An overset mesh-free finite-difference method for seismic modeling including surface topography

Abstract

An overset mesh-free finite-difference method (FDM) is developed for 2D time-domain seismic wave modeling using second-order elastic displacement wave equations in a generally isotropic medium that exhibits complex surface topography and subsurface structures. The complex surface topography is discretized using an overset mesh-free node generation method, thus naturally arranging surface nodes on the surface topography and outperforming the Cartesian grid in terms of geometric flexibility. A Cartesian grid is used to discretize the entire computational region in terms of computational efficiency. The QR-decomposition radial-basis-function FDM (QR-RBF-FDM) and FDM are adopted to solve the equation independently in the mesh-free node and Cartesian grid. The data transfers between them are conducted through QR-RBF interpolation to facilitate mesh-free calculation, thus eliminating the requirement for node-to-grid matching. The improved free-surface boundary condition is implemented in the QR-RBF-FDM. Furthermore, a more appropriate formula for the outward normal direction is developed. The numerical solutions of our method are compared with those of the curvilinear grid FDM and standard FDM to verify the effectiveness of our method. The results indicate that our method avoids numerical scattering induced by staircase approximations of Cartesian grids while saving considerable computational costs. Therefore, this method is a better candidate than the mesh-free FDM for seismic numerical simulation with free surface topography.