Kinematics of Shot-geophone Migration and Riemannian Annihilators

Recent analysis and synthetic examples have shown that many prestack depth migration methods produce non-flat 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 which 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. We use a ray-theoretical analysis to show that shot-geophone migration produces focussed (subsurface offset domain) or flat (scattering angle domain) image gathers, regardless of velocity field complexity, provided that 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. While our analysis is theoretical and idealized, we present a synthetic example which suggests that its implications remain valid for practical implementations, and that shot-geophone prestack depth migration may be a particularly appropriate tool for velocity analysis in complex structure.