Generalization of the concepts of the phase-shift method to media having lateral velocity variations. Wave extrapolation in two steps. In the first step, the wave field is extrapolated by the phase-shift method; in the second step, the actual wave field is computed by interpolation from the reference wave fields. The phase shift plus interpolation (PSPI) method is unconditionally stable and lends itself conveniently to migration of three-dimensional data. Performance is demonstrated on synthetic examples. PSPI migration results are then compared with those obtained from a finite-difference method.--Modified journal abstract.