In a recent paper, Stoffa et al. (1990) presented a split-step Fourier migration method. It takes laterally varying migration velocities into account by splitting the reference slowness into an average slowness, constant within the migration interval, and a perturbation term which accounts for the lateral variations. The method works accurately only if the lateral slowness variations are smooth and angles of propagation are near-vertical. The restriction to steep propagation angles stems from the fact that the wavefield is accurately propagated with respect to the reference slowness but a five-degree approximation is used to accommodate the lateral variations. This note presents a theory that avoids the five-degree assumption and thus generalizes the split-step algorithm.

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