Introduction

The migration of the slant stack of a common midpoint gathers is a method that makes no assumptions that deteriorate with wide offset angles, steep dips, or vertical velocity variations. Events of different dips that intersect are equally well imaged. Hence, Keho and et al 1992 use such migrated $\tau-p$seismic data to do AVO processing.

Ottolini 1982 proposed the equations for and some applications of common midpoint slant stack migration. The migration can be implemented with either FK or the phase shift algorithm.

Gazdag 1984 provided an unconditionally stable method, phase shift plus interpolation (PSPI), taking lateral velocity variations into account.

This paper describes my use of two different PSPI algorithms to implement common midpoint migration of prestack slant stack for velocity variations with depth and also for lateral velocity variations. The migrated sections can be stacked to obtain a migrated image or left unstacked for for AVO analysis.