S. K. Upadhyay

Seismic Reflection Processing

Springer-Verlag Berlin Heidelberg GmbH

S. K. Upadhyay

Seismic Reflection Processing With Special Reference to Anisotropy

With 300 Figures and 15 Tables

~ Springer

S. K. Upadhyay Indian Institute of Technology Roorkee 94 Vigyan Kunj Roorkee - 247 667 Distt. - Haridwar (Uttranchal Pradesh) India e-mail: skues@iitr.ernet.in

and

S. K. Upadhyay Department of Earth Sciences Indian Institute of Technology Roorkee Roorkee - 247 667 Distt. - Haridwar (Uttranchal Pradesh) India e-mail: s_upd@rediffmail.com

ISBN 978-3-642-07414-1 ISBN 978-3-662-09843-1 (eBook) DOI 10.1007/978-3-662-09843-1

Library of Congress Control Number: 2004103474 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>.

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© Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 1 st edition 2004

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protec­tive laws and regulations and therefore free for general use.

Production: PRO EDIT GmbH, Heidelberg, Germany Cover-Design: Erich Kirchner, Heidelberg, Germany Typesetting: K + V Fotosatz, Beerfelden, Germany

Printed on acid-free paper 32/314IDi - 5 4 3 2 1 0

This book is dedicated to the founders and pioneering contributors, C. G. Knott, K. Zoeppritz, M. Muskat, M. W. Meres, C. H. Dix, ]. G. Hagedoorn, O. Koefoed .... , of Reflection Seismology, which is truly today's Energy Resource Seismology.

Preface

Routine reflection processing is based on the assumption of isotropy of the medi­um. It is now well realized that developments in isotropic reflection processing have reached a saturation stage, and something special needs to be done to im­prove accuracy. Anisotropic processing of reflections provides the answer to this. 'SEISMIC REFLECTION PROCESSING: With Special Reference to Anisotropy', aims at bridging the existing gap.

This book puts together the physical concepts, mathematical details and meth­odology for achieving the best results for reservoir modeling either under condi­tion of isotropy or anisotropy. Further, the most common form of anisotropy -the transverse isotropy, is dealt with in detail. Besides, practical aspects in Reser­voir Engineering - such as interval isotropic or anisotropic properties of layered media; identifying lithology, pore-fluid types and saturation; and determining crack/fracture-orientations and density, etc. form the core of discussions. It has the following distinguishing features: - Emphasis on accurate reflection processing - Integration and elucidation of concepts in isotropy with anisotropy - Promoting easy understanding - Bringing together the concept and theme based lead case studies on the ben-

efits of exploring fracture-induced anisotropy - Inspiring futuristic vision.

This book is written with the aim to serve primarily the graduate/postgraduate students and research workers in geophysics desirous of pursuing a career in seis­mic investigations for Hydrocarbon Energy Resources. Members of the various Societies of Exploration/Petroleum Geophysics would benefit from this book. It should be particularly useful to professional geophysicists and engineers involved in interpreting seismic reflection data from geologically complex areas exhibiting fracturing conditions in the reservoir, in search of hydrocarbons, geothermal or ground water resources.

This book is concept oriented. It discusses the latest research breakthroughs in isotropic and anisotropic processing, focuses on requisite precision over isotropic reflection processing, and projects investigation of fracture-induced anisotropy as a new tool for modeling different types of reservoirs.

This book has been composed keeping in view the current research develop­ments and appreciation by all categories of readers. This book should prove to be a very timely publication to teach a regular course in 'Exploration Seismology' to

VIII Preface

graduate/postgraduate students of geophysics at the present level of developments both in isotropic and anisotropic reflection processing and interpretation.

The substance of organization of this book is presented in Chapter 1 (Fig. 1.8). Both basic and practical aspects, for conditions of isotropy or anisotropy, are dis­cussed with suitable emphasis.

This book is the outcome of my involvement in teaching courses and research guidance in the area of seismic prospecting for many years, at the University of Roorkee, Roorkee (now Indian Institute of Technology Roorkee, Roorkee). The realization of the phenomenal growth during the last decade in the field of aniso­tropic reflection processing has inspired me to write a book which is complete to the current level of developments. Although rapid advancements are taking place in this field, it has been my continued effort to incorporate the most recent devel­opments, as far as possible.

My sincere thanks are due to the authors of research papers or books, publish­ers, and organizations for granting permissions to include their published materi­als in this book. Wherever permission could not be received due to changed ad­dress or some other reason, complete reference of the published material used, is given and the same is gratefully acknowledged here.

I have drawn from a number of sources from past to the most recent, and made deliberate efforts to present the ideas in their real forms. However, in case concise presentation has led to distortions of original concepts, suggestions from authors or readers in this regard would be gratefully acknowledged.

My special thanks are due to Dr. Wolfgang Engel, Executive Editor Geosciences, Springer Verlag, Heidelberg, Germany and his colleagues, Helen Rachner, Janet Sterritt-Brunner, Judith-Diemer, Constanze Sonntag and Susanna Pohl (formerly at Springer Verlag) and all others for their continued involvement in the copy edit­ing process, timely publication and excellent quality production of this book.

Sarvesh Kumar Sharma, a member of the technical staff in the Department of Earth Sciences, Indian Institute of Technology Roorkee, Roorkee has provided constant continued support in typing in an excellent manner the difficult text material, including a variety of equations and symbols. Perhaps, his unique en­during patience has made my dream of completing this project come true. I have no words to express my appreciation for his cooperation and performance as a colleague.

N. K. Varshney of the National Institute of Hydrology, Roorkee provided much needed cooperation and all manner of support for the punctual production of ex­cellent tracings. I would like to express my greatest appreciation to him. Santosh Kumar Mishra and Y. D. Gupta (retired) of the Central Building Research Institute Roorkee also traced some figures. I also express my appreciation to them.

I received special support in various forms from Professor R. P. Gupta, Profes­sor, Department of Earth Sciences, Indian Institute of Technology Roorkee, Roor­kee from the initial stage to the completion stage of this project. It is indeed a pleasure and fortune to have such an excellent colleague.

Dr. J. G. Negi (retired) Scientist and subsequently Emeritus Scientist at the Na­tional Geophysical Research Institute, Hyderabad, presently serving as Director General, Institute of Seismological Research, Gandhinagar, Gujrat, India, and my Guru (Ph. D. thesis supervisor) was always a source of inspiration for me. He also

Preface IX

read Chapter 15 and made useful suggestions for which I would sincerely express my gratitude.

The completion of this book has been a long journey occupying me almost full time, for nearly five years with the most intensive efforts. My family mem­bers, Sharada (wife), Kaushal and Kundan (sons), and daughter Anita Mishra and son-in-law R. K. Mishra provided continued support for the completion of this project in its best form. In fact, their contributions are no less than mine. My (late) parents, M. Devi and B.D. Upadhyay, and Sharada's father Dr. S.N. Chatur­vedi always encouraged me to write an excellent book as a contribution to the so­ciety. Their words have always inspired me.

This book should fulfill needs, and generate new ideas and interests in gradu­ate students, academicians, research scientists, and professionals in Hydrocarbon Exploration Industries for better achievement of their goals. I sincerely hope that readers will value it as a timely and useful contribution to science.

Roorkee, June 2004 S. K. UPADHYAY

Contents

1 Introduction . ................................... . 1.1 1.2 1.2.1 1.2.2

1.3

2 2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.4 2.5 2.6

3 3.1 3.1.1 3.1.2 3.2 3.2.1 3.2.2 3.3 3.4 3.4.1 3.4.2 3.5 3.5.1

Seismic Reflections ................................ . Necessity for Processing Reflections .................... . Specialized Processing of Converted Waves . . . . . . . . . . . . . . . . . Failure of Processing for Typical Anisotropic and Structural Conditions ........................... . The Scope and Organization of the Book . . . . . . . . . . . . . . . . . .

Reflection - Data Acquisition ........................ . Components of a Reflection Survey Unit ................. . Seismic Sources ................................... . Detectors ....................................... . Amplifiers, Filters, Analog and Digital Recorders ........... . Surface Shot-Geophone Spreads ....................... . For 2-D Surveys .................................. . For 3-D surveys ................................... . Practical Considerations for Acquisition of Reflection Data .... . Signal and Noise .................................. . Reduction of Noise ................................ . VSP Geometries ................................... . Seismic Surveys using Shear Waves ..................... . Marine Seismic Surveys ............................. .

Reflection Seismograms and Steps in Processing ......... . Creation of a Seismogram ........................... . An Ideal Seismogram-Impulse Response of a Spike .......... . Transient Seismic Pulse and Sweep Signal ................ . Analog and Digital Form Seismograms .................. . Frequency Bandwidth of a Reflected Wavelet .............. . Use of Sampling Theorem ........................... . Digital Recording - Multiplexed Data ................... . Processing Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Space-Time Domain ................................ . Frequency Domain ................................ . Various Kinds of Processing and Their Purposes ........... . Frequency Filtering ................................ .

1 7 8

10 11

15 15 15 21 25 29 29 32 32 35 37 38 40 43

47 47 49 52 54 55 56 60 61 64 65 67 67

XII

3.5.2 3.5.3 3.5.4 3.5.5 3.5.6

3.5.7 3.5.8 3.5.9 3.5.10 3.5.11 3.5.12 3.5.13 3.6 3.6.1 3.6.2

4 4.1 4.2 4.3 4.4

4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.4.7

5

5.1 5.2 5.2.1

5.2.2

5.3 5.3.1

Contents

Demultiplexing ................................... . Gain Recovery and Attenuation Correction . . . . . . . . . . . . . . . . . Deconvolution Before Stacking ........................ . Static Corrections ................................. . Specific Selection of Seismic Traces - Different Types of Gathers including CMP Gathers . . . . . . . . . . . . . . . . . . . . . . . Velocity Analysis .................................. . Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CMP Stacking .................................... . Deconvolution after Stacking ......................... . Migration ....................................... . Wavelet Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Displays of Seismic Sections .......................... . Information Contents of Seismic Sections ................ . Geological Structural Details .......................... . Geological Stratigraphic Details: Concept of Seismic Stratigraphy . Appendix 3A: Problems of Detection of Thin Bed, Horizontal and Vertical Resolution ............................. .

Attributes of Routine Reflection Processing and Pitfalls ..... Introduction .................. . . . . . . . . . . . . . . . . . . . . Seismic Attributes of Reflection Data . . . . . . . . . . . . . . . . . . . . . Complex Trace Analysis to Determine Values of Attributes ..... . Pitfalls in Routine Reflection Processing due to Conditions of Anisotropy: Effects on ............................ . Waveforms and Arrival Times ......................... . Evaluation of Moveout Corrections ..................... . Stacking Velocity .................................. . NMO Velocity .................................... . Interval Velocity .................................. . Reflectivity ...................................... . Imaging ........................................ .

Anisotropy Models of Sedimentary Sections and Characteristics of Wave Propagation ............... . Introduction ................ . . . . . . . . . . . . . . . . . . . . . . Description of Elastic Behaviour ....................... . Elastic Constitutive Relations : Stiffness and Compliance Constants ....................................... . Bond Transformation Matrix ......................... . Algorithm 5.1: Method of Writing Elements of Bond Transformation Matrix ........................ . Exercise 5.1: (On Elastic Stiffness Constants in Rotated Coordinate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Occurrence of Anisotropy and Models for Sedimentary Sections . Layering Induced Anisotropy: VTI Media . . . . . . . . . . . . . . . . . . Problem 5.1: (On Elastic Stiffness Constants for Periodic Layering)

69 70 71 73

75 77 79 88 90 93 97 99

100 103 103

103

109 109 111 117

119 119 121 123 127 130 134 138

143 143 147

151 154

154

156 159 159 165

Contents XIII

5.3.2 Azimuthal Anisotropy: HTI Media. . . . . . . . . . . . . . . . . . . . . . . 166 5.3.3 Limited Equivalence between VTI and HTI Media. . . . . . . . . . . . 168 5.4 Thomsen Parameters for HTI Media (or Equivalent VTI Media) . . 170 5.5 Thomsen Parameters for Orthorhombic Media . . . . . . . . . . . . . . 171 5.6 Weak Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 5.6.1 Phase- and Group-Velocities in VTI Media and Their Linearized

Forms .......................................... 173 5.6.2 Linearized Form of Group (Ray) Velocity for HTI Media. . . . . . . 179 5.7 Wave Equation in Elastic Media: The Christoffel Equation . . . . . . 181 5.7.1 Plane Wave Equation in Isotropic Solid ................... 181 5.7.2 Plane Wave Equation in Anisotropic Solid ................. 184

Problem 5.2: (On Solutions of Wave Equation for Anisotropic Systems) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

5.8 Particle Motion Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 5.8.1 P-Wave Polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 5.8.2 Shear Wave Delays and Polarization Anomalies ............. 195

Problem 5.3: (On Calculation of Rotated Seismograms) ........ 201 Appendix SA: Existence of Degenerate and Non-Degenerate Shear Waves - Shear Wave Splitting ..................... 201

6 Ray Path, Wavefront Curvature, Normal Moveout Velocity (VNMO) and Subsurface Medium Properties ............. 207

6.1 Conventional and Generalized Forms of Snell's Law .......... 208 6.2 The Wave Surface, Ray Parameter and Ray Tracing. . . . . . . . . . . 217

Algorithm 6.1: A Method of Ray Tracing .................. 221 6.3 Surface Emerging Wavefront and Normal Moveout (NMO)

Velocity ......................................... 221 6.3.1 Arbitrarily Dipping Layered Media with Isotropic or Ellipsoidal

Velocity Dependencies ............................... 221 Exercise 6.1: (On Calculation of Radius of Curvature of Surface Emerging Reflected Wavefront) ................. 228 Problem 6.1: (On Determination of NMO Velocity) ........... 232

6.4 NMO Velocity for Transversely Isotropic (T. I.) Media ......... 232 6.5 From Normal Moveout Velocity to Interval Velocities

and Positioning of Reflectors: Isotropic Layers .............. 236 6.6 Normal Moveout Velocity and Reconstruction of Velocity Field

in Anisotropic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

7 Reflection Time Analysis and Velocity for Isotropic Media ... 241 7.1 Reflected Wave Travel Time for Multi-Layer Isotropic Media:

Use of Fermat's Principle of Least Time . . . . . . . . . . . . . . . . . . . 241 7.2 Dix Equation for Interval Velocity. . . . . . . . . . . . . . . . . . . . . . . 244 7.2.1 Vertical Ray Path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 7.2.2 Non-Vertical Ray Path ............................... 250 7.3 Stacking Velocity for a Layered Structure. . . . . . . . . . . . . . . . . . 251 7.4 Hyperbolic Velocity Analysis .......................... 252 7.4.1 Basis of Analysis .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

XIV

7.4.2 7.4.3

8

8.1 8.1.1 8.1.2

8.2 8.2.1 8.2.2 8.2.3 8.3

9 9.1 9.1.1 9.1.2 9.1.3 9.1.4 9.2

9.3 9.3.1

9.3.2

10 10.1 10.1.1 10.2 10.2.1 10.2.2

10.3 10.3.1 10.3.2

10.3.3

10.3.4

Contents

The Semblance Coefficient ........................... . Velocity Spectra ................................... . Appendix 7 A: Concept of Velocity Estimation using Beam Stack: Applicable to Geologically Complex Areas ................ .

Reflection Time Analysis and Velocities for Transversely Isotropic (T.I.) Media .............................. . Skewed Hyperbolic Travel Time Relations ................ . For Single Azimuthally Isotropic or Anisotropic Layer ........ . Generalization to Multi-Layer Medium and Relationship between Bulk Velocities and Interval Velocities ............. . Three Velocity Parameters in Skewed Hyperbolic Analysis ..... . Phase- and Ray-Velocities of SH and P Waves ............. . Skewed Hyperbolic Formula for Travel Time for VSP Geometry .. Three Velocity Parameters in Skewed Hyperbolic Analysis ..... . Apparent Anisotropy and Identification of Lithology ......... .

Analysis of e-x2 Relations .......................... . Single Anisotropic Layer Model ........................ . Wave Surfaces and t2_x2 Curves ........................ . Curved t2 -x2 Graph, Instantaneous Velocity and Intercept Time .. Interpreting t2 _x2 Curves for Anisotropy ................. . Velocity and Depth Errors under Assumption of Isotropy ..... . What Interval and Stacking Velocities correspond to Under Condition of Anisotropy ............................. . Three-Term Taylor Series Approximation of t2 - x2 Curves ...... . Term-wise Interpretation for Isotropy, Anisotropy, and Inhomogeneity ................................ . Recommended Combined Use of SH and SV Waves

254 255

257

261 261 261

263 264 265 267 268 270

275 277 277 278 281 286

287 288

289

to Probe Anisotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

Estimation of Anisotropy and Layer Parameters .......... . Semblance Analysis of Skewed Hyperbolic Time-Distance Curves. Elastic Constants Determination using Layer Stripping Method .. Inversion using Non-linear Fit to e _x2 Curves ............. . Interval Velocity and Elastic Constants for Azimuthal Isotropy .. . Interval Velocity, Elastic Constants and Direction of Symmetry Axis for Azimuthal Anisotropy ........................ . Inversion using Travel Times ......................... . Damped Least Square Formulation ..................... . Jacobian Matrix Formulation: Simultaneous Determination of All Layer Parameters ............................. . Artifacts of Isotropic Travel Time Inversion under Conditions of Anisotropy .................................... . Inversion Algorithms and Model Assessment .............. .

299 299 301 303 305

306 309 309

312

319 322

Contents

11 11.1 11.2 11.3 11.4 11.4.1

11.5 11.5.1

11.5.2 11.6 11.7

12 12.1 12.2 12.2.1 12.2.2 12.3 12.4

13 13.1 13.2 13.3 13.3.1 13.3.2 13.4 13.4.1 13.4.2 13.4.3 13.5 13.5.1 13.5.2 13.5.3 13.6 13.6.1 13.6.2 13.6.3

Dip Moveout Processing and True Amplitude Imaging ..... . Introduction ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common Mid Point Gather and Dip Moveout Operator ....... . Mapping Constant Offset Section to Zero Offset ............ . Kinematics of DMO Equations ........................ . Extension of the NMO-DMO Algorithm of Forel and Gardner (1988) to Elliptically Anisotropic Media .................. . DMO Impulse Response ............................. . DMO Impulse Response for Constant and Varying Isotropic Velocity ........................................ . DMO Impulse Response under Condition of Anisotropy ...... . DMO in Dip Domain ............................... . Dip-Moveout and True Amplitude Imaging ............... .

Basic Reflection Theory for Anisotropic Models .......... . Ray Series and Zero Order Approximation . . . . . . . . . . . . . . . . . Reflecting Interface Separating Two Transversely Isotropic Media Linearized Reflection and Transmission Coefficients ......... . Numerical Results ................................. . Case of Elliptical Anisotropy .......................... . Concluding Remarks ............................... .

Reflection Amplitude and AVO-Interpretation ........... . Introduction .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of Gas Sands . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approximations to Reflection Coefficient Variations ......... . Condition of Isotropy ............................... . Condition of Anisotropy ............................. . Factors Affecting Reflection Amplitude .................. . Geometrical Spreading .............................. . Anisotropy of Incident Medium: Radiation Pattern Effects ..... . Anelastic Effects and Absorption Loss ................... . Estimating Target's Reflection Amplitude Behaviour with Offset .. AVO Correction Factor: Use of Seismic Range Equation ...... . Model Based Amplitude Balancing ..................... . Use of Separable Signal Model ........................ . AVO Interpretation ................................ . AVO Gradient and Intercept for Gas Sands ................ . VplVs Ratio, Anisotropy and AVO Response ............... . Perspective of AVO Intercept and Gradient Interpretation ..... . Appendix 13A: Computer Programs for Approximate Numerical Solutions of P-P Reflection Coefficients between HTI/HTI Media .......................................... .

xv

325 325 326 329 331

337 339

346 348 350 353

359 359 361 363 368 373 375

379 379 380 382 382 388 391 391 394 400 407 408 409 410 412 412 415 418

421

XVI Contents

14 Concepts and Methods in Seismic Migration ............. 425 14.1 Definition and Elementary Considerations ..... . . . . . . . . . . . . 425 14.2 Point Diffractor Model and Application . . . . . . . . . . . . . . . . . . . 428

Problem 14.1: (On Diffraction Hyperbola for Point Diffractor) . . . 429 14.3 Geometric Technique of Migration ...................... 429 14.3.1 Corresponding Wave Number Domain Migration ............ 432

Exercise 14.1: (On Migration of an Illustrative Earth Model in Two Domains) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

14.4 Finite Difference Migration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 14.5 Frequency Domain Migration . . . . . . . . . . . . . . . . . . . . . . . . . . 442 14.6 Exploding Reflector Model (ERM) and One Way Wave Equation 445 14.6.1 Downward Depropagation of Surface-Recorded Reflected Wavefield 447 14.7 Migration using Frequency Domain Form of Wave Equation .... 453 14.7.1 Approximation of Exact Dispersion Equation .. . . . . . . . . . . . . . 453 14.7.2 Wavefield Extrapolation ....... . . . . . . . . . . . . . . . . . . . . . . . 453 14.7.3 Application of Paraxial Equation under Condition of Anisotropy 454 14.8 Slant Stack Migration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 14.8.1 Wave Stack vs. CMP Stack ............................ 457 14.8.2 Plane Wave Stack and p-Gather . . . . . . . . . . . . . . . . . . . . . . . . . 458 14.8.3 Relationship between Common Geophone Gather and p-Gather .. 460 14.8.4 Basis of Slant Stack Migration ......................... 461 14.9 Migration using Explicit Filters for Depth Migration. . . . . . . . . . 464 14.9.1 Isotropic Laterally Varying Earth Model. . . . . . . . . . . . . . . . . . . 466 14.9.2 Anisotropic Earth Model ............................. 469

15 Imaging using Integral Solutions of Wave Equations . . . . . . . 473 15.1 Green's Function and Kirchoff Integral Representation

of the Wavefield in Image Space ........................ 474 15.1.1 Convolutional Form of Solution of Scalar Wave Equation

for Wave Field Extrapolation. . . . . . . . . . . . . . . . . . . . . . . . . . . 477 15.1.2 Imaging of Stacked Seismic Data. . . . . . . . . . . . . . . . . . . . . . . . 479 15.1.3 Imaging of Unstacked Seismic Data. . . . . . . . . . . . . . . . . . . . . . 481 15.2 Simultaneous Migration of P- and S-Waves: Elastic Wave Migration 483 15.3 Migration in Inhomogeneous, Anisotropic Media for Converted

and Non-converted Waves ............................ 487 Algorithm 15.1: Stepwise Development of Imaging Scheme using Non-conventional Velocity Analysis . . . . . . . . . . . . . . . . . . . . . . 494 Appendix 15A: Removal of Distortions in Migrated Image, Caused due to Static Shifting, by using Wavefield Extrapolation . . 495

16 Miscellaneous Interpretation Tools. . . . . . . . . . . . . . . . . . . . . 503 16.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 16.2 Mathematical Operations and Geophysical Applications . . . . . . . . 503 16.2.1 Convolution and Deconvolution ........................ 503

Exercise 16.1: (On Convolution and Deconvolution) .......... 507 16.2.2 Cross-correlation and Auto-correlation ................... 508

Exercise 16.2: (On Correlation) ... . . . . . . . . . . . . . . . . . . . . . . 511

Contents

16.2.3

16.2.4

16.2.5 16.3 16.3.1 16.3.2 16.3.3 16.4 16.4.1 16.4.2 16.4.3 16.4.4 16.4.5

16.4.6

16.5 16.6 16.6.1 16.6.2 16.6.3

17 17.1 17.2 17.3 17.4 17.5 17.5.1

17.6

17.6.1 17.7

17.8 17.8.1

17.8.2

17.8.3

17.8.4

Digital Filtering ................................... . Exercise 16.3: (On Digital Filtering) ..................... . Z-Transform ..................................... . Exercise 16.4: (On Z-Transform) ....................... . Fourier Analysis and Synthesis ........................ . Use of Tomographic Reconstruction .................... . ART for a Weakly Anisotropic Medium .................. . Constrained Dual Tomography ........................ . Tomographic Estimation of Elastic Constants of a T.1. Medium .. Use of Seismic Rock Physics .......................... . Porous Fluid-Saturated Reservoir Rocks .................. . Effects on Seismic Velocities of Reservoir Rock Properties ..... . Influence of Environment Factors and Geological History ..... . V p/V s as an Indicator of Lithology and Porosity ............ . Velocity-Porosity Cross Plot as a Measure of Kerogene Contents of Shales ........................................ . Practical Guidelines Relating Some Significant Rock/Fluid Properties with Seismic Properties ..................... . Use of 3-D Data Analysis ............................ . Objective-oriented Interpretation Tools .................. . Detection of Coal Seam ............................. . Detection of Overpressured Zone ...................... . Anisotropic Property of Shale Formations ................ .

Exploration Value of Fracture-Induced Anisotropy ........ . The objective and Need for Specific Development ........... . Observable Signatures of Seismic Anisotropy .............. . Elastic and Seismic Properties of Fractured Rocks .......... . Stress Anisotropy and Fracturing ...................... . Model of Vertically Fractured and Horizontally Stratified Media .. Schoenberg and Muir Calculus: Quantification of Fracture Compliance ...................................... . An Inverse Method to Separate Fracture Anisotropy from Background Anisotropy ......................... . Example ........................................ . Numerical Method to Model Fracture Anisotropy: Use of a Synthetic Seismogram ........................ . Field System Examples of Reservoir Characterization ........ . Determination of Bulk Density and Strikes of Fractures in Geothermal Reservoir: Use of Shear Wave Splitting ........ . Delineation of Cracked Rock Regime around Boreholes: Use of Velocity Anomalies ........................... . Determination of Fracture Orientation in Marine Seismic Studies: Use of P-Wave AVO ................................ . Spatial Location of Cracks and Crack Density Variations in Coal Bed Methane Reservoir: Use of 3-D AVO ........... .

XVII

512 513 514 515 518 529 530 532 534 535 536 538 540 542

542

543 543 546 546 551 552

557 557 557 559 561 565

566

568 570

572

575

575

578

581

584

XVIII Contents

Appendix 17 A: Combined Application of V NMO and V H

for Fracture Characterization in a Azimuthally Anisotropic Medium.. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

18 Future Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 18.1 Enhanced Scope for Applications in Engineering Geophysics

Problems ........................................ 593 18.1.1 VHR 3-D Shallow Seismic Investigations .................. 593 18.1.2 Necessity for Combined Application of High Resolution

Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596 18.2 Research Areas Requiring Special Emphasis . . . . . . . . . . . . . . . . 599

19 List of References 601

Subject Index .................................... 621