REFERENCES

Aminzadeh, F., Burkhard, N., Long, J., Kunz, T., and Duclos, P., 1996, Three dimensional SEG/EAGE models - an update: The Leading Edge, 2, 131-134.

Biondi, B., and Palacharla, G., 1996, $\mbox{3-D}$ prestack migration of common-azimuth data: Geophysics, 61, no. 6, 1822-1832.

Biondi, B., and Sava, P., 1999, Wave-equation migration velocity analysis: 69th Ann. Internat. Meeting, Soc. of Expl. Geophys., Expanded Abstracts, 1723-1726.

Biondi, B., and Shan, G., 2002, Prestack imaging of overturned reflections by reverse time migration: 72nd Ann. Internat. Meeting, Soc. of Expl. Geophys., Expanded Abstracts, 1284-1287.

Biondi, B., and Symes, W. W., 2003, Angle-domain common-image gathers for migration velocity analysis by wavefield-continuation imaging: Geophysics: submitted for publication.

Biondi, B., and Vaillant, L., 2000, 3-D wave-equation prestack imaging under salt: 70th Ann. Internat. Meeting, Soc. of Expl. Geophys., 906-909.

Biondi, B., Tisserant, T., and Symes, W., 2003, Wavefield-continuation angle-domain common-image gathers for migration velocity analysis: 73rd Ann. Internat. Meeting, Soc. of Expl. Geophys., 2104-2107.

Biondi, B., 2003, Equivalence of source-receiver migration and shot-profile migration: Geophysics, 68, 1340-1347.

Brandsberg-Dahl, S., de Hoop, M., and Ursin, B., 1999, Velocity analysis in the common scattering-angle/azimuth domain: 69th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1715-1718.

Brandsberg-Dahl, S., de Hoop, M. V., and Ursin, B., 2003, Focusing in dip and AVA compensation on scattering-angle/azimuth common image gathers: Geophysics, 68, 232-254.

Claerbout, J. F., 1985, Imaging the Earth's Interior: Blackwell Scientific Publications.

Clapp, R., and Biondi, B., 2000, Tau domain migration velocity analysis using angle CRP gathers and geologic constraints: 70th Ann. Internat. Mtg., Soc. Expl. Geophys., 926-929.

Clapp, R. G., 2001, Geologically constrained migration velocity analysis: Ph.D. thesis, Stanford University.

de Bruin, C. G. M., Wapenaar, C. P. A., and Berkhout, A. J., 1990, Angle-dependent reflectivity by means of prestack migration: Geophysics, 55, no. 9, 1223-1234.

de Bruin, C., 1992, Linear AVO inversion by prestack depth migration: Ph.D. thesis, Delft University.

Etgen, J., 1990, Residual prestack migration and interval velocity estimation: Ph.D. thesis, Stanford University.

Liu, W., Popovici, A., Bevc, D., and Biondi, B., 2001, 3-D migration velocity analysis for common image gathers in the reflection angle domain: 69th Ann. Internat. Meeting, Soc. of Expl. Geophys., Expanded Abstracts, 885-888.

Meng, Z., Bleistein, N., and Valasek, P., 1999a, 3-D analytical migration velocity analysis, Part II: Velocity gradient estimation: 69th Ann. Internat. Meeting, Soc. of Expl. Geophys., 1731-1734.

Meng, Z., Bleistein, N., and Wyatt, K., 1999b, 3-D analytical migration velocity analysis, Part I: Two-step velocity estimation by reflector-normal update: 69th Ann. Internat. Meeting, Soc. of Expl. Geophys., 1727-1730.

Mosher, C. C., Foster, D. J., and Hassanzadeh, S., 1997, Common angle imaging with offset plane waves: 67th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1379-1382.

Mosher, C., Jin, S., and Foster, D., 2001, Migration velocity analysis using common angle image gathers: 71th Ann. Internat. Mtg., Soc. of Expl. Geophys., 889-892.

Ottolini, R., and Claerbout, J. F., 1984, The migration of common-midpoint slant stacks: Geophysics, 49, no. 03, 237-249.

Prucha, M., Biondi, B., and Symes, W., 1999, Angle-domain common-image gathers by wave-equation migration: 69th Ann. Internat. Meeting, Soc. Expl. Geophys., Expanded Abstracts, 824-827.

Rickett, J., and Sava, P., 2002, Offset and angle-domain common image-point gathers for shot-profile migration: Geophysics, 67, 883-889.

Sava, P., and Fomel, S., 2003, Angle-domain common-image gathers by wavefield continuation methods: Geophysics, 68, 1065-1074.

Schultz, P. S., and Claerbout, J. F., 1978, Velocity estimation and downward-continuation by wavefront synthesis: Geophysics, 43, no. 4, 691-714.

Stolk, C. C., and Symes, W. W., 2004, Kinematic artifacts in prestack depth migration: Geophysics, 69, 562-575.

Stork, C., 1992, Reflection tomography in the postmigrated domain: Geophysics, 57, 680-692.

Wapenaar, C. P. A., and Berkhout, A. J., 1987, Full prestack versus shot record migration: 69th Ann. Internat. Meeting, Soc. of Expl. Geophys., Expanded Abstracts, Session:S15.7.

Xie, X. B., and Wu, R. S., 2002, Extracting angle domain information from migrated wavefield: 72th Ann. Internat. Mtg., Soc. Expl. Geophys., 1360-1363.

Xu, S., Chauris, H., Lambare, G., and Noble, M. S., 2001, Common-angle migration: A strategy for imaging complex media: Geophysics, 66, 1877-1894.

A In this Appendix we derive the expression for the residual moveout (RMO) function to be applied to 3-D ADCIGs computed by wavefield continuation.

We start from the 2-D expression for RMO, as derived by Biondi and Symes (2003):  

$${\bf \Delta n}_{\rm 2D-RMO}= \frac{\rho-1} {\cos\alpha_x{'}}... ...a}{\left(\cos^2\alpha_x{'}- \sin^2\gamma\right)} z_0\; {\bf n},$$ (24)

In 3-D, this relationship is valid on the tilted plane shown Figure 3, where the migrated depth of the normal incidence event z₀ is now the depth along the tilted plane z'₀. Therefore, the migrated depth z₀ needs to be scaled by a factor of $1/\cos \alpha_y{'}$,where $\alpha_y{'}$ is the inclination of the tilted plane. In 3-D equation (24) becomes:

$$\begin{eqnarray} \lefteqn{ {\bf \Delta n}_{\rm RMO}= } \nonumber \\ && \frac{\rh... ...amma}{\left(\cos^2\alpha_x{'}- \sin^2\gamma\right)} z_0\; {\bf n}.\end{eqnarray}$$ (25)

When $\alpha_x{'}$ and $\alpha_y{'}$ are available, the RMO function could be directly evaluated using the expression in equation (25). However, in several situations it is more useful to express the RMO function explicitly as a function of the geological dip $\alpha$,the azimuth angle of the normal to the geological dip $\eta$,and the azimuth angle of the reflected event $\phi$(see Figure 13). To derive the desired expression, we use the following two trigonometric relationships among the angles:  

$$\cos \alpha= \cos \alpha_x{'}\cos \alpha_y{'}, \;\;\;\;\;\ {... ...;\ \sin \alpha_x{'}= \sin \alpha\cos \left( \eta- \phi\right).$$ (26)

Substituting equations (26) into equation (25), we obtain the following final result:  

$${\bf \Delta n}_{\rm RMO}= \frac{\rho-1} {\cos\alpha} \frac{\... ...2 \left( \eta- \phi\right)- \sin^2\gamma\right)} z_0\; {\bf n}.$$ (27)