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.