A Two-Dimensional Non-Conforming Multidomain FDM/PSM Hybrid Method for Elastic Wave Simulation

Abstract

Efficient elastic wave numerical simulation is crucial for ground motion and waveform inversion studies. However, using uniform grids in simulations for models with strong velocity contrast interfaces, thin layers, or ring shapes often leads to spatial oversampling, wasting computational resources and reducing efficiency. To address this challenge, we propose a two-dimensional non-conforming multidomain FDM/PSM hybrid approach. This method divides the computational domain into independent subdomains along a specified direction, with overlaps occurring only at the edges. Within each subdomain, a Chebyshev pseudospectral scheme is applied in one direction, while a high-order finite-difference scheme is used in the other. Grid generation for each subdomain is customized based solely on its shape and velocity, without reference to neighboring subdomains. As a result, this non-conforming method allows the grid points on either side of the subdomain interface to remain unaligned. We use Lagrange polynomial interpolation and characteristic boundary conditions to handle non-conforming interfaces. This non-conforming method allows for a direct transition from fine to coarse grid regions, even when the fine grid spacing is one-tenth or one-hundredth of that of the coarse grid. For problems involving strong velocity contrast interfaces and geometrically thin layers, the scheme reduces computational costs in terms of both memory and runtime requirements. Through five numerical experiments, we have confirmed the method's accuracy and efficiency, demonstrating its broad potential for application in seismology and exploration geophysics.