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.
The sparse, efficient and stable representation of the primary propagator is an important aspect of current prestack depth migration techniques. The primary propagator accounts for one-way wave propagation (downward or upward) from one depth level to the next depth level. It does not account for scattering at boundaries. This paper aims at giving a representation of the primary propagator in the wavelet transform domain and at giving a representation of the seismic data in the wavelet domain. An efficient full prestack migration scheme which uses advantageously the structure of the non-standard wavelet transform, will be derived from these representations. Furthermore, it is shown that the wavelet transform enables the user to choose between resolution and efficiency.
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