Three-dimensional seismic wave modelling in spherical Yin-Yang-Zhong grid with irregular topography by a finite difference method

In the simulation of global seismic wave propagation, the curvature of the Earth cannot be neglected. Therefore, solving the seismic wave equation in spherical coordinates is both accurate and efficient. Conventional grid discretization methods encounter singularity issues at the center and poles of the spherical coordinate. To address the grid discretization problem in spherical coordinate models, we employ the "Yin-Yang-Zhong" grid to discretize the model. Yin-Yang grid is an overlapping grid system composed of two sub-grids, and the subgrid named "Zhong" is based on Cartesian coordinate and located in the center of Yin-Yang grid, which together form the "Yin-Yang-Zhong" grid. Additionally, traditional finite difference method (FDM) cannot accurately simulate models with irregular topography. To overcome this limitation, we introduce the curvilinear grid method into the "Yin-Yang-Zhong" grid and implement the free-surface boundary condition for irregular topography using the traction image method. This allows the model to incorporate arbitrary topography. Our algorithm combines the flexibility of curvilinear grid with the computational efficiency of FDM. In this study, the simulation results are compared with those from COMSOL and the spectral element method, confirming the accuracy and efficiency of our algorithm. Furthermore, the results demonstrate the significant influence of topography on seismic wave simulation.