocity increases, as a result of grouting. These changes also represent potential physical effects of grouting on individual Q-parameters. Conservative assumptions of individually improved Q-parameters, like increased effective RQD, reduced number of effective joint sets, and successful grouting of the least favourable joint set, combine to suggest significantly improved

576

Conclusions

effective Q-values. Reduced tunnel deformation, reduced support needs, increased modulus of deformation, and increased seismic velocity are each implied, and seem to be supported by the experience of trouble-free tunnel advance following effective, high pressure pre-grouting.

PART II Chapter 10

Seismic quality Q and attenuation at many scales

10.1 Attenuation can be simply defined as the loss of energy per cycle divided by the maximum energy per cycle in the same rock volume. The wave amplitude versus frequency diagram indicates that frequency determines the maximum wave amplitude. The inverse of attenuation, the seismic quality Q, shows high values when there is little attenuation, and low values when rock conditions and near-surface location causes strong attenuation. The standard definition: E/E 2/Q suggests a minimum theoretical value of seismic Q of about 6, but lower values are reported, including possibly erroneous negative values. Several methods can be used to estimate seismic Q, which can have the forms Q p and Q s when derived from P-wave or S-wave spectral analysis, or Q c when derived from the tail of an earthquake seismogram, termed the coda, to sample the deep hypocentral region.

10.2 Knopoff’s paper ‘Q’ from 1964 with long lists of seismic Q values for solids like steel, glass, lead and celluloid (5000, 490, 36 and 7), suggest that relative stiffness may be involved in some way. It was originally thought that seismic Q was independent of frequency. However, rock with microcracks, joints or fractures, and with different fluid saturation levels, is now known to cause frequencydependent attenuation. Attenuation losses occur due to wave scattering from heterogeneities like joints, faults and rock boundaries, and due to intrinsic losses such as matrix anelasticity, friction at grain boundaries, across microcracks and across joints and fractures, related heat loss, fluid ‘squirt’ from fractures to microcracks to pores, and gas pocket squeezing when partly saturated. The viscous fluid related losses are particularly dependent on frequency due

to the relaxed or unrelaxed state caused by low or high frequency.

10.3 The short period of each wave cycle, and the relatively low levels of dynamic stress, are generally assumed to cause sub-micron size reversible micro deformations and flows. There are those who have denied the early assumption of friction as an intrinsic attenuation mechanism in the earth, but this supposition was partly based on dynamic sub micro-strain work with intact bars of dynamically excited rock. Frictional losses in situ, due to the presence of joints and fractures, plus their contribution to losses by scattering, are now widely cited, and by various authors, when working outside the common intact-medium laboratory limits. Important here is the fact that when the effect of single joints or aligned fractures are inverted from seismic data, the respective contributions of the dynamic stiffnesses of the joints to the wave amplitude and to shear-wave anisotropy, are found to have recognisable magnitudes and the same units (Pa/m) as when working with pseudo-static loading tests. The latter obviously mobilize friction due to their contribution to frictional strength.

10.4 Review of a large body of laboratory data for seismic Q has indicated a close approximation to the pseudostatic Young’s modulus (Estatic) and it’s increase with confining stress and sample stiffness. This was noted when substituting a non-linear seismic Q scale next to numerous sets of experimental data that showed only a linear 1/Q attenuation scale. Laboratory studies frequently show seismic Q increasing from about 10–20 to about 50–100, as confining pressure is increased from near zero to 10, 20, 40, or 70 MPa . Seismic Q magnitudes have great similarity to the variation of Estatic with confining pressure, if seismic Q is expressed as if it were GPa.

10.5 Intact rock samples loaded to failure show consistently increasing seismic Q when measured in the loading direction, as does Estatic, and the same samples show reducing values of seismic Q when measured in the perpendicular

Conclusions

(Poisson expansion) direction. Ultrasonic 0.1 to 1 MHz seismic Q values estimated during normal-stress closure tests on jointed samples, show Qp increasing from about 5 to 80, as normal stress is raised from about 3 to 70 MPa. At another extreme, cracking caused by repeated freeze-thaw cycles in limestone, have demonstrated Qseis steadily declining with increased cracking from about 20–25 down to 10–12, with corresponding reductions in P-wave velocity.

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10.8 With clay and weak rock at one extreme, the deformation modulus range can extend down to 0.1 GPa, representing a strongly absorbing inelastic matrix with UCS  1 MPa, plus the near-surface attenuating effect of clay-filled discontinuities. At the other extreme, with high matrix strength UCS  200 MPa, a depth up to 1 km and negligible jointing, Emass may reach 150 GPa, representing very low attenuation.

10.6 In situ seismic interpretations of seismic Q have revealed a certain tendency for higher seismic Q when the rock mass quality Q-value was also expected to be higher. These commonly used quality parameters are differentiated as respectively Qseis and Qrock. The widely used Qrock value, varies from about 1 to 1000 for heavily jointed to massive almost joint free rock masses. It is composed of three ratios. The first ratio is RQD (% of core pieces 100 mm length) divided by the number of joint sets Jn. The second ratio Jr/Ja describes roughness and alteration, and gives the friction coefficient, which includes the effect of clay-filling. Finally the estimated water pressure (or tunnel inflow) and the stress/strength ratio are evaluated. Qrock RQD/Jn  Jr/Ja  Jw/SRF. The maximum range of Qrock is from 0.001 for fault zones to 1000 for massive joint-free rock masses. Qrock provides quick estimates of seismic Vp, deformation modulus and permeability, and also indicates tunnel support needs in rock engineering projects.

10.7 The first pair of Qrock parameters RQD/Jn, representing ‘relative block size’, have a numerical range of 200 to 0.5. Even this has a certain similarity to the range of Qseis for respectively joint-free to heavily-jointed rock masses. More important is the likeness of the rock mass (pseudostatic) deformation modulus to Qseis, because Emass is readily estimated from Qrock. The great majority of rock masses, from the surface to 1 km depth, from heavily jointed to virtually joint-free rock, have deformation moduli in the approximate range 1 to 150 GPa, as derived from in situ testing and from back-analysis of deep tunnels and shafts. This range closely resembles the typical ranges of in situ Qseis seen in numerous shallow 0 to 2 km deep seismic data.

10.9 In sedimentary, finely layered rock sequences, greater sophistication in broad-band recording has demonstrated a more complex Qseis-deformability response than the above, with seismic Qp indicating that different values are obtained from ultrasonic 500–900 kHz testing of core (mean 27.0), sonic 8–24 kHz testing in boreholes (mean 10.4), cross-hole 200–2300 Hz testing (mean 15.7) to VSP 30–280 Hz testing from surface to borehole (mean 31.3). The rock mass was a finely layered saturated sequence of limestones, sandstones, siltstones and mudstones. The overall range of Qp from the different frequencies and depths was approximately 5 to 40. This remains in a potentially familiar range, if expressed in rock mechanics deformation modulus units of GPa.

10.10 Coda waves from the tail of seismograms, typically in the 20 to 200 seconds time window, after the arrival of P, S and surface waves, have traditionally been used to analyse the seismic Q signatures of both local and distant earthquakes. A large volume of rock surrounding the earthquake source is believed to be sampled by the coda, with the possibility to register changing rock properties or migrating source zones, due to the accumulation or dissipation of stress and resulting strains and possible fluid movements. Coda Qc is frequency dependant, with low frequency 1 Hz content assumed primarily composed of surface waves scattered from shallow heterogeneities, while coda waves at 20 Hz are believed to be from backscattered body waves from deeper heterogeneities in the high Qseis lithosphere. Thus many surface recorded data sets show Qseis lower than 100 at frequencies 2 Hz, while at 10 Hz, Qseis is often as high as 1000 due to the

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Conclusions

combined effect of deeper crustal stress levels, and a presumed more massive rock mass.

10.11 The late coda is assumed to contain a variety of take-off angles from the source. The frequency dependence is presented in the form Qc  Qo f n, with component n often increasing from pre- to post-event values. Component n may be just below to close to 1.0. A greater density of scatterers after a seismic event has been suggested as the reason for greater frequency dependence after a major event, which also suggests that frictional and partial saturation losses will be involved when new discontinuity surfaces are being developed, or extended.

10.12 Temporal variations of coda Qc have been reported in the periods before and following significant earthquakes. From 30% to 300% reduction of coda Q prior to six M 6.0 to 8.0 earthquakes have been reported, with an increase in coda Q in only one case, and the possibility of no obvious relation between coda Qc and a single major earthquake. Temporal variations have more recently been interpreted as due to migrating hypocentres, with an example Qc reduction from 200 to 100 interpreted as a migration during the early period of activity, to after the activity. In rock mechanics terms, this could approximate to changing from a higher modulus, higher stressed zone, to one with lower modulus and lower stress, after the event.

10.13 At the M 7.2 Hyogoken Nanbu earthquake near Kobe, seismic Q c was shown to have reduced following the earthquake. At respective frequencies of 1.5 and 2.0 Hz, Qc reduced from 81 to 68, and from 91 to 78, perhaps representing seismic sampling at increasing depth with higher frequency. At respective frequencies of 3.0 and 4.0 Hz Qc reduced from 132 to 107 and from 186 to 162. All the above resemble feasible deformation modulus trends, but obviously progressing to depths beyond existing Emass data.

10.14 The more recent possibility to record seismic events using down-hole seismometers, to depths of 100’s of meters and even to 2 and 3 km, has made it possible at some localities, notably near the San Andreas Fault, to avoid contamination by seismic and man-made noise, and to avoid much of the ‘site effect’ and it’s unwanted influence on recordings. Amplification in the low velocity near surface, with increased scattering and intrinsic losses, can have had a strong effect on all surface recordings. Attenuation at shallow depths beneath the surface layers, appears to be little influenced by rock type, with similar low values of Qp and Qs in the first 1 to 2 km down wells in widely different rock types like tertiary sediments and crystalline basement. Perhaps each of these dissimilar rocks are nevertheless stiff enough to have a partially common tectonic imprint of jointing and faulting from the same neighbouring major fault.

10.15 Qp values of 20, 30 and 55 from analysis of depth intervals 0–300 m, 300–940 m, and 570–940 m, and Qp increasing to 110–170 from 1 to 3 km depth, are also following the likely pattern of deformation moduli, when Q p values are expressed as if GPa. The actual addition of scattering and intrinsic losses are of course not distinguished in such a simple modulus model, but since the modulus estimate actually includes block size, inter-block friction and effective stress-to-strength ratio, it is in some way sampling important causes and components of both classes of attenuation. Reduced fracture density with depth, reduced friction losses on increasingly stressed fractures, and scattering from a reduced number of fractures, are reported reasons for the increasing Qseis values with depth. These are all recipies for increased deformation modulus too, and a common experience in deep, as opposed to shallow tunnels.

10.16 For cross-continent studies of seismic coda, the so-called Lg phase common on regional short-period seismograms is often used. It is followed by the main coda, which can also be used for determining the magnitude of regional events. The Lg coda at 1 Hz is commonly referred to as

Conclusions

Qo, and has been used to describe deep crustal attenuation across continents and in component plates, orogenic belts and major sedimentary basins. Comparing South and North America on this scale, one sees lower Qo in the Andean Belt (250–450), and in the Basin and Range province west of the Rocky Mountains (250–300). By comparison, there are broad regions of very high Qo spanning the central Brazilian Shield and Amazonian Basins (700–1100), and in the eastern region in the USA below the Great Lakes. 10.17 Higher values of Qo reportedly reflect the length of time since the last major tectonic activity. Low Qo regions are typical of seismically active regions with higher upper mantle temperatures, or the presence of deep hydrothermal fluids, and variable amounts of fluids in major faults. Younger sediments cause local reductions of Qo due to their contained fluids, while older sedimentary rocks which have lost fluid, are less attenuating. A shallow sediment model for explaining shallow and lateral variation of attenuation shows Qseis values of 30, 50, 75 and 100 for sandstones and shales from 0–100 m, 100–300 m, 300–600 m and 600 m. Units of GPa are again suggested in broad terms. 10.18 Seismic Q has become increasingly important in hydrocarbon exploration due to the improved sensitivity to degree of saturation of the ratio Qs/Qp compared to the velocity ratio Vp/Vs. The presence of low seismic Q in petroleum reservoirs can reflect the presence of over-pressure, of fracturing, and oil. Values of seismic Q as low as 10 to 40 at more than 4 km depth are good indications of favourable properties, likewise are pay-zones with overpressured gas giving seismic Q as low as 10 to 40, when the remainder of the sequence shows seismic Q between about 50 and 130. 10.19 In reservoirs where cross-well tomography is performed, there is a possibility of improved definition of the structures, due to the high frequency and multiple ray-path coverage. Transversely isotropic ‘layer-cake’ sedimentary

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inter-bedding is found to be quite attenuating, with good differentiation between shale, limestone and clay. A major, dipping fault zone in a North Sea reservoir, between 1 km and 2 km depth, was interpreted from down-going Pwaves as having a seismic Qp value as low as 45. Analytical modelling suggested a strong inequality between the high dynamic shear compliance, and the more conventional lower normal compliance. Low pseudo-static shear stiffness for fault-scale structures is also a necessary input to numerical distinct element models, where realistic subsidence modelling is to match steep subsidence bowls, in situations where continuum modelling fails to match such measurements.

10.20 In Chapter 13, there are numerous further sets of seismic Q data from laboratory-scale testing, in which the velocity and attenuation data are given side-by-side. Tests at reservoir confining stress levels and with numerous fluids (brine, gas, oil) will also be found. The rock physics data also extends into velocity and attenuation testing of the effects of bedding, foliation and induced fracturing, and the anisotropy caused by these features. In Chapter 15, the treatment of poro-elastic modelling also addresses the dispersive and anisotropic nature of seismic Q, as caused by the coupled dynamic behaviour of hydraulically connected equant pores, microcracks and aligned sets of fractures of various sizes

Chapter 11

Velocity structure of the earth’s crust

11.1 The uppermost 5 km of the crust shows a rapid increase in deformation modulus and density, as pore space and joints are closed. However, the thermal expansion partly balances the increase in seismic velocity, and P-wave velocities above about 6.5 km/s do not appear to be common here. The crust usually varies from 20 to 60 km in thickness beneath continents, while the oceanic crust is much thinner, and is usually about 6 to 7 km thick, beneath an average water depth of 4.5 km. The typical crustal P-wave velocity range is 6.0 to 6.8 km/s. In the upper 5 km, and excluding sedimentary rock with Vp  5 km/s, the most typical range of velocity is 6.0 to 6.2 km/s.

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Conclusions

11.2 An almost linear velocity-depth gradient between 5 and 25 km for the average crust shows a gradient of about 0.6/20  0.03 s1, while the gradient between 5 and 10 km is approximately 0.5/5  0.1 s1. Velocity-depth gradients are more than an order of magnitude steeper than this in the upper kilometre, and much steeper again in the upper 25–100 m. Gradients are even more pronounced in the upper 25 m of weathering-effected rock mass. The reduced gradient at great depth is due to the expansion effect caused by increased temperature.

on a scale larger than the laboratory samples, also giving high permeability throughout the drilled section.

11.6 The P-wave velocity of the sub-ocean crust at and near ridge crests exhibit an increase in velocity with age. Numerous results from the Atlantic and Pacific midocean ridge studies show an obvious link between Vp and age, with an increase of Vp of 2–3 km/s, in the first 40 million years. Deeper older layers do not show systematic increase in velocity.

11.3 Continental-scale velocity-depth profiles show strong visual resemblance to near-surface refraction seismic profiles to 50 m depth in place of 50 km depth. A uniform subtraction of about 2 km/s velocity, and a scale reduction of 1:1000 gives an almost indistinguishable result from the laterally-varying and depth-varying shallow refraction seismic obtained at a rock engineering site.

11.4 For many years, sub-oceanic marine seismic refraction profiles were interpreted as a small number of layers (Layer 2 to 2 km, Layer 3 to 7 km), separated by planar interfaces, with a constant velocity assumption for each layer. Homogeneous layering assumptions from the 1960s were first replaced by much finer layering (2A, 2B, 2C and 3A and 3B), and then in the mid-1970s by continuous gradients in velocity. The first geophysical downhole sonic logging data for oceanic crustal material was near a portion of the mid-Atlantic ridge in a leg of the Deep Sea Drilling Project. Velocities were typically from 1.5 to 4.8 km/s in the upper 200 m of oceanic Layer 2A. Interpreted porosities of 13 to 41% were unexpectedly high.

11.5 The reasons for high porosities were interpreted as being due to a combination of sediments, rubble, and solid basalt in contrast to the compact nature of basalt samples used in laboratory tests, which often showed Vp between 5.5 and 6 km/s and porosities from only about 2 to 8%. Open fractures and voids were assumed to exist

11.7 Early laboratory testing of oceanic basement rocks from deep drilling in the mid-Atlantic ridge highlighted the discrepancy between laboratory seismic properties and in situ, bulk velocities obtained from seismic refraction. Confining pressures of 20, 50, and even 200 MPa were used in early on-board velocity measurements. Laboratory velocities of 5.5 to 6.5 km/s were typically obtained with 50 MPa confining pressure. The comparable, shallow depth refraction-seismic inferred velocity-depth profiles showed only 2.5 to 3.5 km/s in situ velocities, an apparent discrepancy of about 3 km/s relative to the intact rock, but in fact, some of this difference was due to the excessively high confining pressures applied to the intact samples.

11.8 It was subsequently realised that it must be the rapidly increasing (from zero) effective stresses, not the assumed external ocean-depth loads, that were acting on the shallow sub-ocean crust, that was causing the rapid increase in velocity with depth. In other words, the velocity gradients were similar to what is found at the earth’s surface, with rock and (effective) fluid loads both increasing from zero. The theory of effective stress was apparently late in being adopted in this hostile sub-ocean environment. 11.9 Increasing effective stress from the ocean floor was responsible for about 4 s1 velocity-depth gradients, together

Conclusions

with presumed 4 to 5% per 100 m porosity reduction, as seen in the first 200 to 300 m of sub-sea layer 2A. The differences between in situ velocity measurements in the shallow oceanic crust and the higher matrix velocities measured at suitable (low) effective stress levels, was not only caused by moderate changes to the matrix porosity, but also by low aspect ratio jointing and fracturing, which was more stress-sensitive.

11.10 Very high velocity gradients, similar to the above, are typically experienced at the earth’s surface because the rock quality Q-value, as well as the effective stress, are both increasing rapidly with depth. We may have a near-surface Q  0.1 followed rapidly by Q  1 and then Q  10, suggesting nominal ‘near-surface’ theoretical increases in Vp from 2.5 to 3.5 to 4.5 km/s, with the additional effect of increasing depth and therefore increasing effective stress. This dual effect requires ‘curve jumping’ in the Q-Vp-depth relation.

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interspersed by a majority of permeable and therefore low effective-stress-loaded permeable blocks. 11.13 The Vp-Q-value-porosity-depth model uses a plotting format that can readily be compared with the oceanic crust fracture zone data of Layer 2A and 2B. Strong similarity with oceanic data is seen, probably because the rock quality Q-value specifically represents the ‘soft porosity’ or jointing, and models the effect on velocity of gradual joint closure with depth. The very steep Vp-depth gradients typically seen close to the ocean floor, in the first few hundreds of meters of the new crust, can be analysed with this near-surface based empirical method, which was developed from near-surface civil engineering projects. ‘Curve-jumping’ is needed to explain the supposedly ‘anomalously high’ gradients through Layers 2A and 2B. These can be modelled by assuming increased Q-values for deeper, older material. 11.14

11.11 A direct measurement of Upper Oceanic Crust P-wave attenuation was described in 1990, using seafloor hydrophones and large explosive sources. The site was on 0.4 m.y. old crust, and had a seafloor velocity of 2.7 km/s, which increased uniformly to 5.6 km/s at 680 m depth. Gradients as high as 4.6 s1 near the surface and 4.1 s1 at greater depth were estimated. Values of seismic Qp varied from 4 to 275, but mostly clustered between about 10 and 20 in the upper 100 m, similar again to expected deformation moduli in GPa.

11.12 A consistent increase of Qp with depth was not found, but several sets of data for 1/Qp did show a ‘stepped’ trend of 1/Qp reducing with depth in the first 500 m. Values of Qp were mostly from about 8 to 50 in this depth range. The sudden steps up, and down from, very high Qp values like 200–300, even negative 1/Qp steps, leads one to question whether the early ship-board triaxial test routines had an element of (local) correctness. Some volumes of intact basalt could perhaps be subject to high 30 MPa rock-plus-water confinement loads,

East Pacific rise studies were made by many of the researchers known for their mid-Atlantic ridge studies. A linear velocity-depth gradient in the upper 500 to 800 m of young (0 to 4 m.y.) oceanic crust on the flanks of the East Pacific Rise was initially assumed, and an average gradient of between 3.0 and 3.5 s1 for the upper 0.5 to 0.8 km of oceanic crust was estimated, with seabed velocities ranging from as little as 1.9 to 2.7 km/s. The evidence of very low velocities in the upper-most oceanic crust was consistent with visual and photographic evidence from submersibles, of pervasive fracturing in midocean ridge crustal regions, where the basalt layer was exposed. Low velocities were also consistent with drilling and logging results that showed high porosity. 11.15 The problems posed by zero-age oceanic crust with Vp  2 km/s, compared to about 6 km/s for intact basalt continued to provide challenges for theoreticians and practitioners working on the origin, formation and structure of mid-oceanic crust. Low aspect ratio cracks, and their reduced frequency of occurrence and reduction in aperture with depth, and probable sealing with hydrothermal minerals in the case of older oceanic crust, were some

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Conclusions

of the variables confronting those researching the variable structure of mid-ocean crusts. It was theorised that young 120 ka material with Vp  2.5 km/s, must have a porosity of between 24 and 34%. Slower Vp  2.2 km/s zero-age crust was theorised to have a porosity of between 26 and 43%. 11.16 At the beginning of the 1980s, a sub-ocean Deep Sea Drilling Project borehole in the Costa Rica Ridge area, made it possible to correlate core, usually of low % recovery, with downhole sonic logs, borehole televiewer logs, and permeability test results. This was first performed to a depth of 1 km, through layers 2A, 2B and 2C. In the 0–100 m, 100–650 m and 650–1000 m depth zones, Pwave velocities were a ‘familiar’ 3.7, 4.8 and 5.6 km/s, and permeabilities were likewise a ‘familiar’ 106–107, 108–109 and 109–1010 m/s. Based on vertical borehole logging, which would be biased against vertical structure, the upper 50 metres was found to contain numerous horizontal to sub-horizontal fractures, thick basalt flow units, and thin interbeds of pillow structures. 11.17 Large scale three-dimensional tomography was performed on the East Pacific Rise sub-ocean crust at the end of the 80’s, at the location of a fast spreading ridge. This was characterised by a sharp upper-crustal to mid-crustal velocity inversion some 1.5 to 2 km below the seafloor. This was presumed to be the roof of an axial magma lense, with an assumed few percent of melt. Contours of seismic Q at 4 km depth, showed values of Qseis of 25 and 33 nearest the ‘magma’, and values of 50 and 100 at 2 to 3 km off-ridge distances, in older crust. Values of Qseis as low as 8 and 10 have been measured at the Costa Rica Ridge area, caused by local faulting or similar features at 1⁄2 and 1 km depth in the much referred Hole 504B. 11.18 Inversions for individual receivers showed that seismic Q increased from average values of 40–50 in the upper 1 km, to at least 500–1000 at depth greater than 2 to 3 km. One may speculate that this abrupt increase could be due to an undrained increment of effective vertical stress of about 30 MPa representing the ocean load, since

such very high seismic Q values appear here at ‘shallow’ (rock) depth compared to generally greater rock depths on-land. With a thin, warm sub-ocean crust, permeability may be compromised at relatively shallower depths than under tectonically deformed continental crust.

11.19 Age effect reviews for both mid-Atlantic Ridge and Pacific Rise data show that most of the age-dependent increase in seismic velocity occurs ‘rapidly’ with velocities nearly doubling in less than 10 million years. Layer 2A appears to persist as a low velocity capping of the ocean crust, even when more than 15 m.y. old. The trend for increased velocities as age increases is clearly shown by the statistics. A velocity plateau, averaging about 4.3 km/s is indicated, beyond about 7 m.y. There is a clear link between hydrothermal alteration and seismic velocity increase, due to deposition of minerals first in the thinnest cracks and joints. Hydrothermal void filling causes a simultaneous increase in velocity and reduction in hydraulic conductivity, therefore reducing heat flow to the ocean floor.

11.20 In regions with significant sediment cover, the previously open seawater convection cooling system is hindered, and temperatures rise, thereby accelerating the formation of secondary minerals and porosity sealing. The on-axis, zero age upper crustal permeability has been deduced to be about 6  105 m/s, decreasing to about 7  107 m/s within 6 m.y. Seismic velocities for crust of the same age are about 2.2 km/s and 4.0 km/s. Permeability may reduce to about 107 m/s or less, by the time the crust is old enough to have reached the approx. 4.3 km/s ‘plateau’.

11.21 Parallels to the hydrothermal mineral filling of fractures, and increased velocities may be gleaned from civil engineering, where the sealing of jointed rock by pre-grouting with fine-grained micro-cements ahead of tunnels, or the use of industrial, coarser grain size cements in more permeable dam foundations, are common ways of both sealing and improving rock mass properties. Rotations and magnitude reductions of the three principal permeability

Conclusions

tensors, when conducting multiple-borehole 3D hydrotomography before and after grouting have been documented.

11.22 These tensor or principal value rotations are interpreted as due to successive sealing of the most permeable and least stressed joint sets. This process can also be interpreted by small changes in five or six of the rock quality Q-value parameters (ratings in Appendix A), which may cause some dramatic potential improvements in the rock mass properties such as increased modulus of deformation, seismic velocity, and frictional and cohesive strength. There is a degree of correspondence to sub-ocean velocity increase, and their expected geomechanical effects.

Chapter 12

Rock stress, pore pressure, borehole stability and sonic logging

12.1 Hydrocarbon-bearing rocks rely on pore-space and permeability for the possibility of having recoverable reserves that can be produced at a well. The necessary migration of the hydrocarbons from source rocks into potential entrapment structures, without escape to the atmosphere, adds to the adverse statistics of hydrocarbon discoveries. Too close to the surface the sealing properties of shale, salt or clay-smear in faults, may have been compromised by lack of plasticity and too high permeability. Too deep, the pore space and permeability of the reservoir may be compromised, giving a reduced reserve and the need for permeability enhancement and gradient enhancement, or a decision for non-development.

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pore pressure for conversion of the three principal stresses to effective stresses. The appropriate selection of wellbore ‘temporary support’ in the form of mud pressure, using variable mud weight, determines the state of the borehole wall in the different lithologies, prior to setting and cementing the casing.

12.3 Due to various opinions about an alteration zone around deeper wells, there is now widespread acceptance of the need for logging while drilling (LWD) with monopole and dipole tools, to obtain ‘early’ velocity responses, which may differ significantly from subsequent wireline logging. The differences are probably due to stress-fracturing, increased permeability, and consequently accelerated mud-filtrate invasion. A near-wellbore, tangentially-distributed log-spiral-type discontinuum, in case of an insufficiently mud-weight supported weaker formation, may need to be considered when interpreting the two sets of seismic data.

12.4 It is important to consider the components and modifiers of the most fundamental of reservoir parameters, namely the effective stress magnitude. The rock stress and its variations with direction, depth and location, and the pore pressure and sometimes over-pressure which are influenced by compaction and also by fluid type, are the major boundary conditions. Their relative magnitudes affect both the laboratory test simulations, the drilling programme, the production planning, and the reservoir production and depletion, possibly for 80 years or more in a large reservoir.

12.5 12.2 Besides reservoir access for production testing, a drillhole is used for sonic logging and selected side-wall and regular core recovery, to better define the properties of the different lithologies, seals and reservoir rocks. Rock reacts to the drilling of boreholes with a complex interaction of rock stress and strength magnitudes, plus the anisotropies of each, and is affected by the necessary subtraction of

To prevent hydraulic fracturing by high mud-weights, which are needed where there is overpressure, casing will be set to protect the overlying units from fracturing. A change from a pressure-depth axis, to mud-weight-depth format is preferred by drillers, who speak of mud-weight in lb/gal, and try to steer this between the pore pressure gradient and the fracture-gradient. Resistivity, velocity, and density depth-trends will each suffer various degrees

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Conclusions

of deviation from the norm, when there is over-pressure that changes the effective stress.

12.6 The fluid pressure at a well is the sum of normal hydrostatic pressure, plus over-pressure, plus a buoyancy effect caused by the reduced density of any petroleum that is present. Since over-pressure and the presence of petroleum products both increase the pore pressure, the effective stress will also be reduced, which will have the effect of causing a reduction in velocity.

12.7 Over-pressure commonly occurs where low permeability layers such as shale prevent fluid from escaping as rapidly as pore space compacts. Excess pressure in relation to hydrostatic then builds up as newly deposited sediments cause squeezing of the trapped pore fluids, which could be water, oil or gas or two or three of these close together. Models for basin-evolution show that pore pressure effects are seismically visible when the effective pressure is typically less than about 15 MPa, A small % conversion of live oil to gas is sufficient to make the pore pressure equal to the confining pressure. The large changes of predicted velocity are caused by the fact that the dry rock moduli are strongly affected by low effective pressures.

12.8 Minimum rock stress estimation by mini-hydrofracing, if not possible in an open-hole situation, is done by seating the double-packers on either side of shaped-charge perforations of the casing. This is done in the reservoir intervals, and also in the cap-rock interval, to determine the minimum stress difference. Interbedded ‘brittle’ layers like sandstone, and ‘plastic’ layers like shale or salt, will usually exhibit different minimum principal stress levels. This may be an additional reason for oscillating sonic log records in such interbedded strata.

12.9 Shale and salt-rocks may have insufficient shear strength to tolerate a significant principal stress difference. The

minimum of the three principal rock stress magnitudes in the shale or salt will therefore often exceed the minimum stress in the reservoir sandstone by up to several MPa. This is desirable for hydrocarbon containment, and also for vertically limiting massive hydraulic fracture treatments. Rocks such as granite, limestones, stronger sandstones and stronger shales (which are thereby poor seals), tolerate differential stress much better than weaker shales and almost plastic salt rocks. 12.10 Shale or salt may, if encountered at sufficient depth during drilling, require the support of an active mud-weight to prevent creep or squeezing. The drillers choice of mudweight, or the setting of protective casing, becomes critical where support of the well is needed adjacent to a reservoir rock like sandstone or fractured limestone or chalk, which would tend to have a minimum rock stress less than that of these weaker, sealing ‘plastic’ layers. The reservoir horizons could potentially fracture, or have a permeable joint under lower normal stress than the mud-weight needed to keep the plastic materials from squeezing and jamming the drill-string. Invasion of mud or lost circulation, into any reservoir horizon is obviously very undesirable. 12.11 As one approaches the surface, inter-bedded rock types resembling reservoir sequences, show the reverse of the previously discussed differential stress intolerance, because the weaker rocks are no longer ‘over-stressed’. Furthermore, because of their lower deformation moduli, they attract lower stresses from a given horizontal stress field. Hydraulic fracturing tests therefore may give indications of low Ko ratios (h min/v) in the weaker materials like shale and siltstone, and higher values in sandstones and limestones. 12.12 This reversal of Ko trends at a certain depth (it was measured from 100–150 m depth, but might apply from 0 to 500 m), may have implications when comparing stressinduced velocity anisotropy and sonic log velocity ‘oscillation’ near-surface and at greater depth. This reversed behaviour also needs to be considered when evaluating the applicability of shallow borehole seismic testing to

Conclusions

reservoir holes perhaps an order of magnitude deeper, with corresponding reversed Ko behaviour. There may also be consequences for the relative magnitudes of attenuation, as both lower Ko and lower stress levels near the surface, will tend to enhance attenuation. Thus Qp and Qs values must be expected to be lower, and exhibit more anisotropy near-surface than at depth.

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temporary support costs by under-supporting, using for example a constant single layer of sprayed concrete, where two layers were actually needed locally. 12.16

The hydrocarbon reservoir exploration and production industry has long been aware that borehole deformation and failure modes are an important ‘complication’ concerning the interpretation of sonic-logging of wells. There are now acoustic dipole and monopole shearwave producing logging devices that can be used in a logging while drilling LWD mode, that acquire responses from more than one hundred wave forms, some tens of meters behind the drill-bit, in order to delineate formation fracturing response, and virgin conditions further from the walls of the wells, before additional ‘alteration’ has occurred from stress and/or mud-filtrate invasion, as often seen in subsequent wireline logging, when the drill-string is removed.

Due to the smaller size of wells and the use of mud for hole support, the recognition of the behavioural data that can be extracted from anisotropic stress effects on smallscale EDZ round wells, may possibly not be used in the petroleum industry, to the extent it can be used in tunnel engineering. Borehole ellipticity, a much-used historical indicator of the minimum horizontal stress axis, is the surface expression of effects behind the ellipticity. In tunnels it is easy to see the effects of structure-induced wedge release, or stress-fractured ‘lenses’ of rock. It is also possible to install multiple-position borehole extensometers (MPBX), in tunnels and in vertical shafts, to measure the anisotropic radial-distribution of deformation, thereby giving deformation moduli as a function of direction. Velocity variations and permeability variations as a function of position and radial depth around a tunnel or shaft, can also be determined, thereby relating these parameters to eventual stress anisotropy.

12.14

12.17

There are possibilities for local velocity (and seismic Q) enhancement due to tangential (and diametrically-opposite) stress increase in the case of competent rock like limestones, or low porosity sandstones. In the case of over-stressed, fractured (‘dog-eared’) sections of rock, and especially in the case of incompetent rocks like shales, reduction of velocity (and of seismic Q) will occur locally, due to the mini-EDZ (excavation disturbed zone) that form as a result of drilling and possible over-stressing.

There is a strong likelihood that mini-EDZ in the weaker, less well mud-supported zones, have reduced, radialdependent velocity, due to failure and deformation in the over-stressed zones. Stronger inter-beds could show an opposite trend due to tangential stress enhancement of the velocities. Mini-EDZ that might penetrate several diameters can be detected, and circumvented by deeper sensing, shear-wave based, dipole logging tools. The probable discontinuum caused by log-spiral shearing is often referred to only as ‘shale alteration’. Fabric and jointing and bedding planes, may also affect the progress rates for mud-filtrate invasion. The geomechanics of borehole deformation and over-stress, and its coupled MHT effect on permeability, mud-filtration, and LWD-to-wireline logging differences, can be quantified in approximate terms.

12.13

12.15 The mini-EDZ may mean the development of a log-spirally sheared discontinuum, based on physical and numerical modelling results, where the starting point was a continuum. Stress reduction in the radial direction, which may be azimuthally varying, will tend to locally reduce the velocity, and thereby also the seismic Q. It is impossible to support each lithology with the ideal mud-weight, so some suffer the consequences, just as occurs in weak zones in a tunnel where the contractor might be trying to reduce

12.19 Deeper penetration of mini-EDZ, representing ‘shale alteration’, may be the reason for a serious potential

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Conclusions

contrast in logging results, when comparing the 1–2 weeks later result of wireline logging, with the few hours delay represented by LWD, or logging while drilling. More recent shear-wave anisotropy based logging, is capable of imaging a volume of up to several borehole diameters away from the wall, therefore beyond the stress-related fracturing and mud-filtrate invasion or ‘shale alteration’, thereby giving presumed ‘virgin’ formation attributes as well.

followed by frictional mobilization at larger strain. In modified Mohr-Coulomb terms it is a case of ‘c then tan ’, not ‘c plus tan ’. Numerical models that are programmed, or manually-steered, to dissipate cohesion while mobilizing friction, are capable of matching physically observed behaviour. Non-linear fracture mechanics boundary-element based modelling seems to mirror reality extremely well, with log-spiral type fracture development that dissipates over-stress.

12.20

12.23

Variable azimuth drilling in test blocks under 3D stress states, gives failure modes that cannot be obtained when loading a test block with a pre-drilled hole. Deep log-spiral shear failure surfaces have been demonstrated in weak cemented-sand blocks, when the major principal stress was about eight to ten times higher than the uniaxial strength, with the minor and intermediate principal stresses of 60% or 80% of the maximum. This level of over-stress is easily reached in deep wells in relation to shale and salt rocks.

Different degrees of ‘log-spiral-type’ shear failure are demonstrated, depending on the ‘disturbance’ to the isotropic stress distributions, caused by different amounts of jointing or fissuring close to the hole. These geological features dissipate some of the highest, near-wall tangential stresses seen in elastic isotropic analyses. When modelling medium strong brittle rock, principal stresses of only about 35–40% of the uniaxial strengths are needed to start fracturing in the form of initial ‘dogearing’. A brittle sandstone of 50 MPa UCS would be acted on by an equivalent ratio of strength to stress beyond about 1200–1300 m depth, with standard density and pore pressure assumptions, considering a H max value no larger than the vertical effective stress. The existence of dog-earing may provide more information about formation properties than the simple registration of stress-induced ellipticity in a four-arm calliper log.

12.21 With extreme weakness, the failure mode may be nondilatant, and actually contracting-with-shear, or even flow, in the case of clay-rich materials. There are distinctive differences between stress-induced failure of hard dilatant brittle rocks, giving extensional splitting and subsequent crushing or comminution of the rock in the sharp ends of diametrically opposite ‘V-shaped’ corners. In the case of failure in intermediate strength and less dilatant rocks, the traditional ‘dog-earing’ takes on a different shape resembling localized log-spiral shear failure surfaces. Each of these modes can be demonstrated in physical simulations, and with suitable choice of numerical model, though not with conventional rock failure criteria.

12.22 The actual modes of physical behaviour experienced by boreholes and tunnels, are unlikely to be predictable when modelling with conventional Mohr-Coulomb type (c  tan ) shear strength criteria, because intact rock tends to fail first by loss of continuity at small strain, caused by loss of local tensile or cohesive strength,

12.24 Due to the influence of deformation of ‘soft’ as opposed to ‘hard’ porosity, a borehole for hydrocarbon exploration that penetrates variably jointed and faulted ground, will actually experience variable small amounts of deformation, due to different degrees of joint closure, joint opening, and joint shearing. There will also be the pseudo-elastic response, due to both loading (at the diametrically-opposite  max locations) and potential unloading (at the diametrically-opposite  min locations) of the matrix as well as the joints, the latter usually dissipating some of the theoretical (isotropic, elastic) peaks of maximum and minimum tangential stress. This process will occur even with a constant mud-weight, since the mud – unlike rock bolts in a tunnel – cannot prevent joint movements of unequal magnitude at different points around the opening, although the mud may help to make them very small.

Conclusions

12.25 When assessing the rock quality of the walls and arches of tunnels, the observed rock, which is the visible part of the tunnel-scale EDZ, is classified (using the Q-system: see Appendix A), in order to select appropriate rock reinforcement (grouted rock bolts) and tunnel support (sprayed, steel-fibre-reinforced concrete). The latter is the equivalent of the borehole mud pressure, and is badly needed in a complete load-bearing ring, in the rapidly deteriorating and deforming clay-bearing zones, in order to control deformation and prevent local tunnel collapse. Outside the tunnel EDZ, the rock mass would be characterized as a better quality rock mass.

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by a reduced elastic modulus in an annular zone around the borehole, particularly in soft formations such as shales and shaly sands. Entrapment of wave-fronts in the lower modulus damage zones results in ‘bi-compressional arrivals’, or second arrival compressional waves. The bicompressional arrival is a phantom arrival too fast to be a shear wave, and actually caused by trapping of the wavefront by the low-modulus damage zone.

12.29

If one performs both sonic logging and azimuthal dipole sonic logging in a well, the borehole mini-EDZ can be classified by the one tool, while the hydrocarbon-bearing or reservoir sealing formation away from the immediate influence of the hole, can be characterized by the other tool, and show higher velocity and higher seismic Q as well. It appears that this familiar rock mechanics EDZ logic is effectively being applied in modern well logging, with its multi-wave-form acquisition.

Orthogonal dipole transmitters, and the multiple receiver pairs, which are aligned in orthogonal directions, measure the components of slowness in any direction within planes perpendicular to the borehole. They use the principal of shear-wave splitting, and polarization, one of the most valuable of all seismic anisotropy properties for fracture and fracture-fluid investigations. The slow direction (as also with P-waves) is perpendicular to the fracturing – which could be microcracks, cracks, joints or faults – according to the scale of example considered. The rotated direction of the fastest shear waves becomes the fast-shear tool azimuth. Both the acoustic time anisotropy and the slowness anisotropy are sensitive to properties deeper within the formation than the superficial effects caused by drilling.

12.27

12.30

Dipole transmitter tools are designed to generate flexural waves. Flexural waves are shear waves that are polarized into fast and slow directions, and penetrate several hole-diameters into the formation, thereby revealing potential stress-induced ‘alteration’, and/or drilling mud-induced alteration. The need for these tools confirms many of the foregoing suspicions that what we have termed mini-EDZ, are indeed a source of concern in certain formations, and more importantly, that these ‘alteration zones’ can be detected and seismically classified. The shear-wave analysis can also be used when characterizing the formation beyond the damage zone.

The fact that shear wave anisotropy allows the investigation of a volume of the formation up to several diameters from the borehole axis, means that it can sense jointing, and stress-induced fracturing, that are missed by conventional logging tools. This means that it is particularly useful for registering the additional jointing and fracturing that tends to be present on either side of a fault.

12.26

12.28 The ‘altered zone’ around the borehole may continue to develop during the week or so that may separate the two types of logging. The later wireline log may be influenced

12.31 LWD with dipole shear-wave anisotropy analysis is available almost in real-time, some hours behind the drill-bit. It has proved very useful when applied to drilling of horizontal well sections, designed to intersect a maximum amount of structure. Simultaneously one can avoid the less favourable parallel to H max hole direction. Early warning is also given while drilling in formations with rapidly changing pore pressure. LWD

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is then an important aid in choosing appropriate mud pressures. The use of wireline dipole logging in vertical holes, and pipe-conveyed dipole tools for deviated and horizontal wells, has given reservoir geophysicists improved means of calibrating the responses of their rock physics based reservoir models, against these small-scale, but in situ measurements. 12.32 Synthetic seismograms often do not correlate with measured seismograms, when correlating seismic data with acoustic logs. Formation properties inferred from wireline logging measurements may not reflect the true properties, so a realistic description of the mud-filtrate invaded damage zone is important for processing and interpretation of the logs. A problem is caused by the invaded or ‘altered’ zone being deeper than that illuminated by the logging tool, meaning that the velocities will not reflect those of the formation, but of the damaged zone, therefore requiring corrections. 12.33 A standard approach is to correct the acoustic logs via a Biot-Gassmann fluid substitution, to free sonic logs from mud-filtrate invasion effects. It is assumed that the measured velocities are those of the invaded zone, saturated with mud filtrate. By displacing the saturation fluid theoretically, new velocities are obtained, and taken as the virgin formation velocities. Despite theoretical removal of the saturating fluid, one possibly should note from Chapter 15 the failure of the porous-medium based Biot-Gassmann method in the case of split shearwave data in fractured as opposed to unfractured porous formations. 12.34 Ultra high pressure and high temperature (HPHT) wells that are increasingly relevant with high petroleum prices have several unfavourable effects on well stability. One is that the rock skeleton may bear a proportionally greater load, as the effective stress parameter () becomes less than 1.0 (as per Terzaghi), when stress levels have caused reduced porosity and permeability. This higher effective stress causes slower drilling rates.

12.35 Mud cooling systems can be applied, which help to reduce the likelihood of compressive stress-induced failure, as matrix contraction reduces the maximum tangential stress concentration. On the adverse side, there is an increasing possibility of tensile failure and mud loss. Socalled wellbore ‘ballooning’ represents such mud loss, but some of the mud is returned by subsequent heating. If there is no risk of compressive stress failure, then high mud temperatures can be used to control the hydraulic fracturing gradient. Shale and salt rocks pose particular challenges in HPHT environments.

Chapter 13

Rock physics at laboratory scale

13.1 The major exploration-related goals of rock physics research have recently been summed up by King as: ‘to understand how lithology, porosity, confining stress and pore pressure, pore fluid type and saturation, anisotropy and degree of fracturing, temperature, and frequency influence the velocities and attenuation of compressional P- and S-waves in sedimentary rocks’. At the end of this list ‘and vice versa’ was added, emphasising the interactive and complex nature of the reality. The remaining challenges were summed up as ‘relationships between attenuation, anisotropy, fractures and fluid flow, and determining these relationships across the frequency spectrum of core, log and seismic measurements’.

13.2 It was recognized long ago that seismic velocities of rocks were strongly influenced by micro-cracks, and that seismic attributes representative of the intrinsic mineralogy and porosity, could only be obtained by applying pressure to the rocks. Much of the rock physics understanding of reservoir rock behaviour, of both matrix and joints or fractures, has therefore to be achieved at elevated pressure. The importance of elevated temperature is also well recognised, but is less frequently an experimental variable than it actually should be, especially if jointing is also sampled, as it should be in the case of fractured reservoirs.

Conclusions

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13.3

13.6

Age-depth relationships derived from well analysis in sandstone-shale units have a certain grouping of velocities with age, due to variations of porosity and the resulting densities. Hard porosity in the form of pores tends to decrease with age and depth, while soft porosity in the form of joints tends to increase with age due to tectonic influences, but reduces strongly with depth. Only the hard porosity has a significant effect on density. A relatively ordered density-Vp trend for chalk, limestone and dolomite is often seen, and reflects the simple mineralogy. Frequently widely scattered density-Vp data for sandstones is evidence of the variable mineralogy of ‘sandstones’, with 10–15% variation in density possible for the same velocity, particularly in the case of tight gas sandstones. In contrast to these variations, Vp-Vs trends are consistently uniform, as befits characterisation by seismic waves.

Theoretical modelling of porous rock behaviour has been used on many occasions for examining the numerous factors affecting seismic velocities. Theoretical formulations by Toksöz were used to represent the solid matrix, and the assumed spherical to oblate pores, using widely varying aspect ratios to match numerous laboratory data. Small aspect ratios, or flatter voids, caused the greatest reductions to elastic moduli and velocities. The properties of the saturating fluid (gas, oil or water) were found to produce greater effects on the compressional velocities than on the shear velocities. The P-wave velocities were predicted to be higher, and of course were measured as higher, when the rock was saturated with water, than when dry or gas-saturated.

13.4 An early compilation by Faust of well survey results from some 500 petroleum wells in the USA and Canada, included data from about 300 kilometres of well sections. The great majority of data was for mixed shale/sandstone/ shale sections. A non-systematic comparison of shale and sand (sandstone) velocities revealed an average discrepancy of only 350 ft/sec, or 106.7 m/s in velocity between these two, frequently inter-bedded units, the sandstone having the highest velocity by this small average margin. Remarkably close Vp versus Vs trends for water-saturated sandstones and shales, emphasise the remarkably similar seismic velocity signatures of these two ‘dissimilar’ lithologies, when in a compacted state. The necessity of using attenuation, and other techniques, for seismically distinguishing these two most essential reservoir ‘partners’ is clear.

13.5 A useful means of separating such formations is to plot impedance, or the product of velocity and density, versus Vp/Vs. Variation of porosity within such a diagram is a further means of distinguishing different formations, once they have been identified.

13.7 When such theoretical models are fitted to P- and S-wave velocities that have been measured at different pressures, they are found to require pore shapes ranging from spheres to very fine cracks (aspect ratios from 1 to 105) for sandstones, limestones and granites, both under dry and saturated states. As igneous rocks have low porosities, the pore shape has great influence on the elastic and seismic properties, and dry and water-saturated behaviours are often very different as a result. Compressional velocities are predicted and measured, as highest with brine saturation, and lowest with gas saturation. These differences decline with increasing effective pressure. Poisson’s ratios for gas saturated rocks are predicted to be lower than for those with brine saturation, and this difference persists to high pressures.

13.8 From extensive data sets and modelling we can summarize from Toksöz that Vp is likely to be lower: if low water saturation, if dry or gas saturated (in the case of flatter pores), if in the presence of some immiscible gas (in brine), if higher porosity, if over-pressured, if at shallow depth, if containing thin pores, following several cycles of freezing, if at room temperature, if at extremely high temperature. Vp is likely to be higher: with water saturation, when dry or gas saturated (in the case of rounder pores), when saturated with brine, when there is

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no immiscible gas, when of lower porosity, when underpressured, when at greater depth, when consisting of rounded pores, when frozen, when at low or moderately high temperature.

13.9 Water-flooding, and four dimensional seismic monitoring of its effects, relies on the strong dependence of velocity on temperature, and on the significant influence of the relative hydrocarbon and brine saturations. Both the matrix, but especially the joints, will also sense the reduced effective stress, caused by the injection pressure and by the matrix shrinkage caused by cooling.

13.10 Concerning the matrix behaviour in the case of oil sands, the greatest effect of temperature is seen when there is 100% oil saturation, with P-wave velocity reducing by as much as 40% (e.g. 3.4 to 2.0 km/s) from 20° to 150° C. Least and almost zero effect is seen when there is either 100% gas saturation or 100% brine saturation. As oil is removed from these sands, the velocities successively become independent of temperature, with roughly half the effect when 50% oil remains. In viscous tar sands velocity may reduce by more than 50% (e.g. 2.4 to 1.1 km/s) when steam flooding reduces viscosity due to a similar temperature rise.

13.11 At low temperature the higher viscosity means that the oil cannot flow easily, so the dynamic measurement is on the high-frequency, high velocity, unrelaxed side of the local-flow mechanism. As temperature increases, viscosity reduces, so fluid flows more easily, and velocity therefore decreases since measurement is on the relaxed side of the absorption/dispersion mechanism.

13.12 Ultrasonic measurement of the effect of clay content on the P-wave velocity of sandstones may show a 40% or

greater drop in velocity (e.g. 5 km/s to 3 km/s) as clay content rises to 30% or more in a simultaneously increasingly porous sandstone. The relative effects of clay content at frequencies of 10 Hz to 1 kHz (as used in seismic exploration) or frequencies of 10 to 20 kHz (as used in borehole logging), when imaging in situ sandstones, is less clear, due to potential effects of anisotropy. The complex nature of permeability, which depends on porosity, pore size distribution, inter-connectedness of the pores, and tortuosity, means that permeability may be severely compromised by increasing clay content. Variable clay content also typically occurs in bedding-parallel layers, making for strongly anisotropic permeabilities.

13.13 When relating rock physics laboratory data to the in situ reality of frequently inhomogeneous deposition cycles, the technique of ‘fining-up’, to benefit from the more uniform sedimentary environment and diagenetic nature of smaller deposition cycles, gives successively higher Vpn% correlation coefficients. Sorting data into common sediment-compaction and cementation-history categories, using stratigraphy and other matching techniques, also has advantages when establishing relevant relationships between permeability and porosity, and between velocity and permeability. The log of permeability may be linearly related to porosity (e.g. 30%: 1 darcy, 20%: 10 md, 10%: 0.1 md).

13.14 Relationships between velocity and permeability, can be developed more easily by making a more relevant match of porosity and permeability with common sediment compaction and cementation history. Without doing this, velocity and permeability may show poor correlation. Simple ‘classification’ terms can be used. RQI is known as the reservoir quality index, and is composed of permeability (k) in units of millidarcies, and () the fractional porosity. The void ratio (), the ratio of pore volume to solid volume, given by /(1  ), links RQI and FZI, which is known as the flow zone indicator. Rocks with FZI values within a narrow range are found to belong to one hydraulic unit and have similar flow properties. A semi-log plot of porosity versus log permeability tends to show similar FZI values plotting together with distinct log K-VP trends. The FZI

Conclusions

classification can be extended to seismic parameters, to obtain a stronger correlation between velocity and permeability.

13.15 A uniform or smooth variation of velocity with degree of saturation is strictly a function of an assumed or actual homogeneous distribution of saturation, which is possible with lithological uniformity. The more complex and common effects of mixed lithological units, may create a heterogeneous or patchy saturation distribution. This gives different signatures during imbibition and drainage. The drainage process creates a more heterogeneous distribution of saturation. Local full saturation of the crack-like regions of the pore space tend to stiffen these regions in relation to high frequency, but at low frequency these ‘patches’ can drain to the less saturated pore space. The pore fluid lying in thin, compliant pores can flow freely into the dry pore space, in a squirt-flow type of attenuation response. It does not therefore allow reinforcement of the compliant part of the rock at low frequencies, so velocities are low.

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13.18 The sensitive response of () close to the hydraulic fracturing limit may be the result of sealed, over-pressured and under-compacted beds. There may also be additional over-pressure due to increased oil-to-gas conversion at zero effective stress. Vs is (locally) zero as the rock mass is hydraulically fractured and load is born by the fluid. However Vp is not zero, therefore  approaches 0.5. 13.19 It is well documented that pseudo-static moduli of deformation can be significantly lower than the dynamic moduli predicted from P- and S-wave velocities. Knowledge of the non-linear elastic properties that are largely responsible for the differences between dynamic and static moduli is essential for optimal drilling, effective well completions and efficient reservoir management. The frequency of measurement is all important for the geophysical estimate obtained, since Eultrasonic  Elog  Elow freq.  Estatic. 13.20

13.16 At high frequencies, pressure equilibrium cannot occur because the pore fluid relaxation time is greater than the seismic wave period. Pore fluid in thin compliant pores is then effectively trapped, and it therefore reinforces the otherwise compliant pore spaces, resulting in higher apparent modulus and velocity.

13.17 Poisson’s ratios are anomalously high in cases of over-pressure, where effective stress can approach the fracturing (negative) side of the usual lithostatic and pore pressure gradients. The aspect ratio of the cracks and pores and the nature of the saturating fluid determine the magnitude of (). Rocks containing mainly stiff, equi-dimensional pores do not show major variations of () with effective stress. In saturated rocks the compliant pores become stiffened in relation to high frequency waves, so () changes less as effective stress increases. However, at low effective stress, when pore pressures are very high, the effective stress sensitivity is marked, and () increases.

The development of attenuation as a means of improved characterization of reservoir rocks is due to the dispersive, frequency-dependent nature of seismic Q, and the greater sensitivity of the ratio of Qs /Qp to fluid and partial saturation than Vp/Vs. The expected reduction in Vp by reduced brine saturation and increased gas saturation in sandstones is matched initially, by greater attenuation with Qp reducing from e.g. 30 to 10. At the far end of the saturation scale, when samples become ‘room dry’ or reach 100% saturation with nitrogen, the attenuation reduces sharply, and Qp may reach a value of 50. This is related to the eventual absence of squirt flow with increased dryness.

13.21 Ultrasonic (0.1 to 1.0 MHz) laboratory tests on dry and water- or brine- saturated Berea sandstone of 16% porosity, have been used on numerous occasions for investigating how velocity and attenuation vary with ‘differential’ pressure (confining minus pore pressure). The P-wave velocities of this sandstone, when dry and

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Conclusions

when brine-saturated, usually rise rapidly over the first 10 to 20 MPa, eventually reaching a plateau with little stress sensitivity. At high differential pressure such as 50 MPa, equivalent to reservoir conditions, there may be little difference between the dry and brine-saturated values of Vp. By comparison Qp and Qs rise more consistently, even up to high stress levels. They show less attenuation in the dry or methane saturated states, than in the case of brine saturation, where squirt losses can occur.

mechanisms. The saturated rocks always show much stronger attenuation (lower Qp ) than the dry samples. The effective stress level has greatest influence on attenuation when samples are brine-saturated and at the lowest levels of effective stress. The behavioural contrast of Qp compared to Vp, with the former’s greater sensitivity to effective stress level, and to frequency, confirms the importance of attenuation as an excellent diagnostic at reservoir stress levels.

13.22

13.25

Qs is often larger than Qp in the case of the dry and methane-saturated sandstone. In the case of brine saturation, there is a consistently wide separation of Qp and Qs (Qp  Qs). This represents an important means of tracking water-gas fronts during production. The increase of Qp from e.g. 10 to 20 at low effective stress, to values as high as 60 to 80 to 100 at effective pressures of 50 MPa bears a strong resemblance to deformation modulus increases. A lower range of increase seen with brine saturation, might be due to the weakening effect of brine.

Differentiation of Qp values, has also been suggested as a way of distinguishing gas and condensate from oil and water in sandstone reservoirs. In perfectly dry rocks, Qp is very high. In fully liquid saturated rocks Qp is at an intermediate level. In partially saturated rocks Qp is low. Magnitudes of Qp for sandstone reservoirs, based on well log (i.e. sonic frequencies), are usually in the following ranges: gas and gas-condensate bearing sandstone 5  Qp  30, oil bearing sandstones 8  Qp  100, water bearing sandstones 9  Qp  100. The low Qp values may be caused by low effective stress in the case of over-pressure (or by fracturing). These ranges are remarkably similar to laboratory ultrasonic data, when a range of effective stresses are applied.

13.23 Tests with higher porosity sandstones (range 20–25%) tested in dry or brine-saturated states, in triaxial compression, over an effective stress range from 2.5 and 40 MPa, using a range of frequencies (400 to 2000 kHz), show important additional trends when the effect of frequency is shown together with the effect of stress level. The greater sensitivity of Qp than Vp as effective stress levels rise is seen as before. However the effect of increasing frequency shows negative velocity dispersion for the dry samples, meaning velocity decreasing with increasing frequency, while in marked contrast, the attenuation increases (Qp reduces), as the third to fourth power of frequency. This is assumed to be evidence of scattering within the pore spaces between the grains.

13.24 Brine-saturated sandstones show slight, positive velocity dispersion at the lower confining pressures, while attenuation increases (Qp reduces), with only the first or second power of frequency. This change in attenuation-frequency dependence is taken as evidence of local fluid-flow loss

13.26 Classic Biot theory that accounts well for attenuation in clay-free sandstones, fails by an order of magnitude to account for the attenuation effect of clay content. Strong clay-related attenuation is assumed to be due to viscous interaction between the clay particles and the pore fluid. Permeabilities are also strongly dependent on clay-content. The measurement of attenuation of compressional waves in sandstones under confining pressures of 40 MPa at ultrasonic frequencies (0.5–1.5 MHz, shows that intra-pore clay content is important in causing attenuation, and in modifying the permeability. Qp may be as low as 10 with clay contents 10%, rising up to several hundred when clay content is 1%.

13.27 Systematic reduction of Qp from about 80–100 to about 10–20 is seen as the percentage of compliant minerals in

Conclusions

sandstones and siltstones increases from a few percent to nearly 80%. This is attributed to ‘clay squirt flow’. This mechanism may also be important at both seismic and sonic frequencies, in the case of larger scale geologic features such as inter-bedded permeable and impermeable layers.

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as low as 4 to 5, and 3 to 6, at near-surface sites, using seismic frequencies. There is potential for strong squirt flow attenuation with passage of low frequency seismic waves, in dual porosity systems such as jointed limestones. Smaller magnitudes of Qseis may be expected, due to the contrasting moduli at the different scales, with reduced differences at higher stress levels.

13.28 Different rock types such as siltstones, sandstones and limestones may also show a significant range of instantaneous sample deformation as a result of applying high confining pressures. Their deformation moduli are clearly different. Differences between rock types will be accentuated when bedding and jointing is also present, causing increased attenuation, and greater sensitivity to effective stress. This sensitivity may even apply to velocities, which tend to show much less sensitivity to confining pressure than seismic Q when samples are without jointing. 13.29 Dual porosity limestone specimens, with micro-pores and inter-particle macro-pores, show a weak trend for higher attenuation and lower seismic Q when permeability and total porosity are also larger. For example a Qp of 10 roughly correlates with 1–10 mD, while a Qp of 100 roughly correlates with 0.01–0.1 mD. Both distributions of ‘pore’ size are important. The attenuation can be shown to be the sum of Biot-type fluid flow and squirt flow to/from the larger, moderately interconnected inter-granular pores, which may contribute as much as 90% of the total porosity. This permeabilityQp trend is expected to strengthen when the small-scale ‘dual porosity’ also has the contribution of in situ jointing or fracturing. A requisite number of joint sets for connectivity, and well-intersection for verification, are necessary boundary conditions. 13.30 Ultrasonic data (0.7–0.85 MHz) for small ‘intact’ dualporosity limestone samples has uncertain relevance for geophysicists interpreting propagation through dualporosity porous and jointed limestones in the field, at the lower frequencies used in seismic and sonic log surveys (50 Hz to 30 kHz range). Dual-porosity chalk, with higher porosity than limestone, has indicated Qp and Qs values

13.31 A degree of correlation is noticed between seismic Q and the ‘static’ modulus of deformation, expressed in GPa and readily estimated from rock quality Q. This modulus is stress- or depth-dependent, and may range from about 1 to 150 GPa in the upper 1 kilometre, but most frequently from 5 to 100 GPa. The components of the rock quality Q-value reflect many potential attenuation-causing factors, e.g. RQD/Jn for scattering due to relative block size, Jr/Ja concerning the frictional and conductive properties of the joints that are expected to be relevant for squirt flow, including loss mechanisms in clay, Jw as a direct link to permeability, and SRF related to increased attenuation where stress is low, and reduced attenuation where stress is high.

13.32 Over-pressured zones due to rapid sedimentation of alternating sands and shaly sediments present a potential hazard when drilling, due to the risk of shallow water flows (SWF). Effective stresses and compaction of sediments can be minimal, and progressive instability during drilling at a new well can potentially engulf neighbouring wells, also at depths up to a kilometre. Due to very low values of shear wave velocity at low effective stresses in sands, there is an exponential increase in the ratio of Vp/Vs to values beyond 5 and 10, and even beyond 100. Poisson’s ratios increase rapidly to just below 0.5. There is high attenuation of the shear waves at the lowest pressures, as the sand is close to a state of suspension. Distinguishing between unstable sand and sandstone is very clear using the ratio of Qp/Qs plotted versus (Vp/Vs)2. 13.33 Saturated shales tested under over-pressured conditions, show anisotropic velocity and attenuation in ultrasonic

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laboratory testing. Velocities can be 30–40% higher parallel to bedding, where attenuation is also least. There is a general increase in seismic Qp and Qs with increasing differential pressure. Relative proportions of Biot ‘fluidpast-frame’ attenuation, and local squirt flow attenuation are different in the plane parallel to the layering, and in the plane perpendicular to the layering. There is a strong link between the rock framework, the pore geometry and connectivity, and therefore of the response of pore fluid to the propagation of seismic waves in specific directions.

13.34 The surface roughness of joints or fractures may help to maintain some permeability, even at higher confining pressures, corresponding to depths of several kilometres. Permeability parallel to jointing or fracturing may then be much higher than that parallel to eventual sedimentary layering. The additional possibility of pre-peakstrength conjugate shearing of such joint sets, due to anisotropic stress, would allow relative maintenance of joint permeability despite high effective stresses. Elastic property anisotropy, and hydraulic anisotropy may be closely related in terms of symmetry directions, when the two mechanisms share the same cause, such as layering or jointing.

13.35 High pressure polyaxial loading frames have been used to study the seismic signature differences between unfractured matrix and fractured matrix. Parallel fracturing has been developed in the same specimen by holding the minimum principal stress very low and increasing 1 and 2 in unison, to high levels. Velocity increasing steadily parallel to the high biaxial loading direction, contrasts with the fall in velocity in the perpendicular direction, when fracturing initiates. Subsequent reloading of the fractured sample demonstrates stronger stress-velocity dependence perpendicular to the fractures than parallel. Perpendicular to the fracturing direction, seismic Q values change from 40 to 30 as a result of fracturing, and reduce to 10 with unloading, actually resembling potential deformation modulus behaviour, when expressed as GPa. Low permeability sandstones start to develop measurable permeability when velocities start to reduce

in the direction perpendicular to the stress-induced fracturing.

13.36 The coupled stress-permeability-velocity behaviour of smooth-planar and rough-undulating fractures is different. Rough fractures closing due to stress increase contribute to increased velocity, but suffer less than expected reduction in permeability. The reason for the different behaviour of the rough fractures compared to the smooth, may be that E (physical aperture)  e (hydraulic aperture), for the case of rough, high JRC fractures (or joints), while E
e for smooth fractures (or joints). This would mean faster physical closure than hydraulic closure for rough joints, thereby potentially explaining the stronger velocity response and the weaker permeability response to stress increase.

13.37 Reservoir-scale 4D seismic monitoring in fractured reservoirs is most sensitive to production-induced changes at lower effective stress levels. The velocity and particularly the attenuation, are relatively sensitive indicators of small permeability changes. By the nature of jointed reservoirs, there are unlikely to be commercially viable hydrocarbonbearing fractures or joints with very low surface roughness JRC values, as joint closure under stress would preclude both permeability and ‘storage’, if such was needed due to low porosity matrix. Minerally ‘frozen’ stylolites in limestone and chalk are a special case, being both exceptionally ‘rough’, and insensitive to stress change, in comparison to rough, interlocking joints which show greatest stress sensitivity, and greatest apertures (E and e).

13.38 A simple empirical method is suggested for linking seismic Q values, specifically Qp, with hydraulic and rock engineering properties. This is based on the fact that Qseis invariably resembles the static E-modulus in the case of intact samples, and the static deformation modulus in the case of jointed or fractured rock and rock masses. when Qseis magnitudes are expressed in GPa. Despite the dynamic micro-strain basis for spectral analysis estimation

Conclusions

of Qseis, the magnitude of Qseis and its increase with effective stress, does not so closely resemble the dynamic micro-strain based deformation properties such as Edyn as one might expect. It has been found that Qseis cubed and inverted gives first-order estimates of intrinsic permeability, and velocity and compression strength combined (both reflecting stiffness), give independent first-order estimates of Qseis. Chapter 14

P-waves for characterizing fractured reservoirs

14.1 There was very early recognition in petroleum exploration, of velocity increase with depth, and early recognition of a quite systematic trend linking velocity to the geological age, in combination with the present depth of occurrence. The greatest rate of velocity increase was found to occur at shallow depth in the oldest units, which is fundamental early proof of the importance of dual porosity. The likelihood of more joints in the stiffer, older units means that these units are more sensitive to stress change. However, with only Vp as a dynamic indicator of conditions, acoustic closure represents a limit to the stress-sensitivity of velocity, especially for the case of weaker, younger reservoir rocks.

14.2 An early analysis of almost 300 kilometres of well sections, in 500 petroleum well surveys, mostly from the USA, and mostly for mixed shale and sandstone sections, indicated an average P-wave velocity discrepancy of only about 110 m/s in velocity between these two, the sandstone having the highest velocity by this small average margin. The similarity of velocities for these mechanically and hydraulically dissimilar units, is a reminder of the potential ‘non-uniqueness’ of P-wave velocity, and the need for alternative interpretation methods, such as attenuation, and impedence, to distinguish the different lithologies and their fluid-bearing signatures. The closeness of the in situ velocities for shale and sandstone, also seen in rock physics experiments on the matrix of both rocks, is surprising, in view of the greater tolerance of the stronger sandstone to stress anisotropy,

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often resulting in several MPa greater minimum stress in the shale, which is frequently a fluid barrier for the hydrocarbon-bearing sandstone.

14.3 Fine layering of alternating porous and impermeable strata is obviously one of the basic sedimentary systems that contribute to the existence of potential reservoir rocks in sedimentary basins. Fine layering of sedimentary strata means that the dominant wavelength of a seismic or sonic pulse is long compared to the thickness of individual layers. The medium will nevertheless exhibit effective (and real) anisotropy, with a vertical symmetry axis in the case of horizontal layering. In the presence of hydrocarbons this layered medium may show substantial attenuation and velocity dispersion, which will be compounded with the additional presence of jointing or fracturing. With modern seismic techniques a new exploration concept has gradually developed, exploring not just for the presence of reservoir rock containing hydrocarbons, but exploring for the presence of permeable joint-sets and their principal direction.

14.4 A ‘thin bed’ is considered to be 3/8 of a wave length, the limit for a discrete reflection both from the top and bottom of the bed. Wave scattering, attenuation and dispersion occur when the ordered heterogeneities have scale lengths of about 0.3–0.01 of the wavelength, while the smallest scale of ordered heterogeneity, less than 0.01 of the wavelengths, may be the cause of most of the azimuthal and offset dependent velocity. Conventional seismic wavelengths are much longer than the scale lengths of either of the features that govern dual-porosity flow in a reservoir.

14.5 Strong P-wave velocity anisotropy is observed in every geologic environment, with the possible exception of basins under primary deposition and burial. P-wave azimuthal anisotropy, previously ignored and left to the research and technology specialists, is now known to be one of the most significant properties of the acquired

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seismic data. In the marine environment, fully populated offsets in each azimuth bin are less common than on land, but even narrow azimuth data gives an opportunity to see the effects of azimuthal anisotropy. As time goes by more and more reservoirs are being re-classified as severely heterogeneous, as well as fractured and anisotropic.

Qseis/Vp ratios could therefore be used to delineate the difference between unconsolidated sands and jointed sandstones, and between weak plastic shales, and the less desirable fissured/jointed, or indurated variety.

14.9 14.6 Definitions of three common classes of anisotropy are as follows. Transversely isotropic media have a vertical axis of symmetry, and are referred to as TIV: with horizontal axis of symmetry as TIH. The former is typified by fine layering in shales. Transversely isotropic media with a horizontal axis of symmetry, known as HIV, typically have stress-aligned, vertical jointing or fracturing, and/or microcracks. When fast and slow directions have been identified, azimuth sectoring can be applied in these directions. Even isotropic processing codes can function with such azimuth-sectored data.

14.7 Shallow 3D-survey based imaging of seismic velocity and attenuation, shot over several km2, can be used to derive tomographic images of velocity and attenuation at specific depths in shallow reservoirs, using an iterative reconstruction algorithm. The tomograms derived for constant-thickness slices centred at increasing depths show successive increases in both P-wave velocity and Qp with increasing depth (e.g. Qseis  5 when Vp  2 km/s, and Qseis  10 when Vp  3.5 km/s).

At a site in the USA, the P-wave velocity of near-surface jointed limestones determined from near-offset VSP varied from about 3.8 to 4.2 km/s between the shallow depths of 16 and 26 m. This suggests a rock quality Q-value of 2 to 5 from the empirical relation Vp
3.5  log Q relevant to nominal 25 m depth, 100 MPa, low-porosity rock. Qrock  2 to 5 is typical for rock masses with three sets of joints, moderate block size, and with possible weathering of the joint walls: i.e. Q
90/9  2/2  0.66/2.5
2 to 3. A seismic Qp value of about 13–14 can be estimated via the deformation modulus method, when Qrock  2 to 3, and assuming the uniaxial compressive strength of the limestone is around 100 MPa. Alternatively, using just velocity, Qseis can be estimated as 12–16 for this jointed limestone, based on the Vp range of 3.8–4.2 km/s. 14.10 In this ‘circular-logic’ jointed rock prediction, the ratio Qp/Vp, if roughly correct, would be a much lower 3 to 4, compared to the much higher ratios seen in porous, unconsolidated sediments. A 460 m deep cross-well measurement in a very permeable limestone aquifer showed Vp and Qp of 3.5 km/s and 14 at 2 kHz, but at higher frequencies (12 kHz), Qp rose by 350%, while Vp rose by only 3%.

14.8 Smaller scale, shallow cross-well tomography, has been used in reservoir sands (channel-sands) to correlate high values of the ratio Qseis /Vp with the most porous and most permeable zones, and low values with flow barriers, such as shale-rich layers (e.g. sands Qp/Vp  45/3  15, plastic shale Qp/Vp  30/3.7  8). Absence of jointing and high porosity and permeability apparently causes higher values of Qp (i.e. less attenuation without squirt losses), and quite low Vp. This is in contrast to the seismic attributes of jointed sandstones or jointed rock in general. The proposed Vp-UCS-deformation-modulus ‘GPa-model’ for Qp fits the latter and not the former. A contrast in

14.11 There have been many years of oil-industry interest in cross-hole tomographic methods for imaging below the resolution of surface seismic. High frequency waves can be propagated over distances of many hundreds of metres, with minimum loss of energy, when both source and receiver are down-hole, in deep boreholes. The avoidance of near-surface (low Qseis) losses, means that broad band-widths can be used. Very high resolution images are obtained by using second arrivals and reflection imaging.

Conclusions

14.12 At a 260 m deep research well through finely inter-layered limestone, shale, and sandstone sequences, the combined use of a borehole compensated sonic logging tool, a compensated formation density tool, and a formation micro-scanner enabled resolution of much of the detail of finely interlayered rock sequences, where the normally detectable layer thickness using standard sonic tools may be no less than 15 cm. The ability to separate shales, sandstones and limestones, based on down-hole facies recognition and velocity differences, can also be used in a tentative separation of Qp according to facies. With appropriate ranges of increasing uniaxial strengths and velocities for the three rock types shale, sandstone, limestone, one arrives at potentially representative Qp values of 6–7, 10–15, and 20–40, using the empirical Vp-UCSmodulus model.

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include azimuthal variation of attenuation in 4D monitoring, possibly due to conjugate joint shearing. 14.15 Since all seismic data also varies with frequency, there is increasing acceptance that 3D multi-component, multimode and multi-azimuth acquisition may be required and may also be economically justified. A given set of vertically aligned fractures may cause anisotropy with low frequency measurement, signal distortion with mid-frequency measurement, and lead to reflections by the highest frequency waves. The detection of the azimuthal anisotropy attributable to structure, that specifically controls the fluid-flow properties at reservoir scale, is now an important focus of attention. The detection of permeability anisotropy can be considered as one step beyond the detection of vertically aligned fractures, and/or the detection of unequal horizontal stresses.

14.13 14.16 A finely inter-bedded mix of facies as above, may tend to create a ‘weighted’ response in standard logging. Sonic logging (8–24 kHz) gave the lowest Qp with a mean Qp of 10 and a range of about 6–14. A Qp range estimated from the measured velocity range of 3–4 km/s, using the Vp-UCSmodulus method, would be about 5 to 12. The somewhat lower frequencies of cross-hole logging (0.2–2.3 kHz), gave a mean Qp of 15.7 and a range of 12 to 20. The lowest frequency VSP (30–280 Hz), giving presumably the poorest definition of the fine inter-layering, gave a mean Qp of 31.3 and a range of 25 to 45.

There is also a growing trend to instrument selected petroleum wells on a permanent basis, especially offshore, so that 4D seismic can be used relatively more easily, to monitor changes bought about by different water-flood and production practices. Rock physics principles are used to assist in the interpretation of measured changes in velocity, amplitude and attenuation. In-well 3D accelerometer installations were applied in the late 1980’s for permanent installations in deep holes adjacent to the San Andreas fault in California, where the benefit of avoiding near-surface attenuation were recognised.

14.14

14.17

Since sedimentary rocks containing hydrocarbons have proved to be neither isotropic nor homogeneous, but heterogeneous and anisotropic, the seismic wavelength at which the measurement is made, determines what seismic attributes can be measured, and whether the rock looks homogeneous and isotropic or heterogeneous and anisotropic. All seismic data are now known to vary with offset from the well (in VSP) and with azimuth. Besides detecting azimuthal velocity anisotropy due to aligned fracturing or stress, one can now acquire spatial resolution of variable structure, azimuthal resolution of attenuation, and resolution of temporal changes, which may

It is commonly assumed that there is strong correlation between directionality of reservoir flow and the local, presentday orientation of the maximum horizontal stress. Oriented four-arm calliper logs typically show a long axis that is oriented parallel to the minimum horizontal stress direction, if there is stress-induced break-out. However there may be geomechanics-based reasons for carefully evaluating this commonly held viewpoint from case to case. Rock strength, joint or fracture roughness, joint closure under stress, and possible shear-displacement modes need also to be considered. Fractures perpendicular to the H max direction can also be ‘open’ if partially filled

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with mineral cements, and for this same reason, sealed fractures parallel to H max are also numerous. 14.18 The common assumption that the direction of H max is the direction of ‘open’ cracks or fractures also overlooks the possibility that two sets of joints or fractures can be involved in limited conjugate shear-displacement. With one set dominant, the orientation ‘discrepancy’ often reported, regarding the direction of ‘open’ fractures in relation to H max, can be better explained. Dominant directions of fracturing can also be images of the resulting dominant strike of conjugate, steeply dipping sets, in the case of domal structures. 14.19 A further potential source for minor angular discrepancies, is the dilation-related contrary-rotation of fluid lenses contra rock-to-rock contacting asperities, when non-planar joints or fractures are under significant shear stress, and therefore significantly ‘open’. This geometric effect could also potentially cause a minor rotation of shear wave splitting polarization, as argued in Chapter 15. 14.20 Measurements in deeper wells have indicated that seismic Qp based on seismic frequency VSP, may be systematically smaller than Qp based on higher frequency sonic logging. This is the opposite of what has been measured in shallower wells, where attenuation was least for VSP and most for sonic logging, giving lower Qseis. The expected dispersive bias of higher frequency (sonic) waves travelling at higher velocities than lower frequency seismic (VSP) waves, remains consistent when shallow or deep. Individual values of Qp or Qs may change ‘erratically’ with depth unless depth averaging is used. However, rock quality Q-values down recovered core also tend to fluctuate quite strongly, and since linked to deformation modulus, Qp and Qs must also be expected to fluctuate. 14.21 Rock quality differences, and therefore differences in stiffness and susceptibility to failure may play a role in such

fluctuations. In addition, minimum rock stress will tend to be residing in the weaker beds (i.e. shale) at shallow depth, while residing in the stiffer beds (i.e. sandstone) at depths where shale is more plastic, and therefore has a higher h min. Stress concentrations around wells will cause a magnification of tangential stress, in the same direction as major principal stress, and diminution of tangential stress in the perpendicular direction. If these stress concentration effects are strong enough in relation to rock strength, shear failure surfaces may develop, first giving break-out, subsequently a possible log-spiral-sheared discontinuum close to the well.

14.22 Seismic attenuation has come to be recognised as potentially very sensitive to reservoir properties. This is because of its sensitivity to fractures, joints or bedding planes, and in turn, due to their sensitivity to changes of effective stress and to frequency. Attenuation levels are also sensitive to the saturating fluid and petro-physical properties. High dispersion (and low Qseis) values may correlate with permeable sand and carbonate beds within shale. Such beds can be at least ten times as permeable as the host shale formation. The dependence of seismic velocity on frequency can be used for reservoir characterisation, since the dispersion is mathematically related to seismic attenuation. High frequency measurements differ from low frequency measurement due to both elastic scattering and intrinsic attenuation.

14.23 AVO (amplitude variation with offset) and AVOA (amplitude variation with offset and azimuth) indicate that variation of P-wave amplitude can be related both theoretically and in practice, to the presence of fracturing. Appropriate analysis of AVOA gives reasonable estimates of the orientation of fracturing, particularly if only one set is involved, or if one set is dominant. Fracture orientations can be compared to results obtained when using C-waves (P to S converted waves), and the shear-wave splitting and polarization mechanism. The converted P to S waves have the advantage that they can be generated by compressional (i.e. explosive) sources, yet are expected to contain the same information as pure S (or SS) waves, as discussed in Chapter 15.

Conclusions

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14.24

14.27

Although the use of shear waves are theoretically favoured for fracture set detection, there has been some reluctance to use shear waves, due to more expensive acquisition and more expensive processing routines. For these reasons, the use of P-waves for fracture set detection and estimation of orientation, has attracted a lot of interest, even though P-wave travel times need to be detected in many directions to obtain the necessary information.

There is a reported problem of model-dependence in AVAO analyses. The dominant fracture strike direction can be ambiguous, since the azimuthal variation in the near-offset AVO gradient, can be positive or negative, relative to the fracture direction. The direction of the most positive AVO gradient can correspond to either the fracture-normal, or the fracture strike direction, depending on the character of the fracturing, and depending on whether brine-filled or gas-filled. Forward modelling is therefore needed in order to constrain the interpretation of AVOA. Forward modelling using fracture density, fracture aspect ratio, and fracture (additional) compliance concepts, may actually require knowledge of two different fracture apertures: the hydraulic aperture (e) that would govern squirt losses, and the physical aperture (E) that would govern compliance or stiffness and stored volume of fluid, where E  e. This inequality in the case of favourably rough-walled joints or fractures seems so far to have been ignored.

14.25 If seismic data acquisition is conducted parallel to the (geologically suspected) fracture orientation, the fractures will have minimal influence on the reflection properties, regardless of the angle of incidence, or offset. The P-wave particle motion is then parallel to the fractures. If the seismic line is instead oriented more perpendicular to the fractures, at larger angles of incidence than zero, the reflection coefficients will be affected strongly. At the largest angles of incidence, especially perpendicular, the P-wave velocity is also expected to be affected by the acoustic properties of the fluids filling the fractures. Thus in the presence of anisotropy, the reflection amplitude will vary with offset, due to changed angle of incidence, and will also change with azimuth (AVOA).

14.26 When deviation of 20° to even 40° is observed between AVO-determined dominant fracture orientation and the perpendicular-to-break-out based H max direction, and when nearly as large deviation is also obtained between shear-wave polarization and the H max direction, the possibility of conjugate-shearing of joint sets that are intersected by the H max direction should be considered. Although this contradicts the standard industry assumption of ‘open fractures parallel to H max’, it helps to explain frequent angular discrepancies between dominant ‘open’ fracture azimuths, and the perpendicular-tobreak-out based H max direction, At shallow depth, the standard industry assumption, also in civil engineering, is more correctly focussed on maximum permeability, and Vp, being parallel to the H max direction.

14.28 The probability for multiple joint or fracture directions in the neighbourhood of faults, means that the fast velocity is no longer equal to the matrix or bulk rock velocity. The normal elliptical Vfast and Vslow distribution is then replaced by superimposed multiple ellipses, which have the effect of reducing the observed velocity. The previous directionality with a single set of joints or fractures will be lost. Due to rapid changes in fracture frequency, rapid changes in velocity are also seen. Such is actually a response to the rapid changes in rock mass quality Q close to, and across faults, as frequently mapped in tunnelling, and when logging fault-zone core, in each case for rock quality determination.

14.29 There is a multitude of technical jargon in the geophysical industry. Some is exceedingly simple. Converted C waves means explosive or air gun generated P-waves converted to S-waves at an interface or at the sea floor. (Pure S-waves may be referred to as SS). The term 4C means fourcomponent seismic recordings. These consist of one hydrophone, one vertical geophone, one in-line horizontal

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geophone, and one cross-line horizontal geophone. The term 4D means 3D seismic repeated at intervals for monitoring changes caused by production. Repeated 4D surveys can be made cheaper by modifying 4D receivers to also be 4C. There are now some expensive 4D4C installations that make frequent reservoir monitoring much cheaper. The consequence of frequent full-field 4D4C reshoots, as at Valhall, in the North Sea, providing full-field estimates of all required reservoir parameters, is more efficient exploitation of reserves, and a production increment obviously coming sooner than discovery and exploitation of new fields.

14.30 Reservoir monitoring with 4D seismic in its most basic form is the repeated inversion of changing seismic data, to obtain dynamic reservoir properties, which can subsequently be used to predict pore pressure change at a distance from the wells based on the effective stress and fluid sensitivity of laboratory samples of the reservoir rocks. History matching can be used to up-scale the rock physics matrix data, and to calibrate forward modelling of anisotropy and fracture effects. There is high sensitivity to effective stress in shallow reservoirs, but a stress-velocity plateau may be reached at high effective stresses (i.e. beyond roughly 25 to 50 MPa, depending on rock type and on fracture-surface roughness.) A velocity plateau indicates the need for up-scaling using attenuation.

compaction, and reduced layer thickness, i.e. reinforcing effects. Time-shifts of as much as 12–16 ms, between 1989 and 1999, recorded at the Ekofisk field, were related to an estimated 6m of additional compaction at 3 km depth. An uncritical time-lapse comparison between surveys, may give unrealistically large values for compaction and subsidence.

14.33 Extensive casing damage to numerous wells at Ekofisk is evidence of discontinuous behaviour, due to stretching of the overburden and differential bedding plane slip. This was also seen in early discontinuum models. Subtle changes are now known to occur to the overburden velocity, due to the ‘stretching’ of the overburden in response to the incremental compaction between surveys. There are about 150 km3 of obviously discontinuous rock involved in the compaction and subsidence. Further evidence for discontinuous behaviour caused by compaction at Ekofisk can be seen in the results of the 4D seismic. Fault related discontinuities are seen in ‘time lapse’ tomograms of compaction magnitudes. Forward modelling of compaction details, performed in the 1980s, indicated small-scale down-dip shearing of conjugate jointing in the chalk, before evidence of slickensiding had been seen in newly drilled core.

14.34 14.31 Compressible grain-boundary cracks with their low aspect ratios may be partly the result of stress unloading when matrix samples are drilled and bought to the surface. The in situ velocity may not be recovered upon reloading, due to hysteresis caused also by temperature change. Saturated samples containing micro-cracks will tend to project a lower stress sensitivity with laboratory ultrasonics, than with seismic waves, due to greater relaxation, as opposed to stiffening with the ultrasonics.

In water-flooding, for stimulating and driving petroleum production, there is both a local increase in pore pressure at the injector wells, and a reduction in temperature, causing some contraction of the matrix, both of which help to dilate, and possibly shear existing joints, and perhaps create new fractures as well. The conventional and expected mechanism of fracture or fault opening exactly in the direction of Sh min is not as common as expected.

14.35 14.32 When compacting reservoirs are 4D monitored by repeated seismic surveys, time-shifts are registered, which are a combined result of increased velocity due to

There are strong indications from surveys of numerous fractured reservoirs that have been water-flooded, that the reduction of effective stress caused by the water-flood pressure, and the related contraction-cooling effects, could be stimulating shear-displacements on existing joint or

Conclusions

fracture sets, or faults. The direction of H max shows a frequent tendency to have bisected the geologic features that are the basis for the joint rosettes. An implied mechanism of conjugate shear, would show strong parallels to the findings of Zoback and co-workers, concerning the frequency of water conducting discontinuities in deep wells needing to be oriented so that they are under shear stress.

14.36 Mapping of the azimuthal velocity anisotropy of P-waves using a downhole triaxial accelerometer sensor array, and multi-azimuth walk-away (or ‘float-away’) VSP, is a means of reducing the risk of drilling low-productivity wells in unfractured parts of reservoirs. Calibration with oriented core data and with FMS logs improves the likelihood that later producing-wells will intersect ‘open’ conductive fracture sets, where P-wave anisotropy is highest. Azimuthal variation in the shear modulus of the fractured rocks is cited as the reason for the P-wave velocity anisotropy. Dominance of one fracture set orientation, with a nearorthogonal subset, and variation of fracture density in the unequal two-set system, would be reasons for variations in the degree of seismic anisotropy, and demonstrate the benefit of 3D mapping.

14.37 Multi-azimuth walk-away VSP can also be used to map the attenuation anisotropy of a reservoir. A fractured, oilsaturated reservoir is likely to show azimuthal variation in attenuation, in a similar manner to P-wave anisotropy. As examples, we may quote Qp  18 in the fractured part of a reservoir, and Qp  35 to 40 in the overburden, which was assumed to be relatively unfractured, with minimum attenuation correspondingly scattered between wider azimuths. In the particular reservoir, minimum attenuation was some 20° to 30° oblique to both the open conducting fractures and to the h max direction, based on oriented cores and borehole images. Conjugate jointing, perhaps also pre-peak shearing, is again suggested.

14.38 ‘Open’ fractures in a petroleum reservoir would seem to require that the rock is unusually strong and that joints

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are rough, or that there exists a close-to-fracturing pore pressure, or that there is a suitable quantity of hard mineralization to ‘bridge’ and maintain an earlier porosity. Alternatively, if some pre-peak-strength shear displacement of non-planar joints or fractures has occurred, there would be the contribution of dilation to ‘openness’, and the additional influence of a 10° to 20° rotation of the fluid-bearing parts of the fractures in relation to the contacting parts taking the load. This might rotate both the sources of attenuation and the sources of shear-wave polarization.

Chapter 15

Shear wave splitting in fractured reservoirs and resulting from earthquakes

15.1 Vertical and sub-vertical jointing is extremely common in most rock masses. Yet vertical boreholes are usually the first, and seemingly also the second choice, for sampling and gaining access to the sub-surface. The sampling bias caused by the mismatch of borehole diameter and horizontal spacing of vertical structure, and the vertical borehole itself, is extreme and well known. If the economic savings of a vertical well, and the subsequent cost of an extensive seismic survey and its inversion were combined, there would perhaps be reason for rapidly deviating exploration boreholes at least 10° or 15°, in order to sample the increasingly understood relevance of vertical and sub-vertical structure on hydrocarbon production. On the other hand drilling and hole stability problems might be increased by the more frequent joint intersections.

15.2 Shear-wave anisotropy due to splitting and polarization caused by the presence of vertical or aligned structure, (and P-wave azimuthal anisotropy), are miraculous means, in view of the long seismic wave lengths, for rectifying these poor joint or fracture sampling strategies. The central challenge of sub-surface fracture characterization is to obtain data on essential fracture attributes where direct observation has been prejudiced by vertical wells. An early deviation of 10° or more would greatly improve understanding of both the overburden jointing and the reservoir

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jointing. The potential anisotropy of the overburden cannot be ignored in seismic inversion, as indicated in an increasing number of cases, especially where compaction and therefore subsidence are occurring.

15.3 Countless hydrocarbon reservoirs have been discovered, characterised, and monitored by P-waves. However, P-waves cannot solve every seismic imaging or reservoir description problem. The addition of S-waves, usually in the form of converted PS-waves, has given oil and gas companies an enormous quantity of new reserves that could not have been found with P-waves alone. The new reserves have been more effectively exploited by better identification of fracturing, and therefore better placement and deviation of production and water-flood wells. Multi-component recording of shear-wave attributes also provides information where shallow gas has obscured Pwave imaging over central parts of a field, such as at Ekofisk and Vallhall.

15.4 The basic geological source of polarized shear waves can be sets of vertical joints or fractures, or stress-aligned microcracks. These aligned features cause the vertically transmitted shear-waves to split into fast and slow components, registered as time delay, due to the attenuating effect of fracture shear compliance, on the S-wave component that has particle motion perpendicular to the fracture strike. Shear-waves travelling in the parallel direction hardly sense the presence of the cracks, and travel at almost the wave speed of the unfractured matrix. The difference in travel-time between the fast qS1 and slow qS2 components is strongly related to the length of travel path and to the density of the crack population. It is also related to fracture compliance. Numerous polarized shear wave observations show the fast wave polarized parallel (or subparallel), to the accepted local or regional maximum stress field. There can be several reasons for this, and also several reasons for deviation from this direction in other cases.

fluids prop open a population of compliant voids or inclusions that are nevertheless capable of remaining open against the least principal stress. The implication of 3D principal stress anisotropy at depth is that EDA cracks will tend to be aligned in a vertical plane, striking parallel to the major horizontal stress. With this configuration, a microcracked but otherwise isotropic crust would be transversely isotropic, with a horizontal symmetry axis.

15.6 The traditional view was that there were several possible small scales of azimuthal anisotropy that could cause shear wave splitting, such as aligned crystals, lithological anisotropy due to aligned grains, stress-aligned microcracks, and fine layering. Much evidence for the influence of larger-scale joint-set alignment effects on shear wave splitting has subsequently been obtained. These larger scale features obviously dominate drainage potential from the matrix to the joints, and thence to the wells in hydrocarbon production. The micro-scale extensive dilatancy anisotropy (EDA) championed by Crampin and co-workers, would logically dominate drainage from the pores to the microcracks. Relatively large time delays between split shear-waves may also be set up in the top tens to hundreds of meters of rock. These near-surface effects have been termed natural directivity. Principal stress aligned microcracks, or principal stress aligned intra-bed jointing, or aligned jointing from historic tectonic effects including doming and anticlines, each have shear-wave splitting potential.

15.7 It was earlier considered remarkable that, with all the different scales and characters of aligned fluid-filled cracks, inclusions or fractures in sedimentary, metamorphic and igneous rocks, that the differential shear-wave anisotropy varied only within narrow limits (0.5 to 5%). With increasing application at fractured reservoirs, this range, and the earlier assumed limited ranges of fracture density, have each been extended, sometimes by significant margins.

15.5 15.8 The potential of fluid-filled microcracks to react to crustal stress and strain led to the early proposal for extensive dilatancy anisotropy (EDA). The hypothesis was that crustal

The traditional porous medium experience is that shearwave velocity remains unchanged whether a formation

Conclusions

contains gas, oil or water. However, because of the effects of fluid compressibility on the dynamic normal stiffness of fractures, or its inverse compliance, the polarized shear waves passing through a fractured or jointed medium, may actually have the unexpected ability to distinguish between oil and gas, specifically when incident waves and jointing are non-parallel. Regions of gas are characterized by lower magnitude slow shear waves, and regions of oil by higher magnitude slow shear waves. In comparison, classic Gassmann porous medium theory anticipates an S-wave velocity relatively unaffected by the type of fluid.

15.9 A controversial point is whether the fractures and shearwaves can both be vertical, where theoretically only shear compliance would be sensed, because it is uncertain if shear compliance will be sufficiently affected by these contrasting fluid compressibility effects. A more certain effect of fluid compressibility is when normal compliance is involved in the case of sub-vertical fractures or sub-vertical shear-waves, giving a finite angle of incidence. There is evidence that the delay between the split shear waves may decrease with increasing depth, yet an accumulative delay with increasing depth would naturally be expected. This perhaps suggests that stress-sensitive compliances are involved, which would match rock mechanics experience with the non-linear pseudo-static stiffness of joints or fractures.

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are sure to vary, and each split shear wave may therefore split again, giving multiple splitting. The influence of the joint structures near the recording site gives one of the most prominent results. Down-hole instrumentation is needed if possible, in order also to minimise such site effects and the higher frequency filtering due to attenuation.

15.12 High velocities in rock tend to occur where attenuation is low or Qseis is high. This reciprocal relationship between velocity and attenuation is one of the reasons why the leading split shear wave is a very stable phenomenon, because it is travelling in the fast direction and is less attenuated than the slower split shear wave. Sometimes the slow wave is too attenuated to allow calculation of the shear-wave anisotropy. The location along the ray path where the shear-wave splitting is imprinted most strongly is not known a priori, and near-surface effects where jointing is stronger may be a disturbing feature. Well fractured reservoirs may over-print such effects. Lower crack densities implied by many earthquake studies may be a reflection of the sampling of ‘average rock’. In contrast, crack densities interpreted from fractured reservoirs may represent a ‘biased sample’, caused by a rock mass that is more jointed or fractured than the norm, and therefore also a target for exploration and subsequent exploitation.

15.10

15.13

In the case of earthquake recordings, the relative steepness required for the incident wave to make an acute angle to typical sub-vertical structure, means that there is a need for the recording site to be within the shear wave window. This derives from the requirement of angles of incidence less than sin1(Vp/Vs). For a Poisson’s ratio of 0.25, is about 35°. Outside this window the shear-wave waveforms are severely distorted. The epicentral distance from the recording sites must therefore be significantly less than the focal depth of the earthquake.

The geophysicist’s crack density (e) is defined as number (N) of cracks per volume (V) times the crack radius (a) cubed. Crack density was often quoted in the range of e
0.01 to 0.05 in reportedly widely different geological and tectonic regions. This commonly used parameter is unfortunately remarkably ambiguous. Ten million micro-cracks @ 100 m/10 cm cube, give e  0.01, while ten fractures @ 1 m/10 m cube also give e  0.01, and even ten minor faults @ 100 m/1 km3 give e  0.01. These three scenarios, with their theoretically equal ‘crack density’, have very different mechanical and fluid-conducting properties. Nevertheless they theoretically would previously have suggested equal shear wave anisotropy. Alternative methods of forward modelling show this theory to be in error, when extremes of fracture size and compliance are involved, and due to frequency or dispersive effects.

15.11 The large depth of most earthquake sources means that shear waves will pass through a range of rock types with different ages. Velocity and individual joint-set properties

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15.14 The classically assumed limited range of 1% to 5% shearwave anisotropy, was linked to a similarly limited range of assumed crack densities 0.01  e  0.05. The percentage of differential shear wave anisotropy was reportedly about e  100, for a Vp/Vs ratio of about 1.7 or 3. There are now known to be many exceptions to these limited levels of shear-wave anisotropy, and there are order of magnitude larger values of fracture density interpreted in fractured reservoirs. So-called fracture criticality, associated with higher densities, is clearly positive for good reservoir production. The rock mass does not fragment, and the shear strength is not lost, and nor does the pore fluid disperse at higher crack densities, as feared by a prominent author. This is because it is confined by a 3D stress field, and by less permeable boundaries. How-ever rock mass deformability and susceptibility to compaction may obviously increase when looking beyond matrix compaction mechanisms, as at Ekofisk.

Shear wave splitting was also visible in reflections from layers above the reservoirs. More recently, shear wave splitting has been observed to mimic saucer-shaped and oval-shaped sub sea-bed subsidence bowls kilometres above compacting jointed reservoirs. Strength-scaled polarization patterns show excellent correlation to locations where sea depths are changing most rapidly. The amount of detected anisotropy is small above the centre of the compacting field, where the subsidence is largest, and large on the flanks, becoming small again further from the centre. Oriented joint-stretch in the overburden seems likely to be the cause, as a partially cubic polarization pattern resembling intra-bed jointing can be noted. If unconsolidated un-jointed sediments were the actual source of this nearer-the-surface splitting and polarization, then micro-cracks or even macro-cracks in the sediments would need to be invoked to explain the polarization match to the subsidence bowls.

15.17 15.15 Aligned fracturing may be detected and monitored over a huge range of length scales, using polarized shear waves. Dimensions may range from crustal dimensions of 10–100 km, through 1–1000 m reservoir scale fractures and faulting, to millimetre and micron-sized microcracks. The relative stiffness of microcracks, having much higher aspect ratios than inter-locked fractures or joints, means that they cannot respond in the same way as fractures, to a given change in fluid pressure, according to classic geophysics teaching. Recent poro-elastic fluid interaction modelling of the dispersive effects caused by fractures of widely different dimensions, using doubleporosity or triple-porosity models, show that different fracture dimensions can be inverted from given levels of shear-wave anisotropy, based on their different response to changing frequency.

15.16 By the mid-eighties, some oil companies were apparently reporting shear wave splitting in almost all their three-component reflection surveys in sedimentary basins. The phenomenon was assumed to be due to fracture or joint sets within the fractured reservoirs.

On occasion, ‘90°-flips’ in polarization directions are observed from presumed earthquake source zones. It has been postulated that this may be due to extreme build-up of pore pressure, causing the faster split shearwaves that were previously parallel to H max to do a 90°-flip and become the slower wave parallel to h min. From a geotechnical viewpoint a 90°-flip in polarization would appear more likely with extreme H max loading, causing lateral expansion of aligned microcracks in a limited volume of rock. The volume affected by expanding, aligned microcracks may need to be limited, since the rock mass could not absorb this volume increase without a general reversal of the H max and h min directions.

15.18 The progression from seismic propagation in isotropic media, to anisotropic layered media, to transversely isotropic layered media containing one set of vertical fractures, later increased to two sets of perpendicular fractures, then non-orthogonal vertical sets, and finally to non-vertical sets, has resulted in a progression of theoretical papers in the geophysics literature, containing an increasing content and complexity of 6  6 compliance and stiffness matrices. Schoenberg and Sayers are prominent authors.

Conclusions

15.19 The elastic moduli and the density determine the behaviour of seismic waves, assuming a linear, loss-free, elastic behaviour. The presence of fracture sets affects the elastic moduli of the fractured rock, due to the addition of their dynamic compliance. The additional presence of fractures can be expressed as the sum of the compliance of the isotropic back-ground rock and the excess compliance matrix associated with the fractures. The latter is composed of the effects of a fracture-normal compliance ZN, and of a fracture-shear compliance ZT.

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media, in which the shear modulus should be independent of the fluid. In the case of fractured media, oil and gas are distinguishable by the reduced and increased shear wave anisotropy respectively, as the stiffening effect of the oil makes the fracture normal stiffness less contrasted to the back-ground medium. So for dipping joints or fractures, there proves to be a significant decrease in shear wave anisotropy if the fluid has a higher bulk modulus, making the normal stiffness of the fractures greater. The average of the two shear wave velocities is therefore also increased.

15.22 15.20 The simple addition of the three fracture compliance terms (ZN , ZT and ZT) is made in the same diagonal-term (1,1 5,5 and 6,6) locations in the combined compliance matrix. In the context of shear-wave splitting, the stiffness matrix term relating to the fast shear wave propagating parallel to the fractures, is the C44 term, and the slow shear wave propagating perpendicular to the fractures, is given by the C55 term. The Thomsen shear-wave splitting anisotropy parameter () is defined from the elastic stiffness matrix as (C44 – C55)/2C55 (often expressed as a percentage), where qS1  (C44/), and qS2  (C55/). Shearwave splitting anisotropy as defined by Thomsen, is commonly in the range 0    20%. The Crampin definition of the S-wave velocity anisotropy is a contrasting 100  (Vs max – Vs min)/Vs max or 100  (qS1 – qS2)/ qS1. For the case of the vertically propagating waves through the vertical fractures, there is no fracture compliance term in C44, only the Lamé constant for the background rock. This causes the fast shear-wave component to be parallel to the fractures. For the case of the slow shear wave, the more complex C55 term involves ZT, and not ZN. The simpler compliance matrix S55 term is simply 1/  ZT. 15.21 Involvement of ZN in the slow shear wave velocity theoretically requires dipping fractures, or non-vertical wave propagation. When polarized shear-waves sense the different viscosity of oil or gas in the fractures, ZN is more likely to be involved than ZT, which would have a less obvious dependence on fluid viscosity differences. This sensitivity is despite Gassmann’s theory for porous

The shear compliance ZT and normal compliance ZN interpreted from loaded, roughened Lucite (Plexiglas) plates, which were used to simulate ‘a fractured medium’, was apparently responsible for some authors to assume that ZN
ZT for the case of dry, gas saturated cracks. Seismic phenomena observed in highly stressed, finely layered (t 0.7 mm), roughened plates of Lucite, with their extreme ‘crack densities’ and artificial ‘fracture’ surfaces, should however not be used to predict rock joint response to dynamic or static loading. The suggested ‘equality’ of ZN and ZT was propagated in some of the geophysics literature, but may be far from realistic for all but the smallest laboratory specimens. ZN involves ‘micro-closure’ in a stiffening direction, while ZT involves ‘micro-slip’ in a direction that may not involve stiffening.

15.23 An inequality of the joint or fracture compliances would be more consistent with the experience of Ks  Kn, concerning the pseudo-static shear and normal stiffnesses of joints and fractures, where stiffness is the rough inverse of compliance. The magnitude of Kn proves to be a bit less than, but quite close to 1/ZN in good quality unweathered hard rock, while in the shearing direction, Ks  1/ZT, sometimes 1/ZT. However ZT data from geophysics investigations is extremely limited compared to the large body of Ks (pseudo-static) data that has been in use in discontinuum rock mechanics modelling since the late 1960’s, first in jointed FEM studies by Goodman. If pseudo-static stiffnesses and dynamic compliances could be related, despite the different orders of magnitude of dynamic and ‘static’ deformations, then the more

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researched, stress-and-scale-dependent parameter Ks and the stress-dependent Kn might provide shear wave splitting analysts more information than at present. A handful of 40 to 50 mm size laboratory samples of natural joints and stress-induced fractures, and tests on Perspex plates, represent a very uncertain basis for interpreting the equality or inequality ZN  ZT. 15.24 The measured range of Kn(dyn) / Ks(dyn) ratios for approximately 50 mm diameter jointed samples in hard crystalline rock has been shown from limited testing to be about 1 to 4. This means that the ratio of the inverted compliances ZN/ZT for such samples may range from 1 to 0.25. Convenient ‘core-sized’ 50 mm data from state-ofthe art testing of joints in hard crystalline rock seem unlikely to have 1:1 relevance to in situ reservoirs in much weaker sedimentary rock, where jointed block sizes may range from extremes of perhaps 100 mm to 10,000 mm.

15.25 Pyrak-Nolte demonstrated at laboratory scale, that joints that support less flow tend to have higher normal stiffness, and that in principal, joint normal stiffness may be inversely related to the cube root of the permeability. The permeability and seismic response of a joint can therefore be inter-related through the normal stiffness of the joints in question. Joints that attenuate seismic waves most at a given stress level, due to lower normal stiffness, also supported more flow. This implies a second implicit link between the permeability, and both the joint index parameters JRC and JCS, since these can be used to calculate both the normal and shear stiffness, and they independently give estimates of average hydraulic and physical apertures.

15.26 The permeability of the rock mass may also be related to the rock mass modulus of deformation, when permeability and modulus are not reduced by clay. In simplest possible terms permeability is inversely related to Qrock. Seismic quality Qseis and the pseudo-static modulus of deformation Emass expressed in GPa, can each be estimated from Qrock, for the case of jointed rock masses.

15.27 The typical 1012 Pa/m unit for stiffness favoured by geophysicists, converts to 1000 MPa/mm, which is more familiar in rock mechanics. An even better experimental feel for stiffness is given by 1 MPa/ m, each of these being equivalent. In geophysics, the inverse of stiffness, termed compliance is also typically reported in ‘complex’ units such as 1012 m.Pa1, instead of equivalent units of 1 m/MPa, which is much more tangible for any rock mechanics experimentalist.

15.28 Depending on stress levels, rock type, and joint roughness, Kn(dyn) may range from 1012 to 1014 Pa/m, or 1,000 to 100,000 MPa/mm or 1 to 100 MPa/ m, suggesting a mostly very small increment of dynamic displacement. Kn(static) values from a wide range of weaker rock and joint types, may vary from as low as 100 MPa/mm to almost 50,000 MPa/mm. There is therefore a large degree of overlap between the static and dynamic stiffnesses in this stiffest perpendicular loading direction.

15.29 Shear compliance, as opposed to normal compliance is of most relevance in the case of vertical shear-waves and vertical structure, and the resulting degree of shear-wave anisotropy. Of the two dynamic compliances, this is the least understood component. By comparison, it is the pseudo-static shear stiffness that is most researched in rock mechanics. In pseudo-static testing, a whole range of possible static shear stiffnesses are found, that seem generally to be inversely related with the sample size, if there is measurable joint roughness, (and therefore possible permeability even at depth). The degree to which dynamic shear compliances might be related, more weakly but nevertheless directly to sample size, is one of the remaining unsolved areas in this important area of seismic detection of anisotropy, and the subsequent goal of interpreting fractured reservoir permeability.

15.30 Some pieces of the dynamic-permeability jigsaw are complete, but there are missing links between dynamic and

Conclusions

static testing, and between small sample testing and the large sample reality, which causes experimental stressmagnitude problems. The completed parts of the jigsaw are the abilities to estimate both of the pseudo-static stiffnesses Kn and Ks and the less tangible physical (E) and hydraulic (e) apertures, for different sizes of jointed rock block, based on simple index testing. This involves estimation of joint roughness and wall strength, using respectively the un-scaled or scaled JRC and JCS components of the Barton-Bandis joint constitutive model.

15.31 Fracture-induced seismic anisotropy has rapidly evolved from the earlier estimation of fracture orientation, with an assumed indication of major horizontal stress, to fracture intensity, and the attempted prediction of fluid type, fluid saturation, and permeability anisotropy. To make this advance, the sensitivity of the fracture compliances to fluids has to be understood. Theoretical expressions for the fracture compliances ZN and ZT have been developed by Liu and Hudson and co-authors, which indicate strong sensitivity of the ratio ZN/ZT to the bulk modulus of the fracture infill material, with the most rapid change in the compliance ratio, and values closer to 1.0 occurring when the infill bulk modulus approaches zero, such as for gasfilled fractures. One of the geophysics equations suggests that ZN/ZT
1 if fractures are dry, and ZN/ZT
0 if fractures are filled with liquid. With realistically small fracture aspect ratios (i.e. 0.0001), much lower ratios of ZN/ZT than 1.0 are predicted, which would be more in line with rock mechanics pseudo-static experience. Zero is inadmissible for the pseudo-static ratio Ks/Kn, but certainly Kn Ks.

15.32 Although outside this chapter’s focus on shear-waves, Worthington and Hudson modelled the effects on downgoing P-waves, of one or more faults intersecting the transmission path, between 1000 and 2000 m depth in a North Sea reservoir overburden. They used a theoretical compliance model to demonstrate the need for a very large inequality of the shear and normal compliances, suggesting the need for ZN  4.4  1014 m.Pa1, and ZT  1.1  109 m. Pa1. These convert to shear and normal stiffnesses of Kn
20,000 MPa/mm, and

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Ks
1 MPa/mm. This low, back-calculated ‘in situ’ shear stiffness is similar to the values used in large-scale pseudostatic modelling of compaction/subsidence in rock mechanics. In general one may assume that the pseudostatic values of stiffness are lower in the normal direction, and much lower in the shear direction, than the equivalent dynamic values of stiffness.

15.33 Stronger shear wave splitting interpreted from large time delay in locations in the neighbourhood of fault zones, such as the San Andreas fault at Parkfield, suggests that fluid-filled fractures within the fault zone may be more extensive than in the surrounding crust. Fault parallel polarization of the leading split shear wave may indicate that fault-related fractures are aligned by fault shearing rather than by the differently aligned regional principal stress that can be verified further from the fault plane. The internal structure of the fault gouge and transition zone is assumed to be the reason for this rotation. In some cases, only one of the anisotropic shear-wave polarizations is recorded, due to attenuation of the slower component. A change of stress affecting the geometry and fluid in neighbouring discontinuities following larger earthquakes, may be the reason for temporal decreases in time delay.

15.34 Earthquakes with shallower focal depths may show pronounced increase in time delays, suggesting that a stronger anisotropy associated with the fault zone may also be concentrated at shallower depth. Leading shearwave polarizations exhibiting fault-parallel alignments near the fault, but alignments with the regional stress field away from the immediate fault zone were also verified at the Cajon Pass site. In general terms the source of shearwave splitting may be shallower than desired, where conditions of anisotropy are more favourable for this mechanism.

15.35 Stress-monitoring sites in Iceland, using state-of-the-art borehole instrumentation to monitor shear-wave splitting between controlled-source wells and receiver wells are designed to identify the effects of nearly negligible

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Conclusions

changes of stress, which might be capable of monitoring the build-up of stress and other crustal adjustments before earthquakes and volcanic eruptions. Anomalous water level changes and GPS-measured displacement anomalies have been related to various changes in prior and subsequent P-wave and S-wave travel times and delays.

15.36 The ‘90°-flips’ that sometimes occur in source zones, may be due to extreme pore pressure build-up according to Crampin. An alternative explanation is that they could be due to extreme loading in the H max direction, causing an extreme ‘Poisson effect’ due to crack expansion, thereby locally reversing the H max and H min directions. Except in an eventual clay core, a pore pressure reduction appears more likely than the assumed increase of pore pressure, since as shear failure of either intact or jointed rock is approached, dilation is the most likely phenomenon, unless beyond the brittle-ductile transition.

15.37 Major earthquake (Chi-Chi) after-shock monitoring in Taiwan indicated 8% shear-wave velocity anisotropy at a 200 m deep station due to up-going split shear-waves with fast and slow components. Qseis values in the 2–15 Hz frequency band were 61 to 68 in the fast direction, and 43–52 in the slow direction. Such values may closely resemble possible deformation moduli M, expressed in GPa. The anisotropy may have been caused by sub-vertical joint set anisotropy, which causes anisotropy at low seismic frequencies, as opposed to the assumed microcrack anisotropy that is dominant from 1 kHz.

15.38 Shear-wave splitting analysis utilizing local 4 to 5 km deep micro-earthquakes, and P-wave anisotropy measurement with controlled sources, were used in Mid-Atlantic Ridge studies, where anisotropy was attributed to a shallow distribution of vertical, fluid-filled cracks, aligned parallel to the trend of the axial valley. Time delays ranged from 35 to 180 ms, with an average delay of 90 ms. The shear-wave anisotropy was from 8 to 30% in the highly fissured layer. Most of the shear wave delay was attributed to the shallowest 500 m in seismic layer 2A, where the average value

of Vp/Vs was 2.9. There was evidence for only a shallow concentration of P-wave anisotropy, which decreased from 4% at 500 m depth, to zero below 1.5 km depth. Isolated fluid-filled cracks at depths from 500 m to 3 km were too tight to be detected by the P-wave survey, but could contribute to the shear-wave delays. P-wave anisotropy was defined as 100  (Vp max  Vp min)/ Vp average, while S-wave anisotropy was defined as 100  (Vs max  Vs min)/Vs max) following convention.

15.39 Offshore 3D seismic surveys, using compressional P-wave sources converted to PS at the sea-floor, thereafter analysed as S-waves, or use of direct S-waves (SS) generated on land, in walk-away, multi-azimuth VSP, are basic geometries for shear-wave polarization and anisotropy investigations above fractured reservoirs. Split shear waves S1 (or qS1) and S2 (or qS2 ) may occur due to major principal stress aligned dominant fracturing: the conventional interpretation, or perhaps due to stress bisected sets of unequal conjugate fractures, or due to fracture sets that have suffered some permeability-enhancing pre-peak shear displacement, which may also cause a deviation from H max. In walk-around VSP, a circular path of multiple sources at fixed offset, an incident P-wave, when converted to a PS wave that passes through the plane of horizontal symmetry caused by aligned vertical fractures, will show polarity reversal when incident on either side of the fracture strike.

15.40 The overburden may also display anisotropy in the form of azimuthal-dependent velocity. Errors will be introduced when the seismic data are inverted to obtain fractured reservoir parameters, if overburden anisotropy is ignored. Shear-wave splitting and polarization occurs in both cases due to the presence of the relatively compliant fracture properties. For the reservoir, basic structural information such as fracture density, strike and dip (due to symmetries), and some indications of fluid-type (gas or oil) and permeability may also be obtained, due to the relative sensitivities of the fracture normal and shear compliances. Deviation of fracturing from H max, because one of the sets dominates, or because fracture set stiffnesses differ, may compromise relative crack density interpretation.

Conclusions

15.41 Conjugate fracturing with non-vertical dips, as typically found in anticlinal or domal structures, means that samples of both the oppositely-dipping joint sets can be directly sampled, and tested, using vertical exploration wells. Nevertheless, it is a remarkable fact that exploration wells are nearly always vertical despite the target structures often being vertical too. Sidewall cores are therefore used to help locate zones having high fracture intensity; using microfracture and diagenesis data to infer the presence of the macro-fractures.

15.42 Large aperture fractures may require mineral bridges to have preserved conducting porosity. Fractures below a certain characteristic size may be completely filled. ‘Open’ fractures in the sub-surface are not necessarily parallel to maximum compressive stress H max. Fractures perpendicular to this direction can also be ‘open’ if partially filled with synkinematic or post-kinematic mineral cements. Sealed fractures parallel to H max may also be numerous. Effective normal stress induced joint ‘closure’ caused by sufficiently high h min may occur at reservoir depths in less competent rock. There is however an important prepeak shear-displacement mechanism for maintenance of ‘open’ fractures that are non-parallel to H max, in which conjugate sets may be bisected by H max. This interpretation has numerous merits for explaining permeability at depth.

15.43 When fracture densities are as high as 1 to 2, as in welljointed, domal chalk reservoirs, dimming of the amplitudes of the slow shear-wave, due to greater attenuation caused by lower Qseis tend to correlate with the most productive parts of the reservoir, as also experienced where the measurable shear-wave anisotropy is greatest. A down-dip shear mechanism may help to maintain apertures despite high effective stresses in the presence of this weaker, high porosity rock. If the high crack density is contributed to by two sets of oppositely dipping conjugate joints, one can expect shear and normal compliance contributions from both sets to the slowness of the slow shear-wave, which might be 2 km/s when porosity is

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high. The response is strongest when fractures are gas filled, as gas does not stiffen the normal compliance. Attenuation anisotropy should be enhanced in the case of oil-filled fractures, due to the greater contrast of their normal and shear compliances.

15.44 Reportedly the world’s first time-lapse, marine, multicomponent (3D/4C) survey, was performed in 2002 at the Ekofisk jointed-chalk reservoir in the North Sea. This baseline was subsequently compared with a monitoring 4D/4C survey acquired in 2003. Small changes of polarization direction and of shear-wave anisotropy were detected, even after this short 15 months monitoring of more than 30 years production. Azimuthal rotation of the anisotropic attenuation has recently also been detected at neighbouring Valhall, where life time seismic monitoring is established. An unequal conjugate shear mechanism could be a possible explanation for these temporal rotations, especially if the strike of the two conjugate sets was not equally oriented. Potential ‘opposite-rotation’ of fluid lenses and rock-to-rock contact areas due to pre-peak shearing of non-planar joints might also be detected by the shear waves. A much larger rotation of polarization azimuth was detected at a monitored HDR in Cornwall, where joint shearing was also assumed, due to plunging AE activity.

15.45 An important development in the dynamic modelling of the effects if fractures is that of Schoenberg, who modelled elastic wave behaviour using linear slip interfaces. These allow reflection, transmission, conversion, and delay to take place at the modelled interface, with the magnitudes depending on the specific stiffness, the frequency content, and the angle of incidence. The assumption is that when an elastic wave propagates across a fracture, there is a displacement discontinuity that is linearly related to the normal or shear force generated. The seismic particle displacement is discontinuous, while the seismic stresses are assumed to be continuous. This shares several of the interface-stiffness concepts that are basic to discontinuum modelling in rock mechanics, in the Cundall 2D and 3D codes UDEC and 3DEC.

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Conclusions

15.46 Hudson utilised a ‘method of smoothing’ for the effect of modelled cracks, which was capable of representing the elastic parameters of a ‘cracked’ material, in the form of an effective medium. This allowed calculation of the effect of incident dynamic waves of long wavelength. Subsequently, Hudson extended the model to allow for the cracks to be connected via the porosity of a rock matrix. In this extended case, cracks could be deformed by an incident wave in a manner that depended on their aspect ratio and on their orientation with respect to the incident wave. Clearly the modelling of intrinsic attenuation mechanisms such as squirt flow, and its frequency dependence, was transformed by this extended capability. 15.47 Tod extended this model further, by allowing for a continuous distribution of crack orientation and aspect ratios, and by allowing each to depend on the applied stress and on the fluid pressure. At high frequencies, the cracks behave as isolated stiff features, while squirt losses at lower frequencies cause a soft behaviour. Crack density is allowed to decay with an increase in applied stress, from an initial value representing the unstressed state. The model is purely elastic, and relaxes to its original state upon unloading. Crack density is designed to decrease with increasing compressive stress, but cracks with normals lying in the h minimum direction are assumed to remain open. The model is capable of capturing the changed anisotropy caused by fluid pressures and applied stresses, which impact the aspect ratios of the cracks. The non-compliant pores of the Tod model, transfer fluid to the physically unconnected cracks, therefore giving dispersive, or frequency-dependent velocities and attenuation. 15.48 Chapman developed a triple-porosity poro-elastic model, based on the observation that typical laboratory samples, clearly unfractured, nevertheless display dispersion, anisotropy, stress sensitivity, and dependence on fluid type and degree of saturation. When the fractures or cracks were removed from preceding models, a linear-elastic material remained, in contrary to observation. Chapman combined ‘meso-scale’ anisotropic fractures with equant matrix porosity and ellipsoidal microcracks. Due to the

fluid transfer between the different scales of discontinuity, dispersion occurs at lower frequency ranges than those over which the micro-structure dispersion occurs. Introduction of even small fractures causes dispersion to begin at lower frequencies, and the effect increases with increasing fracture sizes. The magnitude of shear wave anisotropy therefore shows fracture size, frequency and azimuth dependence. Attenuation is altered by setting smaller aspect ratios for meso-fractures compared to microcracks, as a result of higher stress, as the fluid cannot ‘squirt’ or flow so easily, in response to the passage of seismic waves.

15.49 Effective medium models appear at present to make no distinction between the assumed mean crack aperture (E), and the theoretical hydraulic aperture (e). In jointed rock (E) controls stiffness and deformation moduli, and the crack aspect ratio should have a similar role. On the other hand, (e) controls the intrinsic permeability, given as e2/12. Both apertures probably influence attenuation, since they effectively define two different aspect ratios, therefore influencing the assumed squirt-flow losses and the assumed stiffness. Dispersion will likely begin at higher frequencies as roughness increases. Incorporating the inequality e  E would be a source of improvement for effective medium modelling of rough-walled, tightly compressed cracks, joints or fractures, for which use of only one aspect ratio is least realistic.

15.50 The traditional EDA focus on microcracks as the source of shear-wave splitting, may need to be re-evaluated, in the light of these new poro-elastic double (or triple) porosity models. Microcracks appear to give a ‘constant’ potential source of shear-wave splitting independent of frequency. Meso-fractures, for instance of 1 m and 10 m radius, apparently have an equally strong role in shearwave anisotropy as microcracks, but specifically at the seismic frequencies appropriate to earthquake studies.

15.51 Shear wave splitting through fractured reservoirs may show a sharp increase of time delay with depth at the

Conclusions

reservoir level, indicating the presence of fractures. The time delays tend to be largest at lowest frequencies (e.g. 5–15 Hz), and smallest at higher frequencies (e.g. 20–40 Hz). However, polarization of the fast S-waves may show no apparent variation with frequency, unless at very low frequency. The time delays between the split shear waves may be decreasing as frequency increases, due to stiffening of the squirt phenomenon in the case of the slow waves. Such data have been used for inverting for the theoretical fracture density (an appropriate re-naming of crack density), and for fracture radius, using nine-component VSP data sets, with one P-wave and two orthogonal S-wave sources. Frequency-dependent anisotropy has also been demonstrated.

Chapter 16

Joint stiffness and compliance and the joint shearing mechanism

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geomechanics concept is provided by deep-well data showing that joints under differential (shear) stress are the conductors, with other directions apparently nonconducting. 16.3 The interpretation of shear wave splitting with possible multiple ‘vertical’ joint or fracture orientations emphasises the need for knowledge of both shear and normal compliances, if poro-elastic modelling is to extend to stress and displacement sensitive aspect ratios for the modelled joints or fractures. Presently, limited sets of laboratory data, and even more limited sonic log and cross-hole data, and a tentative extrapolation to large scale seismic interpretation of fault compliances, strongly suggest a scale effect. Increased compliance in both normal and shear directions is implied, as scale is increased or frequency reduced.

16.1

16.4

Rock mechanics developments in distinct element rock mass deformation modelling, including flow within the deforming joints, can be used to illustrate an extension of the traditional geophysics concept of one set of stressparallel ‘open’ joints in a reservoir. This is important because multiple sets of joints are more usual in rock masses, probably including even deep reservoirs. Multiple joint or fracture sets, such as bedding and two vertical sets also open the possibility of polarization orientations that are not parallel to the H max direction. Two conjugate vertical joint sets intersected by the H max direction can also cause shear wave splitting with polarization that nearly corresponds to this principal stress direction.

A comparison has been made between the presently known normal ZN and shear ZT compliance laboratory and field data, which is a dynamic and micro-deformation response, and the much larger body of laboratory and field data for the pseudo-static response of normal Kn and shear Ks stiffness. Data for joints, tension fractures and clay-filled discontinuities are readily available due to long term use in rock mechanics modelling of jointed rock masses. These pseudo-static measures of stiffness are given in typical units of MPa/mm, and when inverted show resemblance but generally larger magnitude, compared to the geophysicists compliance, given in typical m/Pa units.

16.2

16.5

When reservoir joints or fractures are not parallel to the H max direction, they may be acted on by shear or differential stress, and this implies shear deformation, which may be needed to supplement the often too small conducting apertures which may result when in the traditional parallel to H max direction. This philosophy is based on the fact that unless joints or fractures are mineral ‘bridged-but-not-blocked’, or are very rough and in hard rock, both testing and modelling indicates too small apertures to be considered ‘open’, since conducting apertures may be 5 m, and often 1 m. Support for this

When rock mass and rock joint quality is high, the dynamic modulus Edyn is not of much greater magnitude than the static modulus Emass. The normal compliance ZN may then be within 1 to 1/10 of the magnitude of the inverted static normal stiffness Kn. A typical laboratory-scale ZN range of 1013 to 1014 m/Pa, or Kn (dyn) of 10,000 to 100,000 MPa/mm is therefore found to be 1 to 10 times stiffer than typical Kn (static) data of typically 1,000 to 10,000 MPa/mm (range maybe 100 to 50,000 MPa/mm). In the inverted worlds of geophysics and rock mechanics, 1012 m/Pa is the same

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as 1,000 MPa/mm, with the identical 1 MPa/ m giving a more practical feeling for this level of micro dynamic stiffness. 16.6 Although the large-scale, seismically derived magnitude of shear compliance ZT from reservoirs is presently very uncertain, preliminary indications are that it may be about two orders of magnitude stiffer than large-scale pseudo-static shear stiffness Ks. The lower magnitude of Ks is due to strongly reducing magnitudes as block size increases. A block size increase has a double effect due to reduced peak shear strength and larger displacement to reach peak strength. It is not known whether this fundamental scale effect could also influence the presumed stiffer dynamic shear stiffness, but a weaker dependence than in rock mechanics is suspected. 16.7 A scale effect on ZN or Kn (dyn), as occurs with Ks, is not expected when merely sampling a larger portion of the same feature, However, when comparing ZN or Kn (dyn) on small fractures, larger joints, or faults, a sampling effect must obviously be expected, since the inequality Edyn  Emass is potentially increasing when sampling increasingly large features.

stress reduction from a higher stress level, if sufficiently rough and in sufficiently strong rock. Cooling can have a similar effect. Both ambient and thermal over-closure cause higher shear strength to be registered, due to changes in the thermal expansion coefficient, when joints are included. This causes changes in aperture and permeability, and may therefore complicate the matching of reality and present theory. During heating, stiffness and modulus appear to be less than expected, due to the additional closure. However, following the heating, this thermal over-closure results in stiffer subsequent behaviour. 16.10 Despite insufficient test data from most areas, the utilization of index properties for the joints for guiding the estimation of Kn and Ks, which is well established in rock mechanics, could provide order of magnitude estimates of the dynamic properties, or estimates of the index properties and therefore permeability, by inversion. This would presently be based on the assumed one to two order of magnitude stiffer dynamic behaviour. Index properties JCS and JRC concerning wall strength and roughness, allow estimation of the mechanical and hydraulic apertures under closure and shearing, and also estimation of the pseudo-static normal and shear stiffnesses each, thereby potentially linking dynamic data and in situ permeability. 16.11

16.8 There is present uncertainty in the magnitudes of ZN and ZT because of limited test data at different scales. The uncertainty in the magnitudes of the pseudo-static Kn and Ks parameters used in rock mechanics is much less, and values can be readily predicted using a 1D model for coupled M–H joint behaviour. However, there is an inevitable lack of test data with respect to high pressure and large size, also in the case of pseudo-static testing. 16.9 A further uncertainty with all four joint parameters is that rough joints or fractures tend to be more tightly closed at high temperature, and are also more tightly closed following several load cycles if they have been sampled and unloaded, and cooled. Joints can appear ‘over-closed’ by

Index data for typical reservoir rocks and joints, with variation of both strength JCS and roughness JRC, and consideration of confinement effects on strength, give prediction of very small conducting apertures of micron or less magnitude when modelling closure by an assumed h min of 10 to 40 MPa, unless roughness and strength are both significant. Available coupled M–H test data from the laboratory CSFT apparatus, and from in situ block tests, each including heating, also confirm the extremely small apertures of interlocked joints, unless rough and of high strength, or with aperture preserved by mineral bridging. 16.12 When modelling minor amounts of shear, excellent permeability is predicted in most cases, due to the positive

Conclusions

influence of even pre-peak-strength shear displacements, showing the vitally important beginnings of dilation. One to two orders of magnitude increased permeability is seen in CSFT coupled shear testing, following only 1 or 2 mm of pre-peak or close-to-peak shear displacement. Shearing of non-planar surfaces causes the fluid-bearing lenses on ‘down-slopes’ to have a different average orientation than the ‘up-slope’ rock-to-rock contact areas. This rotation may influence the polarization direction of split shear waves, if they are more sensitive to one or the other of these average directions. Combined with two conjugate but usually unequally developed joint or fracture sets, the resultant polarization directions of the split shear waves qS1 and qS2, can have at least two reasons for not lining up exactly with the classically ‘preferred’ H max and h min directions, and for showing 4D rotations of azimuth.

16.13 Significant contributions from deep-well monitoring and analyses by Colleen Barton, Zoback and Townend and colleagues, has demonstrated the hydraulic flow distinction of joints or fractures that are under differential shear stress, and those that are principally under larger normal stress and insignificant shear stress, due to their mutually different orientations. In general, but quite clearly, the former are found to be water conducting, and the latter are assumed not to be water conducting, based on temperature logging. The wells are of kilometre to several kilometre depths, drilled in mostly crystalline rocks, with several wells connected with San Andreas Fault investigations. This hydraulically differentiated behaviour is despite rock strengths significantly higher than typical reservoir rocks.

16.14 Differential stress magnitudes based on rock stress measurements, indicate that the presently resolved ratios of shear and effective normal stress expressed as mobilized frictional strength , are generally in the range of 0.4 to 1.0 for the case of the above water conducting fractures. On this basis fractured reservoir jointing that was parallel to H max and without mineral ‘bridging’ or sufficient JCS and JRC might well be very impermeable when normally pressured, but perhaps conducting when overpressured.

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16.15 Using non-linear Barton-Bandis shear strength, dilation and aperture interpretation, in place of the linear Byerlee

 0.6 to 1.0 assumption for the shear strength of ‘faulting’, one finds that the conducting ‘fractures’ with

in the range 0.6 to 1.0, require typical to high ranges of both JRCn, and confined strength JCSn. This means a full-scale roughness as high as 10, and full scale confined rock strengths (1  3) as high as 200 to 600MPa or more, to explain this higher range of resisted /
n loading. The subscripts (n) on the index parameters signify in situ strength, and block sizes Ln of perhaps 0.25 to 2.5m. 16.16 It is very difficult to model as high as 1.0 in situ, in jointed or fractured rock at kilometre depths, but easy when near-surface. The joints or fractures must be prepeak or close to peak strength to have sufficient strength to develop implied mobilized friction angles as high as 45°. At the same time they must be sufficiently dilated to be conducting. ‘Fractures’ that are under the lower

range of 0.4 to 0.6 are more likely to have the character of minor faults or have larger block sizes or some clay smear.

16.17 The assumption of co-axial stress and displacement in the classic stress-transformation equations seems to be in error if the joints or fractures or new fault surfaces are non-planar. Since shear displacement is implied when specifying shear strength, or a resisted value of /n
 , then dilation has also inevitably occurred at the highest range of from about 0.7 to 1.0, for which significant roughness or non-planarity is also implied.

16.18 The mobilized dilation angle dn mob estimated from the JRCmobilized concept, needs to be added to the angle  used to define the joint or fracture orientation in relation to the major principal stress direction 1. The addition of the dilation as sin 2( dn mob) and cos 2( dn mob) in the shear and normal stress transformation equations explains the extra difficulty of shearing when dilation

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occurs, and might explain the high end of the interpreted values of in situ .

16.19 An approximate, order of magnitude prediction of permeability in rock masses, can be made using the rock mass Q-value, normalized by the uniaxial strength to the form Qc. This can be equated to the inverse of the Lugeon value, where 1 L is 107 m/s. The resulting Qc  10, K  108 m/s type of estimate appears to be a useful first order estimate, when Qc values range from 0.1 to 1000, implying little complication of clay smear. The range of K is then predicted to be about 106 to 1010 m/s, or roughly 1013 to 1017 m2 if water viscosity at 20°C is invoked, for simplicity.

16.20 Due to the problem of clay-sealing of discontinuities, and due also to the general effect of reduced permeability at significantly increased effective normal stress, a new term called QH20 has been developed, involving an inverted Jr/Ja term, a normalized JCS, together with a simple depth-permeability equation for the ‘soft porosity’ represented by jointed rock. This shows promising fit to shallow civil engineering Lugeon testing, and potentially also to deep-well data, and demonstrates suitable adjustment to lower permeabilities caused by clay-filled discontinuities and increased depths.

Appendix A – The Qrock parameter ratings

Q 

J J RQD  r  w Jn Ja SRF

Definitions of characterization and classification as used in rock engineering CHARACTERIZATION

The six parameters defined RQD Jn



Jr



Ja



Jw



SRF 

is the % of competent drill-core sticks 100 mm in length in a selected domain (Deere et al., 1967) the rating for the number of joint sets (9 for 3 sets, 4 for 2 sets etc.) in the same domain the rating for the roughness of the least favourable of these joint sets or filled discontinuities the rating for the degree of alteration or clay filling of the least favourable joint set or filled discontinuity the rating for the water inflow and pressure effects, which may cause outwash of discontinuity infillings the rating for faulting, for strength/stress ratios in hard massive rocks, for squeezing or for swelling, as appropriate

Combination in pairs RQD / Jn  relative block size (useful for distinguishing massive, rock-burst-prone rock) Jr / Ja  relative frictional strength (of the least favourable joint set or filled discontinuity) Jw / SRF  relative effects of water, faulting, strength/ stress ratio, squeezing or swelling (‘active stress’) An alternative combination of these three quotients in two groups only, has been found to give fundamental properties for describing the shear strength of rock masses – something close to the product of ‘c’ and ‘tan ␸’. By implication Q (and in particular Qc) have units resembling MPa. (Barton, 2002a)

CLASSIFICATION

description of a virgin site (pre-tunnelling attributes and properties) description of a non-virgin site (post-excavation attributes and properties)

For example, in the excavation disturbed zone of a tunnel or steep rock slope, there will be changes in stress, permeability, deformation modulus and seismic velocity. In the case of a tunnel, it may not only be the redistributed stresses that have radial and tangential components. With rock joints present, four sectors of shear stress and joint displacement (roughly at 45° intervals) and the pairs of diametrically opposite maximum and minimum tangential stress, may give a complex perturbation of properties in the EDZ. The tables appearing in the following figures are the ratings for the six ‘Qrock’ parameters. These have been printed as figures, in order to keep the compact style suitable for reproducing together with field logging sheets. The recommended way of recording the Q-parameter ratings is explained in the following notes, based on Barton, 2002a. Footnotes below the tables that follow, also give advice for site characterization ratings for the case of Jw and SRF, which must not be set to 1.0 and 1.0, as some authors have suggested. This destroys the intended multi-purposes of the Q-system, which has a quite different structure compared to RMR. (Bieniawski, 1989)

Notes on Q-method of rock mass classification 1. These tables contain all the ratings necessary for classifying the Q-value of a rock mass. The ratings form the basis for the Q, Qc and Qo estimates of rock mass quality (Qc needing only multiplication

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of Q by c /100, and Qo the use of a specifically oriented RQD, termed RQDo relevant to a loading or measurement direction). All the classification ratings needed for tunnel and cavern design are given in the six tables, where Q only would usually apply. 2. For correlation to engineering parameters as described in this paper, use Qc (multiplication of Q by c / 100). For specific loading or measurement directions in anisotropically jointed rock masses use RQDo in place of RQD in the Q estimate. This means that an oriented Qc value should contain a correctly oriented RQDo for better correlation to oriented engineering parameters. 3. Q-parameters are most conveniently collected using histogram logging. Besides space for recording the usual variability of parameters, for structural domain 1, domain 2 etc., it contains reminders of the tabulated ratings at the base of each histogram. Space for presentation of results for selected (or all) domains at the top of the diagram, includes typical range, weighted mean and most frequent (Q-parameters, and Q-values). 4. During field logging, allocate running numbers to the structural domains, or core boxes, or tunnel sections, e.g. 1  D1, 2  D2 etc. and write the same numbers in the allotted histogram columns, using a regular spacing for each observation such as 11, 113, 2245, 6689 etc. In this way the histograms will give roughly the correct visual frequency of all the assembled observations, in each histogram column. Besides this, it will be easy to find the relevant Q-parameters for a particular domain, core box or

section of tunnel, for separate analysis and reporting. Overall frequencies of observations of each rating (or selected sets of data) can be given as numbers on separate logging sheets. Large data sets can be plotted in e.g. EXCEL when returning from the field. 5. It is convenient and correct to record rock mass variability. Therefore allow as many as five observations of each parameter, for instance in a 10 m length of tunnel or 5 m length of core. If all observations are the same, great uniformity of character is implied, if variable – this is important information. At ‘the end of the day’ the histograms will give a correct record of variability, or otherwise. 6. Remember that logged RQD of 10, including 0, are set to a nominal 10 when calculating Q, to avoid calculating Q  0. In view of the log scale of Q, the histograms of RQD in the logging sheet will be sufficiently accurate if given mean values, from left to right, of 10, 15, 25, 35…85, 95, 100. The log scale of Q also suggests that decimal places should be used sparingly. The following is considered realistic 0.004, 0.07, 0.3, 6.7, 27, 240. Never report that Q  6.73 or similar, since a false sense of accuracy will be given. 7. Footnotes below the tables that follow, also give advice for site characterization ratings for the case of Jw and SRF, which must not be set to 1.0 and 1.0, as some authors have suggested. This destroys the intended multi-purposes of the Q-system, which has an entirely different structure compared to RMR (Leave blank if permeability and stress data is awaited, otherwise estimate Jw and SRF.)

Appendix A – The Qrock parameter ratings

Figure A1 Characterization/classification ratings for RQD, Jn and Jr.

617

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Figure A2 Characterization/classification ratings for Ja and Jw.

Appendix A – The Qrock parameter ratings

Figure A3 Characterization/classification ratings for SRF.

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Figure A4 Graphic presentation of the meaning of Jr/Ja, representing the frictional strength of joints and clay-filled discontinuities. Note tendency for friction angle development like   i, , and  – i, according to whether dilatant or ‘normal’, or contractant joint or discontinuity resistance to shearing.

Appendix A – The Qrock parameter ratings

621

Figure A5 The Q-system of tunnel (and rock cavern) permanent support estimation, based on Grimstad and Barton, 1993, and Barton, 2000. The other widely used ‘rock mass rating’ (RMR) used in engineering geology has approximate correlation to Qrock as shown in the equations. The version ‘RMR  15 log Q  50’ is preferred. Barton, 1995. (Note: B  systematic bolting i.e. grouted steel rebar. Sfr  fibre reinforced sprayed concrete, often called shotcrete).

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Rock quality, seismic velocity, attenuation and anisotropy

Figure A6 The Q-parameter histogram logging sheet, for recording the number of observations of each parameter.

Appendix A – The Qrock parameter ratings

Figure A7 Example of hand-filled Q-parameter ratings from core-logging of part of a deep borehole.

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Rock quality, seismic velocity, attenuation and anisotropy

Figure A8 Example of EXCEL calculation of rock mass quality statistics, for the deep borehole, part of which was logged in Figure A7.

Appendix B – A worked example Q-value and tunnel or cavern support Note the overbreak caused by three joint sets in Figure B1. The joint planes (beneath the sprayed concrete) are planar and weathered or clay-coated, making for poor stability until also reinforced with rock bolts. Q
90/9  1/4  0.66/2.5
0.7 (‘very poor’). Estimate of permanent support requirements from Figure A5: 20 m span requires B (bolting) 1.6 m c/c (spacing)  13 cm S(fr) (steel-fibre reinforced ‘shotcrete’ or sprayed concrete). Q-value used for geophysical estimates 1. With a simple c estimate for the gneiss of 150 MPa, Qrock  0.66  150/100  1.0. Therefore at this shallow (25 m deep) cavern site the following ‘geophysical’ estimates can be made, from Figure 5.36, 5.37, 13.60 and 15.33.

2. Emass (or M)
10 GPa, Vp (seismic)
3.5 km/s, Qseis
12. (A rock mass porosity equal to a nominal 1% has been assumed). 3. From Figures 5.36 and 5.37, the empirically-derived effect of increased depth can be traced; i.e. Vp
5 km/s, and Emass
32 GPa at 500 m depth. 4. By implication, with a (continued, pessimistic) assumption of unchanged rock mass quality with increased depth, the magnitude of Qseis (specifically Qp at seismic frequency) would be expected to be about 30. 5. The reality of improved Q-value at depth (e.g. Jr/Ja
2/1, and SRF  0.5 (high stress) would mean Q
40. With less well-developed joint sets, the rock mass quality Q-value could easily be 100, at 500 m depth. 6. With the 40–100 estimate of Qrock, a more likely range of Vp is about 5.6–6.0 km/s, with Qseis increased to about 60–68 at 500 m depth.

Figure B1 The reality of near-surface construction of tunnels and caverns in rock. Note the three joint sets causing deep over-break. See Plate 17.

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7. The approximate Qseis estimates of about 10 at 25 m depth, and about 60–70 at 500 m depth are mirrored numerous times in this book. Qrock and Qseis appear to be approximately linked via the pseudo-static deformation modulus, which can be estimated from Qrock, as we have seen. The possible

‘explanation’ for this simple (probably too simple) link is that all three parameters (Qrock and Qseis and Emass) are reflecting the ‘soft-porosity’ effects of both structure and joint stiffness, with potentially several joint sets involved, not purely normal loading across one set. For some reason, rock mass dynamic stiffness as reflected in Edyn, is too high for a good correlation.

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References Barton, N. 1982. Modelling rock joint behaviour from in situ block tests: implications for nuclear waste repository design. Office of Nuclear Waste Isolation, Columbus: OH, 96 pp. ONWI-308, September 1982. Barton, N. & Bandis, S. 1982. Effects of block size on the shear behaviour of jointed rock. 23rd US Symp. on Rock Mechanics, Berkeley: CA. Goodman & Heuzé (Eds.). Keynote lecture. New York: Society of Mining Engineers. Barton, N. & Bakhtar, K. 1983. Instrumentation and analysis of a deep shaft in quartzite. Proc. of 24th US Symp. on Rock Mechanics, Texas A&M University. Barton, N., Bandis, S. & Bakhtar, K. 1985. Strength, deformation and conductivity coupling of rock joints. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 22(3): 121–140. Barton, N. 1986. Deformation phenomena in jointed rock. 8th Laurits Bjerrum Memorial Lecture, Oslo. Geotechnique, 36(2): 147–167. Barton, N., Hårvik, L., Christiansson, M., Bandis, S., Makurat, A., Chryssanthakis, P. & Vik, G. 1986. Rock mechanics modelling of the Ekofisk reservoir subsidence. Rock Mechanics: Key to Energy Production, Proc. of 27th U.S. Symp. Rock Mech., Tuscaloosa, AL, Hartman, H.L. (Ed.). Society of Mining Engineers. Barton, N. 1987. Predicting the behaviour of underground openings in rock. Manuel Rocha Memorial Lecture, Lisbon, NGI Publication 172, 1988. Also Geotecnia 53, July 1988 (in Portugese). Barton, N., Makurat, A., Christianson, M. & Bandis, S. 1987. Modelling rock mass conductivity changes in disturbed zones. Rock Mechanics. Proc. of 28th US Symp. Rock Mech., Tucson, AZ, Farmer, I.W., Daemen, J.J.K., Desai, C.S., Glass, C.E. & Neuman, S.P. (Eds.): 563–574. Rotterdam: Balkema. Barton, N., Makurat, A., Hårvik, L., Vik, G., Bandis, S., Christianson, M. & Addis, A. 1988. The discontinuum approach to compaction and subsidence modelling as applied to Ekofisk. BOSS ’88. Proc. of Int. Conf. on Behaviour of Offshore Structures, Trondheim. 1: 129–141. Barton, N. & Bandis, S.C. 1990. Review of predictive capabilities of JRC-JCS model in engineering practice. Rock Joints, Barton, N. & Stephansson, O. (eds.). Int. Conf., Loen, Norway. 603–610. Rotterdam: Balkema. Barton, N. 1990a. Chapter 6, panel of experts for Xiaolangdi Project. Report No. 1 submitted to Yellow River Water & Hydroelectric Power Development Corporation, YRCC, MWR. 26–42. Barton, N. 1990b. Scale effects or sampling bias? Closing lecture. Proc. of First Int. Workshop on Scale Effects in Rock Masses, Loen, Norway. Da Cunah (Ed.). LNEC. Barton, N. 1991. Geotechnical Design. World Tunnelling, November 1991. 410–416. Barton, N., Løset, F., Smallwood, A., Vik, G., Rawlings, C., Chryssanthakis, P., Hansteen, H. & Ireland, T. 1992a. Geotechnical core characterization for the UK radioactive

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waste repository design. 1992 Proc. of ISRM Symp. on EUROCK, Chester, UK. Barton, N., Makurat, A., Monsen, K., Vik, G. & Tunbridge, L. 1992b. Geotechnical predictions of the excavation disturbed zone at Stripa. Proc. of Fourth Int. Symp. on OECD/NEA Stripa Project, 14–16 October 1992, Stockholm, Sweden. 77–96. Barton, N. 1993. Physical and discrete element models of excavation and failure in jointed rock. Keynote lecture presented at ISRM Int. Symp. on Assessment and Prevention of Failure Phenomena in Rock Engineering, 5–7 April, Istanbul, Turkey. Barton, N. & Grimstad, E. 1994. The Q-system following twenty years of application in NMT support selection. 43rd Geomechanic Colloquy, Salzburg. Felsbau, 6/94: 428–436. Barton, N., By, T.L., Chryssanthakis, P., Tunbridge, L., Kristiansen, J., Løset, F., Bhasin, R.K., Westerdahl, H. & Vik, G. 1994. Predicted and measured performance of the 62 m span Norwegian Olympic ice hockey cavern at Gjøvik. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 31(6 ): 617–641. Barton, N. 1995. The influence of joint properties in modelling jointed rock masses. Keynote lecture. Proc. of 8th ISRM Congress, Tokyo. T. Fuji (Ed.). 3: 1023–1032. Rotterdam: Balkema. Barton, N. & Itoh, J. 1995. The Q-system and NMT support techniques. (In Japanese) Tunnels and Underground, Japan Tunnelling Association Publication, November 95. Barton, N. 1996a. Estimating rock mass deformation modulus for Excavation Disturbed Zone studies. Int. Conf. on Deep Geological Disposal of Radioactive Waste, Winnepeg, 1996, EDZ Workshop, 133–144. Canadian Nuclear Society. Barton, N. 1996b. Rock mass characterization and seismic measurements to assist in the design and execution of TBM projects. Proc. of 1996 Taiwan Rock Engineering Symp., Keynote Lecture, 1–16. Barton, N. & Warren, C. 1996. Rock mass classification of chalk marl in the UK Channel Tunnels. Channel Tunnel Engineering Geology Symp., Brighton, September 1995. Barton, N. & de Quados, E.F. 1997. Joint aperture and roughness in the prediction of flow and groutability of rock masses. Proc. of NY Rocks ’97. Linking Science to Rock Engineering. Kim, K. (Ed.). 907–916. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 34: 3–4. Barton, N. 1998. Quantitative description of rock masses for the design of NMT reinforcement. Keynote Lecture, Int. Conf. on Hydro Power Development in Himalayas, Shimla, India. Rotterdam: Balkema. Barton, N. 1999a. General report concerning some 20th Century lessons and 21st Century challenges in applied rock mechanics, safety and control of the environment. Proc. of 9th ISRM Congress, Paris, 3: 1659–1679. Rotterdam: Balkema.

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Index

ABC method 15 ABEM method 15 acid-leaching (model) 470, 480, 481 acoustic barrier 30 emission (see AE) closure of joints 3, 77–80, 166, 369 dipole logging 301, 302, 312–319 impedence (see impedence) log correction, mud-infiltration 317 monopole logging 301, 318 sensors 59 acquisition geometry 7 acute incident angle w.r.t. bedding, foliation in shale 354, 355 adiabatic (dynamic) 183 advance rate (TBM) 150, 158 AE acoustic emission 53, 85, 87, 128, 454 activity 222 arrays 130–131 inaudible to- 435 interpreted velocities 129–131 subsidence causes 454 temporal changes 130 tomography 131 Aegean 220 Afar triangle, Ethiopia (thinnest crust) 245 Afghanistan 228 African Plate 230 age, basement age at mid-Atlantic ridge, and VP 262, 264, 265 at mid-Atlantic ridge, and porosity 263 combined mid-Atlantic, East Pacific data 287–294 effect on Qseis 228 geological 369–371 agglomerate 25 Ahmedabad, India 219 air -dry samples 22, 23 filled 30, 119 guns 254, 261, 438 gun arrays (P-wave sources) 394, 396 gun travel time data 258 large- guns, low frequency sub-basalt imaging 403

-quartz mixture (sand) 254 velocity of 12, 159 Alaska 228 Alaskan lithosphere 243 East-Central Alaskan crust 244 albedo (see earthquakes) Alberta 386 aleurolite 212 Alford rotation 314 for fast-shear tool azimuth 314 for minimizing cross-receiver energies 314 aluminium 198, 424 alluvial clay 26 stream-beds 375 alluvium 12, 142, 374 Alpe Gera dam 77 alum shale crushed 53, 139 fractured 162 alteration 316 chemical near-wellbore- 316 due to discontinuum formation 302–307 mechanical wellbore- 316 zone, time-dependent interactions 319 alterered shale 313 shale compressional arrival 313 un- undamaged formation 313 un- virgin formation compressional arrival 313 zone 303, 305, 307, 308, 310, 311, 313, 316 zone development with time 313 alteration deep- zone 312 drilling mud induced- 312 zone phenomena 311 discussion re influence on logging 311 alternating hard and soft rocks 301, 304, 311 Amazonian Basin 231 ambient and heated tests 514, 515, 527 Ambiesta, Italy, limestones in situ 105 American units 296–298, 320 Amoco 331

656

Index

amphibolite 13, 32, 38, 70 compositionally homogeneous 249 -gneiss contrasts (reflectors) 249 amplitude/magnitude ratio A/Ao 85, 86 ratio versus joint frequency, roughness, clay-filling 85, 86 of waves (with, without fractures) 199, 204 versus frequency: jointed samples 199 versus frequency: bedded coal 201 versus time, S1, S2 reversal 455 amplitude of roughness (a) compared to length (L) 508, 510 ANDRA Andes 72, 231 andesite 26, 28, 29, 70, 72, 73 Andean Belt 231 anelasticity of matrix 182 angle of incidence effect on reflection coefficients 388 in AVO 388 in one- and two-set models 393 Angolan offshore exploratory well 312 angular discrepancies re assumed correlated phenomena polarization, anisotropy, non-parallel ␴Hmax direction 384, 385, 389, 390, 403, 404, 406, 414, 429, 431, 432, 475, 518 anhydrite, VP and density 326 anisotropic 9 attenuation 354 brittle fracturing 36 cuspidal phases 450, 451 domains 445, 446 dilation 36 frequency 384 jointing 9 pattern of wave attenuation 356 permeability 355, 359, 360 permeability, Äspö spiral tunnel 555, 556 pore-pressure propagation due to fractures 464 reflectivity 384 response 304 seismic velocities 3 stiffness 3 stresses 35, 36, 298–300, 305, 358 stress influence on joint shearing 299 structure (EDA microcracks) 432, 428–435 velocity 354 anisotropy 40, 41, 42, 351–364, 394 attenuation- 118, 382 attenuation in presence of- 351–364 azimuthal dependence of- 248 azimuthal- from dipole sonic logging 391 azimuthal P-wave- 405 azimuthal velocity- 35, 248, 382

detection 3, 382 double-effect 35 effects 35, 382 elastic 360 fault zone effect 429 following grouting 170 frequency-dependent- 472, 473 hexagonal 436 horizontal permeability- 382 hydraulic 360 maxima for slate, mica quartz schist, phyllite 248 natural-, layering 387 near-surface model 225 permeability- 357–364, 445, 446 Poisson’s ratio-, due to fracturing at geothermal field 394–396 P-waves, bedding fractures 499, 500 P-waves in failing sample 540 P-wave velocity- correlation with gas productivity 384 productivity direction connection 450 rotation of velocity anisotropy axis (blasting effect) 119 rotation of velocity anisotropy axessaturation reduction effect 480 shear wave-, supposed small range 413, 415 shear wave-, actual larger range 415 theory, basic 373, 374 three classes of-, elastic tensors 374 three-dimensional 38, 39, 355–364 velocity anisotropy 119, 357–364 VP–for 26 rock types at 1 GPa confinement 248 with respect to assumed ␴Hmax 382, 383, 385, 390, 404, 406 anisotropy caused by azimuthal shear modulus 404 cleavage 38, 248 conjugate joint, fracture sets 392, 393 crack content 445, 446 fabric 38, 248, 263 faults, faulting 47, 48, 394 fluid-filled cracks, Mid-Atlantic Ridge 436, 437 foliation 38, 248 fractures, aligned 358–360, 382, 436, 437, 439, 445, 446, 525 fractures, aligned, poro-elastic models 461–481 fractures, aligned, poro-elastic physical models 480, 481 joints and bedding 361–364, 372, 373 heterogeneity 373 horizontal (bedding-plane) fractures 499, 500 horizontal stress anisotropy 382, 439 lower-frequency shear waves 459 micro-cracks 35 micro-cracks in failing sample, P-wave- 540 oriented RQDo and oriented Jr/Ja 411

Index over-burden 440 permeability 382 principal stress difference 129 rock joints in situ 35, 40, 41, 42 stress difference 35 subsiding overburden, joint stretch/stress/strain 453 up-stepping, down-stepping 2nd joint set 523, 524, 551, 552 anisotropically loaded 306–311 fractured 463, 465 anomalies break-out-, not ␴Hmax related 541 fracture zones, sub-ocean 272, 273 high density- 254–257 Poisson’s ratio 270 temperature, conductive fractures 541, 542 velocity- 14, 256, 257 velocity-age reversal 274, 275 anorthosites gabbroic- 242 massive 147 meta- 147 anoxic, sub ocean floor 281 anticlinal structures 381 jointing, fracturing caused by- 381 anticlinal trap 391 Anza, California 222 APE model, Crampin, critique of 415 aperture (fracture/joint) 456 aspect ratio aspect of- 392 closure unless strong rock, rough joints 392 conducting (e) – normal stress, block test 514 conducting (e) – normal stress – temperature, block test 515–517 conducting (e), modelled 309, 310 cubed 161–164, 173 e E 470, 480 e E experimental data 457, 488–490 e E demonstration re grouting 467, 468, 487, 490 e E demonstration re tunnel model 469 e E UDEC-BB modelling 460, 519–521 e E relevance to poro-elastic modelling 392, 456, 457, 467, 474 e E relevance to production rates 453, 456, 487 e E relevance to shearing 474 effect of JRC on-, reservoir BB simulation 533 equation linking e and E by JRC 364, 487, 489 extremely small-, reservoir BB simulations 531, 532 ‘frozen’-, by mineral infill 278 hydraulic, conducting (e) 162, 172, 173, 278, 363, 364, 392 increase linked to dilation 524, 526 indicated by mineralization (ophiolite) 278

kinematic- 441 lenticular-, fluid-bearing lense 414, 525–527 physical (E) 162, 172, 173, 278, 363, 364, 392 reduced with depth 276 scaling for aperture and spacing , micro- and macro- 441 sealed by post-kinematic cements 441 -squared 173 stress-closure measurements of- 527–530 stress-closure modelling of- 392, 531–534 unstressed aperture, equation, discussion 511, 532 Appalachian Basin 370 aquaduct 79, 80 Arabian Plate 230 Archangelsk Region, Russia 439 area/volume ratio of pore space 33 areal well shoot 44 Argentina 163, 244 Arphy dam site, France 159 artificially jointed samples 40, 41 aspect ratio 207 apertures e and E (see aperture) 467 dominant 208 elliptical-crack closure stresses 529 influence in modelling saturation effects 326–329 low- cracks 200, 201, 270, 276, 363, 364, 467 low- cracks sealed 270, 276 low- cracks closed 287 low- fractures 391 means micro-cracks are stiffer than joints 412 of cracks and fissures 266 of fractures, joints 363 of microcracks 226 pore shape spectra 326 asperity (ubiquitous term) crushing 501, 502 role in dilation 519, 520 -weld, aluminium 424 welded-, Lucite, supposition 418 Äspö, Sweden 119, 131–133 access spiral tunnel, permeability 555, 556 Asthenosphere 227, 241 asymmetry of S- and P-wave reflections 438 Atlantic Coastal Plain, USA 231 (North-) fracture zones 273, 274 margin 244, 246, 251, 255, 256 Ocean 244, 246, 251, 255, 256 Shield, South America 231 sub-ocean Mid-Atlantic ridge 261–273 atomic inter- spacing 188 weights 23

657

658

Index

attenuated 8 attenuating effect of cracks 184, 185 effect of cracks nucleating 463 effect of freeze-thaw cycles 184, 185 joints support more flow 425 layer 66 attenuation (see 1/Qseis, 1/Q at Qseis, Q ) across continents 226–231 amplitude 66 -anisotropy 119, 352, 481 azimuthal- anisotropy 405 coefficient 233, 353 data from sub-ocean sites and lab samples 280 difference 118 expressions, after Thomsen 356 extreme, faulted rock, tunnel collapse 558 fluid-flow based- 186 for distinguishing lithologies 369 four components of- 193–194 high and low- regions (plate tectonics) 227 intrinsic 213, 214, 223, 280, 387 intrinsic-, incorrectly assessed 379 intrinsic link to joint processes 490 intrinsic squirt flow (see squirt flow) 236 influence of Ko on- 299, 300 in presence of anisotropy 351–357 lateral variations 228 low, Sugar Loaf, Rio de Janeiro 558 mineral/fabric related 246–248 mechanisms 17, 182, 183, 195, 196, 345 magnitudes 299 maximum 353 measurements in petroleum reservoirs 232–238 mechanisms discussion, earthquakes 219, 220 mechanisms, Coulomb friction, squirt, scattering 282 melt-squirt- 242 near-surface mechanisms of- 224 of velocity components 363 P-wave- 382–396, 459, 481 peak- versus frequency 387 peak (frequency  viscocity rule) 207 peak (aspect ratio range) 207 peaks at low and full saturation 190 problems 49, 51, 57 profiles 387 profile (post-blast) 118 profile (pre-blast) 118 reduced at low frequency, sub-basalt 403 rotation of attenuation anisotropy axis 119 scattering 182, 195–197, 213, 214, 223, 280 scattering mechanisms 202 sensitivity to structure 386 sensitivity to effective stress change 386

sensitivity to saturating fluid 386 separation (intrinsic and scattering attenuation) 213, 214 source of- 5 spectrum 118 structure, sub-ocean ridge area 282 ‘total’- 192 valid mechanism of- 189 viscosity-based- 209 attenuation due to, (note 1/Q and Q considered) alteration-mineralogy 280 axial strain 195–197 bulk modulus 356 clay, clay content 345, 346 clay-rich, clay-free sandstones 349 compliant mineral content 347 confining pressure, (effective) 191–193, 201 crack density 440 depth (near-surface) 202, 203 depth (1 km) 222, 223, 234 depth (few km) 222, 232, 233, 237 depth (many km) 229, 230 depth (extreme, plate-tectonic setting ) 179, 227 differential pressure, stress level 186, 187 distance from epicentre 211, 216, 220, 221 double-porosity limestones 348–350 dry rock, perfectly dry 343 effective stress change 386 E-modulus of specimen (supposition) 191–193, 196, 200, 201, 342 fault zone 235, 427, 428 formation stiffness variations 386 fractures, fracture frequency 224, 280, 286 fracture compliance 408 fracture nucleation 463 frequency of freeze/thaw 185 frequency of coda Q (earthquakes) 211, 214, 217, 223, 228 frequency (ubiquitous topic) 187, 189, 190, 194, 200, 207, 208, 238, 343–345 frequency of measurement (VSP, X-hole, sonic, core) 208, 209 friction 186, 187–189, 195–197, 206, 219, 224 friction, calculated 197 geology/lithology (ubiquitous topic) 206, (222) geometrical spreading losses 386 heterogeneities 191 high porosity and high permeability 349 inelasticity of matrix 387 increased fracturing 280 inter-bedded units when imaging sub-basalt 403 intrinsic links to macro-processes 487 lateral location in crust 229 magnitude, seismic 220 normal stress ( joints) 199

Index over-pressure 350, 351 porosity 186 pore pressure change 193 reflections 386 rock mass quality Q (see J- components) 200–203, 210, 220, 221, 224–226, 350 rough basalt surface 403 saturating fluid 386 saturation with water 186, 189, 190 saturation with gas/brine 341 shear mobilization, friction 507 shear modulus 356 shear strain 189 squirt flow (see squirt) 17, 182, 183, 187, 190, 202, 206, 346, 349, 355, 356, 457, 461, 465–476 stress-aligned micro-cracks 394 strain amplitude 187–189 strain amplitude and confinement 188 structure 386 temporal seismic events (before/after) 215, 216, 218 viscous losses in compliant pores 387 attenuation, intrinsic 182, 195–197 absorption 210 mechanisms 202, 206 attenuation, inverse of Q (see 1/Qseis, 1/Q at Qseis and Q, all categories of data) 1/Q (1/QP ) – frequency data comparison using Biot 209 1/Q (1/QP ) – axial stress-strain, loaded to failure 195, 196 1/Q (1/QP ) – frequency, calculated for fractures /joints of different stiffness 200 1/Q (1/QP ) – frequency, nucleating, coalescing fracture networks 463 1000/QP – frequency dependence(interbedded sand-, lime-, silt- and mudstones) 207 1000/QE – extensional strain amplitude 187 1000/QE and 1000/Qp – confining pressure 191 Q1 or 1/Q or 1000/Q or Qseis1 7, 9, 45, 79, 80, 179, Ch10: 181–239, Ch13: 344, 345, 349, 363 attenuation recorded during earthquakes albedo (Bo) 214 Q1 actually (Qc1) intrinsic (earthquakes) 213, 214 Q1 actually (Qc1) scattering (earthquakes) 213, 214 QS1 intrinsic component 213, 214, depth-dependence 213 Qsc1 (or ScQS1) scattering component 214 total 214 attenuation recorded in fractured reservoirs depth – Q1 (and Q), in fault zone 235 depth – Q1 – VP (interbedded sediments) 234, (380) depth – Q1 – VP –K (fractured shale) 237 (Q in anticlinal chalk) 235 attenuation recorded in sub-ocean ridge areas (see Qseis listings) QS – depth (hole 504B, Costa Rica ridge, 0 to 1600 m, also Qintrinsic) 280

659

Austin, Texas 444 Austria 76, 95 Australia 25, 67, 200, 201 Aveyron, France 39 AVO 369, 388–392, 407 anomalous most positive, most negative gradients 391, 392 attributes, fracture parameters relation 389 gradients, azimuthal anisotropy effects 389 gradient, maximum 390 most positive near-offset- gradient 392 response with additional fracture sets 393 AVOA 369, 388–392 P-wave amplitude 388 azimuth 314 binning 384, 452 fast- changing across fault 315 full- 3D P-wave survey recommendation 384 narrow- data 373 sectoring 374 stacking 452 azimuthal anisotropy (see anisotropy) anisotropy attributable to structure controlling fluid flow 382 anisotropy in subsiding overburden 453, 454 bins of data 384, 437 deviation of S-wave polarization due to O/R 548–552 deviation of S-wave polarization due to unequal conjugate joints 549–552 isotropy (TIV) 451 sensitivity, with single set 393 separation, of reflection coefficients 393 variation of amplitudes 447 variation of travel times 447 velocity anisotropy 3, 40–43, 314, 317, 373, 382 velocity anisotropy signalling aligned fracturing 382 velocity anisotropy signalling anisotropic stress 382 azimuthally differentiated seismic attributes 384 isotropic source and receiver arrays 384 limited seismic attributes 384 axis of ridge (see mid-ocean) axial modulus (␺) 5, 13 strain 195–197, 300, 339 strain amplitude 340 stress (see VP) 300, 339 valley 437 valley floor (mid-ocean ridge) 436, 437 Azerbaijan reservoir, deeply buried sandstones 312 Äspö, Sweden 119, 131–133 access spiral tunnel, permeability 555, 556

660

Index

Bad Creek borehole, permeability 555 Balder formation 15 band width (ubiquitous term) very high- with down-hole instruments 378 Bakhtar calculator curves 526 Ballotini glass spheres 547, 548, 551, 552 Bandis joint strength, scale-effect components 522 Barents Sea 404 Barton-Bandis constitutive model for rock joints, fractures 401, 424, 428, 435, 456, 484, 486, 490, 492, 493, 537 application if clay-fillings, caution 546, 547 conversion of strength criterion to Mohr-Coulomb parameters 539 coupled modelling 506 coupled stress, deformation, dilation, permeability 523, 524, 526 high-stress version, confined JCS 544 modelling of conducting apertures under stress 512, 541 modelling of conducting apertures, closure and shear 531–533 modelling of saturation on shear stiffness 511, 512 Barton-Choubey shear strength criterion 27, 428, 537 application if clay-fillings, caution 546, 547 conversion to Mohr-Coulomb parameters 539 peak shear stiffness estimate 428 basalt 12, 20, 21, 25, 28, 29 artificial surface in- 80 Atlantic margin- 255 breccia 277 Columbia Plateau- 269 Columbia River, dilated joint 520 columnar- 124–127, 366, 500 columnar/flow entablature- , Hanford 124–127 compliance and dynamic stiffness, columnar 500, 503, 504 Eastern North Sea- 269 flows 277 flow-top weathering 163 flow-top permeability 163 intact, distinction from jointed 269, 276 North Atlantic, Faroe Islands 203 permeable, jointed 270 pillow 277 sub- imaging 403 -to garnet transformation 242 unfractured 278 vesicular 22, 23, 265 basalt, mid-ocean 243, 255, 264, 267–270, 273, 277, 280, 285 basement 8, 221 crystalline 220, 222 sub-ocean 244

basic friction angle (see friction) basin (see also plate tectonics) 179 forearc 227 marginal 227 pull-apart 228 Basin and Range province, Western USA 227, 231 Bay of Islands, Newfoundland 262, 264 bathymetric contours 281, 437 beach sand 254, 350, 351 beam footprints 67 Beaumont Tunnel, near Channel Tunnel, S.England 94, 319 beautiful strikingly- (continuous sub-ocean seismic profile) 284 Beaver County, Utah 42 bed, bedding intra- joints 208, 236 intra- joint apertures 208 joints 145 -parallel 352–357 -perpendicular 352–357 plane opening 319, 320 plane slip, subsidence 399, 400, 453, 454 thickness before-and-after-fracturing VP VS Q1 and permeability 362–364 Bekkelaget, Norway 160 bell-shaped curve 190 BEM FRACOD models 306, 307 bentonite seals 129–130 Berea (see sandstone) Berger, Norway 160 Berkeley, California 422 BGS Anisotropy Project, Edinburgh 405, 409 BHA bottom hole assembly 312 BHC borehole compensated logging 379 BHTV 385, 386 biaxial loading of in situ blocks 165–167, 513–517 loading of tension fracture model 105, 524 loading of 1 m3 blocks 509, 545, 553 loading-path, theoretical, corrected for dilation 553 biaxially-loaded direct shear box needing correct stress transformation, dilation added 554 bi-compressional arrival 313, 317 phantom arrival 313 billiard-table planarity, non-producers 549 Biot 183 flow related to shear modulus 356 fluid flow (boundary shear) 183, 349 fluid-past-frame attenuation 356 -Gassmann fluid substitution, mud-filtration 317 generalized theory of poro-elasticity 320

Index poroelasticity equations 209 theoretical prediction of 209 biotite gneiss highly weathered 11 jointed 11 sound 11 weathered 11 birefringence (see shear wave splitting) 445, 446 bit size variation at KTB 251 Blake Spur, North Atlantic fracture zone profile 273 blast/blasting 30 gasses 133 induced fracturing 63, 64 normal- 127, 128 post- 63 pre- 63 smooth- 127, 128 blastability 17 block, blocks (rock) block tests, lab, large-scale 509, 553 inter-block friction coefficient 6 failure 167 falls 304 heated- test, CSM /Terratek 513–517 length, size sheared 493 modelled- 306, 308–310 natural- size 422 of Berea sandstone 137, 315 of diverse sandstones 359–364 relative block-size 6 samples 27 scaling JRC, JCS to –size 401 size effect on stress-strain behaviour, models 523, 524 size, increasing 308 sizes L1 L2 L3 524 size, relative (see RQD/Jn) 225 size scaling of Ks 421, 422, 523 tension fracture- models 524, 551 test, in situ 165–167, 513 test UDEC-BB model 518, 519 Blow-Me-Down massif, Bay of Islands 264 Bluebell Altamont Field, Uinta Basin, Utah 471–475, 525 Blyvoor gold mine, South Africa 131 bolting 621 bolt spacing 621 BOSK effective medium model 457 fracture porosity 457 fracture density 458 gas or brine distinction 457, 458 boring 30 borehole, boreholes 3, 9, 11 ballooning 321 break-out (see break-out)

661

break-out, log-spiral 302–307 break-out, extensional 303 break-out, slotted 303 break-out (stress) 250, 252, 299, 301, 302–311 causing dispersive effects 314 causing frequency dependent effects 314 -compensated sonic logging BHC 47 creep 297, 299 damaged zone 301–311 deep-, conducting fractures study 536, 541, 542 deviated 305 disturbed zone 301–311 effects 271 elongation 472 ellipticity 301 enlargement due to overbreak 299 extensometers, multiple position, MPBX 301 fluid velocity 206 heaters 513 heater test 134–136 images 471 instrumented- 137, 303, 305 large-diameter 133, 307, 309 large-diameter analogue 319 loading test 136–138 logging 249, 252 logging of disturbed zone 312–320 over-break (jointing) 250, 252, 299, 307–310 plastic flow 299, 303 pre-drilled- 302 radial stress gradients 314 research- for seismic studies (see Hole) 207, 208, 299 shallow test- 203 shear or extension failures 299 size reduction 299 stress anisotropy 137, 314 stress concentrations 136–138, 314, 386 stress concentration reasons for VSP sonic mismatch 386 squeezing 297, 299 televiewer logs, logged 277, 384, 385, 541, 542 to seismic spread 14 velocity 70, 73 wall condition 295, 299, 302–311 Borrego Valley, southern California 260 boulders 12 boundary condition one-dimensional strain 392, 401 roller- 401 Boussinesque elastic foundation 162 BP Claire Field 404–406 BP 4D-4C plans 394 BP Devine Test Site, USA 234 BP Valhall reservoir 453 Brazil 173, 174

662

Index

Brazilian contrasts, Sugar Loaf, tunnel collapse 558 Brazilian dam foundation testing 505 Brazilian Shield 231 break-out analysis 383, 386, 432 anomalies 541 borehole- (‘dog-earing’) 302–307 log-spiral shear-failure surfaces 130, 302–307 orientation logs 389 perpendicular to- 390 phenomena, theoretical 303 stress-controlled-, vertical stress 319 structurally-controlled- 319 V-shaped notches (tunnels, shafts) 127, 128, 131, 303 wedge-shaped fall-out 304 breccia, brecciated rock 161 Brenntangen, Norway 160 bridges, long span 19 bright spots 458 brine -filled cracks 326, 327, 329, 426, 457, 458, 479, 480 saturation effects 326–329 brittle 37 failure -ductile transition 36, 37, 257, 311, 312, 537, 539 shear fracturing 312 broad-band dispersion curves 316 of dipole flexural waves 316 of Stonely wave modes 316 broken rock 118 buckling mode of deformation 310, 311 Buena Vista Hills reservoir, California 236, 387, 388 Bulgaria 19 bulk modulus (K) (see also deformation) 5, 13, 71, 104, 109–111, 529 of infill material, relation to ZN /ZT compliance ratio 425, 426 pressure-sensitive-, using excess compliance 397 reduction due to joint frequency 522, 523 buoyancy effect 297 burial present deep- 300 present shallow- 300 Bussesundet, Norway 145 BWIP, Hanford, USA 124–127 Byerlee (frictional-strength) ‘law’ 536, 542 C-waves 369, 388, 389 repeated 3C x 3C, 9C survey 451 cable bottom drag 11 car, Rio 558 Cabril dam site, Portugal 170

Cajon Pass scientific borehole, San Bernadino, California 432, 541, 554 mobilized friction calculations 544, 554 permeabilities 555 calcarenite 100 calcite 509 -filled joints 79, 165, 167 calcium carbonate cement 206 caldera structure, Kenya Rift 394–396 Caledonian quartzites 11 California 21, 22, 23, 210, 212, 386, 429, 431, 432, 541 Southern 228 Californian earthquakes 226 calliper log four-arm 382, 472 long axis parallel ␴h min 382, 383 measurements 250, 252, 304 noise 320 Cambourne School of Mines, Cornwall 169 Cambrian sandstones 11 Cambro-Silurian limestones 11 Canada 22, 57, 61, 87, 117, 127–131, 217, 325, 331, 369–391, 505, 506 cap rock 372 capillary effects 353 capillary pressure (see patchy saturation) carbonate, carbonates beds 387, 388 domal 443 Palaezoic 430 rocks 196 Carboniferous 447 limestone 499, 500–503 sandstone 11 siltstone 11 casing collapse 399 collapse due to overburden stretch 399–401 damage 454 hundreds of- collapses 400 setting of- 297 waiting for – installation 320 cataclastic fault seals 404 flow of sandstones 312 Catalina Island, southern California 260 Caucasan oil reservoirs 439, 450–452 cavern, caverns 16, 43, 53, 55, 76, 123, 224 reinforcement and support needs 93 CDR compensated dual resistivity tool 313 celluloid Qseis value 181 cement, cemented partially-, vuggy 404

Index cementation 26 high degrees of 370 episode 334, 336 Central California earthquakes 213, 214 Central Europe 107 Cerro Prieto Geothermal Field (CPGF) 435, 436 chalcopyrite 23 chalk 7, 12, 53, 54, 76 and cheese 369 artificial surfaces 80 Austin-, Texas 444 base-, Qseis 235 chalk marl, jointed 16, 77, 79 Cretaceous, jointed 203, 204 domal 443 density-VP 325 dual-porosity, low Q 350 Eocene 123 foundation 29 fractured 297, 391 intact 30 jointed 94 jointed, porous Ekofisk- 339–402, 411, 420, 428, 443, 451, 452, 522, 549 low quality 30 Lower- 77 marl 17, 77, 79, 94, 163, 319 melange 30 ooze transition 206 overlying- 234 pore collapse porous 79 porosity - VP 325 remoulded 30 slickensided joints (see jointed, Ekofisk above) stress-conducting aperture, CSFT 529, 530 thin- beds 206 top-, Qseis 235 Upper-Cretaceous 447 VP – density 326 VP – VS 328 water-weakening, Ekofisk 400 Chamoli earthquake, Garhwal Himalaya, India 218 channel, fast velocity 15 Channel Tunnel, between England and France 17, 94, 319 channelling 160 characterization (see classification) 4, 11, 144, 615 Charlie Gibbs, North Atlantic fracture zone profile 273 Cheddar Gorge 118 chert, Mesozoic 153 Chevron 386 Chile 72 China 74, 76, 94, 110, 210, 212, 213, 245 Chinnor Tunnel, Oxfordshire 16, 76, 163

663

chlorite 509 fillings, outwashed 163 Christensen and Mooney global review of velocity-depth structure 244–251 circular openings 303, 305, 307, 308–311 circulation loss civil engineering 3, 24, 161, 390 projects 14, 45, 324, 484 Claire Field, UK offshore, Shetland Islands attenuation anisotropy investigations 404–406 multi-azimuth walk( float)-away VSP 404 classic equations 4 relationships 369–372 stress transformation equations 552 stress transformation equations, modified 553 classic knee-shaped curve for VP – pressure lab data 31, 32, 80, 81, 85, 87, 168, 192, 193, (198, analogue), 201, (250) for VP-depth trends, in situ, on-land and sub-ocean 91, 93, 157, 271, 272, 286, 290, 166, 167, 241, 245, 248, 250, 251, 252–254, 258, 260–262, 264, 266, 267, 274–277, 280, 281, 284–286, 289 classification (of rockmass conditions) 144 schemes (various sources) 19, 21, 26, 28, 69, 71–73, 75, 75, 106, 142–144, 148 system (Q) (see also Q listings) 3, 13, 75, 92, 93, 108, 134, 144, 146, 150, 152, 164, 615–626 classification of fractured reservoirs 333–335, 440, 441 matrix porosity versus fracture porosity, 441 Types I, II, III, IV 440, 441 clastics Palaezoic 430 clay 7, 8, 11, 12 and attenuation 345, 345 and gravel 24 bearing discontinuities 271, 346, 493 bearing, well-jointed, QH2O – K estimation 557 coatings 148 dark- layers, effect on permeability 359 filled discontinuities, break-down of Lugeon-1/Q relation 555 filled discontinuities, displacements to peak 546 filled discontinuities, stiffnesses 427, 428, 505 fillings 169, 170, 543 fillings (artificial) 81 interlayers 101, 102, 212, 234 filled joints 505 low permeability- 268 Maicop 450 Oxford- 49, 51 platelet alignment 451 -rich materials, flow 302

664

Index

clay (contd ) /sand sequences 7 -seal, -smear along faults 295 sealing of joints, absence of 210, 366 silty-sandy- 238 -smear 308, 428 soft/sensitive 53 swellingsilty- 9 viscous interaction between- particles 194, 345 clay content 17, 331–334 differentiation 331–335 - porosity 331–334 - permeability 332–334 - sonic contra seismic detection 332 stratigraphy-guided 332–335 volumetric- content, relation to QP 346 claystone, Triassic, Lower Jurassic 427 Climax mine, USA 135 closed-form elasto-plastic analysis 305 closure (see normal-closure, stress-closure) of microcracks 31 CMP number, lateral 381 CO2 – flooding effect of increased pore pressure 451 effect on reduced velocity 451 Coachella Valley, southern California 260 coal bedded- 201 bituminous (Pittsburgh, Pocahontas, Greenwich) 168 cleated 168 in-seam measurements in- 200 mine, opencast 118 outbursts 60 pillars 60, 61 -seams -seams, shallow 67 Tower colliery 200, 201 triaxial 103, 104 uniaxial 103, 104 cobbles 12 coefficient of friction (see friction, Jr, Ja) 469 cockroaches 373 cohesion (see Mohr-Coulomb) dissipation of- 304 cold water (see water, water-flood) Cole-Cole coupling from dielectrics 194 Colombia River Basalts, Washington State, USA 520 Colorado, USA 139–142, 165, 167 Colorado School of Mines CSM, experimental mine 513–515 Columbia Plateau, Washington State 269 columnar joints in basalt (see basalt)

columns (see basalt) artificially fractured 81–86 collapse, Brazilian tunnel 558 comb-gauge for roughness measurement 510 Comité National Français 159 commercial prospectivity from neural network 384 commercially important azimuthal anisotropy 446 non-viable fractures, low JRC 364 viable fractures, high JRC 364 commonly held viewpoint re Hmax and flow direction 383 compaction, compacting band (borehole failure mode) 303 drive (Ekofisk) 444 link to time shift 398, 402 mechanical-, of porous sandstones 311, 312 modelling with UDEC-BB, Ekofisk 400, 401, 420 monitoring in 4D, Ekofisk 398, 399 one-dimensional strain- modelling 399–401 reservoir, conjugate jointing 420, 485 rubble-ization (Ekofisk) 443 shale, South China sea 301 Companie Général de Géophysique CGG 396 comparison of (ubiquitous term) core and sonic-log, VP – pressure (depth) 348 competent (little weathered) 11 compliance, compliances (of cracks, joints, fractures, faults) 5, 6, 98 additions, to account for joint sets 393 assumptions 204 changes 309 cyclical- in inter-beds 300 dynamic 6 discussion 282 dynamic joint- 184 elastic- tensor 416, 417 estimated from block test (ZN) 515 excess-, due to fractures 417, 461 fault zone 427 fluid-type linkage 425, 426 fracture, joint normal- (ZN) 6, 200, 204, 391, 417–419, 463, 465, 492 fracture, joint shear- (ZT) 6, 391, 417–419, 463, 465, 492 high- voids, propped by fluid pressure 412 Hudson compliance diagonal (scale-effect model) 503, 504, 515, 526 increase with scale 503, 504 in situ- in fault zone 427, 428 laboratory and field data compared 503 link to porosity, supposition 484–486 link to shear-wave splitting, theory 416–417 model 236

Index model for fault 236 non-linear, stress dependent 464, 465 normal-, sub-vertical structure or shear waves 408, 417 off-diagonal component ZNV 506 ratio ZN /ZT 417–426, 463, 465 ratio ZN /ZT of clay-filled discontinuities 506 ratio ZN /ZT relation to aspect ratio, Liu model 426 ratio ZN /ZT (normalized) relation to fluid-type, Liu model 426, 502 ratio ZN /ZT variation with stress, Pyrak-Nolte 426 saw-cut surfaces, limestones, 5–60 MPa load 501–503 saw-cut surfaces, limestones, inverted dynamic stiffnesses 501, 502 shear and normal- relation 407 shear stress application, effect on- 506, 507 stiffness comparison 421–425, 487, 492, 493 theories for resolving fluid type 425, 426 units inversion to compare with stiffness 424, 427 versus fracture scale (logging method), Worthington et al. 503 with off-vertical fractures or incident waves 419, 420 ZN field measurements 499, 500 ZN and ZT excess compliance matrix locations 417 ZN and ZT equality, or not, discussion 417–419, 463, 465 compliant and non- pores 356 bonds 204 cracks 207 minerals, attenuation 346, 347 compressibility (see fluid) compressional and shear wave seismic 7 bi- arrivals 313, 317 bodywaves 4, 5 slowness 316 waves (ubiquitous term) 355, 357, 362 compression wave amplitude 80–86 reflection 7 refraction 7 compressive strength (see UCS) uniaxial 13, 20, 24, 26, 27 of joint walls (see joint wall compressive strength, JCS) compressive strength – porosity (shale) 26 concrete blocks 27 roughness profiles 509 conducting joints, fractures, (see permeability, joints, fractures) some limitations of conventional assumptions 518 conductivity (see permeability) confidence limits 171 confined artificially 268 strength JCS at reservoir depth 534

665

␴1–␴3, Mohr circle diameter 534, 537, 539, 540, 544, 545 confining pressure 22, 31 artificially elevated 265, 269, 281 extreme 1 GPa 246 versus porosity, extreme pressures 312 conglomerates tunnel EDZ in- 121 weathered 148 conjugate fractures 105, 414, 420, 524, 550 jointing, as alternative to EDA 435 joint shearing 414, 443, 444, 450, 550 pair, sub-parallel to dominant set 390 set of joints 130 steeply-dipping sets 442 conjugate joint shearing causing contrary rotation of O and R 414, 527, 550, 551 connected dis- small-scale fissures 359 connectivity 356 joint- needs at geothermal site 436 Conoco Borehole Test Facility 377, 384, 385, 445, 446, 447 consolidated rock layers 4 consolidation 9, 26 consolidation effects 4 constant thickness slices 374 continental divide 140 converted waves P to S termed C 394, 438 mode- with TIV and TIH 394 contact area (joint, fracture walls) 79, 80 ratio Ao/A1 80 continuum modelling 129, 135 becomes a discontinuum 302–307 Conrad discontinuity 241 continent cross- scale 179 continental crust 241–252, 255 crystalline- crust 263, 263 borderland 260 intruded- crust 255 margins 254–261 shelf 242 sub-crust, velocity-depth structures 241, 242, 245–251 continuity loss of- 304 controversial points regarding effective stress 263, 265–267, 269

666

Index

controversial points (contd ) regarding sonic-log velocity oscillations in inter-beds 300, 301 regarding stiffness and compliance magnitudes 282 regarding stress transformation 252–254 contraction when shearing 303, 304, 444 conversion interface 438, 439 converted P-S waves (see P-S) cooling-joints (see joints) copper Qseis 181 core (see drill-core) 70 analysis 249, 499 Inner-, Earth 241 length 13, 75 oriented- 384, 385 Outer- 241 sampled 339 samples 128, 207–209, 334, 525 side-wall 441 sub- samples 357 ultrasonic VP and Qseis on- 380 core logging 9, 12, 76, 115, 623, App.A 615–624 field sheet 622 statistics 624 value if intersecting structure 407, (617) Core (film) 182 coring, slant-hole 377 Cornwall, England 40 borehole data 543 geothermal project 413, 453, 536 cost of construction 141 of support and grouting (relative) 146 Costa Rica ridge area, eastern equatorial Pacific 277–279 Coulomb friction 282 coupled behaviour 165, 166, 487–492 shear-dilation-flow (see CSFT) 474, 488–492, 507 Coyne et Bellier 110 crack, cracks, cracking, cracks per meter 13, 71, 72 closure 35 closure pressure 22 closure under stress, Walsh 364, 528, 529 closure-opening hysteresis 31, 32 compliance (see compliance) 6 critical- density critique 413 dipping- 445 dry- 43 extension- 130 percentage of- 273 relaxation mechanism 387 saturated 43 sealed 270

sizes 130 sizes, maximum plausible 196, 197 tensor technique 40, 41, 42 thick- 270 thin- 270 vertical- 445 crack density 127, 130 ambiguity 411, 413, 468, 469 critical, description 444 critique of geophysics definition 411, 468, 469 critique of limited range 412–415, 434, 442 decay model, Tod 462 Ekofisk chalk example 442 extreme (Lucite plates) 427 sum of two sets 442 theoretical 195, 196 unrealistic values (Lucite laminates) 421 crater 249 creep 297, 299 dislocation climb, salt, HPHT 321 undefined mechanism, salt, HPHT 321 Cretaceous and Eocene, SW Texas 370 chalk 203 limestone 11 sandstone-shale units 371 critical shearing crust concept 542–552 conducting/non-conducting fractures (Zoback and others) 527, 534, 541–544 crack density description 444 mobilization of friction in crust 542–544 pre-peak or post-peak friction mobilization 545–548 shear strength of crust, non-linear 536–540 state line, Barton 537, 539 criticality caused by microcracks, critique of Crampin viewpoint 412, 413 -normality comparison, re tunnel stability, leakage 413 cross-hole logging (see also tomography) 45–46, 49–52, 57, 160, 207–209 cross-hole model simulation 204 reflection imaging 67 seismic 50–52, 66, 106, 117, 119, 120, 125, 380 seismic, for joint compliance ZN 499, 500 seismic, theoretical aspects 477 seismic tomography (see tomography) 374–378, 504 cross-well reflection tomography 66 seismic tomography and permeability 377, 378 attenuation 234 seismic 203 seismic (high frequency) 377, 387 seismic, shallow 377

Index seismic Q 234 high-resolution seismic, Qseis and VP 236, 237 transmission 66 cross-correlation of parameters 21 cross-discipline parallel 310, 333 cross-discipline region (wellbore alteration zone) 319 cross-over of P-wave and S-wave attenuation 343 Cromer Knoll Group 447 crushing due to blasting 61 crushed zones 145 at borehole scale 306, 308 CRUST 5.1 crustal velocity-depth model 252 crust, crustal (see Earth’s crust) 228 age 228, 262–265, 287–294 anisotropy 246–248 large- faults 223 lower 249 middle 249 old 270 phenomena 179 velocity histograms 247 velocity histograms, depths of 5, 10, 15, 20, 25 km 247 thickness: mean, thinnest, thickest 245, 247 thinner, warmer- 223 upper- velocity-age relation, sub-ocean 287–289 young 270 crystalline rocks (ubiquitous term) 27, 203 pre-Cambrian, Ko 299 upper crust 249 Crystallaire well XTLR 90, 91 CSFT coupled stress/shear flow tests 453 shear-flow-gouge 488–492 tests with carbonate-equilibrated sea water 402, 487 tests with hot Ekofisk oil 401, 487 tests with reservoir sandstones, chalk, shale 528–530 tests with Sellafield ignimbrite/tuff 528–530 CT-computed 196 cube, cubic cubic specimens/samples 127, 137, 185, 303, 305, 359–364 law 278 rock volume, one fracture 472, 474 sandstone 419 structure 201 truncated 39 cubic network, idealized 172, 468, 480 cubically jointed 200 Cundall’s distinct element codes 308–310, 365 curve-jumping, Q-jumping 93, 268, 272, 275, 285, 286, 287 cyclic rock properties -effect on sonic log fluctuations 300, 301 cylindrical specimens (ubiquitous term) Cyprus 278

667

Dacite 28, 29 dam 3, 339 abutment 170, 173, 174 arch- 49–51, 88–90, 99, 102 foundations 50, 51, 57, 99, 174, 505 projects 49–51 sites 27, 56, 77, 101, 102–109, 114, 115, 119, 163, 170 site canyons 50, 51, 56, 99 damage zone (see excavation damage zone EDZ) zone confirmed by bi-compressional arrivals 317 crack-related- (freeze-thaw cycles) 185 damaged rock 130, 303–310, 313, 317 damping (see attenuation) Darcy (see permeability) data acquisition, test equipment field tests (cross-hole, tomography) 62, 125 field test (3D permeability) 174, 292 lab tests (rock physics) 59, 192, 197, 361 deep, deeply layer velocities 140, 141, 156 weathered 4 wells in hard crystalline rocks 538, 541–543 well behaviour 179 Deep Sea Drilling Project DSDP 261, 276, 278 Deere 76 deformability of rock masses 97 deformation forced- apparatus 193, 194 macro- testing 184 micro- 184 modelled- 309, 310 moderate 304 radial 304 sub-millimeter size 309 transient 242 deformation modulus (see also dynamic, Young’s, and Qseis-similarity) pseudo-static- (various symbols: Ed, D, M) 3, 5, 17, 20, 21, 46, 47, 49, 56, 92–95, 97–115, 108, 122, 134, 146, 162, 164, 165, 172, 175–177, 293, 300, 307, 339, 348, 524 as function of radial depth 301 changes due to tunnelling 615 dependence on frequency (see dynamic moduli) 339–341 Ee (pseudo-static, rock mass ‘elastic’ unloading modulus) 97–103 gradient 107 high- 22 increased 17 inequality 97–115, 339 low- 113 M-Q- ␴c relation 176, 366

668

Index

deformation modulus (see also dynamic, Young’s, and Qseis-similarity) (contd ) M-VP relation (note: M is pseudo-static estimate) 101, 167, 365, 366 M-VP – ␴c relation 366 M-VP –Qc relation 92, 94, 102, 115, 161, 167, 232, 257, 258, 348, 365, 449 M-VP –Qc-L relation 164, 175, 176, 293, 365, 366 mean- 114 minimum- 114 reduced 5, 93 reduction 118 reduction due to extension fracture 362 ratio of Ee/Edyn (static elastic/dynamic) 107 ratio of Ed/Edyn (static deformation modulus/ dynamic) 107 tests 46, 50, 51 tension fractured model 524 variable 227 deformation modulus, similarity of static Eintact (when GPa units) to seismic Q 191, 192, 355 static Ejointed (when GPa units) to seismic Q 200, 201, 362, 363 static Emass (when GPa units) to seismic Q 202, 203, 210, 220, 221, 224–226, 269, 348, 350, 352, 365–367, 387, 405, 410, 411, 424, 436, 476, 499, 500 e change in hydraulic aperture 489 E change in (mean) physical aperture 489 delta -peak (␦peak) see joints weakly inclined- 302 density 4, 5, 19 -compressive strength (shale) 26 -depth trends (deeper, deeper holes) 111, 252, 253, 255, 264, 267, 298 -depth trends (near-surface) 20, 78, 111 -depth (sub-ocean sediments, Ontong-Java) 206 field- 21 heterogeneities 191 high- anomalies 254–257 of laboratory samples 19–23, 26, 263, 265 scaling, physical models 547 VP data 19–23, 263–265, 267, 324, 326 depth (ubiquitous term) 13 anomaly 14 effects of- on seismic attributes 77–81 estimation error 14 increasing 13 -modulus trends (see also deformation, and Qc ) 222 -pressure aspects of drilling 295–299 to basement 8 to bedrock 9 zone 19

detecting point (receiver) 153 detonator cap 52 deviated hole 299, 300, 305 deviation (see rotation) detector separations 9 Devonian sandstone-shale units 370–372, 370–371 DHI direct hydrocarbon indicator 458 diabase 11, 12, 119, 121 unfractured 278 diagenesis 206 diameter multi- influence, tunnel deformation 304 diametral pair 307 diametrically opposite ␴␪max ␴␪min 306 diatomaceous earth 26 differential pressure, stress (1-3) applied on model rock masses 524 exceptionally low- 351 exceptionally high- 539, 540 high 538 differential weathering diffusivity 464 dike, dikes 277–280, 264 basic 65 fractured, permeable 294 mafic 215 sheeted 264, 278, 279, 281 dilatancy pre-earthquake 233 dilatant 303, 304, 307–310 non- 302, 303–305 strain 190 dilation 4, 84, 86, 169, 212 causing build-up of stress 546 due to triaxial shear failure 540 enhanced- of fracture set 383 for enhanced permeability 435 mobilized-, in stress transformation 553, 554 onset of- 540 peak- angles 525 shear-induced- 390, 392, 406, 414, 444, 520, 522, 523, 525, 526, 527, 531–533, 536, 540, 548, 550, 553 dilatation 5 diluvial clay 26 Diluvium 142 diorite 20, 139–142 Äspö 139–142 Äspö permeability 555, 556 Qseis 181 dipole azimuthal, shear-wave, sonic logging 301, 302, 310, 312–316 dispersion cross-over 315 flexural wave split into fast and slow directions 316

Index modular- tool for radial, axial, azimuthal directions 316 receiver array 314 receiver pairs 313 tool orientation relative to formation 314 tools pipe-conveyed for horizontal holes 315 transmitter tool 312, 314 transmitter pair 314 well-logs 382 directional permeability (see permeability, anisotropy direct hydrocarbon indicator DHI 458 shear test DST 444, 452, 490–492, 510 shear test over-loaded, due to OC 517 shear test, UDEC-model 518, 519 shear test, reconstruction of shear-dilation path 444 wave 383 discontinuity, discontinuities clay-filled different (micro-) scale 418 discovery and exploitation of new fields 396 discrete particle model 203, 204 reflection 372 dissolved air out of solution 133 dispersion (frequency dependence) 182–184, 187, 189, 190, 191, 194 caused by microcracks or fractures, discussion 412, 413, 415 caused by microcracks or fractures, modelling 460–481 for reservoir characterization 387, 388 incorrectly assessed 379 intrinsic 387 profiles 387 dispersive effect of fractures contra micro-cracks 5, 412, 415 displacement (of tunnel) 151 discontinuity 309, 518–520 modelled 309, 310 to peak strength (see joints) 511, 523, 546 to peak, up-scaling 531–533 discontinuity clay-filled 156, 169, 188 spacing 79 discontinuum lies on the floor 319, 320 log-spiral fractured- 303, 305, 386 modelling 400, 401 partly connected 307 discontinuity 189, 200 displacement- events 189 monitoring 134, 135, 151, 152 distinct element model (see UDEC, numerical modelling) Dixie Valley borehole data 543 Dneiper ship lock 117, 118 ‘dog-earing’ (see borehole breakout)

669

dolerite intact 22, 23 joint, stress-closure 494 fissured 22, 23 joint, stress-deformation 495 joint normal stiffness, initial 495 meta- 264 weathered 22 dolomite 12, 32, 61, 100, 114 beds 486, 488, 520, 521 low porosity 31, 32 higher porosity 359 high Qo 231 Ko 299 porosity – VP 325 VP – density 326 VP – VS 328 Webatuck 31 domain 173, 616, 622, 623 domal structure Ekofisk 399, 401 jointing 392 down-dip shear mechanism 401 down-hole acoustic tool 73 mud motor 312, 320 receivers and sources 378 seismometers 221–224 sensor array in overburden and reservoir 404 sources, 4D time-lapse 352 VSP triaxial accelerometer sensor array 404 down-going multiple 383 slab 179, 227, 228 dragline excavators 118 drainage and imbibition 337 in presence of patchiness 335–337 in presence of varied frequency 335–337 Draupne Formation, central Viking Graben, North Sea 352 drift, drifts multiple perimeter- 157 drill-holes (see boreholes, wells) 12 drillability 17 drill-and-blast tunnelling 17, 30, 124, 125, 131–133,151 drillcore (see core) 11, 76, 77 drilling (exploratory) 4, 9 -induced fractures 73 fluid pressure 299 mud 295, 296, 299 rate 150 shallow crust from submersibles 266 super-deep 249, 252 variable azimuth- (physical models) 302, 303, 305 while under stress 305

670

Index

dry 15 boreholes 73 fracture/joint 197–199 fractures, assumed effect on compliance ratio ZN /ZT 426 rock, perfectly dry 343 state 5 state, contra saturated, joint stiffnesses 507–512 drying out 30, 31, 121, 353 Drøbak, Oslo Fjord, Norway 56 DST (see direct shear test) dual porosity, see porosity ductile 37 -barrelling of sandstone samples 312 dynamic bulk modulus K 13, 71, 104, 109–111 compliances (see compliance) cyclical events 373 E-moduli (lab-scale) 201, 339, 340 E-moduli, function of frequency 339 E-moduli, function of axial strain amplitude 339, 340 E-log 339 E-low frequency 339 ejection, tunnel failure 304, 307 field modulus (seismic) EF dyn 105–108 fracture compliances (see compliance) joint compliances (see compliance) joint stiffnesses (see normal stiffness) laboratory modulus (acoustic) EL dyn 108 laboratory Young’s modulus (from VP and VS ultrasonic) 104 laboratory Young’s modulus (from VP and VS ultrasonic, as function of stress) 126 loading 182, 422–424 loading facility 192, 197, 357–359, 359–364, 422–424 micro-excursions 184 moduli 104–110 moduli M1,2 (-ratios at different frequency) 184 modulus Edyn (from VP and VS refraction seismic) 13, 71, 75, 107, 109, 110, 161 modulus Edyn (from AE interpretation) 130 normal stiffness Kn dyn 200, 202, 423, 424, 478 normal stiffness effects on velocity-frequency 478 parameters 7 permeability discussion 425 Poisson’s ratio (see Poisson’s ratio) properties 5 properties of matrix 6 properties of rock mass 6 ratio EL dyn/EF dyn (lab/field: dynamic) 106 ratio Edyn/Estat 340 ratio EF dyn/D (field: dynamic elastic/static deformation modulus) 107, 108 ratio Ks dyn /Ks dyn 423, 424 shear modulus ␮ 5, 13, 71, 104, 109, 111,161

shear stiffness Ks dyn 423, 424 stiffness testing 422–424 stiffness modelling, UDEC 479 testing (ubiquitous term) testing under normal load 197 E and e apertures for joints or fractures (see hydraulic, aperture) Edyn Estat (see dynamic, see deformation modulus) 340, 493, 507 E-modulus (see also Young’s, dynamic, and deformation) 191, 192, 424 earth, Core 182 interior of the- 181 internal structure of the- 52 – science’s favourite continuum theory 306 earth’s crust continental- 241–253 -continental margins 254–261 East-Pacific rise 273–287 mid-Atlantic ridge 261–273 mid-Atlantic ridge and East-Pacific rise ages 287–290 velocity structures 241–291 earthquake, earthquakes 52, 209–219, 257, 428–438 attenuation (coda Qc1, QS1 and albedo: see attenuation, and Q section) attenuation of high-frequency energy 221 back-scattering body waves from- 210 coda (see earthquake coda) damage (caused by acceleration) 218, 219 distant 210, 211 deep 261 deep- zone (sinking lithosphere) 227 deeper heterogeneities above- 210 doublets 215 energy of 181 epicentre 213 epicentral distance 216, 220, 221, 434 event-distance effects 211 focal depth 214 focal depth change 212 frequency (see frequency, and Q section) geometric spreading 215 hypocenter migration 215 hypocentre relocation 257 hypocentral distance 433, 434 hypocentral zone 210 local 210–213, 258, 428–434 magnitudes 213–219 main shock 213 monitoring stations 211 pre-cursory changes 215 QP and QS components 212

Index rays from deep- 261 reduced coda Qc after main shock 213 reduced coda Qc before main shock 213 seismogenic depths 222 seismogram 209 seismometers (three component) 219 seismometers (down-the-well) 221–224 seismometers (closely-spaced) 221–224 separation (intrinsic and scattering attenuation) 213, 214 shallow- 261 shallow heterogeneities above- 210 shallow-layer scattering and resonance 221 site effects 209, 220, 221, 224 small local- 212 spatial variation of amplitude, frequency-content, coda duration 221 swarm 213, 215 take-off angles from source 215 thrust-fault, shallow- 244 travel-time data 258 earthquake coda (see Q section) late- 215 low coda Q 215 high coda Q 215 spatial variation 215 temporal variation during seismic events 210, 212–218 earthquake, aftershock, locations, data, cited Anza, California 222 Chi-Chi, Taiwan 436 Central California earthquakes 213, 214 Cerro Prieto Geothermal Field 435, 436 Chamoli earthquake, Garhwal Himalaya, India 218 Gazil earthquake, Uzbekistan 211 group of locations for Qc-frequency data (Aleutians, Carolina, New England, Southern Norway, Canadian shield, Montenegro-Yugoslavia) 217 group of locations for Qc -frequency data (Afghanistan, Alaska, China, Eastern USA, Friuli: Italy, Guam, Hindu Kush, Iceland, Kinki, Southern California) 228 Ghuj earthquake, Gujarat, India 219 Haicheng earthquake, China 212, 213 Hawaiian earthquakes 213, 214 Húsavik, Iceland 432, 433 Hyogoken Nanbu earthquake (and Tamba region), Japan 217 Iceland 416 Iceland, Station BJA 433, 434 Kuril-Kamchatka earthquakes 213 Loma Prieta earthquakes, California 215 Long Valley earthquakes, California 213, 214 Mamouth Lakes earthquakes, California 212, 213 Mid-Atlantic Ridge axial valley site 436, 437

671

Misasa earthquake, Japan 213 New Madrid seismic zone 428, 430 Norris Lake Community, Georgia, USA 215 North Anatolian Fault Zone, Turkey 220 Oishiyama earthquakes, Japan 210, 211 Olkaria Geothermal Field, Kenyan Rift 394–396 Parkfield Dense Seismograph Array, USGS, California 216, 221–224, 429, 431, 432 Petatlan earthquake 213 Rio Grande Rift earthquakes, New Mexico 210 San Andreas fault zone SAFZ (90, 91, 95) 221–224 Stone Canyon earthquakes, California 210, 211 Southern Germany 220, 221 Tangsham earthquake, China 110, 212, 213 Tsukuba Oishiyama earthquakes, Japan 210 Vamanashi earthquake 213 earthquake monitoring wells in California, specified Cajon Pass 221–224 Varian (array) 221–224 XTLR 91 earth-pressure-balance EPB 4 East Coast Margin Igneous Province ECMIP 254–256 East Pacific rise crustal (see Q and Vp data lists) velocity structures 273–289 East Texas well 441 EDA extensive dilation anisotropy due to cracks/micro-cracks assumed source of shear wave splitting 409, 410, 412, 414, 428, 429, 432, 436, 453 critique 411–413, 470 Edgar Mine 64 EDGE 801 profile, Atlantic margin 256 Edinburgh 405, 409 Edinburgh Castle 118 EDZ excavation damaged zone: 117–138, 151 EDZ excavation disturbed zone 51, 87, 93, 97, 106, 107, 115, 117–138 caused by joints, fractures, bedding planes 306, 308–311 four-sector- 306–308 measurements in tunnels 31, 119–133 multi-diameter- 308 of drill-and-blasted tunnels 119–133 of shafts 119, 121, 123 of slopes 117, 118 of TBM-driven tunnels 123, 306–310 of tunnels in general 301 velocities 140, 157 EDZ, mini-, around boreholes 301–320 azimuthally varying- 301 -discontinuum 302–306, 319 -fluctuation in inter-beds 379 effective stress (ubiquitous term, see also stress) 263, 267, 295–297, 307, 351, 352 Egyptian oil-producing well 315

672

Index

Eikonal solver 16 Ekofisk, Ekofisk reservoir 339, 392, 420, 438, 451, 487 choice of deformation moduli at- 339, 443, 444 choice of shear stiffnesses 427, 428 gas-cloud difficulties 451, 499 geomechanics-based 1D compaction model 399, 420, 443 imaging through shallow gas 394, 396, 399 index testing of conjugate joints 508, 510 joint shearing 399, 401, 420, 443, 522 modelling compaction at- with UDEC-BB 401, 443 modelling subsidence at- with UDEC-MC 400 monitoring with 4D 398, 399 no discovery, no production if 549 pressure reduction 522 world’s first marine 3D/4C, 2002 451 subsidence at- 339 elastic 4 acousto- 137 constants (static) 7, 183 constants (dynamic) 7, 183 continuum theory 9 matrix 360 moduli, modulus 4, 5 -parameters, time dependence in 4D 398 pseudo- response 306 reversible 183 scattering 387 state 59 stiffness matrix 417, 451, 477 stress distribution, borehole 137, 302 stress distribution, tunnel 131 tensors, 3D 374 waves (ubiquitous term) elasticity 373 electrical circuit theory 181 conductivity 174 resistivity (see resistivity) electro-magnet 187 electro-magnetic wave conductivity 169 elliptical yielding zone 311 empirical (ubiquitous term) equations (ubiquitous term) 256, 511 predictions 175 energy loss 18 loss/dissipated per cycle 18, 181 storage 18 engineering geological investigations 76, 469 geologists 58, 442, 469 -scale 179 units 161

England 11, 21, 29, 40, 42, 74, 79, 80, 94, 163 North East 203, 207, 234, 346, 356, 379, 380 Southern- 319, 320, 488, 520, 521 S.W- 488 enhanced oil recovery EOR 66 production techniques 363 environmental, environmentally changes 30 effects 19 sensitive areas 172 Eocene 447 Eocene limestone 11 Eocene and Cretaceous, SW Texas 370 EOR enhanced oil recovery 363 gradient enhancement 295 permeability enhancement 295 epicentre (see earthquake) epidote mineral fillings 278 escalators 4 Ethiopia 245 EU Hydratech Project 237 Eurasia 230 Eurasia regions Altaids 230 Arabian Shield 230 E. European Shield 230 Indian Shield 230 Siberian Shield 230 Ural Mountains 230 Eurasia, tectonic map, types 230, 246 Shields 230 Tethysides-Alpinotype 230 Tethysides-Germanotype 230 European injection pressure limit (grouting) 162 Eurotunnel 94 excavation damage zone (see EDZ) effects 30 method pre- velocities 165 process 30 expansion due to high temperature 246 experimental testing facility (ubiquitous) 192, 197, 357–359, 359–364, 192 explosions nuclear tests as source 251–253 exploratory drilling 4, 295 exploration borehole 306 -development well log display 316 galleries 99, 119

Index infrastructure-led- 320 new- concept 372 on-land 4 marine seismics 4 explosive 63 charges 281 source, sources 9, 243, 244, 254, 269, 389 extension fractures created under biaxial stress 359, 361 rough- 364 VP VS 1/Q and permeability behaviour of- 361–364 extensive dilation anisotropy (see EDA) extensometers 46 extrapolation of properties 49–51 extrusives (ocean-floor) 281 Factor-of-safety 306, 307 zone rotation 306, 307 failure gradient, well pressure related 296 modes, tunnels 304 surfaces, discretized beforehand 310 famous landmark 558 Faroe Islands 203. fast and slow directions 374, 430 and slow qS1 and qS2 directions 313, 314 axis of formation 313 compressional wave 209 direction 38, 128, 276 Fourier transform 84 polarizations 430, 437 spreading ridge 281 fault, faults, faulting 3, 65 active strike-slip- 257 causative 226 compliance 427, 501 cemented- seals 404 domal 391 either side of a- 314 first order transform- 283 gouge 139 known- 24 major 164, 226 major, VP ,L, Qc estimates 226, 556 mature sections of-, no dilation correction 554 minor 14, 164, 175, 510 minor, VP ,L, Qc estimates 226, 556 newer sections of-, dilation correction 554 plane solutions 432 regional fault zone 17, 47, 48, 53, 257 rosettes, water-flood directionality 403 swarm 411

shear strength discussion, JRC, JCS possible 547 throw magnitude, scale-dependency 447 traces from coherency analysis 392 transform-, intra-continental (NAFZ) 220 trap valley-parallel fault swarm 154–156 welded portions of- 427 zone 7, 9, 47, 48, 76, 79, 156, 157, 188 zone compliances 427 zone model, Tod 462 zone, neighbourhood of 306, 308 zones, tunnel collapses, Q 558 fault seals phyllosilicate 404 cataclastic 404 faulted anticline 391 faulted rock 48, 161 severely- 156 ubiquitous at all depths, KTB well 252 faulting adverse- 363 Fenton Hill borehole data 543 permeability 555 Fiji Islands 179, 227 filtering of high frequencies 199 filter paper (artificial fracture filling) 82 finely interlayered sequences 379, 380 first breaks 204 First International Workshop on Scale Effects in Rock Masses 537, 538 fissures, water-filled 266 finger-print, primeval 3D roughness 516 finite difference (see numerical modelling) Finnsjön, E. Sweden 203 first arrivals 437, 479, 481 fissure features 28 fissured bulk samples 22, 23 non-fissured bulk samples 22, 23 rock 21 Fjellinjen road tunnel, Oslo, Norway 53 fjord 56 flat spots 458 Flatey Island, Iceland 433 flatjack loading (see also plate loading) 164–166, 513–516 flexural shear waves 312, 314, 391 polarized into fast and slow directions 312, 314 flow local 183 macro- 183 no-flow criteria re fracture orientations 536, 541, 542

673

674

Index

flow (contd ) simulator 398 versus fracture(joint) stiffness 425 flow zone indicator (see FZI) fluid bearing lenses 414, 527, 550, 551 compressibility effects 397 compressibility effect, oil or gas, ZN , slow S-wave 407, 408 -conducting joint structure 357 crustal, lost with time 231 filled microcracks, preferentially oriented 408 flow monitoring, challenge 359 flow pathways parallel to ␴H max 526 flow rate 166 flow through local discontinuum 317 flow through log-spiral shear surfaces 317 -front monitoring, 4D 252 -lense rotation phenomenon 390 loss 231 -past-frame attenuation 356 path assisted by joint roughness 358 pressure close to ␴H max , critique 416 micro- 282 saturation 8 saturation effects 183 type from compliances, theories 425, 426 velocity of- 30 viscosity 457 fluid substitution theory 407 contrary to the wisdom of- 407 flysch sandstone 25 FMS log, analysis 389, 455, 525 Foidel Creek, Colorado 60 foliation(ubiquitous term) joint 513, 514 planes 355 Folkstone Warren, S.England 320 formation density tool (compensated) 47 fast axis 409 fast axis substitution for ␴H max 409 micro scanner 47 slow axis 409 fossil-spreading direction (sub-ocean crust) 276 fossil flow permeabilities 278 flow porosities 278 spreading direction 276 forced deformation apparatus 193, 194 Forgario: limestones in situ 105 formation damage (see borehole, see EDZ) evaluation 312–319

micro-scanner 379 undamaged- 313 foundations 3, 30, 224, 339 bridge 19 dam- 50, 51, 56, 159, 224 moduli 159 pier 19 powerhouse 172 treatment (grouting) 170–172 four-component 4C acquisition 394, 396 sensing under gas clouds 394 sensors 391 four-dimensional 4D in-well installation 382 full-field 4D4C re-shoots 396 frequent 4D4C surveys 396 monitoring of reservoirs 396, 397 monitoring of compaction 398, 399 need for velocity and attenuation monitoring in 4D 397 repeated surveys 372 seismic in fractured reservoir 364 time-lapse monitoring 352, 353 time shifts, in compacting reservoir 398, 399 frac gradient (see fracture) 296 fractal characteristics 223 earth 179 re vertical wells, vertical structure 441 fracture, fractures (see also joints, cracks, tension-) alignments, alternative to ␴H max 410 aperture (see aperture) azimuth 382–386, 388–396, 401–406, 407–482 behaviour differences, rough and smooth 363 closure cycles 363 closure-velocity stronger result 363, 364 closure-permeability weaker 363, 364 compliance (see compliance) compliance tensor 479 compliant- 407 conductivity (see permeability) criticality (Crampin) 413, 434 densities 224 density:N/V.r3 407 density, inversion for 471, 474 density, need for volume-defined 407, 455 density in reservoir, model 472, 474 density variation between two sets 404 detection 377 dilation, model 444, 519 displacement 87 fluid-flow pathways 373 fluid investigations 314 frequency variation at fault zones 394

Index gradient 296 heavily-, numerical (UDEC-MC) model 308 heavily-, physical model 524 induced-, high pressure triaxial, shear strength 537 investigations 313 like cockroaches (families, all scales) 373 liquid-filled rather than gas-filled- 391 mechanics code (FRACOD) 306, 307 network 172 normal or -strike anomaly, AVO 391 open- (see next) O/R open, rock-to-rock contrary rotations 414, 446, 450 orientations from outcrops, FMS, core 250, 252, 382, 385, 472, 475, 525 orientations (from AVO) 390 pattern, outcrop 448 permeability and stiffness link 425 permeability, changes of 372 permeability, exploring for 372 permeability tensor 479, 480 permeability-velocity-loading hysteresis 363 porosity 457 radius versus density 472, 474 rosettes 385, 403, 404, 406, 441, 448, 475 rosettes, water-flood directionality 403 rosettes, reservoir and overburden 406 rough extension- 363, 406 rough extension- showing ‘open’/‘closed’ rotation 406 sealed- parallel ␴H max are numerous 441 sets, two, perpendicular 447, 448 several- systems (in AVO case) 390 shear and normal compliance ratio 393 spacing (Fm1) 11, 57, 69, 70–72 stiffness (see stiffness, joint stiffness) stress alignment excellent, near-surface 447, 448 strike, dominant 383, 389 strike, production trend mismatch 383 swarms, below seismic detection 455 tensile- traces, from point load 385 tension- , physical models 523, 524, 551, 552 zone 11 zone, mid-ocean ridge 273 fracture characterization from core 382–386, 389, 404–406, 446, 447 borehole logs 382–386, 389, 404–406, 446, 447 outcrop analogues 382–386, 389, 446, 447 fractures, open conducting- 404 conducting- due to shear and dilation 406 critically (shear) stressed crust 541, 542 due to shear strength, dilation, in situ block sizes 534, 535 from 0° to 90° from ␴H max 441 parallel to ␴H max assumption 390

675

parallel to ␴H max measurements 402, 403, 447, 448, 450 rough fractures, hard rock needed for parallel ␴H max 541 fractured badly 163 heavily- 7 heavily-, generic case 309 moderately 11 reservoirs 179, 369–406, 438–459 reservoirs, ‘open’ fractures/joints, tests, models 528–534 petroleum reservoirs 3, 35, 373 petroleum reservoirs, extend current thinking 483 rock mass 5 sample 197–200 zone 73, 153 zone width 73 fracturing anisotropically distributed 304 before-and-after- VP VS Q1 and permeability 362–364 better identification of-, with shear-wave technology 407 development over time 306 due to over-pressure 296, 352 pervasive 273 stress induced- 314 stress-related (see borehole, tunnel) 302 tectonic 273 thermal Franciscan rocks, California 222, 257 QP and QS 222 France 39, 76, 185, 320 freeze 32 -thaw cycles 185 freezing 32, 33, 53, 56, 185 frequency 112, 183, 198 and viscosity (product of ) 207 band 182, 184 dependent 5, 17, 183 dependent cross-well data 378 dependent energy loss 190 domain 118 dominant- 7 dynamic normal stiffness, joints 498 effect on VP with patchiness 335–337 high-, low- differences re scattering, intrinsic attenuation 387 high- propagation over long distance 378, 478 high- P-wave monitoring 301 higher-, shallower viewing LWD velocities 318, 319 independence below 1 Hz assumption 232 influence on attenuation in jointed, bedded rock 207–209 instantaneous-, difference versus depth 459 low-, for imaging, sub-basalt 403 lower-, deeper viewing wireline velocities 318, 319

676

Index

frequency (contd ) negligible- dependence 239 power laws relating seismic Q and f 205, 212, 217–219, 228 predominant- 212 frequency dependence of coda Qc 210–212, 214, 217–219 damage from freeze-thaw 185 Edynamic 339, 340 E moduli (97–105), 339, 340 fluid mobility 194 magnitude spectra, jointed samples 199 Q, Qseis, QP 187, 189, 194, 207 QE 190 1/Q of intact samples 200, 343 1/Q of jointed samples 200 Q, 1/Q in situ 209, 238, 239 1000/Q intact samples 191, 344 1000/Q in situ 208 1/Qc (coda Q,) from earthquakes 210, 211, 214, 217–219, 223, 228 1/Qe,p,k,s 194 strain amplitudes 182–184 VP intact samples (patchy saturation) 337 VP intact samples 343, 344 VP jointed samples) 196 VP in situ (e.g. sonic/VSP) 207, 208, 234, 252, 280, 313–315, 318 friable rock classes 28 friction (cracks, joints, fractures) basic- angle (␸b) 509, 510, 538 basic- angle, effect of moisture 511 coefficient 183, 535, 540, 542, 543, 540, 542–544 crack-tip- 196 critical state- angle, ␸c 538, 539, 544, 547 grain boundaries 183 mobilized- , conducting fractures 542–545 macroscopic- 188 non-linear 17 opposed by 182 residual- angle (␸r) 509–512, 522, 525, 526, 531–535, 539, 547, 548 residual- angle, effect of moisture 502, 509–512 frictional attenuation mechanisms (see attenuation) dissipation 182 mobilization (see JRCmob) mobilization at larger strain 304 sliding at grain contacts, boundaries 188, 219, 220 fused glass beads attenuation – frequency 345 lack of pressure dependence 343 VP – frequency 345 FZI flow zone indicator 333–336

link to RQI reservoir quality index 333 logging-based- 336 relation to permeability 333–336 relation to porosity 333–336 sorted by- 334, 335 Gabbro 11, 12 meta- 264 olivine- 264 pyroxene- 264 unfractured 278 gallery between- seismic 49–51 -to-gallery 49–51 gas and condensate 343 bearing sandstone reservoirs 343 brine, distinguishing 455–458 chimney 456 cloud effect 399 cloud penetration 396 condensate 343 detecting-, (when over-pressure) 343, 349, (350) extraction (earthquake source) 211 filled fractures, compliance ratio discussion 393, 417–421 fractured- reservoir 471–475 generation 296 hydrate sediments 237, 238 oil contact outbursts 60 pockets squeezing 182 producing natural fractures 384 sand 15 shallow- 407 time-sag due to- 381 zone in well, QP and QS separation 345 Gassmann fluid substitution 458 predicted 328 theory for porous rock 421 theory error for fractured porous rock 421, 458 garnet-free 256 Geodia 110 geology 4, 9, 255 steeply-folded- 408 structural 9, 214 geologist engineering- 11 geological investigations 19 profile 9 reality 14, 15 structures, major 65, 169 time/age 370–371

Index geomechanics 179 school of thought 534 geometrical spreading 280 geophone 7 in-line, vertical, cross-line 391, 394, 396 position (VSP) 383 spreads 42 geophysical 3 logging 153 team 9, 169 geophysicist, geophysicists 17, 95, 219, 369, 407, 416, 421, 469 posing questions to- theoreticians 520, 531 Geophysics (journal) 378 geophysics 98, 197 literature 6, 488 principles of 434 geophysics jargon without explanation CMP-gather 234 CMP number 235 NMO-corrected 234 QVO quality versus offset 234 true-relative-spectrum-processed 234 Geoteam 148 geotechnical impossibility(?) 415, 416 investigations 19 geothermal sites Beaver County, Utah 42–44 Cambourne School of Mines, Cornwall 169 Cerro Prieto- Field 435, 436 Olkaria Field, Kenyan Rift 394–396 steam-dominated –field, lower Poisson’s ratio 394 water-dominated –field 394 geothermal gradient 351 -metamorphic depth-permeability curve 555 geotomography (see tomography) Germany 249, 252, 543 Southern (seismicity) 220, 221 Gezhouba hydroelectric project, Yangtze River, China 172 gilsonite dikes 472, 475 Gjøvik (Olympic) cavern, Norway 16, 43, 53, 55, 74, 88, 89 Ghuj earthquake, Gujarat, India 219 glacial post- landslide 95 till 12 glacier glass (see also fused) beads, low Q 205 value of Qseis 181 global

677

measurement locations 246, 251 new- model 249 optimization 445 review of crustal velocity structures 244–251 Glomar Challenge drilling ship 263 gneiss 4, 11, 12, 13, 32, 38, 100, 139–142, 222 CSFT, gouge formation 492 deeply weathered 4 foliated 38 ‘geologically uniform’ 215 in situ 527 jointed (in situ) 16, 70, 88 Ko 299 Mojavi, S. California 261 QP and QS, Cajon Pass drillhole 222 schistose- (EDZ) 123 sequences (KTB) 249 tolerance of stress anisotropy 298 tunnel EDZ in- 121, 122 weathered 107, 108 god-given means 407 Gonwanaland 231 gouge production (see joint) GPS clock 153 graben 238 grain, grains boundaries 182, 183 boundary cracks, due to stress unloading 397 boundary sliding, attenuation 219 boundary weathering 264 contact microcacks 347 density 343 loosely-packed- 206 size 343 size squirt-flow, no fractures 475 granites 4, 11, 12, 13, 61, 100, 139–142, 196, 222 aspect ratio influences 326 Äspö 131–133 Äspö permeability 555, 556 artificial surfaces 80, 82 Barré 36 basement- , Egypt, fault zone 315 Cajon Pass borehole 541, 542 Casco 31 Chelmsford 30 Cornwall (in situ) 40 decomposed 11 deeply weathered 4 in situ, block test 527 intact 11 jointed (in situ) 11, 24, 40, 41, 70, 72, 159, 165, 166 Ko 299 massive 128–131 plutons 243

678

Index

granites (contd ) QP and QS, Cajon Pass drillhole 222 1/Q (1/QP) – axial stress-strain to failure 196 Qseis 182 shear strength in situ 299 Sierra white QE Stripa (quartz monzonite) 133–136, 422–424, 435 stress-conducting aperture, CSTF 529, 530 Tertiary 19, 21 tolerance of stress anisotropy 298, 299 Troy 31 tunnel EDZ in- 121, 122 URL Manitoba 128–131 weathered 20, 21, 24, 77, 107, 108 Westerley 31 granodiorite 7, 8, 12, 72, 100, 203 artificial surfaces 82 Cajon Pass borehole 541, 542 Ko 299 QP and Q S , Cajon Pass drillhole 222 granulite to ecologite transformation 242 gravel 11, 20 formation 205 gravity anomalies 255–257 Great Lakes, Canada, USA 231 Green River (Upper/Lower) reservoir formations 471–475 greenschist sub-ocean floor 281 greenstone 32 GRM generalized reciprocal method 15 Grimsel, Switzerland 124, 169 groundwater pressure drawdown 53 groundlevel 3 grout curtain 57 monitoring (with velocity) 170–172 penetration/take 172, 490 prediction 479, 487, 490 grouting (see also pre-injection) 88, 89, 170 after- 170–175, 292, 293 before- 170–175, 292, 293 efficiency 171 Guadalupe Island 267 guillotine, double-bladed 523, 524, 551, 552 Gullfaks field, North Sea 398 Gulf Coast reservoirs 311 Gulf Coast Plain 231 gypsum samples CaCO3 and water, cement component 547, 548, 551, 552 with flaws 40, 41

Haematite Haicheng earthquake, China 212, 213 Hales method 15 Haltenbanken, Norwegian sector of North Sea 312 hammer seismic 3 Hanford, Washington 119, 124–127 hard (brittle) rock (ubiquitous term) 6, 7, 13, 74, 76, 130, 147, 272 beds (masking) 146 crystalline rocks (ubiquitous term) 210, 527 jointed rock Qc Emass VP 226, 556 massive rock, Qc Emass VP 226, 556 rock sites 12, 70–72, 160 hardness 27 harmonic excitation 181, 205 Hawaii 213, 214 Hawaiian earthquakes 213, 214 Islands 257 ridge 257 head -race tunnels 147, 154–157 waves 16 heated block test 513–519 flow tests 515, 527 joint samples 197 mine-by 135 heater-borehole 134–136 heat-flow assumptions (crustal) 248, 249, 555 heat-producing concrete 130 heavy oil (194) heavily jointed rock mass 9 Helsinki 72–73 Hertz contact theory 23 Heterogeneous Earth 213 heterogeneity 373 heterogeneous conditions 4 re-classified as severely- 373 severely 373 hexagonal-crack, APE model 415 high explosive (see explosive) fluid pressures 320, 321 frequency (see frequency) pressure high temperature well (see HPHT) 320, 321 pressure (ubiquitous term) resolution images (ubiquitous term) 3, 379 -rise building collapses 219 -speed layer 14 strength rocks (see also hard rock) 101, 103 stresses (see stress) 320, 321 temperature 248–250, 320, 321

Index velocity layer 49 voltage sparker 49 highway cutting 25 Hijori deep borehole data 555 Himalayan dam sites 12, 122 history matching to parameter estimation to prediction of performance 396 Hole 418A, Eastern Pacific 276, 279 Hole 504B, eastern equatorial Pacific, Costa Rica Ridge area 276, 277–280 Hole 648B, mid-Atlantic ridge 267 Hole 735B 279 Hole RCF-1 (Sellafield) 387 hole collapse 320 stabilization 305 homogeneous -and isotropic -and isotropic, or heterogeneous and anisotropic 382 isotropic elastic 382 Hong Kong 74, 76 Honshu-Shikoku Bridges 19, 21 Homestake gold mine 60 homogenous zones (tunnel) 149 horizontal drilling 315 stress (see stress) horizontally bedded (ubiquitous term) 374 hornblendite 32 hornfels 38 host rocks 22 hot dry rock project (see also geothermal) 195 HPHT American unit classification 320 extreme- 320 high pressure high temperature 320, 321 Tier I, II, III 320 three-tier classification 320 ultra- 320 HRSN (see Parkfield) HTI (TIH) media 382, 394 HTM modelling effects during water-flooding 401 fully-coupled- of water drive in jointed rock 402 Hudson diagonal (compliance scale-effect model) 503, 504, 515, 526 Húsavik, Iceland 432, 433 Húsavik-Flatey fault, Iceland 433 hybrid machine 4 hydraulic aperture (see aperture) 83, 161–163, 169, 198 apertures in fracture zone 506 conductivity 3, 162, 163 diffusivity 169

679

fractures (as reflectors) 249, 252 fracturing (minifrac: stress measurement) 19, 53, 89, 298–300, 406, 536 fracturing, natural, recent 472 head (ubiquitous term) jacking (of joints or major discontinuities) 162, 163 modellers 133 test/testing 135,161, 174 theory 173 units 333 units sorted by FZI 333–335 hydraulically conductive fractures 541, 542 non-conductive fractures 541, 542 hydrocarbon, hydrocarbons -bearing rocks 295 bearing rock, neither isotropic or homogeneous 382 -bearing structures 369 contact 297 escape to atmosphere 295 exploration 295 migration 295 production, significance of vertical structure 407 prospect 14 hydrologically-predicted pathway 377 hydro-mechanical testing 359–364 hydropower, hydroelectric projects (see also dams, dam sites) tunnels 120, 121, 147, 154–157, 171 hydrophone detectors 62 receiver array 67 receiver, ocean-floor 267, 269, 394 hydrostatic gradient 296, 297 normal- pressure 297 pressure 296, 297 hydrostone, roughness profiles 509 hydro-thermal alteration link to velocity 287 and mechanical hysteresis and over-closure 513 deep- fluids 231 deposition 270 fluid injection 270, 278, 279, 293, 294 fluid circulation 285 hydro-thermo-mechanical in situ block test 513–517 detail, not in models yet 517 hydrotomography 174, 442 Hyogoken Nanbu earthquake (and Tamba region), Japan 217 hypocentre (see earthquake) hypothetical (ubiquitous term) mineralization 336 pore-filling 336

680

Index

Hypabyssal rocks 142 hysteresis affecting velocity-permeability coupling 364 on first-closure cycle 87, 364 Høvik, Norway, quartz lense with shear 551 Ice 12, 249, 253, 254 fern 253 formation 32, 253 -front 32 glacial- 253, 254 occupied by- 33 -wedging 33 Iceland 228, 416, 432–434 Idaho mine, Idaho 321 Idaho Springs, Colorado 64 IFP Picrocol data set 381 igneous rocks 6, 12, 25, 71, 72, 105, 109, 246, 263, 278 massive- 163 fractured-, permeability range 279 garnet-free 256, 257 seismic Q 186 unweathered 13, 72 ignimbrite 94 stress-conducting aperture, CSTF 529, 530 Ikeda rock classes, Japan 142 IKU, Trondheim 470, 480, 481 illite 27, 351 impedence -changes in 4D 252 -contrasts 202, 280 for distinguishing 326, 369 Imperial College, London University 517 polyaxial cell 359–364 Borehole Test Site, NE England 207–209, 234, 346, 356, 379 Imperial Valley, southern California 260 impermeable 555 important insight coupled earth-science behaviour 197 incident angle variations 354, 355, 466, 470, 471, 480, 481 with off-vertical fractures 419, 420 with off-vertical- 419, 420 independent constants 374, 477 index tests (see joint index tests) India 218, 219 N. 302 SE coast of- 219 Indian Peninsula 219 Shield 219, 230 industry assumption, standard 390 regarding permeability, fractures, ␴H max 390

inelastic behaviour inelasticity of matrix, intrinsic attenuation 387 inequality of deformation moduli 97–115, 339 Edynamic  Estatic 104–108, 184, 339, 340 dynamic fracture compliance  (static fracture stiffness)1 184 inertial effects 207 forces 182 infinity (") 182 Inguri arch dam, Georgia 88–90, 102, 170, 171 input signal 118 injection (see pre-injection, grouting) in situ (ubiquitous term) 339 block test, BB-simulation 507 deformability 19 natural block size 507 P-wave velocities 40 scaling of stiffness(shear) 421, 422 strength 19 Institut Français du Pétrole 357–359 instrumentation 165 integrated model 92 interbedded, interbedding (ubiquitous term) 296–300 brittle layers 297–299 plastic layers 297–300 reservoir-type rocks (ubiquitous term) 356 sandstone and shale 207–209, 300, 301 sandstone and shale, numerical model 310 shale/siltstone, Kimmeridge Bay 520, 521 units 369–372 interfaces shallow 7 integrated effects 19 internal friction (dissipation factor) 205 inter-related properties 21, 25 intrinsic absorption (see attenuation) intrusion dike- 277–279 intrusives high MgO 255 mafic 255 invaded zone (see mud infiltration) 316–318 investigation galleries 47, 48 ionic effects (of clay) 169 Iran 107, 108 ISONIC sonic-while-drilling tool 313 isothermal (static) 183 isotropic medium, stiffness matrix 374, 477 isotropic elastic continuum analysis 305 jointed reality not modelled 401 mismatch with discontinuum model 400 mismatch with subsidence bowl 400

Index Israel 54 ISRM congress 97 ISRM commission on failure modes 302, 303 ISRM (1978) describing discontinuities, terminology 419, 469, 511 Italy 60, 77, 101, 102, 171, 228 Jack-up of platforms, Ekofisk 442 Japan 19, 21, 40, 41, 65, 94, 101, 104, 148, 149, 195, 210, 211, 213, 217, 228, 229, 243, 244, 304 N.E.- arc 243 Sea 245 Trench 245 Japanese authorities 19 data 21, 25, 27 Highways classification 21 high-speed railway tunnels 47, 48 rock classes (Ikeda) 142 Java (-Ontong Platform) 206 Jernbaneverket, Norwegian Rail Authority 173 joint, jointed, jointing, fracture, fractured (ubiquitous, and interchanged terms) apertures (see aperture) 17, 80, 82, 84 apertures, intra-bed 208 apertures E and e, JRC related 453 aperture, unstressed, equation 511 artificial saw-cut- 77 bed-limited 208 cleavage 490, 491 closure 13, 19, 81–86, 135, 136, 199, 258 closure effects 285 connectivity needs at geothermal site 436 conjugate 88, 401–403 conjugate- at Ekofisk 401, 452 compliance (see compliance) component sets of- 44, 45 cooling 269 core recovered from Ekofisk 401 cross-column jointing (basalt) 124–127 deformation 161, 162 delta peak (␦peak) 491 density 224 dilation (see dilation) 490, 491 displacement 166 displacement to peak strength 507, 511, 522, 523, 546, 548 displacement discontinuity 518–521 dry or saturated stiffnesses 507–512 due to anticlinal structure 381 effect on attenuation 188 effect on Qseis 197–200 filler, filling 30, 84, 85

681

formation temperature, re thermal OC 516 frequency (F m1, ␭ m1) 12, 13, 16, 17, 41, 43, 69, 77, 81, 82, 83, 84, 85, 88, 89, 150 gouge formation with shear 489, 491, 492, 526 hysteresis, of fractures 87, 364 index tests (see joint index tests) intersecting- affecting stress-closure 364 joint-or-fracture terminology, ISRM 419 mated and unmated behaviour 87, 494, 506 model (UDEC) contact apertures, lengths, angles 521 modelling ignored, when too large scale 401 near-vertical (see sub-vertical) non-conducting 172 non-planar-, counter rotation effect 384 non-vertical- bias, vertical holes 385 normal stiffness 16, 45 number of- 30 numerically-glued 133 open (see fractures-open, stress H max, non-aligned) O/R open / rock-to-rock, contrary rotations of shearing414, 446, 450, 453 orientation 40–45 permeability-shear 491, 492 pole concentration 89 primary- 414, 548, 551, 552 primary cross- 551, 552 related overbreak in boreholes 250, 252 replica roughness profiles, ‘large’ scale 545 rosettes 385, 403, 404, 406, 441, 448, 475 rosettes, water-flood directionality 403 rosettes, reservoir and overburden 406 roughness 11, 83, 84, 85, 169, 197, 422, 451 roughness coefficient (see JRC) roughness coefficient (JRC) profiles, lab, large-scale lab 508, 509, 544 roughness contribution to strength, large scale 544, 545 roughness mobilized ( JRCmob) 489–491, 502 roughness destroyed 491, 502 sample, static, dynamic, flow testing 197–200 saturated or dry stiffnesses 507–512 secondary- 414, 550–552 sensitivity to- 65 set alignments, with ␴H max as bisector 483 sets, more than one (ubiquitous) 483 sets, primary, secondary 523, 524, 551, 552 shear magnitude 308, 433 shearing 110, 165, 299 shearing most where high porosity 402, 433 shearing, modelled 309, 310, 443 shearing, physically modelled 547, 548 shear stiffness (see stiffness, shear stiffness) slickensided, due to compaction, conjugate shear 443, 452 spacing 139, 469, 472

682

Index

joint, jointed, jointing, fracture, fractured (ubiquitous, and interchanged terms) (contd ) sparse 307 sparsely-, massive QH2O – K estimation 557 stiffness (static/pseudo-static,) 5, 6, 45, 79, 98, 106, 184, 418, 420, 463 stiffness changes 309 stiffness, dynamic, effects on velocity-frequency 478 stiffness non-linearity 420 steeply-dipping (ubiquitous term) 357, 401 strength displacement dilation BB-modelling 506, 507 strength, limited 308 stress discontinuity 518–521 stretch in subsidence bowl 412 strike, rotating in domal structure 401 structure effects 285 sub-vertical 40, 41, 42, 359 surface 9 surface area, reason for water weakening 402 testing 282 testing, stress-closure 282 testing, shear-displacement-dilation 282 three sets of- 385 vertical (see sub-vertical) void 119 wall compressive strength (see JCS) water-conducting- 172, 173 weathered, partly 508 weathered, SW, MW joint stiffnesses 496 jointed 304 heavily- 7, 163 less frequently- 19 -rock 30 -rock masses (ubiquitous term) 4, 5, 124–126, 365, 367 -rock masses, coal analogue 168 -rock model sparsely- 7 joint index tests Schmidt hammer 26, 486, 510, 545 tilt tests 401, 508, 510, 513, 514, 545 tilt tests, large-scale 509, 553 wall compressive strength (JCS) 425, 508, 510, 545 wall roughness(JRC) 401, 425, 510, 545 joint industry project 303 Juan de Fuca Ridge 269, 279 Jurassic 185 sandstone-shale units 371 J-parameters from Q-system (see Appendix A for all numerical ratings, descriptions 615–626) Ja -joint alteration, clay-filling rating 6, 53, 92, 144, 169, 175, 225, 293, 350, 447, 448 Jn -number of joint sets rating 6, 53, 92, 144, 169, 175, 202, 225, 250, 293, 350, 447, 448, 469

RQD/Jn as relative block size (see also scattering) 225, 469, 615 Jr -joint roughness rating 6, 53, 92, 144, 175, 225, 293, 350, 447, 448 Jr/Ja as friction coefficient ␮ for joints, fractures, faults 225, 350, 411, 469, 615, 620 Jr/Ja as friction coefficient of clay-filled discontinuities 538, 556, 615, 620 Jr/Ja as directional parameter causing anisotropy 411 Ja/Jr for Qwater and for QH2O 556–558 Jw -joint water inflow rating 6, 92, 169, 175, 225, 293, 350,447, 448 (see SRF for 6th Q-parameter) J-parameters from Barton, Barton-Bandis joint model JCS joint wall compressive strength 79, 83, 203, 258, 359, 420, 422, 424, 425, 428, 451, 456, 485, 492, 495, 496, 507–512, 540 block test 518 JCS and moisture 502, 507, 509, 511, 512 JCSo 526, 543–549 JCSo in CSFT 529, 530 JCSo to JCSn scaling 531–535 JCSn 523, 525, 541, 543–549 ratio JCS/␴n 79, 258, 485, 508, 520, 547 ratio ␴n/JCS in CSFT tests 528–530 scaling equation 511 scaling with block size 523, 525 JRC joint roughness coefficient 83, 84, 86,162, 197, 359, 363, 364, 420, 422, 424, 425, 428, 451, 456, 457, 460, 467, 485, 496, 507–512, 540 back-calculation of- from tilt test 509, 510 block test 518 JRC ‘at right-angles’ 517 scaling equation 511, 544 scaling with block size 523, 525 JRCo 519, 526, 543 JRCo importance in strength-deformation scaling 535 JRCo in CSFT 529, 530 JRCo and JCSo 487, 493, 508, 510, 543–549 JRCo to JRCn scaling 531–535 JRCn 523, 525, 541, 543–549 JRCn estimate from tilt tests 513, 514 JRCn measured in DST and biaxial shear tests 523, 524 scaling- to block-scale JRCn and JCSn 484, 508, 510 JRCmob concept 489–491, 507, 545 applied to model tension fractures 548 applied to stress transformation, corrected 553, 554 Kamioka Mine 65 Kane, North Atlantic fracture zone profile 273 Ko (ratio of ␴h min/␴v) 299, 300, 443 increased by joint shear in 1D compaction 443 reversal at shallow depth 299, 300 kaolinite gouge (artificial filling) 83

Index karst, karsts 4, 196, 197 karstic voids 172 Lawrence Berkeley Laboratory, California 197–200 Kern River oil sand 330 kerogen content 351, 353 -to oil conversion 352 Kielder aquaduct tunnel 79, 80 kinematic, post-kinematic (see aperture, sealing) Kimmeridge Bay, Dorset, S. England 488, 520, 521 King, Imperial College polyaxial cell 361, 365 kink band in physical model 524 Kitakami massif, Northern Honshu, Japan 229 Kn and Ks normal and shear stiffnesses (see normal, shear stiffness) Knopoff ’s seismic Q of selected materials 181 knee-shaped velocity-depth curves 241, 243, 245, 250, 252–254, 260, 261, 262, 264, 266, 267, 271, 274–277, 280, 281, 284–286, 289, 290, 311 Koefels landslide 95 Kola Peninsula super-deep well data 555 KTB super-deep well 249, 250, 252, 542, 543 permeabilities 554, 555 Kuril-Kamchatka earthquakes 213 Kurobe IV dam site 40 Kurtachov, North Atlantic fracture zone profile 273 La Cira-Infantas Oil Field LCI 332, 334 laboratory (see VP and Qseis listings) high pressure tests 22, 31, 58, 59, 248–250, 256, 257, 323–364 samples (ubiquitous term) 259, 323–364, 339 test, large-scale 352, 353 test and large-scale BB-modelling 507 tests on sub-ocean basalts 261, 263 triaxial tests 258 ultrasonic velocity 70, 73, 91, 183, 207–209 Lagerdorf chalk quarry, Germany 420 Lamé’s constants 373, 374, 417 laminar flow 161, 474, 513 laminations, shale 355 Lamont-Doherty Geological Observatory 261 landfill 7 large scale rock properties 165–167 laser scanner micrometer (non-contacting) 84 lateral expansion (see Poisson’s ratio) Latiyan dam site, Iran 107, 108 Lau Basin 179, 227 Lau Ridge 179, 227 Laupies dam site, France 159 layer, layered, layering -cake sequence fine horizontal- 357 inter-beds 3, 45–47, 207–209, 234

683

lattice crystal structures 509 models 265 sequence 233, 234 velocities and densities (sub-ocean crust) 267 layer thickness estimates 14 minimum detectable- 379 reduction during compaction 398–402 Layer 1, 2, 3 sub-ocean divisions 243, 244, 255, 257 Layer 2A 267, 268, 283, 286, 287–289 Layer 2B 278, 283, 287 Layer 2A, 2B, (2C) 265, 267, 271, 272, 277, 283–285, 287 Layer 4, 5, 6, sub-ocean divisions 244 lead, Qseis 181 Lg coda (cross-continent seismic Q) 230, 231 Liaoning earthquake, China 110 Lias shale 11 life of field seismic LOFS (453) lime quarry 61 limestone, limestones 4, 12, 32, 100, 108, 114, 370, 385 aspect ratio influences 326 basic friction angles, dry, wet 511 Bedford 31 Carboniferous 207–209, 346–348, 356, 357 CBTF well- VP – VS – density-permeability-birefringence 445, 446 Corralian 79 crystalline 12, 101, 102 density-VP 325 hard 12 finely interlayered 379, 450 foundations (dams) 49–51, 97, 98 fractured, chalky-lst. 455–458 fractured, well 297, 389 in situ 42, 43, 45, 105 intensely jointed 102–104 interbedded 47, 207–209, 212, 234 joint, initial stiffness 494 joint normal stiffness – stress 496 joint normal stiffness, initial 495 joint, stress-closure 494 joint, stress-deformation 495 jointed 350, 455–458 Jurassic, bedded- 185 Jurassic and carboniferous, compliance, saw-cuts 501–503 Ko 299 low porosity 31, 32 marly 101, 102 medium jointed 102–104 nodular 148 Oncolithic, Grain-, Pack-, Wackestone 349 Oolitic, water, oil saturated 348, 349

684

Index

limestone, limestones (contd ) Permeability extremely high 378 porous 24, 31, 32 porosity – VP 325 Qseis (QP) 181, 186 reduced (␣-coefficient) 321 -shale interbeds 148 soft 12 Solenhofen 31 stress-closure tests on joints 528 thin-bedded (EDZ) 121 Triassic, weathered and jointed 98 tunnel EDZ in- 119 Vajon 108 VP – density 326 VP – VS 328 1000/QE and 1000/QP confining pressure, crinoidal 191 Lincolnshire 42 line -drilling (tunnel excavation) 128, 130 -drilling (of flatjack slots) 513 linear elastic isotropic medium 373 regression 256, 257 liquid- or gas- filled fractures 391 Lista Formation 391 lithological units causing multi-stepped response 336, 337 mixed 335 mixed causing patchy saturation 335–337 lithology 8, 264 changes of 8, 17 range of- 246 lithosphere 227, 241 oceanic 228 thrusting 227 loading-unloading behaviour, intact rock 38, 59 behaviour, rock masses 97, 98 effect on E-modulus 300 joints 485, 494, 495, 516 hysteresis 182, 300, 514–516 thermal 513–517 loam 26 logarithmic 537, 538 logging -based FZI 336 dipole- 312–316 field- 469 while drilling, see LWD wireline 302, 306, 313, 318 log-spiral failure/fracturing 130, 303, 305, 386

shearing 302–307 Loma Prieta earthquakes, California 215 London-Brabant Massif, North Sea 447 Long Valley earthquakes, California 213, 214 Long Valley well data 542, 543 long wall mining 53, 61 pillar 60, 61 shearer 53 Lorraine, France 185 Los Angeles Basin, southern California 260 lost circulation 299 low velocity layer 14 surface sediments 231 zones 71 Lower Cretaceous 391, 447 Hod formation 391 mantle 241 Paleozoic 447 Permian 447 Silesian coal basin 60 Lucite honey-saturated- plates 427 laminate model, critique re ZN and ZT ‘equality’ 417–419 QE -value 188 Lugeon test apertures e and E for grouting design 172–176, 468 conversion to permeability units, approx. 161, 164, 173, 176, 556 in near-surface rock mass 468 inverse of Qc approximation 226, 555, 556 LWD logging while drilling 301, 302, 306, 312–320 for AVO interpretation 315 for OBS tie-in to 4C acquired data 315 for horizontal well sections 315 for shear-wave anisotropy analysis 313–315 for warning of pore pressure changes 315 velocities, compressional and shear 318 velocities compared with wireline 318 Macro deformations 421, 427, 428, 463, 484–486 displacements, micro-displacements discussion 492, 493 fractures 441 permeability 356 pores, inter-particle (oolitic lst.) 348 magma axial- lense 281 magma chamber mid-crustal- 281–282

Index magnetometer relation to true north 314 magnitude earthquake- 213–219 -frequency plots (intact, fractured) 199 sorted by- (Qseis) 181 Makurat CSFT test (see CSFT) Mamouth Lakes earthquakes, California 212 Manitoba 57, 87, 127–131 mantle 243, 244 peridotite 257 Upper 241, 245 Upper-mantle velocity histograms 247 wedge 243 major stress 3 marble 57 artificially fractured columns of- 81 micro-fractured, scattering 195 marketplace economics 396 marl 19, 161 -sandstone 46, 171, 172 interbedded 212 marine environment 373 seismic (ubiquitous term) 232–239, 253–290, 334, 336 Massif Central, France 159 masking 16 massive crystal structures 509 unjointed rock 4, 6 Masua mine 60 mated (see joints, fractures) matrix elastic stiffness- 417, 451, 477 intact 5 format 374, 477 porosity (see porosity) 373 reservoir- 393 silty-sand 12 stiffness- 416, 417 maximum horizontal stress (see stress) temperature (see temperature) entropy method 84 McMurdo Sound, Antarctic 253, 254 measurement-window 194 mechanical over-closure (see over-closure, OC, of joints) medical profession 52 melt, melted fraction 256, 257 mantle- 256 parental- 256

685

partly- rock 281 meso-scale fractures, Chapman model 465–474 modelling reservoir anisotropy 472, 474 role in earthquake studies 470 seismic visibility, contra micro-cracks 499 Mesosphere 227, 241 Mesozoic 25 basement 222 rocks 142, 153 meta-anorthosite 11, 13, 70 meta sediments 243 metal discs (model) 470, 480, 481 metamorphic rocks 6, 12, 25, 72, 109, 142, 246, 247, 256, 263, 265, 278 rocks, seismic Q 186 unweathered 13, 72 methane ejection 60 MHF massive hydraulic fracturing 549 mica 243, 509 micaceous inter-layers, Bandis model 310, 311 mica schist 57 micro cracks closed by ␴1 36, 199 crack system 22 crack density in fault zone 429 crack, elliptical 465, 467 cracked 5, 21 degree of- 182 discontinuities, displacements 5, 45, 416–425 deformation compliances 5, 416–425, 499 excursions 184, 506 flow 190 fracture and macro-fracture orientations 441 fracturing imbalances 5 seismic event (see also AE) 131 seismograms 206 valves 193, 194 velocity probe 128 micro-cracks 31, 127, 128, 184, 195, 196, 201, 407, 418 and micro-voids between sand, clay particles 418 APE model, Crampin (see APE) aspect ratio, stiffness, critique 415, 434 aligned 374 and joints/fractures cause S-wave splitting 408 caused by sampling 397 discussion/critique of universal role 412–415 dominant- 195, 196 stiffness compared to fractures 415 pressure-resistant 226 and weathering 225 micron sub-interaction 188 microstrain 184

686

Index

mid -Atlantic ridge MAR (see VP and Q data sets) 261–273, 287–290 -ocean, axis of ridge 282 -ocean, off-ridge distance 282 -ocean ridge 3, 266 -ocean ridge, transverse 273 -ocean seismic investigations 179, 261–290 migmatite 139–142 weathered 107, 108 mineral, minerals (see hydrothermal) 22 bridging 384, 406, 527 cements deposited in fractures 384 cement injection analogue 291–295 composition 256, 257 deposition of 287–293 effect on VP – age relations 270, 287–293 filling 11 post-kinematic cements 384 synkinematic cements 384 sealing 270, 276 mineralization 270, 287–294, 377–380 bridging (to prevent closure) 406 episode 334, 336 mine, mining 58, 60–62 coal 60, 61 equipment 53 gold 60 hand-mined 128 potash 123 stopes 224 mini-EDZ (see EDZ) minifrac (see hydraulic fracturing) minimum (ubiquitous term) stress (see stress) mining-induced (seismic) 224 Miocene limestone 11 marker 15 Misasa earthquake, Japan 213 Mississippian sandstone-shale units 371 MIT Massachusets Institute of Technology 318 Mjølner (meteor) impact structure, Barents Sea 404 Mobile Bay, offshore Alabama, USA 320 mobility high 183, 194 low 183, 194 model joints (tension fractures) 493 in weak brittle model materials 547 model-prototype scaling 547 shear strength envelopes, peak, post-peak 547, 548 strength, stress, displacement scaling 547, 548, 552 models (see numerical) elasto-plastic 305

parallel-plate 172, 279 visco-elastic, transversely isotropic 351, 353 velocity-depth 266, 267, 271, 274, 275, 276 modelling (see numerical) excellent- results 362 forward 251, 253, 391 modelling (see numerical, and 2D, 3D, UDEC, FRACOD, discrete, distinct) modulus, moduli (see deformation, and Young’s) of deformation (see deformation) 227, 339 dry rock- 296 low- damage zone 313 reduced-, in alteration zone 313 Moho (Mohorovicic velocity discontinuity) 229, 241, 242, 244, 255 Mohr stress representation 542 Mohr stress transformation failure to account for dilation 519 non-coaxial stress and strain 519 Mohr-Coulomb based continuum modelling 304, 319 parameters (c and ␸) 101, 307, 537, 539 parameter combination c plus tan ␸ 304, 461 parameter combination c then tan ␸ 304, 461 strength criterion 304, 305 stress transformation 552 stress transformation, modification 553 theoretical solution 308 moisture content 27, 30 Mojave Desert 90 east and west regions 260 gneiss 261 intrusives 260, 261 moment magnitude 130 monitoring fluid front- 352–353 4D time-lapse 352 monoclinic medium, multiple sets 420 monopole acquisition 316 for radial variation of compressional slowness 316 transmitter-receiver spacings 316 Mongstad oil storage caverns, Norway 147, 160 Monticello reservoir, USA 90 permeabilities 554, 555 MONT-1 well, USA 90–92 montmorillonite 27 monumental study 249 monzonite 21 fresh 19 weathered 19 moraine 11 mountain, mountains Andes 72, 231

Index Rocky Mountains 231 -side deposits 153 -side screes 153 Ural Mountains 231 mountainous 33 Mount Davis, Hong Kong 76 moving source 53 Mratinje da 301,m site, Yugoslavia 49–51, 99, 170 mud pressure induced tensile cracking 299, 321 temperature management 321 mud filtrate invasion 295, 302, 316–319 accelerated 303, 305, 307–311 based on porosity-permeability conversion 317 constant permeability with radius assumption 318 enhanced by mini-EDZ 317 enhanced by log-spiral shear surfaces 317 enhanced by sheared joints 317 scenario, tunnel analogy 320 speed 307 speed highly none-uniform 307 mud temperature management 321 mud-weight 295, 296–298 constant 306 over-balance 299 versus depth 296, 298 mudstones 7, 8, 9, 26, 79, 94 inter-bedded 207–209, 234 Tertiary 19, 21, 304 multi -azimuth walk-away 369 -component 6, 7, 8, 363 -channel (ubiquitous term) 254 -frequency 207–209,373 offset, multi-azimuth, 3C VSP 410 physics approach 318 -source multi-receiver 49–51, 54–67 -wave-form acquisition 310 multi-variable linear regression clay content and porosity, VP 332 melt fraction, VP 256, 257 mineral compositions, VP 256, 257 multiple borehole logging tools 379 fracture directions at faults 394 position borehole extensometers MPBX 301, 367 MWD measurement while drilling 313 mylonite 13, 70, 100 N and S components 484, 485 NaCl (see brine) 342 Nagra 38 Nathpa Jakri hydroelectric project, N. India 302

687

Natih field, Oman 455–458, 469 naturally-fractured gas reservoir 382 near-surface (rock masses) 3, 4, 13, 74, 465 apertures 390 clay 25 conditions 10, 74 data on stiffness 423 extremes (beach sand, ice) 252–254 fully-saturated rocks 211 geotechnical investigations 15 investigations 14 layers of sediment 205 low-Q zone, frequency loss in 378 material 7 measurements 69 ocean-floor velocity structures 261–294 permeability 390 permeability tensors consistent with ␴H max direction 442, 531 seismic Q 203–205 seismic surveys 4 tunnelling 9 velocity structure (refer also VP and Qseis data lists) 8, 10, 20, 46, 47, 51, 52, 55, 75, 76, 78, 79, 88, 89, 91, 92, 93, 203 weathering effects 19 Neogene rocks 142 neural network to infer commercial prospectivity 384 neutron log porosity from- 378 Nevada (nuclear) Test Site 251–253 Nevada Test Site, Yucca Mountain 542, 543 New Mexico 123 Ngendei South Pacific data 275 velocity model 275 NGI 53, 55, 58, 74, 88, 147, 148, 443, 452, 469, 518 NGI borehole failure study 303–305, 311 Nick Barton & Associates 307 nine-component, three-dimensional 9C/3D 455 Nirex (see UK Nirex Ltd) NMO normal moveout 389 ellepticity 390 stretch 389 nomograms (Q, M, K-L, c) 176 nonaligned with ␴H max direction, polarization 384, 385, 389, 390, 403, 404, 406, 414, 429, 431, 432 aligned with ␴H max direction, conductive joints 527, 541, 542 conductive 531, 541, 542 linear shear strength criteria 339, 537–540 uniqueness 271, 369

688

Index

Norfolk, England 29 normal closure (N) 484, 485 closure is least productive condition 488 compaction trend 297 compliance ZN, dynamic, bedding 500 fourth-cycle loading concept 484, 487 loading of joints 484, 485, 487 loading and hysteresis 484, 485, 487 normal stress 79, 198, 199 closure BB model 487 closure, shear/dilation, aperture e, permeability, BB modelling 531–533 deformation, rock plus joint 495 permeability BB model 487 normal stiffness 17, 198, 199, 202, 485, 487, 494–499, 515–517 and shear stiffness Kn, Ks 485, 492–499 and shear stiffness, clay-filled discontinuities 505 apparent reduction with temperature 516, 517 apparent ‘zero’ with thermal OC 516 -compliance discussion 421–425, 492 constant in DST 490, 492 dynamic versus frequency 498 dynamic/static data, stress-dependent 496 estimated from block test 515–517 fracture zone in URL 506 high stress levels 495, 496 initial (Kni) 494 interlocked joint 494 mismatched joints 494 normal stress 498 reduction, apparent, with temperature 515–517 -shear stiffness ratio, dynamic 497 -shear stiffness ratio, static, scale dependent 498, 499, 502 normal moveout (see NMO) normalized surface of invasion 360 normally-pressured 352 Norris Lake Community, Georgia, USA 215 North America, American 231, 246 deep gas reservoirs 320 plate boundary 258 reservoir rocks, stress magnitudes 298, 299 North Anatolian Fault Zone, Turkey 220 North Cape Tunnel 147 North Caucasus oil fields 450–452 North Sea 352 reservoirs 235, 311, 312, 391, 396, 397, 398, 412, 420, 427, 447, 451, 452, 504 salt dome (Zechstein) 381 sands 326 sandstone 359 UK-sector 235

Northern Appalachians 231 Norway 13, 16, 43, 53, 55, 56, 70, 74, 88, 144, 147, 160, 161, 170, 212, 216, 217, 408, 518 Norwegian Geotechnical Institute, Oslo (see NGI) Norwegian Petroleum Directorate 401, 452 Norwegian Road Authority 147 nuclear waste disposal investigations 124–136, 161, 363 related research 165 numerical models, modelling BB modelling of coupled stress-closure, shear-dilation, apertures 531–533 BEM boundary element method 306 Cellular automaton model, scattering, Vlastos-Narteau 463–465 Cundall continuously yielding joint model 460 Cundall distinct element modelling developments 460, 461 distinct element DEM (finite difference)- 306, 308–310, 421 elastic flexural 257. elasto-plastic flexural 257 FEM, 2D, with Goodman joint elements 460 FEM, 3D, dam foundation modelling 460 finite element, jointed- 421 FRACMAN, Dershowitz, Golders, 3D fracture-flow code 460 FRACOD 306, 307, 461 geomechanics 1D-strain model, Ekofisk 399, 400 HMT fully-coupled, water-flooding in fractured medium 402 NAPSAC, AEA Harwell, 3D fracture-flow code 460 orthogonal sugar-cube model, permeability-seismic integration, Brown et al. 479, 480 poro-elastic (see next) synthetic jointed/fractured reservoir models 393 3DEC 365, 454, 460 UDEC (see UDEC) 365 UDEC dynamic attenuation 478, 479 UDEC-MC 306, 308 UDEC-BB 460, 469 UDEC-BB, HM block test 518, 519 UDEC-BB, deformation of jointed rock masses 484–486 UDEC-BB, reservoir compaction modelling 401, 420, 443, 452, 453 UDEC-MC, reservoir subsidence modelling 400, 427, 428, 454 UDEC-BB, tunnel/borehole modelling 306, 309, 310 numerical poro-elastic models 236, 377, 391, 407, 459–477 Angerer, shear-wave anisotropy changes 451 Biot squirt-flow attenuation 236 BISQ Biot and squirt-flow model 378 BOSK effective medium model 457, 458

Index Chapman, triple-porosity 405, 415, 465–475 Hudson effective medium model 461 Nishiwaza TI cracked medium model 362 SeisRox visco-elastic model, Johansen et al. 375, 376 super-k poro-elastic- 377 Tod effective medium, crack decay model 462 Nurec deep borehole data 555 OBC ocean bottom cable 391, 394, 396, 397, 452 hydrophone 391 geophone, in-line, vertical, cross-line 391 OBS ocean bottom seismometer 237, 281 observed rock classified not characterized 310 ocean -bottom hydrophone OBH 275, 281 (analogue AOBH, digital DOBH) 281 -bottom receiver array 281 -bottom seismic instruments 254, 261 depths 227 Drilling Program ODP 206, 276 floor (ubiquitous term) 261–293 floor rock quality 285 sub- basalts 261–293 oceanic crust fracture zones 271–272 young 276, 282 oceanic lithosphere 228 age of- 228, 262–265, 287–294 down-hole sonic logging 261 old 228, 287–291 young 228, 287–291 oceanic sub-ocean layers Layer 1, 2, 3 243, 244 Layer 2A, 2B, 2C 277, 283–285 Layer 4, 5, 6, etc. sub-ocean divisions 244 Oceanografer, North Atlantic fracture zone profile 273 Oddatjørn dam site, Norway 170 offset and azimuth, variation of seismic data 382–396, 401–406, 407–482 (Ch15) by shear mechanism 414, 518, 523, 524, 541–543, 550, 552 fully-populated- 373 large 273 small 273 offshore geophysics 94, 243–245, 251, 253–294 regions 260 oil bearing rock (ubiquitous term) 233 bearing sandstone reservoirs 343 dead- 296 live- 296

689

prices per barrel 320 sand 330 saturation changes in 4D 397 saturation mapping in 4D 397, 398 storage cavern 53, 54 -from gas, distinguishing 455 -to-gas conversion 296 well (see wellbore, borehole) oil sand heavy-, steam injection time-lapse 379 effect of temperature on VP 330 effect of oil/gas %, Kern River- 330 effect of oil/brine %, Venezuelan- 330 oil field, fields complexity of recently discovered- 323 heterogeneous distributions of parameters 323 spatial variability 323 spatial variability of porosity, clay-content, fracture density 323 oil-water contact 369 Oishiyama earthquakes, Japan 210, 211 Okayama, Japan 48 Oklahoma, SE 374 oldest units 369–371 olivine crystals aligned- in Upper Mantle 276 Olkaria geothermal field, Kenya Rift 394 Oman 455–458, 469 one-dimensional strain compaction modelling 399–401 of unjointed chalk 400, 401 onshore sites 19 ooze-chalk transition 206 open joints parallel to ␴H max assumption (see fractures-open, parallel, stress ␴H max, non-aligned) options for open joints, fractures 549 ophiolite, on-land, Troodos, Cyprus 278 O/R open, rock-to-rock contrary rotations 414, 446, 450, 453, 527 possible source of polarization rotation 414, 446, 450, 474, 525–527, 550, 551 Ordovician sandstone-shale units 370–372, 370 ore bodies 22 organic matter 352 oriented core (see core) orientation discrepancy re anisotropy axis and stress 383, 384 discrepancy re reflection S1 and polarized S1 475 unfavourable 14 orogens (geologic structures) 246 orthogonal (joint/fracture) directions (three) 25, 172, 353–363, 479, 480 orthorhombic material 374 orthotropic 46

690

Index

oscillating 5 point (sources) 153 Oslo downtown 139 Fjellinjen Tunnel 54, 139 numerical model 469 fjord 56, 217 Otsuki fault zone, Japan 47, 48 outcrop mapping 76, 455, 456 output signal 118 overburden (see also stress) layers 15 gradient 296–300 stress 299 stretching of-, subsidence 399, 400 velocity anomalies 14 over-closure, over-consolidation episode, in DST preparation 517 heated in situ block tests 513–517 heated lab tests 513 mechanical- (of joints) 87, 513, 517 ratio, effect on shear strength 517 thermal- (of joints) 87, 513–517 over- pressure, over-pressured (see pore pressure) 295–298, 350, 351, 352, 450, 452 detecting-, factors 350 example from tunnel 319, 320 reduced velocity-depth gradient due to- 450, 452 thinly-bedded strata with- 320, 452 time-sag due to- 381 top of- 297 shale, lab tests 354–356 zones 268 Oxford clay 49, 51 Oxfordshire 77 oxides SiO2, MgO 256, 257 FeO, CaO, Al2O3, Na2O 256 P-wave (see VP annotated results) 4, 5 amplitude 81–86 amplitude/magnitude spectra 198, 199 and S-waves 6, 7 and S-wave anisotropy 37 and S-wave surveys 70 and S-wave velocities 6 anisotropy (azimuthal) 35, 179, 382–406, 438 anisotropy definition 438 axial- 36 cancelled between fractures 466 energy 130 joint use of- and C-wave 396 multi-directional 38, 39 particle motion 5, 438

phase velocities 480 reduction of P-wave velocity due to rock failure 36 signal propagation 481 survey, surveys 70, Ch14, 384, 526 travel time, temporal 433 travel-times, for AVO 388 travelling obliquely to fractures, shear properties of rock 404 velocity anisotropy 38 velocity contrasts 8 velocities 11 Pg and Pn direct and refracted waves 242, 246 P-S converted (C) waves 369, 388–390, 438–440, 452 polarity reversal across strike 440 pac-ex packer-extensometer unit 505 Pacific plate 243, 245, 258 boundary (southern California) 258 Pacific ocean 243, 245, 246 sub-ocean East Pacific rise 281–290 western 206 packer, packers double- 162 quadruple- 174, 292 test 378 Pahute Mesa, Nevada Test Site 251–253 Paleocene 447 Palaeogene rocks 142 Paleozoic 25, 72 rocks 142, 211 sediments, Ko 299 parallel bedding- Q 352 not- to stress direction 384 to aligned fractures, faster P-waves Ch3, 382 to bedding 354–357 to fractures, minimum influence on reflection 388 to major jointing 35, 46 to schistocity 38, 39 to ␴H max assumption 179 to ␴H max assumption (microcracks) to H max assumption (open joints, fractures) 384, 526, 541 to stress direction 35 parallel and/or perpendicular loading (and ray paths) w.r.t. layering, bedding, schistocity, foliation 38, 39, 46, 354–357 w.r.t. extension fracture 362 w.r.t. fracrure orientation 389 seismic Q in fractured shale reservoir 236, 237 parameter combinations 271 non-unique- combinations 271, 272 ratings (see Q-value, see various J-parameters, see Appendix A) Paraná Basin 231

Index Parkfield Dense Seismograph Array, (HRSN) USGS, California 216, 223, 224, 429, 431, 432 particle motions 5, 437 size (grouting) 487 velocity histories 479 passive source (see AE acoustic emission) patchy shooting 391, 394 patchy saturation 335–337 causing frequency dependence 336, 337 capillary pressure-saturation estimates 336 discussion re compliance, squirt, attenuation 336 due to rock joint 336 due to macroscopic patch 336 mixture 336, 337 with ‘homogeneous’ mix of lithologies 336, 338 path length 30 Pb3O4 red lead, model additive 547, 548, 551, 552 PC-element liner 151 ring building (TBM tunnel) 94 peak shear strength (see joint, shear strength) singularity of ␦peak and beyond peak 554 peat 26 pebbles 12 pegmatite 13, 70, 73 weathered 107, 108 Peko Oil USA 374 penetration rate 78, 139, 149, 158, 321 strength 79 Pensylvanian sandstone-shale units 370–372 performance of TBM 158 peridotite 19 permeable 169 fractures 179 sub-ocean crust 266 zones, Qseis/VP correlation for sands 376, 377 permeability, permeabilities 77, 159–165, 169, 170, 203, 331–337 and storage 364 anisotropic- 358, 359, 382, 425 anisotropic-, Äspö spiral tunnel 555, 556 access spiral tunnel as function of confining pressure 359 as function of direction 359 before and after grouting 173–175, 292, 293 changes due to tunnelling 615 -clay-content 331–337 comparisons 278 core-plug- 237 depth dependent deep well- data, land-based 555 depth data (1600 m of oceanic crust) 279

691

depth dependent- 164, 490, 555, 557 dominant direction, fracturing 455 enhanced 133 e2/12-based- 173, 474, 513 enhancement with pre-peak shear 554 estimation from QH2O 554–558 FZI data 333–335 high-permeability zones 17 influence of conjugate shearing on- 358 influence of shear stress on- 517–536 low-, due to shale 236, 237, 296 lower 151 Lugeon test of- (see Lugeon) Lugeon – K conversion, approx. 161, 164, 173, 176, 556 macro- 356 maintenance of joint- 358, 359 maintenance due to shear 402 matrix- 373 matrix-, normalized 360 max. and min. 174 measurement facility 359–361, 363, 364 measurement value, if intersecting structure 407 micro- 202 of matrix too low, Ekofisk 401 of mineralized ophiolite (estimated) 278 of rock mass 173–175, 292, 293 of rock mass, one set 533 orthogonal- 358, 359 parallel to joints, fractures 358, 359, 362, 363, 363 principal magnitudes (tensors) 278, 291, 292 Qwater, modification for- 556 QH2O – depth – permeability 557, 558 ratio of principal-, in situ 174, 292 ratio of principal-, around borehole 318 sandstones compared 343 scatter curves 334, 335 stress behaviour 179 stress behaviour (in situ tests) 165, 166, 527 stress behaviour (lab tests on coal) 168 stress behaviour (large-scale lab) 527 super-k method of prediction 378 tensors 359, 360 tensor rotation 174, 292 test, testing 9, 88, 159–176, 292 test holes 513, 514 three-axis 357–364 variable- (crustal scale) 231 -velocity behaviour 168 virgin- 278 Permian sandstone-shale units 371 perpendicular and parallel loading (and ray paths) w.r.t. layering, bedding, schistocity, foliation 38, 39, 46, 354–359

692

Index

Perspex (see Lucite) buffer rod 501, 502 perturbation of stresses, properties in EDZ 302–321, 615 Petatlan earthquake 213 petite-sismique 110, 112 petroleum exploration for deeper – reserves 320 geologist 369 industry 301, 323, 523 industry benefit from shearing mechanism 549 oil prices 320 source rock 351–353 well surveys 369 petroleum reservoir, reservoirs (see VP and Q data) 232–239, 369–406, 438–459, 471–475 conventional wisdom 531 depth-log of Q -VP -K fractured shale 237 familiar warmth of a-, re thermal OC 516 ‘open’ joints, difficulties with conventional direction 526–536 ‘open’ joints from mineral-bridging 384, 406, 523 ‘open’ joints from shear and dlation 523–536 plot of depth-1/Q-VP 233, 234 plot of low Q, high Q1 in fault zone 235 plot of Q-VP 234 plot of Q in anticlinal chalk 235 pressure-depth-gradient-buoyancy aspects 296–297 rocks, rough, hard end of spectrum 515 where rock strengths are limited 384 petrophysicist 369 phase velocity of wave 198 phi-r r residual friction (see friction) Phillips Petroleum Company (Conoco Phillips) 452 phyllite 12, 32, 38, 247 quartzitic 122 slatey 122 unweathered 12 weathered 12 physicists 184, 282 physical aperture (see aperture) laws of behaviour 16 models (borehole drilling) 303, 305 model (poro-elastic, dual porosity) 470, 480, 481 models using tension fractures 523, 524, 551, 552 Piani di Ruschio dam site, Italy 101 Picrocol data set at salt dome 380, 381 piezoceramic vibrator source 61 piezoelectric bender transducers, high resolution 375 source 52 transducers 192, 292, 361 vibrator 62

pillow (see also basalt) lavas 277, 279 pilot drilling 150–152, 319, 320 pipeline 3 Piper Alpha platform disaster, UK sector of North Sea 320 Pirapora dam site, Brazil 173, 174 plagioclase 243 plastic deformation 93, 303 failure (irreversible) 183, 303 model material 302 replicas of shear-dilation path 527 zone 140, 303 plate (jacking) load test 46, 50, 51, 74, 97–105, 112–114, 122 parallel- (see aperture) tectonics 179, 226, 227 plate tectonics structures Benioff zone 227 bulge 227 forearc basin 227 remnant arc 227 seismic belt 227 subduction complex 227 trench 227 volcanic arc 227 platforms geologic structures 246 jack-up of- due to subsidence 400 Pleistocene rocks 142 points of contact (joints) 30 Poisson expansion 133 Poisson’s ratio (dynamic, from VP and VS) 5, 6, 7, 8, 9, 57, 100, 104, 106, 107, 109–111, 130, 161, 263, 264, 270, 280, 337–339, 363, 394, 396, 529 azimuthally-dependent-, 0 to 5 km, Kenya Rift 394, 396 anomalous 270, 337 -depth, sub-ocean Hole 504B, Costa Rica ridge 280 depth, 0 to 5 km, Kenya Rift 396 differential pressure 338, 339 dynamic (function of axial stress) 126 effect of low differential pressure on- 339 effect of hydraulic fracturing on- 338, 339 effect of brine, crude oil, gas/dry on- 338, 339 extremely high- , below ocean floor 286 lateral expansion, rock masses 485 mass-, lateral expansion exceeds 0.5 523, 524 pseudo-static 9, 105 theoretical relationships 6, 7, 104, 338 tomogram 379 Poisson’s ratio – depth (shallow) 8, 111

Index Poland 60 polar diagram, 1/Q of fractured medium 405 histogram 385 polarization (see shear wave) direction not parallel ␴H max 432 fault-parallel alignment 432 inversion, orientation 404 90°-flips of- 415, 416 90°-flips of-, alternative, axial over-load 416 parallel to fast formation axis 314 rotation due to deep well injection 413, 414 rotation due to O/R concept (see O/R) 548–551 shear-wave arrivals 448 temporal changes in Cornwall HDR 413–415 polarized shear waves (see shear waves) polyaxial stress state loading 302–305, 358–364, 419 polyurethane foam 305 Pont Ventoux hydroelectric project, Italy 154 headrace tunnel (TBM) 154–157 polluted sludge 25 Ponte Cola dam site, Italy 101 pore, pores collapse, accelerated due to water 400, 402, 442, 540 collapse and fracture stiffness discussion 426, 538, 540 compressibility 452 filling minerals/materials (clays) 331–337, 349 flat 190, 205 fluid 5 geometry 356 size distribution 332 space compaction 296 space compressibility 351 space compromised by depth 295 space occupied by ice 33 water flow, attenuation 282 pore pressure 17, 169, 295–298 analyst 295 change, prediction of away from wells 397 coefficient 268 -decline, effect on bulk modulus 397 divided by confining pressure 355 effects 268, 355, 356 elliptic propagation 464 excess- 298, 352 excess-, effect on QP 352 excess- effect on VP and VS 298 gradient 296, 297 independent application of- 355, 359 reduction prior to water-flooding 401 regime 273 poroelastic modelling (see numerical) poroelasticity 209

693

porosity 9, 13, 27, 29, 270 age-depth, young oceanic crust 263, 276, 369 bi-modal- 349, 350 correction 92, 93, 163, 167 critical, suspension limit 324 dual- 369 dual- physical model 480, 481 equant 465, 467 high- sediments 206 hard 272, 276 lack of crack- 31 loss of- at extreme depth 311, 312 matrix 24, 285, 373 ranges of- 311 -reduction due to water saturation weakening 399 sandstones compared 343 secondary, crack- 270 soft 272, 276 total 21, 22, 24 porosity – uniaxial compressive strength (crystalline and volcanic rocks) 28 porosity – uniaxial compressive strength (diverse soil, rock) 26 porous granular media 23 macro- 373 micro- 373 rock (ubiquitous term) porphyry 13, 70 strongly jointed 148 porphyrite 20 Portugal 170 post-peak region of stress-deformation curve 36 post-stack seismic time section 14, 15 potash 123, 124 power law, frequency components 205 Pratt-Swolfs in situ block tests, USA 165–166 precipitation (see sealing, minerals) pre- and post-fracturing effects on VP and VS components 362 effects on 1000/Q 363 effects on permeability 364 pre- and post-peak displacement condition permeability enhancement 554 relation to resisted mobilized friction magnitude 554 pre-Cambrian 211 basement 429, 430 crystalline, Ko 299 preferred orientation of clay particles 354, 355 pre-injection/pre-grouting (of cements) 4, 56, 118, 153, 172, 173, 175 analogue for hydrothermal sealing, VP – age relations 287–291, 291–294

694

Index

pre-injection/pre-grouting (of cements) (contd ) pre-peak region of stress-deformation curve 36 pre-slot (unloading of block) 167 pressure, pressured 30 chamber test 97, 107, 108, 115 dependence (ubiquitous term) 346, 348 excess- 296 lack of pressure sensitivity 31 over- 296–299, 350, 351 pore- (see pore) 296, 297 -tunnel 119 under- 351 primary joints 551, 552 principal directions of loading 355, 357, 359, 361–363 directions of velocity measurement stress (see stress) 361–363 prismatic sample, 16-sided 481 probe drilling 139, 151–153, 162 processing software 7 production assistance 438 production rates damaged by excessive- 363, 453 effect on jointing 487 profile (see roughness) propagation direction 353–363, 451 increase of velocity with non-vertical- 451 of body waves 5 of stress waves 17 proton accelerator foundation 29 Prodozakonov f-value 76 psuedo-static macro-deformations 6, 421–425, 456 normal and shear stiffness in CO2 flood 451 parallels 9 pulse echo method 346 pulse generator testing 350 pumping test (extraction) 162, 173, 174, 378 Pure and Applied Geophysics 230 push-down 14, 15 push-up 14, 15 pyrite 23 pyrrhotite 23 Q rock mass quality (termed’ rock quality Q’ or Qrock ) 179, 269 Q-calculation example 225 Q-calculation example, Sugar Loaf, Rio de Janeiro 558 Q-calculation example, faulted rock, tunnel collapse 558 Q-histogram core logging 224, 622–624 Q-logging, absence of 208, 224, 386 Q-logging of caverns 53, 94, 625 Q-logging of core 74, 94, 274, 386, 387, 623, 624

Q-logging of outcrops 94 Q-logging of tunnels 94 Q-parameter ratings re rock quality, (see J-parameters, see Appendix A) 615–624 Q-prime (Q ) 469 Q-jumping (quality-depth; see curve-jumping) 93, 268, 272, 275, 285, 286, 625 Q-system of rock mass characterization 4, 250, Appendix A Q-system for selecting support 163 Q-system support pressure 140 Q-variation with depth 386, 387 Qo oriented rock quality 411, 615, 616 Q-values (logged or estimated) 6, 7, 11, 13, 16, 17, 18, 43, 47, 48, 53, 56, 58, 69, 70, 74, 75, 76, 78, 88, 92, 93, 113–115, 131, 132, 141, 144, 147, 148, 150, 153, 157, 158, 160–164, 167–172, 203, 225, 246, 250, 268, 273, 285, 287, 348, 377, 387, 425, 447–450, 469, 499, 500, 515, 556–558, 615–626 Q-values converted to Qc (normalized by UCS) 92–95, 114, 144, 148, 209, 215, 216, 220, 225, 246, 250, 252, 259, 268, 272, 274, 285, 287, 348, 625 Qc – M 92, 108, 113, 114, 132, 134, 269, 425, 449, 625, 626 Q-VP–UCS 449, 625, 626 Qc-VP relationship 6, 13, 18, 47, 74, 92, 93, 108, 134, 147, 148, 478 Qc-VP –depth 93, 157, 233, 271, 290, 447, 449, 625 Qc-VP –depth – porosity model 92, 134, 157, 233, 268, 450, 452, 465 Qc-VP –Lugeon relationship 159–165, 167, 170, 171, 172, 175–177 Qc-VP –M (depth) model 161, 167, 232, 257, 258, 348, 387, 449, 499, 500, 515 Qc-VP –M–L model 163, 164, 176, 425, 556 Q-VP–PR trends (TBM tunnelling) 151 Qo 615, 616 Qtbm rock-machine quality factor 17 Qtbm model 149 Qwater, QH2O – depth model 556–558 Q seismic quality (also refer to attenuation, earthquakes) (see itemized data below alphabetic order) Qseis (and attenuation 1/Qseis ) analysis methods 238, 239 Azimi second, third laws 239 Cole-Cole 239 Futterman causal operator 238 Kjartansson 239 Kolsky-Futterman 239 peak amplitude ratio 238 power law 239 pulse-broadening technique 238 spectral (amplitude) ratio method 199, 201, 238, 386, 464

Index rise-time method 238 velocity dispersion formula 386 Qseis (Q or QP or QS) (alphabetic order) 17, 66, 179, 181–239, 342–353, 354–357, 363–367 anisotropy near-surface 300 anomaly, anomalous 204, 205, 342 crustal lateral variation (also QS) 229 elastic components of attenuation1 Qe and Qk and Qp and Qs 193, 194 enhancement by tangential stress 301 extremely low Q 179, 205, 227 high-Q 179, 227 laboratory samples, sandstones 186–195, 341–351 laboratory joint/fracture samples 200, 361, 363, 364 low-Q 179, 227 near-surface gradient 211 near-surface- (rock) 201–203 Qgas/Qbrine versus frequency, BOSK model 458 Qseis from VP , finely interbedded rocks 380 Qseis from VP from Qrock 377 Qseis proportional to Edyn 387 Qseis/VP ratios, distinguish sand, jointed sst. 376 sub-ocean sediments (ooze-chalk) 206 unconsolidated sediments 205, 206 variation, erratic, of QP and QS with depth, as Q, Emass 386 variation with confining pressure 192 variation with frequency 200 Qseis similarity of magnitude to static Eintact (if GPa units) 191, 192, 342 static Ejointed (if GPa units) 200, 201, 362 static Emass (if GPa units) 202, 203, 210, 220, 221, 224–226, 232, 269, 348, 350, 352, 365–367, 377, 379, 387, 405, 410, 411, 499, 500 Earthquake sources Qc coda (earthquake sources) 209–219 Lg coda 230, 231 Qc coda – frequency 217 Qc coda – temporal variation 215 Qc coda – before/after earthquake 218 Qc coda-azimuth-depth-distance-magnitude-time 216 Qc1 coda attenuation related to coda wave 209–219 Qc1(earthquake sources) Qc1coda – frequency data sets 211, 214, 218, 228 Qc1coda – temporal variation 218 Qc1 coda – before/after earthquake 218 QS versus QP coda components 212 Qo (Lg coda at 1 Hz) 230, 231 QP (earthquake-based) QP – depth (Cajon Pass, Varion wells, Parkfield) 222–224 QP – depth (0 to 35 km) and lateral variation (0–200 km) 229 QP – depth (0 to 1200 km) and VP, from a) body waves, b) surface waves QP – distance – magnitude (NAFZ) 220

695

QS (earthquake-based) QS – depth (Cajon Pass, Varion wells, Parkfield) 222–224 QS – depth (0–35 km) and lateral variation (0–200 km) 229 QS total – frequency (earthquakes), 223 Qscatter – Qintrinsic (earthquakes), 213, 214, 224 QS fast, QS slow 0–200 m depth, Chi-Chi 436 Mid-ocean ridge QP, QS QP – QS – depth East Pacific Rise 14°S 286 QS – depth (hole 504B, Costa Rica ridge, 0 to 1600 m, also Qintrinsic) 280 1/Q – depth (sub-ocean basalts, mid-Atlantic ridge, 0 to 700 m) 269 1/Q – depth – laterally (sub-ocean basalts and magma chamber, 3D tomography) 282 Reservoir Q Q – depth (sedimentary rocks to 2.4 km depth) 232 Q – interval stacking velocity (VP) sedimentary reservoir rocks 234, 235 Q – VP equation: fit to some sedimentary rocks 235 Q-VP – K log, fractured reservoir, shale, 4000–4350 feet 237 QP and QS ranges, sandstone reservoirs bearing: gas, gas condensate, oil, water 343, 345 QP – QS – porosity differentiation, gas zone indicator in well 345 QP/QS crossed behaviour with gas contra water/oil saturations 343, 349 1/Q – depth, anomalously low (Lower Triassic sandstone at 4 km depth) 233 1/Q – frequency, modelled reservoir fractures 238 Q⫺1 in North Sea fault zone, anomaly 235 Non-earthquake field results for seismic QP and QS QP – freeze-thaw cycles, Jurassic limestone, relevance to field 185 QP – depth into tunnel wall (EDZ), columnar basalts, 40 m depth 127, 367 QP – angular frequency and shear strain level, clay 189 QP – frequency and geophone interval variation, sediments 205 QP – QS dual-porosity chalk, low values near-surface 350 1/Q (1/QP) – frequency data comparison using Biot 209 Petroleum related field results QP – depth slice (mean 32, 96, 106 m and laterally, quaternary, alluvial stream beds, lithified sands-sandstone) 374, 375 QP – pressure (equivalent to depth) ultrasonics (interbedded sand-, lime-, silt- and mudstones) 207 QP – depth w.r.t. sonic logging (interbedded sand-, lime-, siltand mudstones) 207 QP – depth, also VP – depth, also QP /VP – depth, 210–400 m, sands and sand channels 375–377

696

Index

1/Q – depth (sedimentary rocks to 2.4 km depth) 232 1/Q – depth (0 to 5.5 km depth, Lower Triassic sandstones deepest 1.5 km) 233 1000/QP – frequency dependence(interbedded sand-, lime-, silt- and mudstones), field 207

1/QP – frequency, calculated for fractures/joints of different stiffness, quartz-monzonite 200 1/QP – permeability: various limestones: packstone etc. 349 1/QS – permeability: various limestones 349 Rock physics/poro-elastic modelling 1/Q – frequency, fracture nucleation, automaton model 463 1/Q – frequency,Chapman, fracture size variation 471 1/Q(components) – frequency, SeisRox TIH model 476 qS1 and qS2 examples parallel and perpendicular 390, 445

Rock physics data (sandstones) QP , VP – frequency – effective pressure, dry or brine saturated, Berea sst. 344 QP – differential pressure, Berea sst. 352 QP , VP – frequency – effective pressure, dry or brine saturated, Boise sst. 344 QP,, VP – frequency – effective pressure, dry or brine saturated, Massilon sst. 344 1000/Q and Q – 3D confining pressure – permeability, cubic specimens, Penrith sst. 363 QP – clay content (volumetric) – permeability, sandstones, equation 346 QP – differential pressure, as additional function of frequency, Berea sst. 187 QP – % compliant minerals, effective pressure 5 or 60 MPa, sandstones, siltstones 347 QP and VP – effective pressure, microcracked sandstone 347 QP and QS – differential pressure, Berea sst. 342 QP/QS – (VP/VS)2 and pore pressure, to distinguish sand and sandstone 351 QE – confining pressure and saturation, resonant bar technique 186 QE – saturation and frequency, resonant bar technique 190 QE – strain amplitude, resonant bar technique 187

quarry 27, 28, 42 blasting (damage) 170 quartz 27, 243, 254, 509 cement, precipitation of 311 content in three sandstones 343 diorite 27 mineral fillings 278 monzonite (Stripa Mine) 134–136, 422–424 monzonite (Stripa), joint behaviour 197–200 monzonite, stiffness, dynamic/static data, stress-dependent 496 quartzite, quartzites 13, 38 bedded, steeply 301, 367 jointed 93 Ko 299 massive (South Africa) 224 quartzitic sandstones 144 quaternary active faults (Japan) 217 deposits 447

Rock physics data (various rock types) QP – axial stress (sat. and dry), basalt 127 QP – pressure: sandstones 193, bedded-coal 201 QP – pressure, also Ppore/Pconfining 0°, 30° and 90°, over-pressured shales 355 QP – porosity: igneous and metamorphic rocks, limestones and sandstones 186 Qph and Qpv – confining and pore pressure, sandstones 192 QP – compliant minerals %: 5 and 60 MPa confinement, siltstones and sandstones 347 QS/QP – degree of saturation, lab 189, 232 QS/QP – VP/VS – degree of saturation, sandstone 189 QP – QS calcareous-, dolomitic-, siliceous-limestones 349 QP – QS – oil or water saturated: limestones, bi-modal porosity 350 QP – QS – kerogen %: modelled Kimmeridge shale, 0° and 90° 353 QS – axial stress (sat. and dry) basalt 127 1/Q (1/QP) – axial stress-strain, loaded to failure, tuffaceous sst. 195, 196 1/Q – pressure (with three Q⫺1 anisotropy parameters 357

R equivalent roughness of rockfill 538 Rabcewicz 76 radial rock property variations 316 stress (see stress) unequal- stress gradients 315 rail tunnel, high-speed 17 Rangely anticline, Colorado 167 ray curved- paths 44 paths 16, 59, 61, 62, 130, 261 paths parallel and perpendicular to assumed fractures 384 paths crossing max. no. joints 124–127, 367 tracing 153 Rayleigh scattering attenuation 196, 480 wave scattering 480 rebound hammer (see Schmidt) 101 receiver, receivers lines (3D-4C) 391

Index permanently installed in seabed 396 reconstructed shear-dilation path 527 recording station (earthquakes) 210–225, 261 vessel/boat 396 recovery factor 373 recrystallization of firn 254 reflected P-wave 438 primary 383 S-wave 438 upgoing multiple 383 reflection 283 amplitude changes in 4D 352 amplitude varies with azimuth AVOA 389 amplitude varies with offset AVO 389 coefficients, azimuthal P-wave 393 coefficients, for split shear waves 393 coefficients in one- and two-set models 393 coefficients in AVO 388, 389 enhanced-, subtraction of seismograms 382 methods 4 seismic, comparison to polarisation 475 seismic, exotic uses 403 -strength change, in 4D 398 wide-aperture seismic- 285, 286 reflector 249, 255, 383 deep-, difficulty of imaging, sub-basalt 403 in-tunnel 153 refraction seismic inversion 16 land-based 274 on-bottom- 282 reversed deep-sea (historic) 242, 243 shallow 3, 4, 5, 9–16, 74, 160, 203 refractor 4 imaging 15 refuse transfer cavern 76 regional variations of Q 231 regression lines 171 relaxation 182 mechanisms 183 relaxed 183 -pore fluid in super-k regime 378 reloading of fractured cube 363 repeated surveys (see 4D) replicas of shear-dilation paths 527 remnant arc 227 Rendalen hydro electric project, Norway 147 research, experimental (ubiquitous terms) borehole 207, 303, 305, 308, 346, 356 reserves efficient exploitation of- 396

reservoir anisotropy investigations 404–406 characterization 295 characterization using dispersion 387, 388 compaction 183, 295 completion 295 depletion phenomena 397 detection of- compaction in 4D seismic 397 detection of- subsidence 4D seismic drawdown (dam sites) 88–90 description 295 dynamic- properties 397 engineer 369 fractured/unfractured water-flood survey 402, 403 heterogeneities 372, 373 horizons 297 impounding (dam sites) 88–90 management 394, 396 parameters, estimates of from 4D4C 396 phenomena 179 pressure 295–299 production 295 production increment 396 rock scenarios 535 residual friction angle (see friction) 507–512 shear strength (see joints, fractures) 507, 522 resistivity – depth plot, sub-ocean Hole 504B, Costa Rica ridge 280 logging 169 resistivity – depth relation 20, 297, 298 temperature effect 297 tomograms 169 Reskajeage, Iceland 503, 504 resolution -problem 7 vertical 7 resolving kernels 262 resonance decay measurements 187 extensional- tests 186–188 resonant bar techniques 187–190 REV effect 223 rhyolite artificial surfaces 82 ridge (see mid-ocean) rift structure Rio Grande- SW USA 230 earthquakes, New Mexico 210 ripping 30 river 162 rms (root mean square error) 472, 474

697

698

Index

RMR -rock mass rating 7, 11, 56, 70, 76, 144, 163, 469, 615, 621 core-logging 387 correlation to static deformation modulus (Ed or M) 111–113 correlation (approx.) to rock mass quality Q-value 113, 163, 621 -variation with depth 386, 387 rock anchor foundation 51, 52 bedded 304 beneath our feet 558 blocks 156 boundaries 202, 226 burst prone areas 52 caverns, models 551 classes 139–141, 152 classes and rock types 142–144, 148–150 conditions (adverse for tunnelling) 151 country- 157 cover 147 deformation, large scale 400 fabric orientation, from Point Load 384, 385 finely-layered sequence of 207–207 framework 356 hard jointed 164 hard massive 93, 164 hard massive, completely intact, km depths 365 hard porous 164 heavily jointed 145 importance of rock type 3 joints (ubiquitious term, see joint) 493 mass (see rock mass) massiv-, negligible jointing, QH2O – K estimation 558 matrix 30 model, biaxial tests of fractures 422 non-brittle 304 non-dilatant 304 outcrops 11 partially molten- 242 quality 5, 88 qualities (A to F) and velocities (VP) 143 quality Q (see Q-value) skeleton 320 salt, VP and density 326 stimulant, unrealistic 417, 418 slope 30 slope, modelled 517, 551 soft 93, 304 soft, massive 304 soft plastic 304 strength 3, 92, 150 strength, reduced 309 stresses 295–300

stresses, principal components 320 support, high crack density 444 type 9, 11, 27, 173 types for JRC, JCS, ␸r determination (11) 509 unstable- 160 rock engineering 3, 30, 106, 215 parallels 226 parallels to sub-ocean gradients 286 project, projects 35, 110, 423 rock failure 127 dilatant- 302–312 non-dilatant- 302–305 rock mass 30 characterized not classified, outside EDZ 310 characterization method 202 classification method, Chinese 74, 76 condition 9 deformability (pseudo-static) 97–115, 161, 162 failure (under plate load) 102–104 near-surface-, attenuation 226 parallels (shallow crustal seismic attenuation) 224–226 quality 6, 7, 17, 92, 95, 225, 273, 282 quality improvement (due to grouting) 170–175, 292, 293 quality, low 158 rapidly changing- qualities 10, 203 rapidly changing- qualities at fault zones 394 velocity increase 293 rock mechanics 5, 45, 75, 119, 227, 309, 424 background, logic 191, 310, 390, 407, 418, 427, 434, 442, 444, 463, 465, 502, 523 developments 197 effect 192 engineers 189 experience 407 modelling (see numerical) 133, 420, 427, 460, 461 rejection of elastic isotropic behaviour 382 units (e.g. MPa/mm) 200 wellbore (borehole) studies 302–311, 319 rock physics 45, 179, 192, 295, 350 at laboratory scale 323–367 goals, exploration related (King) 323 high pressure testing needs 323 model for computing change of density, from VP and VS 398 more ordered relationships of- 323 reduced sensitivity for – at great stress 320 shallow perspective of- (see Ch. 2) weathering and alteration in near-surface – (see Ch.2) Rocky Mountains 231 roof fall 60 room temperature 30 Rose area, East Pacific rise 275 Ross ice shelf 253

Index Ross Sea 253 rotating S-wave transducer 356, 357 rotation counter- of fluid lenses and rock-to-rock contact with shear 384, 527, 548–551 roughness (see joint, fracture) profiles 508–510, 514, 545, 551 RQD rock quality designation 6, 7, 11, 12, 13, 16, 43, 53, 69–72, 74–76, 78, 83, 88, 89, 92, 101, 105, 106, 126, 144, 169, 175, 202, 225, 293, 447, 448, 469 RQDo oriented 225, 411, 616 absence of- logging 208 RQD/Jn relative block size 469 scattering related 225 RQI reservoir quality index 333 link to FZI flow zone indicator 333, 335 rule-of-thumb (Crampin) fracture density link to S-wave anisotropy 413, 415, 442 particle size d95 x 4 ⬍ E aperture for groutability 487, 490 Rulison Field 384 Russia, 88–90, 102, 117, 119, 170, 439 RSR 76 S-wave (see shear wave) anisotropy definition 438 lower propagation velocity 438 particle motion 5, 438 phase velocities 480 pure S-wave, SS-wave 389, 438 safety factor (F. of S.) 307 salt 12 bedded- 123 bedded, Ko 299 creep 321 creep, dislocation climb 321 creep, undefined mechanism 321 -dome 380, 381 Ko 299 seal for hydrocarbons 295 shear strength in situ 299 -water (see brine) weaker-, intolerance of stress difference 298 sample boundary closure 193 boundary opening 194 damage 516, 528–530 disturbance, shale 354 loaded to failure 195 shortening, modulus 347 sampling (seismic) bias, for rock physics testing 397

699

bias, vertical wells, vertical structure 407 dense- near fault zones 394 dense- near fracture zones 394 sampling-induced microcracking 347 initial stress release when coring 347 San Andreas fault zone SAFZ 90, 91, 95, 221–224, 257, 382, 429, 431, 432, 470 San Francisco Bay Area 257, 259 San Joaquin Valley, southern California 260 sand 11, 12 beach- 254, 350, 351 cemented-, model material 302, 303, 305 distinguishing- and sandstone 351 fast- 15 oil-, heavy 379 sandstone, sandstones 12, 26, 31, 32, 94, 137, 325, 327 (i) sorting by name (see also Q and VP listings) Bandera- VP static/VP dyn and Young’s modulus versus axial strain magnitude 340 Berea- 37, 58, 59 Berea- borehole studies 314, 315 Berea- QP -confining and differential pressure, visible bedding 191–193 Berea- QP -confining and differential pressure, frequency 187 Berea- QP -differential pressure 352 Berea- QE -strain 188 Berea- QE – % saturation, confinement 186, 187 Berea- QP and QS -differential pressure 342 Berea- VP static/VPdyn and Young’s modulus versus axial strain magnitude 340 Berea- VP and QP -frequency -effective pressure, dry or brine saturated 344 Boise- VP -VS -temperature 331 Boise- VP static/VPdyn and Young’s modulus versus axial strain magnitude 340 Boise- VP and QP -frequency -effective pressure, dry or brine saturated 344 Castlegate, jointed 165, 167 CBTF well- VP – VS – density-permeability-birefringence 445, 446 Crossland Hill- VP and VS versus 3D confining pressure, before/after fracturing, cubic specimens 362 Crossland Hill- VS – permeability, before/after fracturing, cubic specimens 364 Gypsy sands, tomography, QP and VP, also QP/VP 375–377 Kern River oil sand, VP-temperature, oil/gas % 330 Massilon- 1000/QE -velocity-strain magnitude 187 Massilon- VP and QP -frequency -effective pressure, dry or brine saturated 344 Michigan- QP – confining and differential pressure 191–193

700

Index

sandstone, sandstones (contd ) North Sea- 3D qP-normalized permeability, stereograms 390 Pecos- VP static/VP dyn and Young’s modulus versus axial strain magnitude 340 Penrith- 1000/Q and Q versus 3D confining pressure, versus permeability, cubic specimens 363 Ohio- VP static /VPdyn and Young’s modulus versus axial strain magnitude 340 Troll sand 326 Venezuela oil sand, VP-temperature, oil/brine % 330 Whitchester- VP -pressure/depth, core and sonic log comparison 348 (ii) sorting by geological dating Carboniferous 207–209, 346, 356 Cretaceous 231 Lower Jurassic 427 Mesozoic- 153 Mississippian 343, 344 Permian- 72 Pliocene 343, 344 Triassic- 72, 427 (iii) sorting by category porosity-velocity 24, 311 high porosity, velocity-porosity data 325 high porosity, velocity-density data 327 high pressure-porosity tests 312 porosity-permeability 334, 343 porosity-permeability-FZI 335 sandstone, sand, Tertiary data numerous engineering properties 19, 21 porosity-permeability, core correlation 334 well log, VP -core porosity-core permeability 334 sandstone, theoretical model VP-pressure-brine/gas saturation 329 Poisson’s ratio-pressure-brine/gas saturation 329 sandstone, tight gas stress-strain data 339 3D, spherical, VP and permeability 357–359 lenticular, reservoir, VSP 471–475 velocity-density data 327 VP –VS data 328 tight gas, 3D VP – confining pressure, spherical samples, layering/jointing, dry, saturated 358 tight gas, 3D permeability – confining pressure, spherical samples, layering/jointing 359 (iv) sandstone, diverse (alphabetic, see also Q and VP lists) 12, 26, 31, 32, 94, 137, 325, 327 artificial surfaces 80, 82 aspect ratio influences for- 326 basic friction angles, dry, wet 511 bedded and jointed- 207–209, 346–348 block of- 137, 545 brittle- 306

brittle-ductile transition for- 312 -carbonate beds 387, 388 cataclastic flow of- 312 channel sand 375–377 clay content in 24 clay content %, VP –porosity 331–333 clay-rich- 349 clay-rich- (reduced ␣-coefficient) 320 clean, porosity-velocity, sand suspension 324 deeply buried 312 density and velocity data 326, 327 epoxy-, model 470, 480, 481 fine clay layering 357–359 finely interlayered, distinguished from other rocks 379 grain-crushing of coarse-grained- 311, 312 hydrocarbon-bearing 370 interbedded- 47, 145, 207–209, 212, 346–348, 450 joint, initial stiffness 494 joint normal stiffness – stress 496 joint normal stiffness, initial 495 joint, stress-deformation 495 Ko 299, 300 lithified (sands) 374 low porosity 31, 32 low matrix permeability 357–359 -marl sequence 46, 171, 172 meta- 146 mixed shale- units 369 -mudstone, interbedded 100 multiple clean/shaly sand composites, VP – saturation, patchiness data 337, 338 North Sea- 359, 360 Poissons ratio-pressure, dry, brine, crude oil 338, 339 porosity – VP (see listings following) 325 porosity-permeability (see listings following) QP – clay content and permeability 346 QP -% compliant minerals, effective pressure 347 QP and VP -effective pressure 347 Qseis (QP) magnitude only 181, 182, 186 QP/QS –(VP/VS)2 and pore pressure, to distinguish sand and sandstone 351 1/Q – axial stress-strain, tuffaceous sandstone 195, 197 1000/QP and 1000/QE versus pressure, saturated 191, 192 1000/QE and 1000/QP confining pressure 191 quartzitic 144, 146 reservoir 297 reservoir Q values 343 roughness profiles 509 sand/sandstone 47, 324 sand-shale proportions, each well 377 saturated 12, 191, 192, 207–209 shear strength in situ 299 ␴h min from minifrac testing 298 stress-closure tests on joints 528

Index stress-conducting aperture, CSTF 529, 530 stronger- tolerance of stress difference, shear stress 297–299 strongly jointed 148 suspension, sand 324 tuffaceous VP – % gas/brine 341 VP –pressure data, dry, saturated 32 VP –VS data 328, 329, 372 VP –VS data, varied effective stress 329 VP/VS – differential pressure, also to extremely low pressure 351 San Gabriel ranges 259 saprolite 4 Santa Barbara Channel, southern California 260 saturated, saturation 8, 17 complete 151 contra dry, joint stiffnesses 507–512 degree of- (calculated) 126, 127 degree of- (measured) 21, 29, 135 effect of- (gas/brine%, oil/gas%) 329, 330, 343, 345 effect of- on VP 337, 338 effect of- on VP, VP/VS and Qs/Qp cross-plot 189 effect of- on VP, QP for bedded-coal 201 effect of- on Kn and Kn dyn normal stiffnesses 202 fully 15, 190 glycerol- (glass beads) 205 heterogeneity with patchiness 336, 337 ‘homogeneity’ with multiple units 336, 338 honey- Lucite plates 427 liquid-, high pore pressure 394 partially 182, 189 partly- 5, 15, 17, 194 state of- of flat pores 190 top of saturated zone 9 under-saturation 123 unsaturated 8 vapour-, low pore pressure 394 water- (ubiquitous term) 352, 353 zone 9 saw-cut fractures, samples 70, 540 S/C (ratio) subsidence/compaction high- with discontinuum modelling 400, 454 low- with continuum modelling 400 scale -effects (see joints) 507, 510, 522, 537, 538 lack of-, assumed 400 -length 373 (scale dependent, see shear stiffness) Scandinavian rocks 6, 13, 71 SCARABEE 110 scattering (see also attenuation) 182, 195–197 attenuation, calculated 197 attenuation, dual/triple poro-elastic models 461–481

attenuation, source of 306 losses (RQD/Jn related) 202, 225, 350 losses (Jr/Ja related) 350 Rayleigh wave 196 wave 191 Schlumberger 58, 206, 316 Schmidt hammer tests 26, 27 in (TBM) tunnels 148, 149 L-hammer 486, 509, 510 N-hammer 27, 28 rebound r and R 509, 510 schist 12, 32, 38, 100, 139–142 clay- 145 (metamorphic) 212 Pelona, S. California 261 schistocity 3 Schmidt net stereographic projection 358, 360 scour-holes, sediment-filled 56 SCV, Stripa 133, 169 sea 147 floor interface 438 -floor, rough 282 water 15 seabed/sea bottom 56 cables (OBC) 391, 452 cable array, permanent 453 hydrophones 53, 56 seismic 56 sealed fractures parallel H max are numerous 441 sealing bulkheads 129–131 plastic layers 295, 297–299 with hydrothermal minerals 270, 276 with syn-kinematic, post-kinematic cements 441, 442 seasonal fluctuations reservoir level 89 water level 89 sediment, sediments 3, 20, 205, 206, 221, 274 Cretaceous 231 deep accumulations of- 231, 232 hard 249 Mesozoic 231 newly deposited 296 post-rift (Atlantic margin) 255 soft 249 thick-, effect on continental Lg coda 231 unconsolidated- giving low Q 231 unconsolidated- giving very low velocity 231 sedimentary environment (ubiquitous term) basin 179, 260 diagenetic-based cycles 333 ‘fining-up’ sorting technique 333–335 layers, layering 14 stratigraphy matching 333

701

702

Index

sedimentary environment (ubiquitous term) (contd ) sedimentary rocks (ubiquitous term) 8, 25, 207, 263, 265, 299 Ko values 299 Q and Q⫺1 values to 2.4 km depth 232 Q versus interval stacking velocity 234, 235 sedimentation 300 -erosion, effects on E-modulus hypothesis saturated –rocks 207 Segunda Angostura dam site 163 seismic anisotropy (see anisotropy) 40, 41, 42, 394 anomalies 4 attenuation (see attenuation) attenuation as sensitive indicator 386 attenuation tomography 281 coda waves (from earthquakes) 209–219 -data, variation with offset and azimuth 382–396, 401–406, 407–482 (Ch 15) detection of subsidence 400 disappearance 24 fissurization index K 70 global measurement locations 246, 251 high resolution- reflection 254 impedence (see impedence) method, shortcomings of 14 modelling (numerical) 204 profile 7, 9, 11, 12 profile, continuous 283 profile, high-resolution 282 profiling (horizontal HSP) 153–155 profiling (tunnel TSP) 153–155 processing (ubiquitous term) Q (ubiquitous term) Q and similarity to Qrock when deep, intact 365 Q , low values with fracturing 365–367 Q , low values with jointing 222, 223 quality (inverse of attenuation) 17, 65, 127, 181–239 quality factor Q and components (see Q , Ch 10, and Ch 13) reflection (see reflection) 254 reflection tomography (see tomography) refraction method, survey, profiles (ubiquitous term) 4, 10, 13, 14, 70, 76, 115, 155, 166, 173, 245–290 refraction, deep (0–35 km) 229 response, temporal 307 risk mitigation 189 shallow refraction- 3, 4, 9, 76, 115, 176 shallow refraction, in tunnel 122, 153 shallow refraction, beach sand 253 sonde 151 sources 189 spectroscopy 118 spread 140 survey (ubiquitous term)

tomography (see tomography) transmission across joints 79, 80, 82 wave blockage 231 velocity (ubiquitous term, see VP, VS and data lists) velocity changes due to tunnelling 615 vessel 394, 396 wave scattering (see scattering) 231 velocity gradients (see VP-depth) 107, 246 seismically visible 3, 296 seismicity (ubiquitous term) base of- thermally controlled 257 seismogram, seismograms earthquake- 213 plane-layer- models 231 subtraction of-, horizontal well sections 382 synthetic 231 synthetic- not correlating with measured 317 synthetic- modelling 266 three-component 437 three-component, before/after rotation, fast/slow 437 seismology broad-band 207–209 seismometers borehole 221–224 in-well, in-borehole 209, 221–224 wide band-width- 221–224 selective firing Sellafield site, N.W. England, UK Nirex Ltd. 57, 94, 224, 309 Rock Characterization Facility (planned) 528–530 sequence shear zones 3 sequential firing in perpendicular directions 313 serpentinite 23 Severn Estuary, second crossing 11 SH-wave 354, 357 shaft 87, 121, 123 deep 93 erosion 156 shale, shales 12, 27, 32, 94, 146 Antelope-, fractured 236, 237, 387, 388 attenuation in- 354–356 Brown-, sigmoidal fractured 236, 237, 387, 388 bulk-, not matching Qseis Emass model 387, 388 CBTF well- VP – VS – density-permeability-birefringence 445, 446 clay-particles in- 418 compacting 301 Cretaceous 231 dense 38, 39 finely interlayered, distinguished from other rocks 379 fine layering in-, TIV symmetry 374 ‘fining-up’ sorting 333 Fiqua, Oman 456, 457 interbedded 47, 234, 298, 300

Index kerogen rich-, state of maturation 379 Ko 299, 300 Kimmeridge Bay, Dorset 488 Kimmeridge-, North Sea 351–353 -limestone interbeds 148, 234 low permeability- 268 Mancos 167 mixed-sandstone units 369 mud-filtrate example 317 overlying- 393 over-pressured, lab test 354–356 Palaezoic 430 Qseis 181, 182 Reskageage, Iceland 504 -rich layers 376 -sandstone units 370–372 saturated 12 sealing, caprock 295, 298–300 shear strength in situ 299 ␴h min from minifrac testing 298 -smear sealing 372 stress-conducting aperture, CSTF 529, 530 thin-bedded 300 Tournemire tunnel EDZ in- 121 VP and density 326 VP –VS data 372 weaker-, intolerance of stress difference 298 shale alteration 302, 312, 313, 317 shallow depth 147 gas (see gas) layer velocities 140, 156 sites 7, 74 water flows SWF 350 shear, shearing and dilation 390 body-waves 5 box (DST) 510 box samples 524 causing dilation 249, 258, 259 causing maintenance of permeability 258, 259 compliance 346 deformation zones 308 direct- tests (DST) 401 direction 39 displacement 9, 84 displacements to peak, joints, discontinuities, many scales 546 displacements, and stick-slip 435 down-dip-, compaction mechanism 392 failure 9, 130 failure of matrix during water-flooding 403 failure of model rock masses 105 failure surfaces observed 305

703

fracture microseismicity, Ekofisk 443 fracturing, mini-EDZ, fluctuating sonic velocities 379 log-spiral- 302–307 micro shearing 282 modulus and fluid type 420 on bedding planes 304 permeability, effect on 517–536 relaxation 187 slowness 316 strain 189 tests, laboratory tests, in situ/field 20, 101 zones 9 shear modulus (␮) (see also deformation) 5, 13, 71, 104, 109, 111, 161 pressure-sensitive-, using excess compliance 397 shear stiffness KS (joints, fractures) 45, 346 clay-filled discontinuities, normal stress 505 equations 511 dynamic- (see dynamic) 282, 423, 424 pseudo-static 282, 422, 492–499 reductions with block size 483, 484, 523, 524 reductions with stick-slip, assumed 435 scale (block-size) dependent- 6, 492, 493, 501 scale effects discussion 421, 422 shear strength displacement dilation curves 507, 510, 526 displacement dilation modelling, Barton-Bandis 506, 507 equations 511 loss of- 241 low- of suspension 350 peak- of joints 491, 507, 510–512 peak- to match mobilized friction, conductive fractures 544, 545 pre-peak or post-peak friction mobilization 545–548 residual- of joints 491, 507, 510–512 shear strength envelope for filled (clay-) discontinuities 538 intact rock, high stress 538, 540 intact rock, numerous data, high stress 539 induced fractures, extreme (tectonophysics) stress 537, 538 induced fractures, high stress 538 rock joints, lab and in situ, engineering stress 537, 538 rockfill/crushed rock 538 sandstones, high stress 312 shear stress 5, 52, 165 change of 217 displacement 507, 510 dissipation, through log-spiral failure 306 limiting value of 227 maximized 308 -normal stress envelopes, induced fractures, extreme stress 537, 538

704

Index

shear stress (contd) -normal stress envelopes, joints: lab and field, engineering stress levels 537, 538 resistance to 227 effects on velocity 40 shear wave, waves 7, 32, 36, 37, 81 ability to penetrate gas cloud 391 amplitude 110 amplitude decrease 350 amplitude, effect of stick-slip, sliding 435 anisotropy 9 anisotropy and fluid type, gas, brine 456, 457 anisotropy and fracture dip 445 anisotropy % linked to crack density 413 anisotropy %, fracture porosity, gas or brine 457 anisotropy % linked to pore pressure, 90°-flip model 416 anisotropy % linked to frequency and fracture sizes 467, 470, 472 anisotropy linked to permeability 445–446 anisotropy logging 302, 312–316 anisotropy sources (see anisotropy) 409 converted from P-S waves 391 detection of oil or gas, compressibility re ZN 407 energy 130 fast- with longer wave length 314 fast- parallel to formation fast axis 313, 314, 417 fast- parallel to structure 313, 314 flexural- 312–316 frequency 81, 110, 112 frequency anisotropy 459 leading split- stable, fast direction 411 monitoring of fracture closure 364 monitoring of fracture closure cycles 364 polarization 82, 313, 357, 359, 361, 445, 446, 448–477 polarization affected by shear stress, shearing, speculation 517–521, 525–527 polarization in principal stress direction 359, 361 polarized- 393 processing, demands of 438 slow- perpendicular formation fast axis 314, 417 slow- (perpendicular to structure) 314, 408 slow-, with gas in fractures 456 source 439 splitting (see shear-wave splitting) surveys 12 technology, belated application, mature reservoir 452 teleseismic- 410 three-component sensors, 1  v, 2  h 438, 439 (with hydrophone 4C) 438, 439 time-delay, temporal 433 travel-time, temporal 433 velocity anisotropy 408 velocity transition 231 velocity (less than fluid velocity) 206

velocity (VS) examples (laboratory measurements/rock physics) 6, 7, 8, 29, 32, 36, 37, 81, 87, 109, 131, 136, 189, 265, 298, 328, 329, 331, 351, 353, 354, 364, 372 velocity (VS) examples (field surveys, all depths) 6, 7, 8, 9, 12, 32, 64, 70, 71, 75, 92, 92, 90, 104, 105, 111, 161, 229, 241, 249, 250, 251–253, 264, 266, 267, 270, 275, 277, 280, 281, 286, 379, 395 shear wave splitting (and polarization) 82, 179, 313, 314, 354, 355, 357, 369, 372, 386, 388, 389, 407–481 above sedimentary hydrocarbon basins 408 above earthquakes 428–438 above small earthquakes 408 anisotropy parameter 451 anisotropy parameter range 451 argillaceous rocks 450–452 as function of (joint, fracture) shearing 518–520, 522 correlated with subsidence bowl 412 due to component sets 386 due to conjugate sets 483 due to high ZT, low KS supposition 512 due to intra-bed joint stretch (supposition) 453 due to microcracks or joints, discussion 432 due to ‘stress or strain’ 453 due to subsidence, bed stretch, intra-bed jointing (supposition) 451–453 due to sub-vertical fractures 450 focussed on structural domain with VSP 410 influenced by sub-recording station structure with earthquakes 410 matrix with relevant compliances 417 mechanism explained 439 Mid-Atlantic Ridge 437 multiple- 410 Natih field, Oman 455–458 New Madrid seismic zone 428, 429, 430 non-parallel ␴H max direction 384, 385, 389, 390, 403, 404, 406, 414, 429, 431, 432 parallel ␴H max direction 429, 436, 437, 439, 446, 447, 448, 450 Parkfield seismic monitoring array 429, 431, 432 petroleum reservoirs 438–440, 442–460 polarization examples 430, 431–433, 437 polarization in anisotropic zone 439 shallow, 15–30 m 447, 448 shallow, subsided overburden, Valhall 453, 454 sources of- 410 temporal changes 410 using near-offset VSP 445 Valhall overburden 453, 454 shear wave window above earthquakes 409, 428, 436, 437 epicentral distance less than focal depth 409

Index Shell 456–458 Shetland Islands 404 shields (geologic structures) 246 Canadian 217 Indian 219, 230 shield area 217 Shinkansen high speed railway, Japan 47 shooting vessel/boat 396 shortest path through best rock 14 shotcrete 80 steel-fibre reinforced 621 Siberian Shield 230 silicate host rocks 23 silica fume (see micro-silica) Qseis 181 Siljan Ring, Sweden, borehole data 543 silty flood-plane 375 siltstones 26, 146 above shale, caprock 454, 455 basic friction angles, dry, wet 511 Carboniferous 207–209, 234, 346–348, 356, 357 inter-bedded 207–209, 234, 346–348 Ko 299, 300 joint, initial stiffness 494 joint, stress-deformation 495 joint normal stiffness – stress 496 joint normal stiffness, initial 495 layered sequence 234 stress-closure tests on joints 528 Tertiary 304 Triassic, North Sea 427 Lower Jurassic, North Sea 427 single -bit run 312, 313 singularity P-wave cancellation 466 zero attenuation 466 sinusoidal shear strain 5 Site 977, ODP Leg 161 (Shipboard Scientific Party) 334 SKB 131–136, 203 Skien river, Norway 161, 162 skarn ore 65 slate, slates 12, 38 cleavage fractures 362 cleavage, stress-closure 494 joint normal stiffness, initial 495 joint, stress-deformation 495 Mesozoic 153 high-grade 248 stress-closure tests on joints 528 strongly jointed 148

705

slickensides on conjugate joints under compaction, Ekofisk 443, 452 sliding on crack faces 182, 190 stable- on fracture surface 540 slip coupling of normal and tangential- 420 on conjugate joint sets 308, 420 on pre-existing faults 130 slope reinforcement 117 slow compressional wave 209 direction 128 shear wave depends on fluid in fractures 457, 458 smectite 352 SMS stress monitoring site, Iceland 432, 433 Snow 3D network model 172, 173, 487, 490 Snell’s law 438 soft (porous) rocks 48, 79, 101, 103, 113 softening behaviour 303 soil 9, 11 clayey 12 engineering 106 silty 12 to clay 24 vegetation 24 solution channels 378 sonar buoys 11 sonobuoys 261, 275 sonic and ultrasonic tests 191 log 45–47, 52, 69, 234, 271, 301 log, core correlation 277 log fluctuations 301, 310 logging 380, 386, 387 logging of boreholes 97, 119, 129, 207–209, 261 logging tool 313 probe 129 shear and compressional- log 301 Soultz deep borehole data 555 soundings 9 source, sources -and receiver (pairs) 204, 205 at the tunnel face 154 calibration shots 394 lines (3D-4C) 391 micro-earthquakes 209–232, 394 multiple, fixed offset 440 of error 169 on the surface 154 P- and two orthogonal S-, nine component 471 quarry blasts as- 394 receiver lines, three for strike detection 446

706

Index

source, sources (contd ) S (SS)-wave source, sea-bed suction anchor 438 synchronise- 153 separation of- 9 vibrator, 1000 positions/day 455 source rocks 372 South Africa 110, 112, 131 South America 230, 231 South Carolina 90, 92 South China Sea, sonic log of reservoir 301, 313 South Dakota 60 South Korea 109, 111, 169 Southern California 228, 258 spacing (see joints, fractures) span (of tunnel or cavern) 151 sparker 67 spatial resolution 382 of variable structure 382 of temporal changes 382 specific stiffness, pseudo-static (see also normal stiffness) 198 spectral amplitudes/magnitudes 198, 199 ratios 199, 212 ratio method (see Q analysis) 353, 362 split shear wave (see shear wave splitting) spreading mid-ocean ridge (see mid-) spherical hemi- projection 358, 360, 445 samples 357–360 squeezing (see tunnels, boreholes) 297, 299 squirt clay- flow 346 flow 17, 183, 187, 206, 346, 349, 457, 461, 465–476 flow in poro-elastic models 461–481 flow absence when dry 341 flow absence when saturated 341 flow mechanism 384 flow reduced by pressure, closure 346 flow related to loss in bulk modulus 356 flow related to small loss in shear modulus 356 losses (Jr, Ja related) 202 phenomena 182, 190 SRF stress reduction factor (Q-parameter) 92, 175, 225, 293, 350, 447, 448, App. A, 615–625 stability poor 144, 145, 149 steam driven TBM 319 -flood injection 66 injection cycle 379 infection-front imaging 378, 379

steam-flooding 329 causing local heating 329 steel indentor 59 Qseis 181 steeply-dipping faults 257 joints (see vertical) planes 257 stick-slip 110 on saw-cut 540 onset of- 540 stiffness (see joint, fracture, normal, shear) stiffness (of joint or fracture) anisotropy Kn dyn  Ks dyn 518, 519 -compliance comparisons 418–425, 427, 428 data gaps 424, 425 dynamic and static (Kn) comparison 422–424 -fracture flow relation 425 matrices 374, 477 mechanical 169 normal Kn 6, 17, 198, 199, 202, 282, 418, 421–424 normal Kn greater with stiffer fluid 420 normal Kn much greater than Ks 550 inequality of Kn and Ks 421–424 real and imaginary parts 475 ratios of Kn/Ks 418, 421 ratios of Kn/Ks, model fractures, prototype stress 552 ratios of Kn/Ks interpreted for fault zone 427 ratios of Kn/Ks, in situ, saturated, weak rock 512 relations to ZN and ZT compliances 418 shear- Ks 6, 418, 428 shear- Ks for large scale features, faults 427, 428 specific- of joints 422 welded asperity Lucite-laminate assumption 418 Stirling Castle 118 stochastic simulation of oil saturation changes 398 Stone Canyon earthquakes, California 210, 211 Stoneley wave 316 Straight Creek Tunnel, Colorado, USA pilot bore 139–142 strain 4 amplitude 183 amplitude, axial 340 amplitude, importance of 183, 187–189, 193, 194 amplitude-frequency plot 183 axial- (see also axial) 339 larger- territory 183 microstrain (see microstrain) radial 339 tangential 304, 305, 307

Index uniaxial 5 volumetric 5 strength (see also rock, joint, fracture, compressive, uniaxial) 27 corrosion 304 deformation components 520, 522, 523 high 22 post-peak- loss 304 resisting critical crack density worries 413 strengthening-by-confinement 537–539 stress (pressure in some contexts) aligned, fluid-filled cracks 409 anisotropy 9, 115, 297–300 anisotropy, rotated 160 axial 339 azimuth, as fracture azimuth? 382–386, 388–396, 401–406, 407–482 changes due to tunnelling 615 closure tests on joints 198, 485, 487, 494, 495 confining-, excessively high 265 confining-, pressure 248, 250, 257, 263, 265 deformation loading of joints 422–424 deformation loading of jointed rock 484–486 deformation loops 97, 98 deformation gradients 184 dependent velocity 35 deviatoric- contours 131 deformation flow monitoring, URL fracture zone 505, 506 difference 297–299 difference intolerance by weak rock 297–299, 302–304 differential- 37, 268 differential- contra effective- 356 discontinuity, re splitting 518–520 -displacement behaviour (joints, fractures) 87 dissipation into rock mass 305 distribution 129 effective- 88–90, 263, 266, 267, 269, 295–297 effective- coefficient (Biot) 191 effective-, extremely low 350, 351 effective- gradients 267 effective- increase prior to water flood 401 effective- reduction as result of cold water injection 414 -gradients 60, 61 -gradients, radial 314, 315 high- 22 high- gradients 61 high- monitoring 60 high- region 59 horizontal- 128, 135 horizontal, below quarry floor 500 horizontal- enhancement, over magma-chamber 282 indentor- 59

707

-induced failure, tunnels 304 -induced fracturing 127 -induced joint closure 13 level 3, 16, 30 low horizontal- 367 locked-in- (grouting) 172 maximum horizontal- ␴H max 88, 382, 429, 472 maximum horizontal- ␴H max direction re water or not 384 minimum 296–300 minimum horizontal- ␴h min 88, 298–300, 406 mis-alignment with major- 506 monitoring site, Iceland 432–434 negative effective- 278 normal (joint or fracture) 79, 198, 199 principal- 115, 128, 132, 136, 137 principal- directions 137, 313, 315, 409 principal- directions, above/below shearing joint 519–521 principal- directions, assuming horiz./vert. 409. principal-, modelled 309, 310 radial 30, 120, 615 radial stress release 123 redistribution (ubiquitous) 30, 125 sensitivity assumption, collective 397 shear- (see shear stress) -slabbing, thin-walled 304 -strain curves 37, 195, 300 -strain loops, cusped to elliptical 188 strength ratios (␴n /JCS), CSFT tests 528–530 tangential stress 30, 93, 115, 120, 122, 123, 127, 129, 132, 136–138 tangential stress concentration 301, 379 tangential stress close to wall 310, 615 tangential stress compaction effects 156, 301, 379 tangential stress enhanced properties 316 tangential stress maxima and minima 306 tangential stress components of similar magnitude 311 thermally-induced- 135 3D stress state (ubiquitous state) 302 total 298 transfer (across joints) 172 vertical ␴H max direction bisected/intersected by 390 bisecting water-flood directionality 403 comparison with fractures 404 non-alignment with- 527 stressing post- (effect of grouting) 170 stress transformation equations 552 error for all dilating geotechnical materials 554 error for dense rockfill, sand, OC-clay 554

708

Index

stress transformation equations (contd ) error for non-planar rock joints, fractures 554 stress transformation equations, modified 553 Stripa Mine, Sweden 119, 133–136, 197–200, 422–424 structural, structurally controlled fall-out 319, 320 geology (see geology) orientation data integrated 384, 385 St.Venant principle, violation non-coaxial stress and strain due to dilation 552 subduction zone, oceanic 179, 226–228 sub -fjord 56 -sea link 320 -sea sediments 9, 56 -surface 3, 4, 7 -surface interfaces 438, 439 -surface resolution, improvement 378 -surface topography 4 sub-ocean, sub-oceanic floor attenuation 268, 269, 281, 282, 286 Layer 1, 2, 3 sub-ocean divisions 243, 244 Layer 2A, 2B, 2C 277, 283–285 Layer 4, 5, 6, sub-ocean divisions 244 spreading ridge velocity modelling 261–294, 317 velocity structures 262–290 subsidence bowl 453 match to continuum modelling 400 match to discontinuum modelling 400 match to shear wave splitting 453 subsidence/compaction S/C (ratio) high- with discontinuum modelling 400, 454 low- with continuum modelling 400 submersible 266, 273 subway station 4 Sudbury, Ontario 61 sugar-cube model representation 479, 480 Sugar-Loaf, Rio de Janeiro, estimated Q, QP, K 558 sulphide orebody 61, 62 superficial deposits 12 superimposed multiple ellipses at faults, re elliptical Vfast and Vslow 394 super-k poroelastic model 377 support pressure (tunnels, caverns) 92, 118 supposition influence of ‘average rock’ (earthquake source) 442 influence of ‘biased sample’ (fractured reservoir) 442 O/R contrary reflection/polarization rotations 414, 446, 450, 453, 474 surface ejection of water and sand 219 liquefaction 219 -magnified ground deformation 219 outcrop joint orientations 384–386

survey ships 243 suspension sand in state of- 324, 350, 351 Sweden 77, 119, 197, 203, 543, 555 Switzerland 38, 76, 124, 161, 169 symmetry deviation from higher- 360 directions defined, MON, ORT, TI 360 monoclinic MON 357, 358, 360 orthorhombic ORT 360 plane 440 plane of circular- 355, 356 transversely isotropic TI 360 vertical- axis 45, 372 synthetic sandstone crack model 480, 481 Taiwan 205 tangent and secant slopes/gradients 98, 101, 198 tangential stress, see stress Tangsham earthquake, China 110 Tanzania 72 target horizon 15 fracture zone 389, 391 tar sands steam flood in- 331 reduced viscosity close to wells 331 VP reduction with heating 331 TBM (see tunnel boring machine) tunnel EDZ, modelled 309, 310 JRC logging in – tunnel 543 Technical University of Trondheim 457 tectonic stresses (ubiquitous term) reginal- at San Andreas fault zone 432 tectonophysicists 210, 246 televiewer (see borehole) temperature anomalies, conductive fractures 541, 542 applied to HTM block test 514–517 corrected 256 effect on resistivity 297 effects on joint apertures 198 effects on VP of oil sands 330 effects on VP and Poisson’s ratio of oil sand in situ 379 elevated- testing needs 397 gradient in crust 242 low- 33 -VP of oil sands in presence of oil/gas/brine 330 -VP and VS , Boise sandstone 331 temporal variation of anisotropy 454, 455 attenuation 413, 414 attenuation, differential 454, 455 GPS displacements 413

Index polarization directions 413, 414, 452, 453 pressure in well 433 qS1 reversal with qS2 454, 455 seismic events (before/after earthquakes) 215, 216, 218 S-wave time-delays 429, 433 S-wave travel-times 433 tensile fracture traces 385 strength (see rock) tension, tensile fractures 81, 87, 299 fractures, models 524, 527, 548, 551, 552 hydraulic- 299 tensor elements 374 fourth and second rank- 417–419 geometric 174, 292 hydraulic 174, 292 Terlingham Tunnel 94. terrain mountainous- 33, 56 steep 56 TerraTek, Salt Lake City (now Schlumberger) 509, 513–515, 518, 552, 553 Tertiary rocks 142 granites 19 mudstones 19, 27, 304 oil shale Ko 299 rocks 142 sandstones 27, 144 sandstones Ko 299 sandstone-shale units 370–372 sedimentary rocks 25 siltstones 304 shale Ko 299 tuff Ko 299 Terzaghi, theory of effective stress 268, 320 test apparatus, equipment (diagrams) rock physics 59, 192, 197, 361 Texaco 374 Texas 203, 386 Texas, fractured carbonate gas field 536 Theories reviewed (brief, biased selection, see references) APE, Zatzepin, Crampin 416 Aki conjecture 228 Aki and Richards crack relaxation mechanism 387 Bandis hyperbolic joint closure model 428, 485, 486, 494, 528 Bandis shear strength scale effects 522 Barton-Bandis joint constitutive laws 435, 511 Barton-Bandis strength-displacement-dilation, scaled 487, 493, 507, 509, 511, 526, 531–535 Barton-Choubey peak shear strength, JCS, JRC, stiffness 485, 507–512, 514

709

Barton,Colleen, Zoback, Moos,Townend, conducting joints under shear stress 541–543 Barton, e and E apertures from JRC 364, 489 Barton, JRC-mobilized concept 435, 491, 548 Barton, M and Qseis similarity for jointed rock masses 202, 203, 210, 220, 221, 224–226, 269, 348, 350, 352, 365–367, 387, 405, 410, 411, 424, 436, 476, 499, 500 Barton, natural block-size scaling of Ks 422 Barton, non-linear strength envelopes, JRC, R, log- formulations 538 Barton 90°-flip ␴h min to ␴Hmax reversal, alternative theory 416 Barton, Qrock to Lugeon inversion 175, 176, 366, 555, 556 Barton, Q-system of rock mass classification 615–624 Barton, QH2O permeability estimation, depth dependent 556–558 Barton, roughness profile, tilt test for JRC 508–510, 514 Barton, shear stiffness scale effect 493 Barton, stress transformation equations with dilation 552, 553 Barton, thermal over-closure of joints 513–517 Barton, VP Qc M linkage 146 BISQ Biot and squirt-flow, Dvorkin 378 BOSK saturated, fractured medium model 457 Crampin EDA shear-wave anisotropy, basic theory 429 Crampin 90°-flip excess pore-pressure theory 416 extended-Kuster-Toksöz, velocity-crack aspect ratio modelling 276 extended-Walsh, velocity-crack aspect ratio modelling 276 Gassmann (Biot-) fluid substitution for porous media 317, 420 (error for fractured porous rock) 420, 457, 458 Johnston, spectral amplitudes, dispersive waves 198 Jones, dispersive squirt flow model 208 Hudson (seismic) effective cracked-media model 196, 461 Hudson (seismic) normal and shear compliance model 427, 503 Hudson and Crampin P-wave anisotropy, fracture density 503, 504 Hudson and Schoenberg compliance formulation for faults 504 Liu, fluid-type, fracture compliance, aspect ratio theory 426 Mohr-Coulomb shear strength criterion 461 Nur, velocity anisotropy due to loaded micro-cracks 36 Nur, critical porosity 324 Rüger reflection coefficients with TIH 390 Schoenberg, slip-interface, displacement discontinuity 200, 461, 501 Schoenberg-Sayers excess compliance theory 416, 417, 503, 504 Stratification-percolation model for apertures 498

710

Index

Theories reviewed (brief, biased selection, see references) (contd ) Tod crack density decay model 461 Walsh elliptical crack closure model 364, 529 Walsh friction dissipation in micro-cracks 182 Zoback hydrostatic not lithostatic pore pressure in crust (references) thermal gradient 242 over-closure (see over-closure of joints) relaxation 183 thermally-induced stress 135 thermal expansion cofficient of contained water 321 coefficient of contained fluids 351 coefficient, importance of included joint 516 effect on crustal velocities 248–250 thin bed in relation to wave length 372 Thomsen, weakly transversely isotropic 356 1000/QP and Q scale comparison 380 3D finite difference modelling 196 measurements (axis-by-axis) 354–357, 359–364 multi-azimuth walk-away 369 full-azimuth, full-offset P-wave survey 526 multi-component, multi-mode, multi-azimuth acquisition 382 P-wave velocity tomograms 375 repeated- multi-component survey 453 seismic survey 399 spherical sample measurements 358–360 3DEC 133, 365, 454 3D-4C (OBC data acquisition) 391, 396 4D (see four) three -component sources 7 -dimensional failure surfaces 306 -dimensional P-wave measurements 357–360 -dimensional seismic (ubiquitous term) 281, 282 thrust fault 244 Tibetan Plateau, China (thickest crust) 245 Tier I, II, III classification (see HPHT) 320, 321 tight (fractured) gas reservoir 384, 471–475 sandstones 357 sandstones, lenticular 471–475 TIH (also HTI) 374, 390, 394, 417, 477 tilt test for JRC estimation (see joint index tests) 514 time delay (between split shear waves) 313, 314, 409, 412, 398, 399, 429, 432–434, 436, 437 delay from micro-earthquakes (Iceland, Hawaii, San Andreas Fault) 436

delay increase in reservoir formation 471, 473 delay-depth intervals: anisotropic, isotropic, anisotropic 473 delay variations 445 distance inversion method 275 distortion 14 average equation 30, 119, 121, 323, 324 lapse comparison 399 lapse cross-well data 379 lapse survey 66, 451 lapse, time shifts, hysteresis, in-outside reservoir 484 separation, increase with path length 439 sag, gas or over-pressure 381 shift in compacting reservoir 398, 399, 402 TIV 374, 390, 394, 451 tomograms acoustic 59 alternative 64, 65 amplitude attenuation- 65 difference- 63 error- 63 fence- 64 for blast monitoring 61, 63, 64 non-co-planar- 64 Poisson’s ratio- 64 Pulse broadening- 65 S-wave- 64 2D and 3D comparison 259 time-lapse S-wave-, stable through fluid change 379 velocity difference- 61, 63 velocity difference- at fault zone 394 VP-, and Poisson’s ratio- 379 VP and QP-, depth slices 375 VP/VS- 64 tomographic, tomography (cross-hole seismic) 40, 49, 52–65, 92, 94, 131, 132, 139, 154, 156, 169, 257, 374–378 amplitude- SAT 83 back-projection- 231 blasting effects 63–64 attenuation- 18 cross-continental 230, 231 cross-hole- 52–58, 61, 74, 88 cross-hole- (deep boreholes) 57, 94, 115 cross-pillar- 60, 61 cross-well- 233 cross-well-, with permeability 377, 378 -inversion 56 post-blast 63, 64 pre-blast 63, 64 radar attenuation difference- 169 radar slowness- 169 shallow 3D- 374, 375 3D velocity- 259

Index 3D attenuation-, sub-ocean floor basalts, magma chamber 281, 282 time-lapse imaging 60 velocity- SVT 83, 169 Tonga Ridge 179, 227 Tonga Trench 179, 227 tool x- and y-axis 313 topography exact 15 Tor Formation 391 Tournemire experimental tunnel, Aveyron, France 39 Tower Colliery, Wollongong, Australia 200 Tracer injection 359 transducer pressure 174 temperature 174 transient crater 404 transition dry-saturated- 14 transmitter-receiver 62 distance 120 sonde 125 Trans Manche Link 94 transmissivity 161, 492 shear displacement effect on- 492 transversely isotopic (see TIH, TIV) travel distance 30 inversion 15 path length 198 travel time 15 difference, fast and slow S-waves 408 -distance-depth plots 14 increase perpendicular to failure zone 540 inversion, orientation 404 post-stack changes of- 398 pre-stack changes of- 398 two-way- 447 Trawsfynydd nuclear power station 9 Triassic 447 crystalline basement 220 mudstone 11 sandstone 11, 72 siltstone 11 triaxial (see stress) cell, conventional 362 confinement 192 compression 343 ship-board 263, 269 stress 267 tests, high pressure 312 triple-porosity, matrix, micro-, meso-fractures 465–474 Troll sand, North Sea 326 Troodos ophiolite, Cyprus 278

711

tropical terrains 4 Tsukuba Oishiyama earthquakes, Japan 210 tsunami waves 404 tube waves 44 tuff 26 breccia 26 jointed, numerical model 309 roughness profiles 509, 545 stress-conducting aperture, CSTF 529, 530 Tertiary 211 welded 94, 510 tunnel, tunnels 3, 25, 30, 52–56, 80, 93, 94, 224, 339, 413, 615–621 ahead of- 151–156 arch 4, 141 boring machine TBM 4, 17, 24, 131–133, 140, 148–157, 321 boring machine TBM back-up 312 by-pass- 56 collapse 4 data (VP – UCS, weak rock) 25 deep 24 deformation (see also displacement) 173 deformation back-analysis 192 difficulties, major 156 engineering 301 experimental- 117, 118, 124–133 exploratory- 107, 119 exploratory boreholes 46, 109, 111 face 139 face, ahead of the- 153 face collapse 153 face-log 94 failure modes, multiple 304 hydropower 120–122, 148–150 in-tunnel reflection (see seismic profiling, HSP, TSP) logging 615–626 measurements 71, 80, 120–133, 139–158 models 306, 307–311 mountain 56, 111, 153–157 pilot 53 pipeline 146 pressure 300, 536 rail 47, 48, 141–143, 408 reinforcement and support 93, 141–143, 145–149, 152, 156 road (see also sub-sea) 53, 54, 56, 146 sealing experiment 129–131 stability despite ‘critical’ crack density 413 sub-sea road- 56, 139, 144–147 support 140–142, 143, 145–149, 151, 152 wall 30 water supply 72–73, 146 wedge release 301

712

Index

tunnelling 4, 48, 52–56, 109, 161, 444 in squeezing rock 306 rock quality variations in- 394 turbidite 9 2D two-dimensional models 307–310, 369 Tydeman North Atlantic fracture zone profile 273 Type A, B, C rock mass load-deformation 485 Type I, II, III, IV reservoirs 373 type curves 164 Tytherington quarry, Bristol, SW England 500, 503 UCS (uniaxial compressive strength, ␴c ) 70, 92, 93, 144, 150, 164, 225, 263, 305–307, 320, 365, 366, 448, 449, 486, 507, 510, 556 effect of moisture 511 UDEC 365 attenuation modelling , fractured 478, 479 joint interactions in- 393 -MC modelling of tunnels, boreholes 308 -MC modelling of subsidence 400, 401, 454 -MC 306, 308 UDEC-BB modelling of compaction 400, 401, 443, 452 of compaction, displacing secondary set 550 of jointed rock masses 484–486 of HM(T) block test 518, 519 of tunnels, boreholes 133, 306, 309, 310, 467, 469 in rock mechanics 484, 508 UK 16, 57, 404 -France 17 Nirex Ltd. 57, 94, 224, 309, 310, 387, 528 ultimate strength 37 ultrafine cement 170 ultramafic rocks 12 ultrasonic frequencies (ubiquitous term in Ch 13) 269, 339, 340 frequency, relevance to sonic, seismic exploration 349 logging 120 P- and S-wave components 355, 361, 362 measurements 44 pulse echo technique 356, 357 pulse transmission 38 pulse transmission equipment 192 reflection technique 355, 356 stress sensitivity with-, less than with seismic 397 testing 372 velocity (ubiquitous, Ch13) unconsolidated 4 marine clastic sediments 430 sediments 7, 15, 205, 206, 243, 249 sands 375–377 undamaged rock 130

under-pressured 351 - and over-pressured 351 underground research laboratory URL, Manitoba, Canada 57, 87, 117, 127–131, 505 fracture zone study 505, 506 undisturbed medium 5 undrained shear strength 303 undrained behaviour assumed high Q data-anomalies for metasediments 234 low Q⫺1 data-anomalies for sub-ocean basalts 269 unexpected events (TBM tunnelling) 158 uniaxial (see also one-dimensional) compressive strength (see UCS) compression testing (see also VP -) 23, 25, 26–28, 195 cycling 339 loading of in situ blocks 165–167, 513, 514 loading of borehole test blocks 137, 315 strain testing, of core plugs 400 University of Berkeley 197–200, 464 University of Cergy-Pontoise 464 University of Edinburgh 450–452, 464 units compliance-stiffness discussion 423, 424, 487 friendly-, MPa/micron 500 recognisable- of stiffness 189, 202, 421 resemblance to- of GPa (see QP similarity) 191, 192, 200–202, 203, 210, 220, 221, 224–226, 232, 269, 348, 350, 352, 365–367, 377, 379, 387, 405, 410, 411, 499, 500 unloaded 30 unloading 30, 97, 106 unmated fractures/joints 86, 87 up-hole shooting 14 Upper Cretaceous chalk 447 Upper Permian 447 upper crust, New Madrid seismic zone 430 upper mantle 228, 241 anisotropy 276 anisotropy due to aligned olivine 276 crustal velocities (see sub-ocean) 283 high- temperatures 231 Ural Mountains 230 URL, Canada (see underground) USA, United States of America 42, 60, 90–92, 102, 123, 165–167, 203, 210–216, 230, 320, 325, 369–371, 382, 384, 385, 386–388, 444, 536, 545 Central 228 continental 228, 249 East Coast 254–256 Eastern 228 North Western 451

Index Western 210–216, 221–224, 227, 228, 244, 245, 251–253, 513–515 West Coast (Oregon, Washington, California) 231, 257–259 South-Western 210, 230 US Bureau of Mines 64 US Department of Energy 382 US Geological Survey 216 Uzbekistan 211 Vacuum Field, New Mexico 451 Vajon dam site 108 Valhall reservoir 391, 392, 396, 438, 453–455 Vamanashi earthquake 213 Vardø sub-sea road tunnel, Norway 145 Vatnajökull eruption, Iceland 434 Veas sewage treatment caverns, Slemmestad, Norway 148 velocity, velocities (see also numerous data sets at: VP) anisotropy 129, 299 anisotropy due to fractures 358–360 anisotropy due to foliation 38, 248 anisotropy due to joints and bedding 361–364 anisotropy expressions 356 anomalous, supposedly 271 anomaly 14, 256, 257 azimuthal anisotropy 40–44, 129 contoured, continuous profile 284 contrast 15 density space 22 depth models 369 depth and crustal type, to 50 km 251 depth-age models 369–372 depth models 266, 267, 271, 274, 275, 369 discrepancy, lab to in situ 263, 265, 268, 276, 281 dispersion (see frequency dependence) 45, 386 dispersion due to absorption 386 dispersion, negative 343, 344 distribution 4 false 146 fluctuation in interbedded strata 379 gradient 4, 6, 52, 91–95, 265, 268, 271, 272, 273, 285, 348, 370–371, 381 gradient, extreme 14, 283, 286 gradient, large, steep 15, 60, 222, 268, 269, 274, 277, 278, 348, 371 grid 16 high- where Qseis and Qrock also high 410, 411 high- regions 129 higher- with water than oil, in 4D 397 hysteresis 31 increase with age 261–263, 276, 282, 287–290 increase due to compaction 398, 402

713

independent- analyses in each azimuth 384 interval stacking- 234 inversion (sub-ocean floor) 281 lateral- variations 257, 258, 381 lithology 48 low- zones 71 low- layer 140, 141 model 93, 154, 157, 212, 219, 252, 253 model, multi-layer, sub-ocean 243, 252, 253, 258, 262, 266, 267, 269, 274, 289 model, multi-layer, altered zone 317 nine (or more) components of- 355, 361 oscillation in well logs 299–301, 316 permeability, of joints, of fractures 363, 364 porosity-permeability 332–334 rock condition (Japan) 48 reduction in subsiding reservoir 399 residual- tomogram 57 rosette 40 thickness anomaly 256 tomograms (see tomography) undisturbed 313, 319 versus radius (see EDZ) 120, 318 velocity-depth (see VP, by category) curves 91, 92 discussion 271, 272 gradients (see also velocity gradients) non-uniqueness 271 structures, sub-continental crust 241, 242, 245–251 structures, continental margins 254–261 structures, geothermal fields 394, 395 structures, mid-Atlantic ridge 261–273, 287–290 structures, East-Pacific rise 273–290 velocity ratios (see VP and VS categories following) (Vo/VP)2 with azimuth (granites) 41 (V/Vmax) with azimuth (limestones) 44 (V’/V) w.r.t. incident angle to fault 48 (VF/VL) field to lab 69, 73 (VF/VL)2 field to lab squared 69, 74 Vema, North Atlantic fracture zone profile 273 Venezuelan oil sand 330 Ventura Basin 260 vertically-aligned fractures, jointing 374, 407, 409, 477 causing anisotropy with low frequency 382 causing biased sampling with vertical wells 407 causing signal distortion with mid-frequency 382 leading to reflections with high frequency 382 missed by vertical wells 407, 408, 441 progression in complexity of matrices 416 vesicules, vesicular (see basalt) gas-filled 265 Vibrometric 56

714

Index

vibration longitudinal 5 torsional 189 vibrator (see source) Vicker’s microhardness 78 Viking Graben, North Sea 352 viscosity visco-elastic 183, 475 viscous damping 190 dissipation 190 void (see joint void) formation due to blasting 61 -space due to blasting 118 volcanic porous- rocks 27, 142, 251–253 soil 25 volume comparison compaction-subsidence- with core plugs 400 volumetric joint count 167 velocity (see VP and VS , and all categories below) azimuthally-dependent- 301 depth trends (see VP-depth, etc) 297 elliptical Vfast and Vslow replaced at faults 394 fast- not equal matrix at faults 394 P-wave-, see VP specification below radially-dependent- 302 reduction, source of 306 zone of changed- 302 VP (see also P-wave) alphabetic listing of categories (see itemized data below alphabetic order) VP – age, sub-ocean, spreading ridge data 262, 264, 265, 287–289 VP air-dry – VP saturated (dolerite) 23 VP anisotropy (parallel) and VP (perpendicular) slate 38 VP anisotropy (maximum) parallel to major joint set 40 VP – angle of incidence (anisotropic rocks, dry or saturated) 38 VP – artificially jointed: frequency, roughness, clay-filling, dilation/shearing 85, 86 VP – azimuthal 360° (in situ sparsely jointed granite) 40 VP – azimuthal 360° (in situ jointed granite limestones) 40, 42, 43 VP – azimuthal 360° (in situ jointed) 44 VP – azimuthal 360° 3D VSP (0 to 520 m) 44 VP – axial load (pre- and post-failure, coal) 104 VP – axial stress (perpendicular, parallel: foliated gneiss) 39 VP – axial stress (indentor, sandstone, tomography) 59 VP – axial stress (basalt 126), (quartz-monzonite 136) VP – axial stress (lab- and field-scale comparison, granite) 166 VP - axial stress-strain, loaded to failure (tuff-sandstone, granite) 195, 196

VP – biaxial and axial stress (in situ jointed block of granite) 166 VP – biaxial and axial stress (in situ jointed block of sandstone) 167 VP – confining pressure (diverse rocks) 31 VP – confining pressure: sandstones, dry and saturated 32, bedded-coal, dry, saturated, 3-axis testing 201 VP – confining pressure and pore pressure (sandstones) 193 VP – cross-hole (not tomography) 50–52, 66, 67, 106, 119, 120, 134–136 VP – cross-hole (time of heating and cooling) 135, 136 VP – cross-hole tomography 54, 55, 58, 62–64, 132, 234 VP – cross-pillar tomography in mining 60, 61, 65 VP – density 19 VP – density (dolerite) 22 VP – density (extreme confining pressure) 23 VP – density (Tertiary foundations) 21 VP – density (sulphide ores) 23 VP – density (basalt, gabbro, serpentinite peridotite, 20 my) 265 VP – depth (see multiple categories below) VP – Ee and Ed (pseudo-static: limestones and diverse rock types 99–103 VP2 –Ee and Ed 100 VP – Emass (pseudo-static) and other parameters, Tertiary bridge foundations 21 VP – Edyn (diverse sources) 107 VP – extensional strain amplitude: sandstone 187 VP – failure stress (plate loading to failure) 104 VP – fractures per meter in drill holes 73 VP – joints per meter (diverse rocks, countries, weathering) 72 VP – joint spacing, penetration strength, chalk 79 VP – joint spacing, depth, shallow tunnel in chalk 79 VP – load-unload (slate) 38 VP – Lugeon value (permeability) 159, 160 VP – orthogonal directions (jointed blocks of granite: dry or wet) 40 VP – penetration rate (TBM) 149 VP – permeability (see listings below) 159–177, 333–337 VP – permeability – FZI 333–335 VP – porosity (see listings below) 19, 21, 24 VP – porosity (clean sandstones, and suspension) 324 VP – porosity (crystalline, volcanic rocks) 28 VP – porosity – clay-content (sandstones) 25, 331–333 VP – porosity (of rock mass, Tertiary foundations) (nr %) 19, 21, 22, 24 VP – Q-value, core logging, cavern site 76 VP – QP – depth plots (1800 to 2800 feet) 234 VP – QP – depth trends (1 to 20 km) 230 VP – QP – depth trends (1 to 1200 km) 245 VP – rock quality Q-value (see listings below) 13 VP – rock quality – deformability 24

Index VP – RQD – joints per meter, or core lengths (hard rocks, near-surface) 6, 13, 71, 72, 75 VP – rate of penetration, hardness, RQD, density 78 VP – reduction with freeze-thaw cycles 185 VP – saturation (foundation) 21 VP – Schmidt N-hammer rebound (crystalline, volcanic rocks) 28 VP – seabed tomography 56 VP – support type 141, 147, 149 VP – temperature (ambient to freezing, sandstone) 33 VP – three dimensional incident angles (truncated cube, shale) 39 VP – time of drying out (granite) 31 VP – time of heating and cooling 185 VP – uniaxial compressive strength (crystalline, volcanic rocks) 28 VP – uniaxial compressive strength (dolerite) 23 VP – uniaxial compressive strength (diverse) 25 VP – uniaxial compressive strength (Tertiary mudstones, sandstones) 27 VP – uniaxial compressive strength (shale) 26 VP – water level fluctuations (reservoir dam site) 89, 90 VP – water saturation – porosity (crystalline, volcanic rocks) 29 (i) VP – depth, extreme depth VP – VS – depth (0–6300 km) crust to inner core 241 VP – VS – confining pressure (extreme, 5–10 kb) 32 (ii)VP – depth (continental crust, deep) V P – depth (0 to 8 km, six geothermal fields, Kenya Rift) 395 V P – depth (0 to 9 km, KTB super-deep well, sonic and VSP) 249, 250, 252 VP – depth (5, 10, 15, 20, 25 km histograms) 247 VP – depth (0–25 km, 0–50 km) 247, 248, 250, 251 VP – depth (0–35 km) and lateral variation (0–200 km) 229 VP – depth (0 to 50 km) five types of continental crust, with lab-sample comparison 250 VP – depth (0 to 50 km) Proterozoic, Phanerozoic, Platform, Oregen crust 251 VP – depth (5, 10, 15, 20, 25 km) orogens, shields and platforms, continental arcs, rifts, extended crust, average crust 248 VP – depth (0 to 50 km) continental crust, USA N.W.Montana to Washington State 251 VP-VS – depth, on land (0 to 9 km, KTB super-deep well, sonic and VSP) 249, 250, 252 VP – VS – QP–QS - depth (0 to 35 km, and laterally 0 to 190 km) Japan 229 VP (variation) for 29 crustal rock types, 309°C, 20 km equivalent depth 249 VP (anisotropy) matrix, high pressure, high temperature 248

715

(iii) VP – depth (continental crust, shallow) VP – depth – fractures/m (900 m XTLR well, crystalline rocks near SAFZ) 90, 91 VP – depth (0 to 1.6 km, nuclear waste site tomography) 58 VP – depth (0 to 5.5 km, Lower Triassic sandstone in deepest 1.5 km) 233 VP – VS – depth, on land (0 to 7 km, porous, jointed volcanics, tuff, NTS) 251–253 VP – VS – depth – fractures/m – VP/VS ratio (1100 m MONT-1 well, jointed granodiorites) 90, 92 VP – VS – transmissivity, and VP/VS (400 to 1800 m deep boreholes in marl) 161 (iv) VP – depth (continental margin) VP – depth (and density) (0 to 45 km, also laterally 240 km) US East Coast 255, 256 VP – depth (4.4 to 6.0 km) Hawaiian ridge 258 VP – depth (0 to 6 km), NE Atlantic, sub-basalt profile 403 VP – depth (0 to 30 km) San Francisco Bay area crust 259 (v) VP – depth (sub-ocean, spreading ridge) VP – depth East Pacific rise 273–287 VP – depth WAP 10, 52 km, East Pacific rise 284–286 VP – depth 14°S on East Pacific rise 286 VP – depth Mid-Atlantic ridge 243–245, 261–273 VP – depth Ontong-Java 206 VP – depth 0 to 1 km, East Pacific rise, linear gradient assumption 275 VP – depth sonic log, Hole 504B, Costa Rica ridge 280 VP – depth – age young oceanic crust 276 VP – depth – permeability – porosity, Hole 504B, Costa Rica E.Pacific ridge 278 VP – depth – porosity – permeability (0 to 500 m of sediments) marine logging and modelling, Site 977, ODP Leg 161, Shipboard Scientific Party 336 VP – VS –depth, VSP, Hole 504B, Costa Rica ridge 280 VP – VS –depth, VSP, Hole 504B, Costa Rica ridge, and lab comparison 281 VP – VS –depth 264, 266, 267, 275, 277, 280, 281, 286 VP – VS – Poisson’s ratio, young crust 270 (vi) VP – depth (petroleum reservoirs, shallow, deeper) VP – depth, also QP /VP – depth, 210–400 m, sands and sand channels 375–377 VP – depth (0 to 5500 feet) (also Q) Melville Island, Canadian Arctic 233 VP – depth (0 to 6 km), NE Atlantic, sub-basalt profile 403 VP – depth (0 to 2.3 km), limestones, clays, over-pressured, two wells 450, 452 VP – depth (1800 to 2800 feet) (also Q) mixed lithology, BP Devine Test Site 234 VP – depth (4000 to 4350 feet) (also Q) fractured shales, Buena Vista Hills 237

716

Index

VP – depth (0 to 5 km) high pressure well, over-pressure effects 298 VP – depth (0 to 5 km) and lateral, at salt dome, North Sea 381 VP – depth (850 to 1000 m) also core porosity-core permeability 334 VP, VS – depth (0 to 1 km), CBTF well, also density, permeability, birefringence 445 (vii) VP – depth (near-surface, land-based) VP – depth (0–50 m) and lateral variation, various sediments and rock 10 VP – depth slice (mean 32, 96, 106 m and laterally, alluvium, lithified sands-sandstone) 374, 375 VP – depth (1–15 m, shallow soils) 24 VP – depth (5–15 m, 6 m,120 m, 200 m, mostly rock) 79, 52, 52, 20 VP – depth (0–60 m approx., jointed gneiss, tomography) 55, 56, 88, 89 VP – depth (mine-drift walls) 70, 73 VP – depth (10–500 m approx., into tunnel walls: EDZ related) 119–121, 123–125, 127–129, 133 VP – pressure/depth, core and sonic log comparison, Whitchester sst. 348 VP – VS (0 to 35 m) (also dynamic elastic parameters) 111 VP – VS (5 to 40 m) hard igneous, metamorphic rocks 6, 105 VP – VS – depth (0 to 60 m), Conoco borehole, fractured limestones, impermeable shales 448 VP – VS large number of rock types, near-surface refraction seismic assumed 12 VP – VS from fine resolution of sonic logs, interbedded shale, sandstone, limestone 379 VP/VS – depth (0 to 70 m) clay over mudstones 8 VP/VS ratio: near-surface 6, 9, 161, 252 VP/VS ratios, six geothermal fields, 0 to 8 km, Kenya Rift 395 VF/VL ratio of field (seismic) /laboratory (ultrasonic) 105, 106 (viii) VP,VS rock physics data sets specified sandstones VP – porosity, Troll sand 326 VP (and QP) – frequency – effective pressure, dry or brine saturated, Berea sst. 344 VP (and QP) – frequency – effective pressure, dry or brine saturated, Boise sst. 344 VP (and QP) – frequency – effective pressure, dry or brine saturated, Massilon sst. 344 VP – VS – temperature, Boise sst. 331 VS – permeability, fracture closure, cubic specimens, Crossland Hill, Fontainebleau, Springwell sst. 364 VP – VS – axial strain (Berea sandstone) 37 3D qP – normalized permeability, stereograms, North Sea sst. 390 VP static/VP dyn and Young’s modulus versus axial strain magnitude, Berea sst. 340

VP static/VP dyn (and Young’s modulus) – axial strain magnitude, Boise sst. 340 VP static/VP dyn (and Young’s modulus) – axial strain magnitude, Pecos sst. 340 VP static/VP dyn (and Young’s modulus) – axial strain magnitude, Ohio sst. 340 VP and VS – 3D confining pressure, before/after fracturing, cubic specimens, Crossland Hill sst. 362 Vph and Vpv – confining and pore pressure (Berea, Michigan sandstones) 192 sandstone, tight gas stress-strain data 339 velocity-density data 327 VP –VS data 328 3D VP –confining pressure, spherical samples, layering/jointing, dry, saturated 358 3D permeability –confining pressure, spherical samples, layering/jointing 359 unspecified sandstones VP – porosity, high porosity sandstones 325 VP – density, high porosity sandstones 327 VP – density, sandstones 326, 327 VP – porosity clay content % 331–333 VP – porosity-velocity, clean sst. and sand suspension 324 VP – porosity, sandstone and sand suspension 324 VP – saturation % gas/brine, sandstones 341 VP – saturation, patchiness data, multiple clean/shaly sand composites 33, 337 VP – frequency – 1000/Q fused glass beads 345 VP – VS data, sandstones 328, 329, 372 VP – VP/VS – degree of saturation, sandstone 189 VP and VS versus differential pressure 298 VP and VS versus excess pore pressure 298 VP (and QP) – effective pressure, microcracked sandstone 347 VP/VS)2 – QP/QS – (and pore pressure) to distinguish sand and sandstone 351 VP/VS – differential pressure, also to extremely low pressure, sands 351 oil sands/tar sands VP – temperature – oil/gas %, Kern River oil sand 330 VP – temperature – brine/oil %, Venezuelan oil sand 330 VP – temperature, Canadian tar sand 331 diverse rock types VP – porosity, limestones, dolomites, chalks 325 VP – density, limestones, dolomites, anhydrite, rock salt, shale 326 VP – density, limestones, dolomites, chalks 327 VP – VS limestones, dolomites, chalks 328 VP – VS shales, mudrock 372 VP – VS – kerogen %, Kimmeridge shale, North Sea, 0° and 90° 353

Index VP – pressure, shale, 0°, 45 ° and 90° VP – VS (and Vsh and Vsv) – pressure, shale, 0°, 45 ° and 90° 354 VP – (and Vsh and Vsv) – 0° to 90° from bedding, and stereographic, shale, 354 qP component P-wave velocities through truncated cube, shale 39 VP – VS – axial stress (quartz-monzonite 136) VP – VS – confining pressure, Barré granite 36 VP – VS – density (basalt, gabbro, serpentinite peridotite 20 my) 265 VP – VS – confining pressure, marble columns 81 VP – VS (dry, crystalline, volcanic rocks) 29 VP – VS – group velocity versus stress, mated, unmated tension fractures 87 VP and VP/VS for dry, partly saturated, saturated: extension tests 189 VP/VS diverse data VP/VS energy ratio (Es/Ep) 131 VP/VS ratio: theory 6, 7, 109 VP – rock quality reversed- 17 VP – Q – depth – porosity (strength) relation 271, 273, 274, 285, 285 VP – Q – M (deformation modulus) model 83, 92, 94, 108, 132, 134 VP – Q – M – L (Lugeon) model 164, 225, 291 VP – Q – M – permeability, near-surface model 225, 291 VP – Q – M – permeability, near-surface model, curve jumping 291 VP – Q or Qc model 6, 7, 13, 18, 47, 74, 115, 271 VP – Qc – gradient, sub-ocean basalts 287 (ix) rock physics/poro-elatic modelling VP – qP – VS – frequency, matrix and 10 cm fractures 466 VSP 14, 49, 207–209, 249, 369, 377, 380, 387 azimuthal- 384, 385 diametrically-opposed- 445 down-hole receivers 382, 383 effect of subsidence on- 400 far-offset 439 -for horizontal well sections 382 for QP and QS analysis 386 for analysing velocity differences re sonic 386 limited offset- 383 multi-azimuth- 382, 383 multi-azimuth- for fracture anisotropy detection 382–386 multi-azimuth reversed- 385, 447 near-offset- 377, 384–386, 445, 446 nine-component- 385, 471–475 opposite-azimuth- for fracture dip 445 -QP less than sonic-based QP 386

717

shear wave splitting with- focussed on domains 410, 439 surface shot points, single azimuth 382, 383 vertical-cable seabed- 446 walk-around- 383, 439, 440 walk-away- 382, 383, 439 walk-away- for S-wave acquisition 439 wide-aperture layout- 383 zero offset- 383 vug, vugs 196, 197 exact structure 196 vuggy porosities 196 Wales 9, 11, 160 walkaway VSP (see VSP) WAP 10 (52 km profile), East Pacific Rise, mid-ocean ridge 283–285 water 4, 12, 254. bearing joint set 42 bearing sandstone reservoirs 343 cold- injection, HDR 414 conducting joints, spacing with depth 488, 490 conducting joint/fracture/fault directions 384, 541–543 conducting fracture directions under shear stress 402, 541, 542 content 27, 169 depth 296 expulsion 135 fault-eroding water pressure 154, 156 filled fissures 22 filled structure 281 filled holes 61, 73 flooding (see water flooding) fresh- effect 297 ground- 11 ground-water pressure 159 injection tests 162 injection into reservoir, effect on joints 487 inrush 151 pressure anomaly, in well 433 pumping test (extraction) 162, 173, 174 saturated joint samples 509, 510 saturation (see saturated) 7, 9, 27, 29, 200, 201, 352, 353 saturation weakening of chalk 399–402 sensitive reservoir rocks 402 table 8, 15, 124 velocity of- 159 weakening modelling, chalk 399, 400, 402 water-flood, -flooding 329 causing local cooling and aperture increase 329, 402 causing contraction of matrix 402 caused reduced velocity, amplitude, frequency 353 conjugate shearing 390, 522 directionality 402

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Index

water-flood, -flooding (contd) directionality of flow assumed 402 directionality of flow measured 403 faster break-through due to 402 fracture and fault opening due to- 402 HTM effects during- 401 model of intermittent- 353 pressure-drive effect 264 tracking- injection fronts 397 water injection 402 for compaction control, Ekofisk 399–402, 442 wave, waves cut platform (photo) 488 paths, horizontal 371 scattering 5, 372 transient 17 wave fronts 16 wave length comparison, reflection, teleseismic 410 dominant- long compared to 372 in relation to thin bed 372 wave speed expressions 5, 477 weak rock at reservoir depth 534 confined (␴1- ␴3) increase 534, 539 crossing critical state line 534, 539 improved JCS at reservoir depth 534 intolerance of stress difference 297–299, 302–304 limits of strength increase due to pore collapse 534, 539 weakness zones 145 weathered 4 constituent minerals 24 deeply 4, 30 extremely- 103, 114 in place 4 seams 14 unweathered 13, 71, 74 zone 19, 20 weathering 3, 26, 27, 324 caused by microcracks 225 degree of-, joint/rock rebound ratio r5 /R5 510 gradational 56 seafloor (sub-ocean) 281 zone of- 28 weight weighted-average Qseis response w.r.t . finely interbedded rocks 380 wellbore (see borehole, well) alteration (see alteration) ‘ballooning’ (see HPHT) 320, 321 damage (see EDZ) 301, 317 stability 339 Wellenberg, Switzerland 161 wellhead 43, 44

well (see also borehole) better placement, deviation, with shear-wave technology 407 data, typical VP , QP , n% 345 deviation 305 deviation for improved sampling of structure 407, 408 diameter, largest 304 flow-rate versus P-wave anisotropy % 405 high flow-rate- 405 high pressure- 298 horizontal section of-, collapse analogue 320 location in reservoir 297 -logging developments, dipole 302, 313, 314 -logging interpretation 302 -logging while drilling, LWD 301, 302, 312–320 low flow-rate- 405 rock/fluid pressure aspects 295–299 sections 369 size 309 Wendover, Utah 238 Widemouth Bay, Bude, Devon, England 488 Wilmington Field, Long Beach, Caliornia 400, 454 WIPP, New Mexico 123 wireline (sonic) logging 302, 311, 313, 499, 500 monopole and dipole logs 318, 319 monopole and dipole log comparison with LWD 318 temperature limits 320 velocities compared with LWD velocities 318 velocities, compressional and shear 318, 319 Wood’s metal 197 world first TBM tunnel 319 map 246, 251 map model tiles 550x550 km 249 record speeds (TBM) 17 supply of oil, gas, water (e⬍E detail) 488 -wide compilation 244–251 Worthington, Lubbe, Hudson range of compliances 503, 504, 506 Wulff ’s stereogram 39 Wyoming, USA 165 Xiaolangdi multipurpose dam, China 74 X-hole (see cross-hole) 208 X-ray computerized tomography 196 diffraction technique 359, 360 XTLR well, Mojave Desert 90, 91 Yangtze river, China 172 yield pillar in coal 60, 61 Yo-yo mid point 67 Young’s modulus (see also deformation, dynamic) 273

Index axial dynamic modulus (␺) 5 E-modulus (from elastic pseudo-static stress/strain of intact specimen) 191, 198 static (see deformation modulus) 339, 340 Edyn (from VP and VS) 13, 57, 75 Yuan-Lin site, Taiwan 205 Yucca Mountain borehole data 543 Yugoslavia 49–51, 97, 98, 101, 102, 109, 171 Zavoj dam site 171 Zechstein (salt dome) North Sea 381

719

ZEDEX (zone of excavation disturbance experiment) 131, 132 zero age crust, velocities 267, 276, 285 -offset vertical seismic profiling 383, 434 ZN and ZT (see compliance) Zoback and colleagues stress measurements 429 Zoback and colleagues conducting-fracture measurements 541, 542

721

Plate 1 Deep (1000–1200 m) cross-hole tomography at the UK Nirex Ltd Sellafield site. (Schlumberger GeoQuest, Nirex Report S/94/007, by kind permission). (Figure 4.10).

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Plate 2 An igneous intrusion (dike) tends to have elevated permeability due to the number of joint sets (typically four: Jn  15). High-modulus mineralized veins may be fractured by subsequent tectonic deformation, helping to maintain some permeability despite the ‘sealing’ process. (Figure 11.75).

(a)

(b)

Plate 3 Fracture development over time in a FRACOD model of a circular opening in a jointed zone. Note the ‘rotation’ of the diametral-pair of red regions, which represent low factors of safety against shear failure. Further fracturing dissipates and displaces the low F. of S. zones, suggesting that more fracturing could occur across the ‘E-W’ diameter. Changed seismic response over time is easy to imagine, also a mud-filtrate invasion speed that could be highly non-uniform, due to developing permeability in the partly connected discontinuum. Nick Barton & Associates 2005 contract report. See Figure 12.15 for input data. (Figure 12.16).

723

Plate 4 Comparison of a) detailed seismic-based (4D time-shift) compaction interpretation (with adjustment for the velocity reduction caused by a subsiding overburden), with b) geomechanics-based one-dimensional strain compaction model, that included porosity reduction due to weakening effect of water saturation. Smith et al., 2002. Note gas cloud effect in centre of seismic model. (Reproduced by kind permission of Norwegian Petroleum Society, NPF). (Figure 14.29).

(a)

(b)

Plate 5 Two examples of attenuation modelling with a set of vertical aligned fractures, using Chapman’s dynamic poroelastic matrix-andfracture-set model. See Chapter 15 for a description of this model. Maultzsch et al., 2005. (Reproduced by kind permission, Maultzsch pers. comm. 2005). (Figure 14.37).

724

(a)

(b)

Plate 6 Bluebell-Altamont Field anisotropy interpretation, from Liu et al., 2003a, with kind provision of files from Liu, pers.com. 2005. a) Except at low frequency (0–10 Hz), a reasonably constant polarization at 40° to 45° is shown. b) Time delays show three intervals: gradient, flat, gradient, implying anisotropy, isotropy, anisotropy. (Figure 15.56).

(a)

(b)

Plate 7 Bluebell-Altamont Field anisotropy interpretation, from Liu et al., 2003a, with kind provision of files from Liu, pers.com. 2005. a) Steep time delay gradient in reservoir interval, with frequency dependence. b) Interpretation of anisotropy percentage as function of frequency. (Figure 15.57).

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(a)

(b)

Plate 8 a) The relative error between the predicted and measured time-delay/depth, evaluated over four frequency values for a range of possible fracture densities and sizes, for comparing with multi-component shear wave VSP data acquired in the Bluebell-Altamont field in Utah. b) The rms error zoomed around the minimum, where the error is less than 5%. (Chapman model application, by Maultzsch et al., 2003 and Liu et al., 2003b). (Figure 15.58).

(c)

Plate 9 A wave-cut platform in a jointed dolomite bed. These beds occur at intervals in the Kimmeridge shale, outcropping in Kimmeridge Bay, Dorset, England. The joints show a) implied JCS  c due to weathering and preferential wave erosion, and b) implied (local) JCS  c, due to subsequent mineralization of dominant conducting joints. c) A fine example of joint cementation which may prevent the use of normal joint characterization techniques. Widemouth Bay, near Bude, Devon, England. (Figure 16.5).

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Plate 10 The photograph is a fine example of contrasting JRC values from an interlocked joint and a minor fault in welded tuff, with respective JRCo values of about 15 and 1. (Figure 16.28).

Plate 11 Hydraulic aperture (e), versus normal stress (n), versus average rock temperature (T° C) in the permeability test volume of the TerraTek heated block test, CSM mine, Colorado. Note aperture (e) reductions from 30.0 m to 18.3 m, to 12.9 m and finally to 9.1 m as a result of temperature rise, despite constant applied stress. This gives an apparent reduction in the normal stiffness in this test, but in the warmth of a deep petroleum reservoir, would have allowed joints to remain stiffer since their formation. Barton, 1982. (Figure 16.33).

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Plate 12 Interlocked and sheared joints in ‘wavy’ columnar basalt, demonstrating the role of asperities and dilation on aperture distribution. Columbia River Basalts, Washington State, USA. (Figure 16.37).

Plate 13 Vertical view through the inter-bedded bituminous shales and dolomite bed, in Kimmeridge Bay, showing a) complex, b) ordered sub-vertical joint patterns. Dorset coast, S. England. (Figure 16.39).

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Plate 14 Normal and shear stresses for fractures identified as hydraulically conducting (closed symbols) or non-conducting (open symbols). Cajon Pass (triangles), Long Valley (circles), Nevada Test Site (squares). Townend and Zoback, 2000, with data also from Colleen Barton et al., 1995. (Zoback, 2006 pers. comm., by kind permission). (Figure 16.63).

Plate 15 Normal and shear stresses for fractures identified as hydraulically conducting or non-conducting, using borehole imaging. Cajon Pass (red diamonds and dots), Nevada Test Site (green circles and dots), Long Valley (yellow triangles and dots), KTB (Germany – blue squares and dots). Inset shows  /n for combined data set. Zoback and Townend, 2001, with data from Ito and Zoback, 2000, and from Colleen Barton et al., 1995. (Zoback, 2006 pers. comm., by kind permission). (Figure 16.64).

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Plate 16 a) An example of a massive rock mass with rock quality Q
1000 and a deformation modulus in excess of 100 GPa. A very low attenuation is implied. b) The fault-collapse blocking the tunnel on the right would give almost the lowest rock quality Q
0.001, and a modulus of deformation lower than 1 GPa. It is perhaps ‘off-the-scale’ regarding the conventional definition of Qseis, and would need to be under stress to allow spectral analysis of measurable amplitudes. Its Q-value would then be higher too. (Figure 16.79).

Plate 17 The reality of near-surface construction of tunnels and caverns in rock. Note the three joint sets causing deep over-break. (Figure B1).