Controlling amplitudes in 2.5D common-shot migration to zero offset

Configuration transform operations such as dip moveout, migration to zero offset, and shot and offset continuation use seismic data recorded with a certain measurement configuration to simulate data as if recorded with other configurations. Common-shot migration to zero offset (CS-MZO), analyzed in this paper, transforms a common-shot section into a zero-offset section. It can be realized as a Kirchhoff-type stacking operation for 3D wave propagation in a 2D laterally inhomogeneous medium. By application of suitable weight functions, amplitudes of the data are either preserved or transformed by replacing the geometrical-spreading factor of the input reflections by the correct one of the output zero offset reflections. The necessary weight function can be computed via 2D dynamic ray tracing in a given macrovelocity model without any a priori knowledge regarding the dip or curvature of the reflectors. We derive the general expression of the weight function in the general 2.5D situation and specify its form for the particular case of constant velocity. A numerical example validates this expression and highlights the differences between amplitude preserving and true-amplitude CS-MZO.