Recursive wavenumber-frequency migration

There are many approaches for migrating seismic data using velocities varying only with depth. These methods are capable of accommodating quasi-continuous vertical velocity variation at the expense of a considerably larger amount of computation than with the Stolt method, which assumes a constant velocity for the subsurface of the earth. However, the errors involved in estimating migration velocities from seismic data are often too large to justify such a large amount of computational effort. Furthermore, because there is a resolution limit in velocity estimation, a time-depth curve based on the velocity estimates may be represented by a series of line segments that typically are much larger than the migration step size. For a time-depth curve segmented in this way, we may successively apply the fast Stolt method interleaved with phase shift for downward continuation. This approach, recursive wavenumber-frequency (k-f) migration, retains the speed of the Stolt method and produces from seismic data a subsurface image as good as that from the phase-shift method. The recursive k-f method is a powerful tool, particularly for the migration of 3-D data.