Fast Poynting-Vector based wave-mode separation and RTM in 2D elastic TI media

The wave-modes in isotropic elastic media are easy to get separated by using Helmholtz decomposition. This method, however, fails in TI (transverse isotropic) media due to the anisotropy, and more sophisticated operators are required. Most of these existing operators are implemented and limited in FD (finite-difference) stencil. We propose a Poynting-vector based method, which separates wave-modes pointwisely, independent of the modeling stencils. In TI media, the Poynting-vector indicates the group-velocity direction while the wave-modes get separated in the polarization-vector direction. We write the relationship between these two directions into a small numerical table by exploiting the phase-velocity direction as a bridge prior to wavefield propagation. During the modeling process, it is easy to estimate the group-velocity direction from the Poynting vector, and then we can get the polarization-vector direction to separate wave-modes by checking the numerical table. We test our method on several TI models. We furthermore apply our method to elastic reverse-time migration (RTM) in TI media.