Seismic Interferometry

Gerard Thomas Schuster0521871247, 9780521871242, 9780511540912

Seismic interferometry is an exciting new field in geophysics utilizing multiple scattering events to provide unprecedented views of the Earth’s subsurface. This is the first book to describe the theory and practice of seismic interferometry with an emphasis on applications in exploration seismology. Exercises are provided at the end of each chapter, and the text is supplemented by online MATLAB codes that illustrate important ideas and allow readers to generate synthetic traces and invert these to determine the Earth’s reflectivity structure. Later chapters reinforce these principles by deriving the rigorous mathematics of seismic interferometry. Incorporating examples that apply interferometric imaging to synthetic and field data, from applied geophysics and earthquake seismology, this book is a valuable reference for academic researchers and oil industry professionals. It can also be used to teach a one-semester course for advanced students in geophysics and petroleum engineering.

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Table of contents :
Cover……Page 1
Half-title……Page 3
Title……Page 5
Copyright……Page 6
Contents……Page 7
Preface……Page 11
Acknowledgments……Page 12
1.1 Seismic interferometry……Page 15
1.1.1 Multidimensional seismic interferometry……Page 23
1.1.2 Generalization of seismic interferometry……Page 25
1.2 Benefits and liabilities……Page 26
1.3 Historical development of seismic interferometry……Page 29
1.4 Organization of the book……Page 32
1.5 Exercises……Page 33
1.6 Appendix 1: Basics of exploration seismology……Page 37
Seismic processing……Page 39
Key problem with migration images……Page 40
1.7 Appendix 2: Fourier identities……Page 41
1.8 Appendix 3: Glossary……Page 42
1.9 Appendix 4: MATLAB codes……Page 43
2 Reciprocity equations of convolution and correlation types……Page 44
2.1 Green’s functions……Page 45
2.2 Reciprocity equation of convolution type……Page 46
Born forward modeling……Page 48
2.3 Reciprocity equation of correlation type……Page 50
2.3.1 Far-field approximation……Page 52
2.4 Stationary phase integration……Page 54
2.5 Seismic migration……Page 58
2.7 Summary……Page 63
2.8 Exercises……Page 64
2.9 Appendix 1: Causal and acausal Green’s functions……Page 67
2.10 Appendix 2: Principal value contribution of dipoles……Page 68
2.11 Appendix 3: Sommerfeld radiation conditions……Page 70
2.12 Appendix 4: Adjoint operator……Page 71
2.13.1 Loudspeakers and forward light cones……Page 72
2.13.2 Loudspeakers, sinks, and backward light cones……Page 73
2.14 Appendix 6: MATLAB codes……Page 74
3.1 Introduction……Page 75
3.2 VSP………Page 76
3.3 Stationary phase analysis……Page 77
3.3.1 Stationary phase contributions……Page 79
3.3.2 Stationary phase contribution of R………Page 80
3.4 Benefits……Page 81
3.5 Liabilities……Page 84
3.6 Numerical implementation……Page 86
3.6.1 Computation of the reciprocity equation by finite differences……Page 87
3.7.1 Synthetic example……Page 89
3.8 Summary……Page 91
3.9 Exercises……Page 93
3.11 Appendix 2: Interferometric imaging = RTM……Page 94
3.12 Appendix 3: Source wavefield deconvolution……Page 96
3.13 Appendix 4: 3D reciprocity equation by quadrature……Page 97
4.1 VSP………Page 100
4.1.1 Transforming VSP multiples into SSP primaries……Page 103
4.2.1 Benefits……Page 107
4.2.2 Limitations……Page 108
4.3.1 Partial cure for truncation artifacts……Page 109
4.3.2 Quantifying illumination region……Page 110
4.4 Numerical examples……Page 112
4.5 Summary……Page 119
4.6 Exercises……Page 120
4.7 Appendix 1: Computer codes……Page 122
5.1 Introduction……Page 123
5.2 VSP………Page 124
5.2.1 Practical implementation of redatuming……Page 125
5.3 Transforming VSP traveltimes into SSP traveltimes……Page 127
5.4 Numerical results……Page 128
5.4.1 Synthetic traveltime redatuming……Page 129
5.4.2 Synthetic waveform redatuming……Page 130
5.4.3 Field data waveform redatuming……Page 131
5.6 Exercises……Page 134
5.7 Appendix 1: MATLAB codes……Page 137
6 SSP………Page 138
6.1 Transforming SSP multiples into SSP primaries……Page 139
6.2 Benefits……Page 142
6.3 Interferometric interpolation of seismic data……Page 145
6.4 Numerical examples……Page 146
6.4.2 Interpolation of shot gathers in field data……Page 147
6.4.3 Imaging primaries and free-surface multiples……Page 149
6.4.4 Retrieving the source wavelet from SSP data……Page 151
6.4.5 Prediction and least squares subtraction of surface waves……Page 152
6.4.6 2D deconvolution of downgoing multiples……Page 155
6.5 Summary……Page 157
6.6 Exercises……Page 158
6.7 Appendix 1: Computer codes……Page 159
6.8 Appendix 2: Surface wave prediction by the SSP………Page 160
7.1 VSP………Page 161
7.2 VSP………Page 164
7.3 Interpolation and extrapolation of VSP and OBS data……Page 166
7.4 Numerical results……Page 170
7.4.2 OBS tests……Page 171
7.5 Summary……Page 174
7.7 Appendix 1: Computer codes……Page 175
8.1 SSP………Page 176
8.2 SSP………Page 178
8.3 Natural Green’s functions……Page 179
8.4 Numerical examples……Page 180
8.4.1 SSP………Page 181
8.4.2 SSP………Page 183
8.4.3 Redatuming SSP data with pseudo-VSP traces……Page 185
8.4.4 Migration with VSP Green’s functions……Page 187
8.5 Summary……Page 188
8.6 Exercises……Page 190
9.1 Introduction……Page 191
9.2 Theory……Page 192
9.2.2 SSP………Page 194
9.2.3 VSP………Page 196
9.3.1 SSP………Page 198
9.5 Exercises……Page 201
10 Stochastic interferometry……Page 203
10.1.1 Random source distributions……Page 204
10.1.2 Random scatterers……Page 206
Reflectivity from random sources……Page 208
Reflectivity from microtremors in a desert region……Page 210
Reflectivity from drill-bit sources……Page 212
Reflectivity from UPRC drill-bit source……Page 213
Shear-velocity distribution from earthquake correlograms……Page 215
10.3 Summary……Page 218
10.4 Exercises……Page 219
10.5 Appendix 1: Processing steps for drill-bit data……Page 222
10.6 Appendix 2: MATLAB codes……Page 224
11.1 Source imaging condition……Page 225
Numerical results……Page 227
11.2 Summation imaging condition……Page 229
Locating trapped miners with a natural Green’s function……Page 232
11.3.1 Super-resolution……Page 235
11.3.2 Super-stacking……Page 239
11.4 Summation imaging condition and correlated traces……Page 240
11.5 Summary……Page 241
11.6 Exercises……Page 242
12.1 Introduction……Page 243
12.2 Theory……Page 248
12.2.1 Earthquake waveform redatuming equations……Page 249
12.2.2 Source aliasing……Page 251
12.2.4 Imaging SmS reflections……Page 252
12.3.1 Synthetic earthquake data……Page 256
12.3.2 Earthquake data example……Page 259
12.5 Exercises……Page 262
References……Page 264
Index……Page 273