Angle-domain common image gathers for anisotropic migration

I present a general methodology for computing Angle-Domain Common Image Gathers (ADCIGs) in conjunction with anisotropic wavefield-continuation migration. The method is based on the transformation of the prestack image from the subsurface-offset domain to the angle domain by use of slant stacks. The processing sequence is the same as for the computation of ADCIGs for the isotropic case, though the interpretation of the relationship between the slopes measured in the prestack image and the aperture angles are more complex. I demonstrate that the slopes measured by performing slant stack along the subsurface-offset axis of the prestack image are a good approximation of the phase aperture angles, and that they are exactly equal to the phase aperture angles for flat reflectors in Vertical Transverse Isotropic (VTI) media. In the general case of dipping reflectors, the true aperture angles can be easily computed as a function of the reflector dip and anisotropic slowness at the reflector. I derive the relationships between phase angles and slopes measured in the prestack image from both a “plane-wave” viewpoint and a “ray” viewpoint. The two derivations are consistent with each other, as demonstrated by the fact that in the special case of flat reflectors they lead to exactly the same expression. The ray-theoretical derivation is based on a novel generalization of kinematic migration to the computation of prestack images as a function of the subsurface offset. This theoretical development leads to the linking of the kinematics in ADCIGs with migration-velocity errors, and thus it enables the use of ADCIGs for velocity estimation. I apply the proposed method to the computation of ADCIGs from the prestack image obtained by anisotropic migration of a 2-D line extracted from a Gulf of Mexico 3-D data set. The analysis of the error introduced by neglecting the difference between the true phase aperture angle and the angles computed through slant stack shows that these errors are negligible and can be safely ignored in realistic situations. On the contrary, group aperture angles can be quite different from phase aperture angles and thus ignoring the distinction between these two angles can be detrimental to practical applications of ADCIGs. 1email: [email protected]