We first have to transform the wavefield in the CMP gather from the (x,t) domain to the domain. Let d(x,t) be the wavefield and be the transformed slant stack wavefieldClaerbout (1985), so that
A lot of care needs to be taken to construct a high-quality slant stack CMP gather. Kostov 1990 lists several methods of obtaining a high quality gather. Poor quality is probably caused by very coarse offsets and missing offsets beyond the ends of the cable. Those offsets that are missing must be interpolated or extrapolated before slant stack transformation.
The double-square-root equationOttolini (1982) for the downward continuation of common midpoint slant stacks is
The solution of equation (2) is