Elastic wave-mode separation in 2D transversely isotropic media using optical flow

Wave-mode separation is a critical step in anisotropic elastic-wave imaging. To avoid high computational costs and additional corrections, we apply a separation formula in the space domain that projects Cartesian components of the elastic wavefield onto the polarization vectors in the orthogonal direction. By solving the Christoffel equation, we implement the conversion from the phase velocity direction to the polarization direction. We use similarity between the seismic wave propagation and the optical flow problem to calculate the phase angle based on the Horn-Schunck algorithm. Compared with the conventional Poynting vector, the optical flow vector is more robust, particularly for complex underground structures. We demonstrate the performance of the proposed approach for two-dimensional transversely isotropic media with three numerical examples and discuss the potential extension to three-dimensional media.