Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media

Wave-mode separation and vector decomposition are significantly more expensive than wavefield extrapolation and are the computational bottleneck for elastic reverse time migration in heterogeneous anisotropic media. We have expressed elastic-wave-mode separation and vector decomposition for anisotropic media as space-wavenumber-domain operations in the form of Fourier integral operators and developed fast algorithms for their implementation using their low-rank approximations. Synthetic data generated from 2D and 3D models demonstrated that these methods are accurate and efficient.