Seismic wavefield simulation in anisotropic media using a high-order SBP finite-difference method

Subsurface complex media are characterized by coupled factors such as anisotropy, irregular topography, and undulating interfaces, which significantly affect the simulation of seismic wave propagation. We established a comprehensive theoretical framework for high-accuracy seismic wavefield simulation in such complex media. In particular, we developed high-order (4th, 6th and 8th order) summation-by-parts finite difference methods (SBP-FDM) to solve a pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media with complex topography. We used a body-fitted gridding scheme to discretize TTI models with complex topography and derived the strong conservation form of the wave equation in curvilinear coordinates, along with the convolutional perfectly matched layer (C-PML) absorbing boundary condition, the numerical stability condition, and the numerical dispersion relation. The primary innovation lies in the method's significantly enhanced tolerance to grid quality, thereby improving computational accuracy compared to previous SBP-FDM applications. The proposed method allows for acute angles in non-rectangular meshes as small as (compared to in previous work) and tolerates a grid-size variation ratio of up to 200% (compared to 30% previously). Numerical examples demonstrate that the proposed high-order SBP-FDMs can stably and reliably simulate seismic wavefields in topographic TTI media.