Seismic Imaging and Inversion: Volume 1

Application of Linear Inverse Theory

By: Arthur B. Weglein, Robert H. Stolt

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Hardcover | 9 February 2012

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418 Pages

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Extracting information from seismic data requires knowledge of seismic wave propagation and reflection. The commonly used method involves solving linearly for a reflectivity at every point within the Earth, but this book follows an alternative approach which invokes inverse scattering theory. By developing the theory of seismic imaging from basic principles, the authors relate the different models of seismic propagation, reflection and imaging - thus providing links to reflectivity-based imaging on the one hand and to nonlinear seismic inversion on the other. The comprehensive and physically complete linear imaging foundation developed presents new results at the leading edge of seismic processing for target location and identification. This book serves as a fundamental guide to seismic imaging principles and algorithms and their foundation in inverse scattering theory, and is a valuable resource for working geoscientists, scientific programmers and theoretical physicists.

Industry Reviews

'... suitable for use as a textbook for a graduate-level geophysics course ...' Michael McCormack, The Leading Edge

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Preface and acknowledgments	p. ix
Introduction - modeling, migration, imaging, and inversion	p. 1
Seismic data contains information	p. 1
Models for propagation and reflection	p. 1
Going forward to go back	p. 3
Seismic and non-seismic imaging	p. 3
Motivation for migration	p. 4
Time and depth migration	p. 6
Migration velocity	p. 6
Full-wave and asymptotic migration	p. 8
Seismic migration and inversion	p. 9
True amplitude migration	p. 9
Linear and nonlinear processes	p. 10
Basic migration concepts	p. 11
Migration as a map	p. 11
Ray-theoretical migration concepts	p. 16
Downward continuation	p. 25
Reverse time migration	p. 33
Claerbout one-way difference-equation migration	p. 37
Frequency-wavenumber migration methods	p. 44
Other methods	p. 52
Time migration	p. 55
Summary	p. 60
Exercises	p. 60
Prestack migration	p. 62
Prestack migration concepts	p. 62
Prestack f-k migration in two dimensions	p. 63
Prestack slant-stack migration in 2.5 dimensions	p. 73
Prestack ray-theoretical migration	p. 75
Prestack f-k migration in three dimensions	p. 80
Prestack reverse-time migration	p. 86
Exercises	p. 89
Migration limitations	p. 90
Perfect and imperfect migrations	p. 90
Effects of finite bandwidth	p. 90
Space-domain image amplitude renormalization	p. 102
Effects of spatial sampling	p. 102
Effects of maximum dip	p. 103
Effects of finite spatial aperture	p. 103
Extra and missing data	p. 113
Effects of a finite time window	p. 114
Undermigration and overmigration	p. 118
Exercises	p. 121
Models for wave propagation and reflection	p. 122
The need for models	p. 122
Wave equations	p. 123
Building reflections	p. 128
A scattering-theory model for reflection data	p. 131
Exercises	p. 134
Green's functions	p. 135
The general Green's function	p. 135
The scalar Green's function	p. 137
The acoustic Green's function	p. 140
The elastic Green's function	p. 142
Local wavenumbers	p. 144
Multipath Green's functions	p. 145
Green's functions in a layered medium	p. 146
Exercises	p. 154
The scattering potential	p. 155
The scattering potential as a function of angle	p. 155
The scalar scattering potential	p. 157
The acoustic scattering potential	p. 158
The elastic scattering potential	p. 159
Summary	p. 171
Exercises	p. 172
Reflectivity	p. 174
Point reflectivity	p. 174
A scalar reflectivity function	p. 176
An acoustic reflectivity function	p. 179
Elastic reflectivity functions	p. 181
A general formula relating scattering potential and reflectivity	p. 186
Summary of linearized reflectivity functions	p. 187
Exercises	p. 189
Synthesizing reflection data	p. 190
The Born model for seismic reflections	p. 190
A constant background	p. 190
Restricted data sets	p. 197
A depth-variable background	p. 207
A generally variable background	p. 212
Summary	p. 219
Exercises	p. 222
Frequency-wavenumber migration	p. 223
Full constant-velocity migration	p. 223
Partial f-k migration	p. 229
Residual f-k migration	p. 233
Migration in a depth-variable medium	p. 236
Exercises	p. 248
Asymptotic modeling and migration	p. 249
Migration and modeling as mapping	p. 249
Traveltime and depth functions	p. 250
Single-valued modeling and migration	p. 252
Relating the forward and inverse mappings	p. 255
Constant-angle migration	p. 258
Special cases	p. 263
Exercises	p. 270
Residual asymptotic migration	p. 271
Combining modeling and migration	p. 271
Transition zones	p. 276
Exercises	p. 277
Asymptotic data mapping and continuation	p. 278
Combining forward and inverse migration	p. 278
Constant-velocity depth extrapolation in 2-D	p. 280
MZO and DMO	p. 285
Exercises	p. 287
Least-squares asymptotic migration	p. 289
Direct versus least-squares inversion	p. 289
Multipathing	p. 290
The asymptotic modeling operator in three and two dimensions	p. 291
Least-squares migration in 2.5-D	p. 292
Three-dimensional common-angle least-squares migration	p. 297
Exercises	p. 305
Conventions and glossary of terms	p. 306
Coordinates, vectors, and identities	p. 311
Fourier and Radon transforms	p. 316
Surface and pointwise reflectivity	p. 324
Useful filters	p. 327
The phase integral and the stationary phase approximation	p. 353
The diffraction integral	p. 366
Wave-based, ray-based, and reflector-based coordinates	p. 385
References	p. 397
Index	p. 401
Table of Contents provided by Ingram. All Rights Reserved.

Seismic Imaging and Inversion: Volume 1

Application of Linear Inverse Theory

At a Glance

Hardcover

Industry Reviews

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