Finite-element Simulation of Seismic Ground Motion with a Voxel Mesh

Abstract

— Accurate simulation of seismic ground motion for three-dimensionally complex topography and structures is one of the most important goals of strong motion seismology. The finite-element method (FEM) is well suited for this kind of simulation, since traction-free conditions are already included in the formulation, and the Courant condition is less strict than for the finite-difference method (FDM). However, the FEM usually requires both large memory and computation time. These limitations can be overcome by using a mesh consisting of voxels (rectangular prisms) with isotropy built into the explicit formulation of the dynamic matrix equation. Since operators in the voxel FEM are the combinations of ordinary FDM operators and additional terms, the method keeps accuracy of the same order as FDM and the terms relax the Courant condition. The voxel FEM requires a similar amount of memory and only takes 1.2∼1.4 times longer computation time. The voxel mesh can be generated considerably faster than the popular tetrahedral mesh. Both ground motions and static displacements due to a point or line source can be calculated using the voxel FEM approach. Comparisons with the reflectivity method and theoretical solutions demonstrate the successful implementation of the method, which is then applied to more complex problems.