3-D prestack migration of constant-offset data can be formulated in the frequency-wavenumber domain as a stationary phase approximation to equivalent Kirchhoff expressions. This formulation constitutes a proof of Dubrulle''s (1983) heuristic algorithm. Numerical implementations are 3-D extensions of his algorithms and lead to very efficient migration under the assumption of lateral invariance in velocity and acquisition geometry.
Dubrulle (1983) presented a method for migrating 2-D common-offset data in the frequency-wavenumber domain. His algorithm for finite offset data is based on a heuristic extension of an algorithm devised for zero offset data. The phase shifts required to migrate the data are computed by the numerical solution of a pair of algebraic equations relating the traveltime and midpoint ray parameter of a diffraction event to the offset and migration displacement.