A fast pointwise strategy for anisotropic wave-mode separation in TI media

The multi-component wavefield contains both compressional and shear waves. Separating wave-modes has many applications in seismic workflows. Conventionally, anisotropic wave-mode separation is implemented by either directly filtering in the wavenumber domain or nonstationary filtering in the space domain, which are computationally expensive. These methods could be categorized into the pseudo-derivative family and only work well within Finite Difference (FD) methods. In this paper, we establish a relationship between group-velocity direction and polarity direction and propose a method, which could go beyond modeling by FD. In particular, we are interested in performing wave-mode separation in a Spectral Element Method (SEM), which is widely used for seismic wave propagation on various scales. The separation is implemented pointwise, independent of its neighbor points, suitable for running in parallel. Moreover, no correction for amplitude and phase changes caused by the derivative operator is required. We have verified our scheme using numerical examples.