Prestack plane‐wave Kirchhoff depth migration using a cluster of workstations

Abstract

We describe here a method of prestack migration that is based on a Kirchhoff Helmholtz formulation for the propagation of the wavefield. Both the source and receiver wave fields can be expanded in terms of plane waves and their interaction to a material discontinuity can be expressed by a surface integral over the discontinuity. A similar formulation can also be used to propagate the wavefield from the recording surface to the subsurface where they originated. We use plane wave transformed data and geometrical ray theory to model the source wavefield and propagate the receiver plane waves to the subsurface using an appropriate phase shift. The source travel time and the receiver plane wave travel time are computed at each grid point in the subsurface using finite difference approximation of the Eikonal equation. Thus the method is valid for a general inhomogeneous medium, but we restricted our travel time calculations to first arrivals only. The support of the plane wave is arbitrary and thus a constant plane wave gather can be migrated rapidly. Since each plane wave section can be migrated independently, the method is ideal for implementation on parallel computer architectures. We illustrate the method with several numerical examples and note that the method has the potential of being used effectively as a migration velocity analysis tool. Several constant ray parameters migrated images can be compared to estimate subsurface velocity structure in a laterally varying medium.