Preface and acknowledgments |
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ix | |
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1 Introduction -- modeling, migration, imaging, and inversion |
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1 | (10) |
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1.1 Seismic data contains information |
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1 | (1) |
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1.2 Models for propagation and reflection |
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1 | (2) |
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1.3 Going forward to go back |
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3 | (1) |
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1.4 Seismic and non-seismic imaging |
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3 | (1) |
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1.5 Motivation for migration |
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4 | (2) |
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1.6 Time and depth migration |
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6 | (1) |
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6 | (2) |
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1.8 Full-wave and asymptotic migration |
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8 | (1) |
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1.9 Seismic migration and inversion |
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9 | (1) |
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1.10 True amplitude migration |
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9 | (1) |
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1.11 Linear and nonlinear processes |
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10 | (1) |
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2 Basic migration concepts |
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11 | (51) |
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16 | (1) |
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2.2 Ray-theoretical migration concepts |
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16 | (9) |
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2.3 Downward continuation |
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25 | (8) |
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2.4 Reverse time migration |
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33 | (4) |
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2.5 Claerbout one-way difference-equation migration |
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37 | (7) |
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2.6 Frequency-wavenumber migration methods |
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44 | (8) |
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52 | (3) |
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55 | (5) |
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60 | (2) |
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60 | (2) |
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62 | (28) |
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3.1 Prestack migration concepts |
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62 | (1) |
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3.2 Prestack f-k migration in two dimensions |
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63 | (10) |
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3.3 Prestack slant-stack migration in 2.5 dimensions |
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73 | (2) |
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3.4 Prestack ray-theoretical migration |
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75 | (5) |
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3.5 Prestack f-k migration in three dimensions |
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80 | (6) |
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3.6 Prestack reverse-time migration |
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86 | (4) |
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89 | (1) |
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90 | (32) |
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4.1 Perfect and imperfect migrations |
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90 | (1) |
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4.2 Effects of finite bandwidth |
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90 | (12) |
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4.3 Space-domain image amplitude renormalization |
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102 | (1) |
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4.4 Effects of spatial sampling |
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102 | (1) |
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4.5 Effects of maximum dip |
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103 | (1) |
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4.6 Effects of finite spatial aperture |
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103 | (10) |
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4.7 Extra and missing data |
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113 | (1) |
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4.8 Effects of a finite time window |
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114 | (4) |
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4.9 Undermigration and overmigration |
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118 | (4) |
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121 | (1) |
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5 Models for wave propagation and reflection |
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122 | (13) |
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122 | (1) |
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123 | (5) |
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128 | (3) |
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5.4 A scattering-theory model for reflection data |
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131 | (4) |
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134 | (1) |
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135 | (20) |
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6.1 The general Green's function |
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135 | (2) |
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6.2 The scalar Green's function |
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137 | (3) |
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6.3 The acoustic Green's function |
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140 | (2) |
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6.4 The elastic Green's function |
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142 | (2) |
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144 | (1) |
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6.6 Multipath Green's functions |
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145 | (1) |
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6.7 Green's functions in a layered medium |
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146 | (9) |
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154 | (1) |
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7 The scattering potential |
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155 | (19) |
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7.1 The scattering potential as a function of angle |
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155 | (2) |
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7.2 The scalar scattering potential |
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157 | (1) |
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7.3 The acoustic scattering potential |
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158 | (1) |
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7.4 The elastic scattering potential |
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159 | (12) |
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171 | (3) |
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172 | (2) |
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174 | (16) |
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174 | (2) |
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8.2 A scalar reflectivity function |
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176 | (3) |
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8.3 An acoustic reflectivity function |
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179 | (2) |
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8.4 Elastic reflectivity functions |
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181 | (5) |
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8.5 A general formula relating scattering potential and reflectivity |
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186 | (1) |
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8.6 Summary of linearized reflectivity functions |
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187 | (3) |
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189 | (1) |
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9 Synthesizing reflection data |
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190 | (33) |
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9.1 The Born model for seismic reflections |
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190 | (1) |
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9.2 A constant background |
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190 | (7) |
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197 | (10) |
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9.4 A depth-variable background |
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207 | (5) |
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9.5 A generally variable background |
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212 | (7) |
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219 | (4) |
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222 | (1) |
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10 Frequency-wavenumber migration |
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223 | (26) |
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10.1 Full constant-velocity migration |
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223 | (6) |
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10.2 Partial f-k migration |
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229 | (4) |
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10.3 Residual f-k migration |
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233 | (3) |
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10.4 Migration in a depth-variable medium |
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236 | (13) |
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248 | (1) |
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11 Asymptotic modeling and migration |
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249 | (22) |
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11.1 Migration and modeling as mapping |
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249 | (1) |
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11.2 Traveltime and depth functions |
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250 | (2) |
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11.3 Single-valued modeling and migration |
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252 | (3) |
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11.4 Relating the forward and inverse mappings |
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255 | (3) |
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11.5 Constant-angle migration |
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258 | (5) |
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263 | (8) |
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270 | (1) |
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12 Residual asymptotic migration |
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271 | (7) |
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12.1 Combining modeling and migration |
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271 | (5) |
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276 | (2) |
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277 | (1) |
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13 Asymptotic data mapping and continuation |
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278 | (11) |
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13.1 Combining forward and inverse migration |
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278 | (2) |
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13.2 Constant-velocity depth extrapolation in 2-D |
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280 | (5) |
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285 | (4) |
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287 | (2) |
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14 Least-squares asymptotic migration |
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289 | (17) |
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14.1 Direct versus least-squares inversion |
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289 | (1) |
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290 | (1) |
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14.3 The asymptotic modeling operator in three and two dimensions |
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291 | (1) |
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14.4 Least-squares migration in 2.5-D |
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292 | (5) |
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14.5 Three-dimensional common-angle least-squares migration |
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297 | (9) |
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305 | (1) |
Appendix A Conventions and glossary of terms |
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306 | (5) |
Appendix B Coordinates, vectors, and identities |
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311 | (5) |
Appendix C Fourier and Radon transforms |
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316 | (8) |
Appendix D Surface and pointwise reflectivity |
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324 | (3) |
Appendix E Useful filters |
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327 | (26) |
Appendix F The phase integral and the stationary phase approximation |
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353 | (13) |
Appendix G The diffraction integral |
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366 | (19) |
Appendix H Wave-based, ray-based, and reflector-based coordinates |
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385 | (12) |
References |
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397 | (4) |
Index |
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401 | |