Modal expansion of one‐way operators in laterally varying media

Abstract

One of the main benefits of prestack depth migration in seismic processing is its ability to handle complicated medium configurations. When considerable lateral variations in the acoustic parameters are present in the subsurface, prestack depth migration is necessary for optimal lateral resolution. However, most migration algorithms still deal with lateral variations in an approximate manner because these variations are in many cases moderate compared to the profound variations in the depth direction. From other areas of science (e.g., optics, oceanography, and seismology), it is known that lateral variations can be dealt with by a decomposition of the wavefield into wave modes. In this paper, we explore the possibility of applying this concept to the construction of one‐way wavefield operators for depth migration. We expand the Helmholtz operator on an orthogonal basis of wave modes and obtain one‐way wavefield operators that are unconditionally stable and significantly increase the lateral resolution of the result.