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Chapter 1 3D Data Geometries ................ ........................ ............... .1 Introduction....................................................................1 Data coordinates .................. .. ..................................... 1 Marine data geometries........................................................... .2 Land-data geometries ..... ................... . ............................... .5 Narrow-azimuth versus wide-azimuth geometries ... . . . .. . . . ......... . . . . . . . . . .... . . . . 6 Sorting and binning..............................................................7 References............................. ... ..... ...... ....................... 8 Chapter 2 Full Prestack Migration Using Kirchhoff's Methods ................................. 9 Introduction...................................... .............. .... .. ...........9 Constant-velocity migration ...................... ................................. 9 Migration in complex media...................................................... 12 Computational cost of prestack migration .................... .................... 16 References.................... ................. . ..... ....................... 17 Chapter 3 Approximations of Full Prestack Migration........................................... 19 Introduction................................... ...........................19 Normal moveout ................ .. .... ....... ..................... ......19 Dip moveout ................... .............. ........................... 22 Azimuth moveout ..............................................................25 Two-pass 3D prestack migration....... ......... ..................................32 References..................................... ...........................38 Chapter 4 Principles of Wavefield-continuation Migration ........... .................. . . . . . . . . . . . . 39 Introduction......................................................... ......... .39 Reverse-time migration...........................................................41 Downward-continuation migration................... ...................... ... . 43 References. ................. .................................................50 Chapter 5 Downward-continuation Methods................................................. 51 Introduction............................................. ......................51 Frequency-wavenumber domain (o-k) methods. ................ ................. .51 Mixed frequency-wavenumber/space (ci-k/ o-x) methods................. ........... 51 Frequency-space (w-x) methods................ ..............................60 References....................................................................64 Chapter 6 Common-image Gathers ........................................... ........ ...... 65 Introduction. ....................................... ...... ..................... 65 Common-image gathers by Kirchhoff migration ...................................... 65 Angle-domain common-image gathers by wavefield continuation ........................ 72 References..................................... .... .......................81 Chapter 7 Efficient Wavefield-continuation Methods for Prestack Migration ................. ...... 83 Introduction ...................................................................83 Migration of synthesized generalized-source gathers. ........ . ...... ............ . . . 84 Source-receiver migration in midpoint-offset coordinates ................ . . . . . . . . . . . . . . . 88 References.................................... ..................... ...................... 102 Chapter 8 Imaging and Aliasing ................. ................................ . .... 103 Introduction ..................................... .. . ..........................103 Aliasing fundamentals .................... ... .......................... 103 Aliasing in Kirchhoff migration ....................... ..................... 105 Aliasing in wavefield-continuation migration. ................... . . . . .... . . . . . . . . 115 References ........................ ........................................... 121 Chapter 9 Imaging and Partial Subsurface Illumination ......... ...................... . .... 123 Introduction.................... ..............................................123 Equalization of imaging operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Filling illumination gaps by model regularization and preconditioning.................... 131 Regularized inversion of prestack migration ........................................137 References ................................................................... 140 Chapter 10 Principles of Velocity Analysis ......................... ... .............. ........ 143 Introduction........................ ..................... ............... 143 Flat reflectors in V,,ms (r) media .................................. ........... 144 Dipping reflectors in Vrms (T) media............................ ............. 145 Dipping reflectors in smooth Vrms (r, x, y) media ..................................... 147 Traveltime reflection tomography.................... .......... .............. 149 References................ ................... ......................... 157 Chapter 11 Migration Velocity Analysis ................. ................... ................. 159 Introduction. ................... ...................................... .... 159 Time-migration velocity analysis .......................... .... ........ ..... 160 Extracting velocity information from prestack images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Vertical interval-velocity updates from measured average-velocity errors................ . 171 Tomographic migration velocity analysis ........................................... 173 References ................................................................. 183 Chapter 12 Migration Velocity Analysis by Wavefield Methods......... ... ....................... 185 Introduction. ................... ....................................... . .... 185 Objective function of wavefield migration-velocity analysis ............... ........... .. 187 Linearization of wave propagation with respect to the velocity function......... ......... 189 Convergence of wavefield migration velocity analysis. . . . . . . . . . . . .. .... . . . . . . . . . . . . . . . 193 A robust WEMVA method ................... ............................. 196 Examples of subsalt wave-equation MVA ................... ................... ... 199 References.................. .................... ......................... 205