Three-dimensional depth migration by a generalized phase-shift method

We present a three-dimensional post stack migration algorithm which is based on an extrapolation in depth with the acoustic wave equation. The new method is designed to handle vertical as well as lateral velocity contrasts. The migration is carried out in the space-frequency domain. The wave equation is solved by a new expansion technique which virtually assures the same type of accuracy which is obtained with the phase-shift method for laterally uniform structures. The new method was implemented on the Cray XMP48 computer. The structure of the algorithm allows for easy utilization of vectorization and multitasking. Multitasking is achieved by allowing each task to perform calculations for different frequencies Vectorization is achieved by performing identical calculations along parallel lines within each frequency plane.