High-order kernels for Riemannian Wavefield Extrapolation

Discussion

Accurate wave-equation migration using Riemannian wavefield extrapolation requires a choice of coordinate system that exploits its higher extrapolation accuracy. An effective choice of coordinate system would be one that minimizes the difference between the extrapolation direction and the direction of wave propagation. If this condition is fulfilled, we can achieve high-angle accuracy using low-order extrapolation kernels. Otherwise, we need to extrapolate seismic wavefields with high-order kernels, like the ones described in this paper.

Shot-record migration requires selection of coordinate systems for the source and receiver wavefields. Optimal selection of coordinate systems in this situation is not a trivial task, since the source and receiver wavefields are optimally described by different coordinate systems which also vary with location. However, if we employ high-order extrapolation kernels, different seismic experiments may share the same approximately optimal coordinate system. An easy way to illustrate this idea is represented by imaging in (tilted) Cartesian coordinate systems, which are just special cases of Riemannian coordinates (Sava and Fomel, 2006). A complete treatment of this topic remains subject for future research.

High-order kernels for Riemannian Wavefield Extrapolation