Angle-domain common-image gathers from anisotropic migration

Abstract

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 transforming the prestack image from the subsurface-offset domain to the angle domain using slant stacks. The processing sequence is the same as that for computing ADCIGs for the isotropic case, though the interpretation of the relationship between the slopes measured in the prestack image and the aperture angles is more complex. I demonstrate that the slopes measured by performing slant stacks along the subsurface-offset axis of the prestack image provide a good approximation of the phase aperture angles, and they are exactly equal to the phase aperture angles for flat reflectors in vertical transversly isotropic (VTI) media. In the general case of dipping reflectors, the angles computed using slant stacks can be easily corrected by applying the relationships that I present in this paper, and the accurate aperture angles can be determined as a function of the reflector dip and anisotropic slowness at the reflector. I derive these relationships from both plane-wave and ray viewpoints. This theoretical development links the kinematics in ADCIGs with migration-velocity errors. I apply the proposed method to compute ADCIGs from the prestack image obtained by anisotropic migration of a 2D line recorded in the Gulf of Mexico. I analyze the error introduced by neglecting the difference between the true phase aperture angle and the angle computed through slant stacks, showing that, at least for this data set, these errors are negligible and can be safely ignored. In contrast, group aperture angles can be quite different from phase aperture angles; thus, ignoring the distinction between these two angles can be detrimental to practical applications.