Three-dimensional migration of zero-offset data using a depth-variable velocity can be performed in one pass using Fourier transforms of time slices. The migration process is carried out entirely in the two-dimensional spatial Fourier domain. Three-dimensional time-slice migration is inherently a parallel algorithm and maps perfectly onto the natural layout of processors on the Connection Machine. This method is especially suitable for target-oriented migration of a subset of a three-dimensional data volume.
The exploding reflector concept leads to a model that enables migration to be described as a surface integral. The basic step in this formulation is the summing of energy over the diffraction surface of a scattering point and placing the result at the apex of that conic. Thus migration causes the energy which was spread over the surface to be concentrated at one point. The way in which this is achieved determines efficiency and accuracy. This paper shows an implementation of the algorithm on a massively parallel computer, for which the algorithm is well suited.