Kinematics of shot-geophone migration

Abstract

Recent analysis and synthetic examples have shown that many prestack depth migration methods produce nonflat image gathers containing spurious events, even when provided with a kinematically correct migration velocity field, if this velocity field is highly refractive. This pathology occurs in all migration methods that produce partial images as independent migrations of data bins. Shot-geophone prestack depth migration is an exception to this pattern: each point in the prestack image volume depends explicitly on all traces within the migration aperture. Using a ray-theoretical analysis, we have found that shot-geophone migration produces focused (subsurface-offset domain) or flat (scattering-angle domain) image gathers, provided there is a curvilinear coordinate system defining pseudodepth with respect to which the rays carrying significant energy do not turn, and that the acquisition coverage is sufficient to determine all such rays. Although the analysis is theoretical and idealized, a synthetic example suggests that its implications remain valid for practical implementations, and that shot-geophone prestack depth migration could be a particularly appropriate tool for velocity analysis in a complex structure.