SEISMIC DATA ANALYSIS OZ YILMAZ
INTRODUCTION
Processingof Seismic Data, 4
Inversion of Seismic Data, 10
Interpretation 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, 28
Frequency Aliasing, 30
Phase Considerations, 34
Time-Domain Operations, 36
Convolution, 38
Crosscorrelation and Autocorrelation, 39
Vibroseis Correlation, 41
Frequency Filtering, 41
Practical Aspects of Frequency Filtering, 44
Bandwidth and Vertical Resolution, 46
Time-Variant Filtering, 48
1.2 The 2-D Fourier Transform, 48
Spatial Aliasing, 51
1.3 Worldwide Assortment of Shot Records, 67
Wave Types, 70
1.4 Gain Applications, 81
Geometric SpreadingCorrection, 81
Programmed Gain Control, 85
RMS Amplitude AGC, 85
Instantaneous AGC, 87
Relative Trace Balancing, 89
1.5 Basic Data Processing Sequence, 90
Preprocessing, 91
Deconvolution, 92
CMP Sorting, 93
Velocity Analysis, 93
Normal-Moveout Correction, 94
Multiple Attenuation, 94
Dip-Moveout Correction, 94
CMP Stacking, 95
Poststack Processing, 95
Migration, 95
Residual Statics Corrections, 122
Quality Control in Processing, 122
Parsimony in Processing, 124
Exercises, 150
Appendix A: A MathematicalReview of the Fourier Transform, 153
A.1 The 1-D Fourier Transform, 153
A.2 The z-Transform, 155
A.3 The 2-D Fourier Transform, 156
References, 156
Chapter 2 DECONVOLUTION
2.0 Introduction, 159
2.1 The Convolutional Model, 162
The Convolutional Model in the Time Domain, 167
The Convolutional Model in the Frequency Domain, 170
2.2 Inverse Filtering, 171
The Inverse of the Source Wavelet, 172
Least-Squares Inverse Filtering, 173
Minimum Phase, 175
2.3 Optimum Wiener Filters, 179
SpikingDeconvolution, 180
Prewhitening, 181
Wavelet Processingby ShapingFilters, 183
Predictive Deconvolution, 185
2.4 Predictive Deconvolution in Practice, 190
Operator Length, 190
Prediction Lag, 193
Percent Prewhitening, 203
Effect of Random Noise on Deconvolution, 207
Multiple Attenuation, 209
2.5 Field Data Examples, 211
Prestack Deconvolution, 213
Signature Deconvolution, 217
Vibroseis Deconvolution, 219
Poststack Deconvolution, 222
2.6 The Problem of Nonstationarity, 222
Time-Variant Deconvolution, 227
Time-Variant Spectral Whitening, 231
Frequency-Domain Deconvolution, 233
Inverse Q Filtering, 234
Deconvolution Strategies, 241
Exercises, 247
Appendix B: MathematicalFoundation of Deconvolution, 249
B.1 Synthetic Seismogram, 249
B.2 The Inverse of the Source Wavelet, 251
B.3 The Inverse Filter, 252
B.4 Frequency-Domain Deconvolution, 253
B.5 Optimum Wiener Filters, 255
B.6 SpikingDeconvolution, 258
B.7 Predictive Deconvolution, 260
B.8 Surface-Consistent Deconvolution, 262
B.9 Inverse Q Filtering, 266
References, 270
Chapter 3 VELOCITY ANALYSIS AND STATICS CORRECTIONS
3.0 Introduction, 271
3.1 NormalMoveout, 274
NMO for a Flat Reflector, 274
NMO in a Horizontally Stratified Earth, 280
Fourth-Order Moveout, 280
NMO Stretching, 283
NMO for a DippingReflector, 285
NMO for Several Layers with Arbitrary Dips, 287
Moveout Velocity versus StackingVelocity, 288
3.2 Velocity Analysis, 288
The Velocity Spectrum, 292
Measure of Coherency, 295
Factors AffectingVelocity Estimates, 302
Interactive Velocity Analysis, 311
Horizon Velocity Analysis, 312
Coherency Attribute Stacks, 318
3.3 ResidualStatics Corrections, 324
Residual Statics Estimation by Traveltime Decomposition, 336
Residual Statics Estimation by Stack-Power Maximization, 344
Traveltime Decomposition in Practice, 345
Maximum Allowable Shift, 346
Correlation Window, 361
Other Considerations, 362
Stack-Power Maximization in Practice, 365
3.4 Refraction Statics Corrections, 370
First Breaks, 374
Field Statics Corrections, 375
Flat Refractor, 375
DippingRefractor, 377
The Plus-Minus Method, 377
The Generalized Reciprocal Method, 379
The Least-Squares Method, 379
ProcessingSequence for Statics Corrections, 381
Model Experiments, 382
Field Data Examples, 395
Exercises, 432
Appendix C: Topics in Moveout and Statics Corrections, 437
C.1 The Shifted Hyperbola, 437
C.2 Moveout Stretch, 439
C.3 Equations for a DippingReflector, 441
C.4 Traveltime Decomposition for Residual Statics Estimation, 442
C.5 Depth Estimation from Refracted Arrivals, 444
C.6 Equations for a DippingRefractor, 445
C.7 The Plus-Minus Times, 447
C.8 Generalized Linear Inversion of Refracted Arrivals, 448
C.9 Refraction Traveltime Tomography, 453
C.10 L1-Norm Refraction Statics, 456
References, 460
Chapter 4 MIGRATION
4.0 Introduction, 463
ExplodingReflectors, 467
Migration Strategies, 470
Migration Algorithms, 471
Migration Parameters, 474
Aspects of Input data, 475
Migration Velocities, 475
4.1 Migration Principles, 476
Kirchhoff Migration, 481
Diffraction Summation, 484
Amplitude and Phase Factors, 485
Kirchhoff Summation, 485
Finite-Difference Migration, 486
Downward Continuation, 486
DifferencingSchemes, 488
Rational Approximations for Implicit Schemes, 489
Reverse Time Migration, 491
Frequency-Space Implicit Schemes, 492
Frequency-Space Explicit Schemes, 493
Frequency-Wavenumber Migration, 494
Phase-Shift Migration, 498
Stolt Migration, 500
Summary of Domains of Migration Algorithms, 501
4.2 Kirchhoff Migration in Practice, 502
Aperture Width, 502
Maximum Dip to Migrate, 509
Velocity Errors, 509
4.3 Finite-Difference Migration in Practice, 520
Depth Step Size, 521
Velocity Errors, 525
Cascaded Migration, 525
Reverse Time Migration, 530
4.4 Frequency-Space Migration in Practice, 530
Steep-Dip Implicit Methods, 535
Depth Step Size, 537
Velocity Errors, 544
Steep-Dip Explicit Methods, 549
Dip Limits of Extrapolation Filters, 549
Velocity Errors, 552
4.5 Frequency-Wavenumber Migration in Practice, 559
Maximum Dip to Migrate, 559
Depth Step Size, 566
Velocity Errors, 567
Stolt Stretch Factor, 572
Wraparound, 575
Residual Migration, 575
4.6 Further Aspects of Migration in Practice, 579
Migration and Spatial Aliasing, 581
Migration and Random Noise, 619
Migration and Line Length, 621
Migration from Topography, 626
Exercises, 626
Appendix D: MathematicalFoundation of Migration, 628
D.1 Wavefield Extrapolation and Migration, 628
D.2 Stationary Phase Approximations, 638
D.3 The Parabolic Approximation, 639
D.4 Frequency-Space Implicit Schemes, 641
D.5 Stable Explicit Extrapolation, 644
D.6 Optimum Depth Step, 646
D.7 Frequency-Wavenumber Migration, 649
D.8 Residual Migration, 651
References, 652
Chapter 5 DIP-MOVEOUT CORRECTION AND PRESTACK MIGRATION
5.0 Introduction, 655
Salt-Flank Reflections, 657
Fault-Plane Reflections, 657
DMO and StackingVelocities, 657
Turning-Wave Reflections, 665
5.1 Principles of Dip-Moveout Correction, 668
Prestack Partial Migration, 670
Frequency-Wavenumber DMO Correction, 672
Log-Stretch DMO Correction, 677
Integral DMO Correction, 679
Velocity Errors, 681
Variable Velocity, 684
Turning-Wave Migration, 685
5.2 Dip-Moveout Correction in Practice, 692
Salt Flanks, 692
Fault Planes, 693
DMO and Multiples, 705
DMO and Coherent Linear Noise, 716
Other Considerations, 716
Aspects of DMO Correction — A Summary, 722
5.3 Prestack Time Migration, 725
DMO Correction and Common-Offset Migration, 728
Salt Flanks, 729
Fault Planes, 742
Common-Reflection-Point versus Common-Reflection-Surface Stacking, 769
5.4 Migration Velocity Analysis, 775
Prestack Stolt Migration, 776
Common-Offset Migration of DMO-Corrected Data, 777
Prestack Kirchhoff Migration, 788
Velocity Analysis UsingCommon-Reflection-Point Gathers, 788
FocusingAnalysis, 798
Fowler’s Velocity-Independent Prestack Migration, 803
Exercises, 815
Appendix E: Topics in Dip-Moveout Correction and Prestack Time Migration, 817
E.1 Reflection Point Dispersal, 817
E.2 Equations for DMO Correction, 820
E.3 Log-Stretch DMO Correction, 823
E.4 The DMO Ellipse, 826
E.5 Nonzero-Offset Traveltime Equation, 827
E.6 Prestack Frequency-Wavenumber Migration, 831
E.7 Velocity Analysis by Wavefield Extrapolation, 833
References, 834
Chapter 6 NOISE AND MULTIPLE ATTENUATION
6.0 Introduction, 837
Coherent Linear Noise, 838
Treatment of Coherent Linear Noise by Conventional Processing, 840
Reverberations and Multiples, 843
Treatment of Reverberations and Multiples by Conventional Processing, 857
Spatially Random Noise, 876
6.1 Multiple Attenuation in the CMP Domain, 877
Periodicity of Multiples, 877
Velocity Discrimination Between Primaries and Multiples, 887
Karhunen-Loeve Transform, 887
Modelingof Multiples, 896
6.2 Frequency-Wavenumber Filtering, 898
Random Noise and Frequency-Wavenumber Filtering, 904
Statics Corrections and Frequency-Wavenumber Filtering, 905
Dip Filteringof Coherent Linear Noise, 905
Frequency-Wavenumber Multiple Attenuation, 907
6.3 The Slant-Stack Transform, 920
Physical Aspects of Slant Stacking, 920
Slant-Stack Transformation, 923
Practical Aspects of Slant Stacking, 924
Slant-Stack Parameters, 928
Time-Variant Dip Filtering, 931
Slant-Stack Multiple Attenuation, 932
6.4 The Radon Transform, 938
Velocity-Stack Transformation, 942
The Discrete Radon Transform, 943
The Parabolic Radon Transform, 944
Practical Considerations, 945
Impulse Response of the Velocity-Stack Operator, 948
Field Data Examples, 948
Radon-Transform Multiple Attenuation, 953
6.5 Linear Uncorrelated Noise Attenuation, 960
Design of Spatial Prediction Filters, 966
Field Data Examples, 966
Exercises, 976
Appendix F: Multichannel Filtering Techniques for Noise and Multiple Attenuation, 977
F.1 Analysis of Guided Waves, 977
F.2 Wavefield Extrapolation in the τ − p Domain, 980
F.3 Mathematical Foundation of the Discrete Radon Transform, 982
F.4 Free-Surface Multiple Attenuation, 989
F.5 Water-Bottom Multiple Attenuation, 992
F.6 Spatial Prediction Filter, 995
References, 998
Chapter 7 3-D SEISMIC EXPLORATION
7.0 Introduction, 1001
The Need for Imaging in Three Dimensions, 1003
7.1 3-D Survey Design and Acquisition, 1010
Migration Aperture, 1010
Spatial Sampling, 1017
Other Considerations, 1018
Marine Acquisition Geometry, 1018
Cable Feathering, 1019
3-D Binning, 1019
Crossline Smearing, 1020
Strike versus Dip Shooting, 1027
Land Acquisition Geometry, 1028
7.2 Processing of 3-D Seismic Data, 1030
3-D Refraction Statics Corrections, 1036
Azimuth Dependence of Moveout Velocities, 1036
3-D Dip-Moveout Correction, 1046
Inversion to Zero Offset, 1048
Aspects of 3-D DMO Correction — A Summary, 1050
Velocity Analysis, 1050
3-D Residual Statics Corrections, 1050
3-D Migration, 1051
Trace Interpolation, 1065
7.3 3-D Poststack Migration, 1073
Separation versus Splitting, 1073
Impulse Response of the One-Pass Implicit Finite-Difference 3-D Migration, 1074
Two-Pass versus One-Pass Implicit Finite-Difference 3-D Migration in Practice, 1076
Explicit Schemes Combined with the McClellan Transform, 1082
The 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, 1112
Crossline Migration, 1129
3-D Migration Velocity Analysis, 1131
Aspects of 3-D Prestack Time Migration — A Summary, 1137
7.5 Interpretation of 3-D Seismic Data, 1156
Time Slices, 1156
3-D Visualization, 1156
Removal of Opacity, 1158
Seed Detection, 1159
Structural Interpretation, 1161
Stratigraphic Interpretation, 1171
Exercises, 1195
Appendix G: MathematicalFoundation of 3-D Migration, 1198
G.1 Implicit Methods, 1198
G.2 Explicit Methods, 1200
G.3 3-D Phase-Shift Migration, 1203
G.4 3-D Stolt Migration, 1204
G.5 Trace Interpolation, 1204
G.6 3-D Nonzero-Offset Traveltime Equation, 1208
References, 1209
Chapter 8 EARTH IMAGING IN DEPTH
8.0 Introduction, 1213
Lateral Velocity Variations, 1222
8.1 Layer Replacement, 1226
Wave-Equation Datuming, 1229
Poststack Layer Replacement, 1230
Prestack Layer Replacement, 1231
Field Data Example, 1237
8.2 2-D Poststack Depth Migration, 1238
Image Rays and Lateral Velocity Variations, 1238
Time versus Depth Migration, 1244
Iterative Depth Migration, 1247
Iteration with Zero-Offset Data, 1250
Iteration with CMP-Stacked Data, 1258
Iteration with Prestack Data, 1265
Iteration in Practice, 1265
8.3 2-D Prestack Depth Migration, 1273
Shot-Geophone Migration, 1274
Shot-Profile Migration, 1280
Sensitivity of Image Accuracy to Velocity Errors, 1280
Field Data Examples, 1295
8.4 3-D Poststack Depth Migration, 1304
3-D Poststack Time versus Depth Migration, 1304
Two-Pass versus One-Pass 3-D Poststack Depth Migration, 1313
Implicit versus Explicit 3-D Poststack Depth Migration, 1314
3-D Poststack Datuming, 1321
8.5 3-D Prestack Depth Migration, 1321
Kirchhoff Summation, 1324
Calculation of Traveltimes, 1324
The Eikonal Equation, 1325
Fermat’s Principle, 1331
Summation Strategies, 1331
Migration Aperture, 1333
Operator Antialiasing, 1333
3-D Common-Offset Depth Migration, 1335
Exercises, 1342
Appendix H: Diffraction and Ray Theory for Wave Propagation, 1342
H.1 The Kirchhoff Integral, 1342
H.2 The Eikonal Equation, 1346
H.3 Finite-Difference Solution to the Eikonal Equation, 1349
References, 1351
Chapter 9 EARTH MODELING IN DEPTH
9.0 Introduction, 1353
Inversion Methods for Data Modeling, 1355
Inversion Procedures for Earth Modeling, 1356
Velocity-Depth Ambiguity, 1357
Model Representation and Visualization, 1360
9.1 Models with Horizontal Layers, 1365
Dix Conversion, 1365
Coherency Inversion, 1369
Near-Surface Layer with Laterally VaryingVelocities, 1382
9.2 Modelwith Low-Relief Structure, 1387
StackingVelocity Inversion, 1392
Coherency Inversion, 1404
Velocity Resolution, 1404
9.3 Modelwith Complex Overburden Structure, 1404
Image-Gathers, 1406
Constant Half-Space Velocity Analysis, 1415
9.4 ModelBuilding, 1415
Time-to-Depth Conversion, 1416
Time Structure Maps, 1416
Interval Velocity Maps, 1417
Depth Structure Maps, 1425
Calibration to Well Tops, 1426
Layer-by-Layer Inversion, 1433
Structure-Independent Inversion, 1450
9.5 ModelUpdating, 1450
Residual Moveout Analysis, 1462
Reflection Traveltime Tomography, 1469
Limitations in Resolving Velocity-Depth Ambiguity by Tomography, 1479
Turning-Ray Tomography, 1512
Exercises, 1524
Appendix J: Data Modeling by Inversion, 1525
J.1 The Generalized Linear Inversion, 1525
J.2 The GLI Formalism of Deconvolution, 1526
J.3 Applications of the GLI Technique, 1530
J.4 Dix Conversion, 1534
J.5 Map Processing, 1539
J.6 Reflection Traveltime Tomography, 1545
J.7 Threshold for Velocity-Depth Ambiguity, 1553
References, 1554
Chapter 10 STRUCTURAL INVERSION
10.0 Introduction, 1557
10.1 Subsalt Imaging in the North Sea, 1558
Estimation of the Overburden Model, 1562
Estimation of the Substratum Model, 1562
Model Verification, 1563
10.2 Subsalt Imaging in the Gulf of Mexico, 1574
Layered Earth Model Estimation, 1574
Sructure-Independent Model Estimation, 1577
10.3 Imaging Beneath Irregular Water Bottom in the Northwest Shelf of Australia, 1597
Earth Modelingand Imagingin Depth, 1597
10.4 Imaging Beneath Volcanics in the West of Shetlands of the Atlantic Margin, 1597
Earth Modelingand Imagingin Depth, 1607
10.5 Imaging Beneath Shallow Gas Anomalies in the Gulf of Thailand, 1620
Earth Modelingand Imagingin Depth, 1620
10.6 3-D StructuralInversion Applied to Seismic Data from the Southern North Sea, 1626
Estimation of the Overburden Model, 1626
Model Representation by Tessellation, 1630
3-D Coherency Inversion, 1630
3-D Poststack Depth Migration, 1637
Estimation of the Substratum Model, 1638
10.7 3-D StructuralInversion Applied to Seismic Data from the CentralNorth Sea, 1651
3-D Coherency Inversion Combined with 3-D Poststack Depth Migration, 1665
3-D StackingVelocity Inversion Combined with 3-D Image-Ray Depth Conversion, 1674
10.8 3-D StructuralInversion Applied to Seismic Data from Offshore Indonesia, 1674
Model Building, 1678
Model Updating, 1678
Imaging in Depth, 1690
Volume-Based Interpretation, 1690
10.9 3-D StructuralInversion Applied to Seismic Data from the Northeast China, 1703
3-D DMO Processing, 1720
3-D Prestack Time Migration, 1720
From RMS to Interval Velocities, 1742
Structural Inversion, 1742
Structural and Stratigraphic Interpretation, 1744
Exercises, 1778
Appendix K: Seismic Modeling, 1779
K.1 Zero-Offset Traveltime Modeling, 1779
K.2 Zero-Offset Wavefield Modeling, 1781
K.3 Nonzero-Offset Wavefield Modeling, 1781
K.4 Elastic Wavefield Modeling, 1790
References, 1792
Chapter 11 RESERVOIR GEOPHYSICS
11.0 Introduction, 1793
Elastic Waves and Rock Properties, 1794
11.1 Seismic Resolution, 1801
Vertical Resolution, 1801
Lateral Resolution, 1803
Reflection and Refraction, 1808
Reflector Curvature, 1813
AVO Equations, 1816
ProcessingSequence for AVO Analysis, 1839
Derivation of AVO Attributes by Prestack Amplitude Inversion, 1851
Interpretation of AVO Attributes, 1862
3-D AVO Analysis, 1863
11.2 Analysis of Amplitude Variation with Offset, 1807
11.3 Acoustic Impedance Estimation, 1863
Synthetic Sonic Logs, 1864
ProcessingSequence for Acoustic Impedance Estimation, 1865
Derivation of Acoustic Impedance Attribute, 1866
3-D Acoustic Impedance Estimation, 1872
Instantaneous Attributes, 1896
11.4 VerticalSeismic Profiling, 1907
VSP Acquisition Geometry, 1907
Processingof VSP Data, 1907
VSP-CDP Transform, 1908
11.5 4-D Seismic Method, 1911
Processingof 4-D Seismic Data, 1912
Seismic Reservoir Monitoring, 1913
11.6 4-C Seismic Method, 1915
Recordingof 4-C Seismic Data, 1919
Gaiser’s CouplingAnalysis of Geophone Data, 1922
Processingof PP Data, 1926
Rotation of Horizontal Geophone Components, 1926
Common-Conversion-Point Binning, 1933
Velocity Analysis of PS Data, 1946
Dip-Moveout Correction of PS Data, 1959
Migration of PS Data, 1961
11.7 Seismic Anisotropy, 1961
Anisotropic Velocity Analysis, 1965
Anisotropic Dip-Moveout Correction, 1968
Anisotropic Migration, 1980
Effect of Anisotropy on AVO, 1998
Shear-Wave Splittingin Anisotropic Media, 1999
Appendix L: MathematicalFoundation of Elastic Wave Propagation, 2001
L.1 Stress-Strain Relation, 2001
L.2 Elastic Wave Equation, 2007
L.3 Seismic Wave Types — Body Waves and Surface Waves, 2008
L.4 Wave Propagation Phenomena — Diffraction, Reflection, and Refraction, 2012
L.5 The Zoeppritz Equations, 2014
L.6 Prestack Amplitude Inversion, 2019
References, 2024