An efficient structured grid generation scheme for seismic wave simulation in regions with extreme topography

ABSTRACT Using curvilinear structured grids, the finite-difference method (FDM) can effectively simulate seismic wave propagation in regions with irregular topography. However, generating high-quality curvilinear structured grids in regions with extreme topography, such as mountains or nearly vertical reservoir dams, is not an easy task and limits the application of FDM in seismic wave simulation. Grid quality is crucial for finite-difference simulations, as it directly affects the accuracy, stability, and efficiency of the simulation. Therefore, achieving an efficient and automatic generation of high-quality structured grids is essential for applying FDM to seismic wave simulation in regions with topography. The grids used for seismic wave simulation have a special feature compared with other computational problems: only the shape of the free surface is fixed, whereas the shapes of the other boundaries are free to be set. Based on this feature, we develop an efficient and automatic grid generation scheme that integrates the hyperbolic grid generation method and the algebraic interpolation method. Initially, the grids are generated using the hyperbolic method, starting from the given free surface and expanding layer by layer along the depth direction. However, when dealing with extreme topographies, the resulting grids exhibit poor smoothness in the depth direction. To enhance the grid quality, we redistribute the grid points using an interpolation approach along the depth direction. We design two models with extreme topography and use the Foothills model to test the grid generation scheme and its application in seismic wave simulation. The results of the grid quality assessment indicate that the scheme can efficiently generate high-quality grids. Seismic wave propagation simulations reveal that these high-quality grids significantly improve computational efficiency with sufficient simulation accuracy.