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Series: Investigations in Geophysics,

Volume I

Michael R. Cooper, Series Editor

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SEISMIC DATA ANALYSIS

Processing, Inversion, and Interpretation of Seismic Data

ÖZ YILMAZ

Volume I

Stephen M. Doherty, Editor

Society of Exploration Geophysicists

Post Office Box 702740, Tulsa, OK 74170-2740

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To Mother In Memoriam

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TABLE OF CONTENTS

PREFACE TO THE FIRST EDITION

PREFACE

Volume I

INTRODUCTION

Processing of Seismic Data, 4Inversion of Seismic Data, 10Interpretation of Seismic Data, 18

From Seismic Exploration to Seismic Monitoring, 22

Chapter 1

FUNDAMENTALS OF SIGNAL PROCESSING

1.0 Introduction, 25

1.1 The 1-D Fourier Transform, 26

Analog versus Digital Signal, 28Frequency Aliasing, 30Phase Considerations, 34Time-Domain Operations, 36Convolution, 38Crosscorrelation and Autocorrelation, 39

Vibroseis Correlation, 41Frequency Filtering, 41Practical Aspects of Frequency Filtering, 44Bandwidth and Vertical Resolution, 46Time-Variant Filtering, 48

1.2 The 2-D Fourier Transform, 48

Spatial Aliasing, 511.3 Worldwide Assortment of Shot Records, 67

Wave Types, 701.4 Gain Applications, 81

Geometric Spreading Correction, 81Programmed Gain Control, 85RMS Amplitude AGC, 85Instantaneous AGC, 87Relative Trace Balancing, 89

1.5 Basic Data Processing Sequence, 90

Preprocessing, 91Deconvolution, 92CMP Sorting, 93Velocity Analysis, 93Normal-Moveout Correction, 94Multiple Attenuation, 94

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viii Seismic Data Analysis

Dip-Moveout Correction, 94CMP Stacking, 95Poststack Processing, 95Migration, 95Residual Statics Corrections, 122

Quality Control in Processing, 122Parsimony in Processing, 124Exercises, 150

Appendix A: A Mathematical Review of the Fourier Transform, 153

A.1 The 1-D Fourier Transform, 153A.2 The z-Transform, 155A.3 The 2-D Fourier Transform, 156

References, 156

Chapter 2

DECONVOLUTION


2.1 The Convolutional Model, 162

The Convolutional Model in the Time Domain, 167The Convolutional Model in the Frequency Domain, 170

2.2 Inverse Filtering, 171

The Inverse of the Source Wavelet, 172Least-Squares Inverse Filtering, 173Minimum Phase, 175

2.3 Optimum Wiener Filters, 179

Spiking Deconvolution, 180Prewhitening, 181Wavelet Processing by Shaping Filters, 183Predictive Deconvolution, 185

2.4 Predictive Deconvolution in Practice, 190Operator Length, 190Prediction Lag, 193Percent Prewhitening, 203Effect of Random Noise on Deconvolution, 207Multiple Attenuation, 209

2.5 Field Data Examples, 211

Prestack Deconvolution, 213Signature Deconvolution, 217Vibroseis Deconvolution, 219Poststack Deconvolution, 222

2.6 The Problem of Nonstationarity, 222

Time-Variant Deconvolution, 227

Time-Variant Spectral Whitening, 231Frequency-Domain Deconvolution, 233Inverse Q Filtering, 234Deconvolution Strategies, 241

Exercises, 247

Appendix B: Mathematical Foundation of Deconvolution, 249

B.1 Synthetic Seismogram, 249B.2 The Inverse of the Source Wavelet, 251B.3 The Inverse Filter, 252B.4 Frequency-Domain Deconvolution, 253

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Contents ix

B.5 Optimum Wiener Filters, 255B.6 Spiking Deconvolution, 258B.7 Predictive Deconvolution, 260B.8 Surface-Consistent Deconvolution, 262B.9 Inverse Q Filtering, 266

References, 270

Chapter 3

VELOCITY ANALYSIS AND STATICS CORRECTIONS


3.1 Normal Moveout, 274

NMO for a Flat Reflector, 274NMO in a Horizontally Stratified Earth, 280Fourth-Order Moveout, 280NMO Stretching, 283NMO for a Dipping Reflector, 285NMO for Several Layers with Arbitrary Dips, 287

Moveout Velocity versus Stacking Velocity, 2883.2 Velocity Analysis, 288

The Velocity Spectrum, 292Measure of Coherency, 295Factors Affecting Velocity Estimates, 302Interactive Velocity Analysis, 311Horizon Velocity Analysis, 312Coherency Attribute Stacks, 318

3.3 Residual Statics Corrections, 324

Residual Statics Estimation by Traveltime Decomposition, 336Residual Statics Estimation by Stack-Power Maximization, 344Traveltime Decomposition in Practice, 345

Maximum Allowable Shift, 346Correlation Window, 361Other Considerations, 362Stack-Power Maximization in Practice, 365

3.4 Refraction Statics Corrections, 370

First Breaks, 374Field Statics Corrections, 375Flat Refractor, 375Dipping Refractor, 377The Plus-Minus Method, 377The Generalized Reciprocal Method, 379The Least-Squares Method, 379Processing Sequence for Statics Corrections, 381

Model Experiments, 382Field Data Examples, 395

Exercises, 432

Appendix C: Topics in Moveout and Statics Corrections, 437

C.1 The Shifted Hyperbola, 437C.2 Moveout Stretch, 439C.3 Equations for a Dipping Reflector, 441C.4 Traveltime Decomposition for Residual Statics Estimation, 442C.5 Depth Estimation from Refracted Arrivals, 444C.6 Equations for a Dipping Refractor, 445

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x Seismic Data Analysis

C.7 The Plus-Minus Times, 447C.8 Generalized Linear Inversion of Refracted Arrivals, 448C.9 Refraction Traveltime Tomography, 453C.10 L1-Norm Refraction Statics, 456

References, 460

Chapter 4

MIGRATION


Exploding Reflectors, 467Migration Strategies, 470Migration Algorithms, 471Migration Parameters, 474Aspects of Input data, 475Migration Velocities, 475

4.1 Migration Principles, 476

Kirchhoff Migration, 481Diffraction Summation, 484Amplitude and Phase Factors, 485Kirchhoff Summation, 485Finite-Difference Migration, 486Downward Continuation, 486Differencing Schemes, 488Rational Approximations for Implicit Schemes, 489Reverse Time Migration, 491Frequency-Space Implicit Schemes, 492Frequency-Space Explicit Schemes, 493Frequency-Wavenumber Migration, 494Phase-Shift Migration, 498

Stolt Migration, 500Summary of Domains of Migration Algorithms, 5014.2 Kirchhoff Migration in Practice, 502

Aperture Width, 502Maximum Dip to Migrate, 509Velocity Errors, 509

4.3 Finite-Difference Migration in Practice, 520

Depth Step Size, 521Velocity Errors, 525Cascaded Migration, 525Reverse Time Migration, 530

4.4 Frequency-Space Migration in Practice, 530

Steep-Dip Implicit Methods, 535

Depth Step Size, 537Velocity Errors, 544Steep-Dip Explicit Methods, 549Dip Limits of Extrapolation Filters, 549Velocity Errors, 552

4.5 Frequency-Wavenumber Migration in Practice, 559

Maximum Dip to Migrate, 559Depth Step Size, 566Velocity Errors, 567Stolt Stretch Factor, 572

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Wraparound, 575Residual Migration, 575

4.6 Further Aspects of Migration in Practice, 579

Migration and Spatial Aliasing, 581Migration and Random Noise, 619Migration and Line Length, 621Migration from Topography, 626

Exercises, 626

Appendix D: Mathematical Foundation of Migration, 628

D.1 Wavefield Extrapolation and Migration, 628D.2 Stationary Phase Approximations, 638D.3 The Parabolic Approximation, 639D.4 Frequency-Space Implicit Schemes, 641D.5 Stable Explicit Extrapolation, 644D.6 Optimum Depth Step, 646D.7 Frequency-Wavenumber Migration, 649D.8 Residual Migration, 651

References, 652

Chapter 5

DIP-MOVEOUT CORRECTION AND PRESTACK MIGRATION


Salt-Flank Reflections, 657Fault-Plane Reflections, 657DMO and Stacking Velocities, 657Turning-Wave Reflections, 665

5.1 Principles of Dip-Moveout Correction, 668

Prestack Partial Migration, 670Frequency-Wavenumber DMO Correction, 672Log-Stretch DMO Correction, 677

Integral DMO Correction, 679Velocity Errors, 681Variable Velocity, 684Turning-Wave Migration, 685

5.2 Dip-Moveout Correction in Practice, 692

Salt Flanks, 692Fault Planes, 693DMO and Multiples, 705DMO and Coherent Linear Noise, 716Other Considerations, 716Aspects of DMO Correction — A Summary, 722

5.3 Prestack Time Migration, 725

DMO Correction and Common-Offset Migration, 728

Salt Flanks, 729Fault Planes, 742Common-Reflection-Point versus Common-Reflection-Surface Stacking, 769

5.4 Migration Velocity Analysis, 775

Prestack Stolt Migration, 776Common-Offset Migration of DMO-Corrected Data, 777Prestack Kirchhoff Migration, 788Velocity Analysis Using Common-Reflection-Point Gathers, 788Focusing Analysis, 798Fowler’s Velocity-Independent Prestack Migration, 803

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Exercises, 815

Appendix E: Topics in Dip-Moveout Correction and Prestack Time Migration, 817

E.1 Reflection Point Dispersal, 817E.2 Equations for DMO Correction, 820E.3 Log-Stretch DMO Correction, 823

E.4 The DMO Ellipse, 826E.5 Nonzero-Offset Traveltime Equation, 827E.6 Prestack Frequency-Wavenumber Migration, 831E.7 Velocity Analysis by Wavefield Extrapolation, 833

References, 834

Chapter 6

NOISE AND MULTIPLE ATTENUATION


Coherent Linear Noise, 838Treatment of Coherent Linear Noise by Conventional Processing, 840Reverberations and Multiples, 843Treatment of Reverberations and Multiples by Conventional Processing, 857Spatially Random Noise, 876

6.1 Multiple Attenuation in the CMP Domain, 877

Periodicity of Multiples, 877Velocity Discrimination Between Primaries and Multiples, 887Karhunen-Loeve Transform, 887Modeling of Multiples, 896

6.2 Frequency-Wavenumber Filtering, 898

Random Noise and Frequency-Wavenumber Filtering, 904Statics Corrections and Frequency-Wavenumber Filtering, 905Dip Filtering of Coherent Linear Noise, 905Frequency-Wavenumber Multiple Attenuation, 907

6.3 The Slant-Stack Transform, 920Physical Aspects of Slant Stacking, 920Slant-Stack Transformation, 923Practical Aspects of Slant Stacking, 924Slant-Stack Parameters, 928Time-Variant Dip Filtering, 931Slant-Stack Multiple Attenuation, 932

6.4 The Radon Transform, 938

Velocity-Stack Transformation, 942The Discrete Radon Transform, 943The Parabolic Radon Transform, 944Practical Considerations, 945Impulse Response of the Velocity-Stack Operator, 948

Field Data Examples, 948Radon-Transform Multiple Attenuation, 953

6.5 Linear Uncorrelated Noise Attenuation, 960

Design of Spatial Prediction Filters, 966Field Data Examples, 966

Exercises, 976

Appendix F: Multichannel Filtering Techniques for Noise and Multiple Attenuation, 977

F.1 Analysis of Guided Waves, 977F.2 Wavefield Extrapolation in the τ − p Domain, 980F.3 Mathematical Foundation of the Discrete Radon Transform, 982

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F.4 Free-Surface Multiple Attenuation, 989F.5 Water-Bottom Multiple Attenuation, 992F.6 Spatial Prediction Filter, 995

References, 998

INDEX, xxv

Volume II

Chapter 7

3-D SEISMIC EXPLORATION


The Need for Imaging in Three Dimensions, 10037.1 3-D Survey Design and Acquisition, 1010

Migration Aperture, 1010Spatial Sampling, 1017

Other Considerations, 1018Marine Acquisition Geometry, 1018Cable Feathering, 10193-D Binning, 1019Crossline Smearing, 1020Strike versus Dip Shooting, 1027Land Acquisition Geometry, 1028

7.2 Processing of 3-D Seismic Data, 1030

3-D Refraction Statics Corrections, 1036Azimuth Dependence of Moveout Velocities, 10363-D Dip-Moveout Correction, 1046Inversion to Zero Offset, 1048Aspects of 3-D DMO Correction — A Summary, 1050

Velocity Analysis, 10503-D Residual Statics Corrections, 10503-D Migration, 1051Trace Interpolation, 1065

7.3 3-D Poststack Migration, 1073

Separation versus Splitting, 1073Impulse Response of the One-Pass Implicit Finite-Difference 3-D Migration, 1074Two-Pass versus One-Pass Implicit Finite-Difference 3-D Migration in Practice, 1076Explicit Schemes Combined with the McClellan Transform, 1082The Phase-Shift-Plus-Correction Method, 1088

7.4 3-D Prestack Time Migration, 1099

3-D DMO Correction Combined with 3-D Common-Offset Migration, 1112Crossline Migration, 1129

3-D Migration Velocity Analysis, 1131Aspects of 3-D Prestack Time Migration — A Summary, 1137

7.5 Interpretation of 3-D Seismic Data, 1156

Time Slices, 11563-D Visualization, 1156Removal of Opacity, 1158Seed Detection, 1159Structural Interpretation, 1161Stratigraphic Interpretation, 1171

Exercises, 1195

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Appendix G: Mathematical Foundation of 3-D Migration, 1198

G.1 Implicit Methods, 1198G.2 Explicit Methods, 1200G.3 3-D Phase-Shift Migration, 1203G.4 3-D Stolt Migration, 1204

G.5 Trace Interpolation, 1204G.6 3-D Nonzero-Offset Traveltime Equation, 1208References, 1209

Chapter 8

EARTH IMAGING IN DEPTH


Lateral Velocity Variations, 12228.1 Layer Replacement, 1226

Wave-Equation Datuming, 1229Poststack Layer Replacement, 1230Prestack Layer Replacement, 1231Field Data Example, 1237

8.2 2-D Poststack Depth Migration, 1238

Image Rays and Lateral Velocity Variations, 1238Time versus Depth Migration, 1244Iterative Depth Migration, 1247Iteration with Zero-Offset Data, 1250Iteration with CMP-Stacked Data, 1258Iteration with Prestack Data, 1265Iteration in Practice, 1265

8.3 2-D Prestack Depth Migration, 1273

Shot-Geophone Migration, 1274Shot-Profile Migration, 1280

Sensitivity of Image Accuracy to Velocity Errors, 1280Field Data Examples, 12958.4 3-D Poststack Depth Migration, 1304

3-D Poststack Time versus Depth Migration, 1304Two-Pass versus One-Pass 3-D Poststack Depth Migration, 1313Implicit versus Explicit 3-D Poststack Depth Migration, 13143-D Poststack Datuming, 1321

8.5 3-D Prestack Depth Migration, 1321

Kirchhoff Summation, 1324Calculation of Traveltimes, 1324The Eikonal Equation, 1325Fermat’s Principle, 1331Summation Strategies, 1331

Migration Aperture, 1333Operator Antialiasing, 13333-D Common-Offset Depth Migration, 1335

Exercises, 1342

Appendix H: Diffraction and Ray Theory for Wave Propagation, 1342

H.1 The Kirchhoff Integral, 1342H.2 The Eikonal Equation, 1346H.3 Finite-Difference Solution to the Eikonal Equation, 1349References, 1351

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Chapter 9

EARTH MODELING IN DEPTH


Inversion Methods for Data Modeling, 1355

Inversion Procedures for Earth Modeling, 1356Velocity-Depth Ambiguity, 1357Model Representation and Visualization, 1360

9.1 Models with Horizontal Layers, 1365

Dix Conversion, 1365Coherency Inversion, 1369Near-Surface Layer with Laterally Varying Velocities, 1382

9.2 Model with Low-Relief Structure, 1387

Stacking Velocity Inversion, 1392Coherency Inversion, 1404Velocity Resolution, 1404

9.3 Model with Complex Overburden Structure, 1404

Image-Gathers, 1406

Constant Half-Space Velocity Analysis, 14159.4 Model Building, 1415

Time-to-Depth Conversion, 1416Time Structure Maps, 1416Interval Velocity Maps, 1417Depth Structure Maps, 1425Calibration to Well Tops, 1426Layer-by-Layer Inversion, 1433Structure-Independent Inversion, 1450

9.5 Model Updating, 1450

Residual Moveout Analysis, 1462Reflection Traveltime Tomography, 1469Limitations in Resolving Velocity-Depth Ambiguity by Tomography, 1479

Turning-Ray Tomography, 1512Exercises, 1524

Appendix J: Data Modeling by Inversion, 1525

J.1 The Generalized Linear Inversion, 1525J.2 The GLI Formalism of Deconvolution, 1526J.3 Applications of the GLI Technique, 1530J.4 Dix Conversion, 1534J.5 Map Processing, 1539J.6 Reflection Traveltime Tomography, 1545J.7 Threshold for Velocity-Depth Ambiguity, 1553

References, 1554

Chapter 10STRUCTURAL INVERSION


10.1 Subsalt Imaging in the North Sea, 1558

Estimation of the Overburden Model, 1562Estimation of the Substratum Model, 1562Model Verification, 1563

10.2 Subsalt Imaging in the Gulf of Mexico, 1574

Layered Earth Model Estimation, 1574

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xvi Seismic Data Analysis

Sructure-Independent Model Estimation, 157710.3 Imaging Beneath Irregular Water Bottom in the Northwest Shelf of Australia, 1597

Earth Modeling and Imaging in Depth, 159710.4 Imaging Beneath Volcanics in the West of Shetlands of the Atlantic Margin, 1597

Earth Modeling and Imaging in Depth, 1607

10.5 Imaging Beneath Shallow Gas Anomalies in the Gulf of Thailand, 1620Earth Modeling and Imaging in Depth, 162010.6 3-D Structural Inversion Applied to Seismic Data from the Southern North Sea, 1626

Estimation of the Overburden Model, 1626Model Representation by Tessellation, 16303-D Coherency Inversion, 16303-D Poststack Depth Migration, 1637Estimation of the Substratum Model, 1638

10.7 3-D Structural Inversion Applied to Seismic Data from the Central North Sea, 1651

3-D Coherency Inversion Combined with 3-D Poststack Depth Migration, 16653-D Stacking Velocity Inversion Combined with 3-D Image-Ray Depth Conversion, 1674

10.8 3-D Structural Inversion Applied to Seismic Data from Offshore Indonesia, 1674

Model Building, 1678

Model Updating, 1678Imaging in Depth, 1690Volume-Based Interpretation, 1690

10.9 3-D Structural Inversion Applied to Seismic Data from the Northeast China, 1703

3-D DMO Processing, 17203-D Prestack Time Migration, 1720From RMS to Interval Velocities, 1742Structural Inversion, 1742Structural and Stratigraphic Interpretation, 1744

Exercises, 1778

Appendix K: Seismic Modeling, 1779

K.1 Zero-Offset Traveltime Modeling, 1779K.2 Zero-Offset Wavefield Modeling, 1781K.3 Nonzero-Offset Wavefield Modeling, 1781K.4 Elastic Wavefield Modeling, 1790

References, 1792

Chapter 11

RESERVOIR GEOPHYSICS


Elastic Waves and Rock Properties, 179411.1 Seismic Resolution, 1801

Vertical Resolution, 1801Lateral Resolution, 1803

11.2 Analysis of Amplitude Variation with Offset, 1807Reflection and Refraction, 1808Reflector Curvature, 1813AVO Equations, 1816Processing Sequence for AVO Analysis, 1839Derivation of AVO Attributes by Prestack Amplitude Inversion, 1851Interpretation of AVO Attributes, 18623-D AVO Analysis, 1863

11.3 Acoustic Impedance Estimation, 1863

Synthetic Sonic Logs, 1864

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Processing Sequence for Acoustic Impedance Estimation, 1865Derivation of Acoustic Impedance Attribute, 18663-D Acoustic Impedance Estimation, 1872Instantaneous Attributes, 1896

11.4 Vertical Seismic Profiling, 1907

VSP Acquisition Geometry, 1907Processing of VSP Data, 1907VSP-CDP Transform, 1908

11.5 4-D Seismic Method, 1911

Processing of 4-D Seismic Data, 1912Seismic Reservoir Monitoring, 1913

11.6 4-C Seismic Method, 1915

Recording of 4-C Seismic Data, 1919Gaiser’s Coupling Analysis of Geophone Data, 1922Processing of PP Data, 1926Rotation of Horizontal Geophone Components, 1926Common-Conversion-Point Binning, 1933Velocity Analysis of PS Data, 1946

Dip-Moveout Correction of PS Data, 1959Migration of PS Data, 1961

11.7 Seismic Anisotropy, 1961

Anisotropic Velocity Analysis, 1965Anisotropic Dip-Moveout Correction, 1968Anisotropic Migration, 1980Effect of Anisotropy on AVO, 1998Shear-Wave Splitting in Anisotropic Media, 1999

Exercises, 2000

Appendix L: Mathematical Foundation of Elastic Wave Propagation, 2001

L.1 Stress-Strain Relation, 2001L.2 Elastic Wave Equation, 2007L.3 Seismic Wave Types — Body Waves and Surface Waves, 2008

L.4 Wave Propagation Phenomena — Diffraction, Reflection, and Refraction, 2012L.5 The Zoeppritz Equations, 2014L.6 Prestack Amplitude Inversion, 2019

References, 2024

INDEX, xvii

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PREFACE TO THE FIRST EDITION

The seismic method plays a prominent role in the searchfor hydrocarbons. Seismic exploration consists of threemain stages: data acquisition, processing, and interpre-tation. This book is intended to help the seismic analyst

understand the fundamentals of the techniques used inprocessing seismic data. In particular, emphasis is givento the practical aspects of data analysis.

Topics in this book are treated in two phases. First,each process is described from a physical viewpoint,with less emphasis on mathematical development. Indoing so, geometric means are used extensively to helpthe reader gain the physical insight into the differentprocesses. Second, the geophysical parameters that af-fect the fidelity of the resulting output from each pro-cess are critically examined via an extensive series of synthetic and real data examples. For the student of re-

flection seismology and new entrants to the seismic in-dustry, this book tries to provide insights into the prac-tical aspects of the application of the theory of time se-ries and waves. For experienced seismic explorationists,this book should serve as a refresher and handy ref-erence. However, it is not just meant for the seismicanalyst. Explorationists who would like to gain a prac-tical background in seismic data processing without anymathematical burden also should benefit from it. Nev-ertheless, for the more theoretically inclined, a mathe-matical treatise on the main subjects is provided in theappendixes.

The seismic analyst is confronted daily with the

important tasks of:

(1) selecting a proper sequence of processing steps ap-propriate for the field data under consideration,

(2) selecting an appropriate set of parameters for eachprocessing step, and

(3) evaluating the resulting output from each process-ing step, then diagnosing any problems caused byimproper parameter selection.

There is a well-established sequence for standardseismic data processing. The three principal processes— deconvolution, stacking, and migration — make upthe foundation of routine processing. There also aresome auxiliary processes that help improve the effec-tiveness of the principle processes. Questions often ariseas to the kind of auxiliary processes that should be usedand when they should be applied. For example, if shotrecords contain an abundance of source-generated co-herent noise, then dip filtering may be valuable beforedeconvolution. Beam steering may be necessary to im-prove the signal-to-noise ratio while reducing the num-ber of channels in processing by a factor of as much asfour. Residual statics corrections often are required forimproving velocity estimation and stacking. In a dailyproduction environment, many questions arise concern-

ing the optimal parameter selection for each process.Some of the most repeatedly asked questions are: Whatis a good length for the deconvolution operator? Whatshould the prediction lag be? What should the de-sign gate for the operator be? How should the corre-lation window be chosen in residual statics computa-tions? What kind of aperture width should one select inKirchhoff migration? What is the optimum depth stepsize in finite-difference migration? Many more questionscould be included in this list of questions. To help an-swer these questions, a large number of examples us-ing both field and synthetic data and describing a wide

range of processing parameters are provided.Since the old adage “a picture is worth a thousand

words” is especially apt in a discussion of seismic dataprocessing, figures make up the major portion of thistextbook. In preparing some of the figures, I receivedgreat assistance from my colleagues at Western Geo-physical Company. Thanks are due to Darran Lucas,Mike Cox, Greg Godkin, Dave Nichols, Tania Bachus,Tomaso Gabrieli, Dave Hill, and Raphael Tortosa.

xix

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xx Seismic Data Analysis

Thanks also are due to the oil companies and contrac-tors for supplying data and some figures for which spe-cific acknowledgment is made in the figure captions. Iexpress my deep appreciation to: Soraya Brombacher,Mark Wilson, Wayne Johnson, Mike Jungnickel, and

Pam Jakubowicz for the artwork on most of the figures.I also extend my appreciation to Meg LaVergne, whoput the final touches on many figures and computer-drafted the flow diagrams. Thanks also to the mem-bers of the playback group at Western’s London Dig-ital Center: Stephen Blick, John Byrne, Mike Byrne,Chris Godsave, Steven Grace, and Tony Leventis. SallyHumphreys, Jan Mitchell, and Vivian Millson helpedkey the text into the word processor.

I acknowledge with great appreciation the reviewwork done by Jon Claerbout, Sven Treitel, John Sher-wood, Fred Hilterman, and Greg Godkin. I also thankthe following individuals who participated in review-ing parts of the earlier drafts: Ron Chambers, Aftab

Alam, Bruce Cassell, Karl Millahn, Tony Kudrna, DaveBrown, Darko Tufekcic, Pete Bibby, John Ferguson,Mark Doyle, Wendell Wiggins, Jeff Resnick, Walt Lynn,Bill Dragoset, Mai Yang, Patrick Ng, Steve Cole, LarryScott, Ken Larner, and Helmut Jakubowicz. Special

thanks are due to Diane Parker, who did an outstanding job of editing for style, proofreading, and preparing thecamera-ready copy of the book. Thanks to Lynn Grif-fin for helping to bring the text up to the SEG stan-dards of publication. Special thanks also are due to myeditor, Steve Doherty, for his excellent and comprehen-sive review. I also appreciate his valuable recommenda-tions in revising the text and the help he provided inbringing clarity to the text. I extend my deepest andwholehearted appreciation to my wife, Hulya, for hereverlasting encouragement. And finally, thanks are dueto Western Geophysical Company of America for thesupport provided to me in writing this textbook.

¨ Oz Yilmaz

London, July, 1987.

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PREFACE

The first edition, entitled Seismic Data Processing , was

published in 1987 by the Society of Exploration Geo-

physicists. Thereafter, I began to work on the second

edition almost immediately. My objective was to cap-

ture continuously the new developments that were tak-ing place in the seismic industry. The second edition

is the culmination of this continuous update over the

past ten years. The updating process was based on ex-

haustive model- and real-data experiments with the re-

sults of the research and development work of my own

and many others. I have also drawn an extensive and

demonstrative set of real-data examples from the nu-

merous case studies that I conducted during the course

of the update. Another source of update was of course

the prolific literature on exploration seismology.

This second edition embodies the broad scope of

seismic data analysis — processing, inversion, and inter-

pretation of seismic data. I shall give a brief summary of

the most important new developments in seismic data

analysis during the past 15 years. To begin with, the

3-D seismic method took a centrally dominant position

in the exploration and development of oil and gas fields.

Algorithms for 3-D seismic data processing, including

3-D dip-moveout correction, 3-D refraction and residual

statics corrections, and 3-D migration have now become

an integral part of the applications library of the seis-

mic data processing systems in use today. Additionally,

noise attenuation based on prediction filtering is now

applied routinely to seismic data. Techniques for multi-

ple attenuation based on the Radon transform and waveextrapolation have been successfully demonstrated on

field data.

Shortly after 3-D migration, we also began to image

the subsurface before stacking. Efficient workflows for

3-D prestack time migration are in use today not only

to image the subsurface more accurately in the presence

of conflicting dips with different stacking velocities but

also to generate common-reflection-point gathers that

can be used to perform prestack amplitude inversion

and thus obtain attributes associated with amplitude

variations with offset. 3-D prestack time migration also

paves the way for estimating a 3-D rms velocity field

that can be used to perform Dix conversion and thus

obtain a 3-D interval velocity field.Concurrent with prestack imaging, we began to im-

age the subsurface also in depth to account for strong

lateral velocity variations. During the last decade, years

of effort in research and development conducted in pre-

vious decades have led to practical inversion methods

for earth modeling and imaging in depth. Using appro-

priate inversion methods, we derive a seismic represen-

tation of an earth model in depth, described by two sets

of parameters — layer velocities and reflector geome-

tries, for low-relief, complex, and complex overburden

structures. The power of 3-D visualization has given us

the ability to create an earth model in depth with the

accuracy needed to image in depth, and that within an

efficient work schedule. Additionally, the rapid growth

in computer power has enabled us to generate an earth

image in depth from 3-D prestack depth migration of

large data volumes, again within acceptable work sched-

ules.

To get the most out of the image volumes derived

from 3-D prestack time and depth migrations, we now

make extensive use of 3-D visualization in seismic in-

terpretation. Using a volume-based interpretation strat-

egy, not only do we pick time or depth horizons to de-

lineate the structural model of the subsurface, but we

also make use of the seismic amplitudes to infer thedepositional model of the subsurface.

The road ahead for exploration seismology includes

three main topics — 4-D seismic method, 4-C seismic

method, and anisotropy, all aimed at seismic character-

ization of oil and gas reservoirs and eventually moni-

toring their depletions. By recording 3-D seismic data

over the field that is being developed and produced at

appropriate time intervals, we may detect changes in

the reservoir conditions, such as fluid saturation and

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xxii Seismic Data Analysis

pore pressure. Such changes may be related to changes

in the seismic amplitudes from one 3-D survey to the

next. Time-lapse 3-D seismic monitoring of reservoirs

is referred to as the 4-D seismic method. The fourth

dimension represents the calendar time over which the

reservoir is being monitored. Potential applications of the 4-D seismic method include monitoring the spatial

extent of the steam front following in-situ combustion

or steam injection used for thermal recovery, monitoring

the spatial extent of the injected water front used for

secondary recovery, imaging bypassed oil, determining

flow properties of sealing or leaking faults, and detect-

ing changes in oil-water contact.

Some reservoirs can be identified and monitored

better by using shear-wave data. For instance, acoustic

impedance contrast at the top-reservoir boundary may

be too small to detect, whereas shear-wave impedance

contrast may be sufficiently large to detect. By record-

ing multicomponent data at the ocean bottom, P -waveand S -wave images can be derived. Commonly, four

data components are recorded — the pressure wave-field

and inline, crossline, and vertical components of par-

ticle velocity. Thus, the multicomponent seismic data

recording and analysis is often referred to as the 4-

C seismic method. Potential applications of the 4-C

seismic method include imaging beneath gas plumes,

salt domes, and basalts, delineating reservoir bound-

aries with a higher S -wave impedance contrast than

P -wave impedance contrast, differentiating sand from

shale, detection of fluid phase change from oil-bearing to

water-bearing sands, detection of vertical fracture orien-

tation, mapping hydrocarbon saturation, and mappingoil-water contact.

Until recently, exploration seismology at large has

been based on the assumption of an isotropic medium,

albeit we have been cognizant of anisotropic behavior

of reservoir rocks. Seismic anisotropy often is associated

with directional variations in velocities. For instance, in

a vertically fractured limestone reservoir, velocity in the

fracture direction is lower than velocity in the direction

perpendicular to the plane of fracturing, giving rise to

azimuthal anisotropy. Another directional variation of

velocities involves horizontal layering and fracturing of

rocks parallel to the layering. In this case, velocity in thehorizontal direction is higher than the vertical direction,

giving rise to transverse isotropy.

In addition to a continuing effort to improve the

existing 3-D time- and depth-domain applications, cur-

rent research and development in seismic data analysis

is focused on time- and depth-domain analysis of 4-D

and 4-C seismic data while accounting for anisotropy.

Topics in this book are organized to reflect the in-

creasing degree of complexity in the data analysis and

the progress made in exploration seismology. Volume

I is devoted to 2-D conventional processing based on

the three principle processes — deconvolution, stack-

ing, and migration. Volume I is devoted to topics be-

yond 2-D conventional processing — 3-D seismic explo-

ration, seismic inversion for earth modeling and imag-

ing in depth, 4-D seismic method, 4-C seismic method,and anisotropy. Each chapter is accompanied by an ap-

pendix that includes a mathematical treatise of selected

topics from the chapter itself. As such, practical aspects

of seismic data analysis are treated within the chapters

themselves without the burden of the theoretical details.

When used as a textbook in a university, I recom-

mend Volume I for a first-semester senior-level course

and Volume II for a second-semester senior-level course

or a first-year graduate course. Optionally, you may con-

sider an additional one-semester senior- or graduate-

level course on the applied theory of exploration seis-

mology based on primarily the appendixes.

If you are a seismic analyst using this book as areference, you can study the practical aspects of seis-

mic data analysis in relation to the projects you are

conducting to get helpful hints on the algorithms and

workflows. If you are a research geophysicist using this

book as a reference, you can study the practical aspects

of a specific application of interest to get helpful hints

on what assumptions can be made in relation to that

application. Also, you can study the appendixes to initi-

ate yourself into the basic theory on the subject of your

interest.

I have a passion for the seismic method that I have

maintained throughout my career. While the source of

this passion is indisputably my teacher and life-longfriend, Jon Claerbout, I have been very fortunate to

have worked with some of the most talented individu-

als who have fueled my enthusiasm for exploration seis-

mology. Most appropriately, I wish to express here my

heartful gratitudes to each of these individuals.

To begin with, I am deeply grateful to Steve Do-

herty, my technical editor and life-long friend, for his

incisive, meticulous, and prompt editing of this entire

work. Steve’s editing brought clarity and precision to

the text. He was also the editor of the first edition; on

that occasion and now, he gracefully shared the experi-

ence with me. Thank you, Steve, for your dedication andeffort. As part of the technical editing, I also received

great assistance from Zhiming Li, who edited Appen-

dices A through J, Joe Stefani who edited Appendix

L, and John Toldi who edited Chapter 11. I thank all

of you wholeheartedly for your careful editing of the

text, debugging the equations, and introducing clarity

to derivations.

Next, I wish to express my sincere gratitude to

Judy Hastings, my technical copy editor, for her im-

pressively consistent editing of the entire manuscript

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Preface xxiii

and her diligence in keeping me on schedule. Thank you,

Judy, also for your graceful handling of my frustrations

with the s and a s. I wish to extend my thanks to Ted

Bakamjian, Publications Manager of SEG, for his sup-

port and excellent coordination of the tasks involved in

the publication process.

Now I wish to extend my special thanks to Cyril

Gregory, Irfan Tanritanir, Ferudun Kilic, Orhan Yil-

maz, Fugen Zhou, Ma Xae Ling, and Huseyin Ozdemir,

who helped me with several of the case studies, and

model- and real-data experiments. Specifically, Cyril

helped me create the case studies for my 1996 SEG Dis-

tinguished Lecture Tour; these case studies are included

in Chapter 10. Cyril has been involved in many of the

projects over the past ten years associated with this

work. Irfan, Ferudun, and Fugen all worked with me on

several case studies which are also included in Chapter

10. Orhan did the processing of the 4-C data presented

in Chapter 11. I feel very fortunate to have had such

exceptionally talented individuals helping me to bear

the burden.

I wish to extend my special thanks to David Lum-

ley, 4th Wave Imaging, and Chevron for contributing

examples to the section on 4-D seismic method. I wish

to express my sincere appreciation to Moshe Reshef for

creating some of the synthetic data sets I used in my

experiments described in Chapters 3 and 8. Likewise, I

extend my sincere gratitude to Evgeny Landa for cre-

ating the synthetic data sets I used in my experiments

described in Chapter 9. Extending the list, I express my

thanks to Ed Crase, Chris Taylor, Dave Nichols, Du-

ane Dopkin, Gerald Kidd, Rob Bond, Cerys Biancardi,

Davud Babayev, and Lee Bell for providing examples

or helping me create them. I am sure that I am unableto recall many of the names associated with the update

going back ten years; I thank all of you most sincerely.

I am very grateful to Chevron, Mobil, Britannia,

Talisman, Husky Oil, BP-Amoco, Shell, AGIP, Total,

BHP, Gulf Canada, ONGC, Shengli Oil Field of CNPC,

Saudi Aramco, and many other companies who may or

may not have preferred to be anonymous for providing

field data that enabled me to conduct my experiments.

I wish to sincerely thank Damir Skerl and West-

ern Geophysical, Rutt Bridges and Landmark, Schlum-

berger Geco-Prakla, Walt Lynn and PGS, and espe-

cially Eldad Weiss and Paradigm Geophysical for their

most invaluable support and encouragement in myquest to complete this work.

And now the last word, but a special tribute to

my wife, Hulya, and my son, Esen. I am wholeheartedly

grateful to you both for your enduring love and support.

This work undoubtedly demanded sacrifice; and it was

definitely a sacrifice on your part. You demanded very

little of me, and you gave the whole of your love to me.

I shall cherish it all my life.

¨ Oz Yilmaz

London, May, 2000.

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