Virtual topography: A fictitious domain approach for analyzing free-surface irregularities in large-scale earthquake ground motion simulation

摘要

This paper presents a numerical scheme based on a fictitious domain framework for the numerical modeling of earthquake-induced ground motion in the presence of realistic surface topography of the Earth's crust. We show that by adopting a non-conforming octree-based meshing approach associated with a virtual representation of the surficial irregularity, we can obtain accurate representations of ground motion. From the computational point of view, our methodology proves to be also efficient, and more importantly, it allows us to preserve the salient features of multi-resolution cubic-shaped finite elements for wave propagation applications. We implemented the non-conforming meshing scheme for the treatment of realistic topographies into Hercules, the octree-based finite-element earthquake simulator developed by the Quake Group at Carnegie Mellon University. We tested the benefits of the strategy by benchmarking its results against reference examples, and by means of numerical error estimate analyses. Our qualitative and quantitative comparisons showed a close agreement between our numerical results and the reference results, and also, that the order of convergence of the displacement field is preserved in the presence of surface topography. Moreover, this performance was obtained by using the same mesh refinement techniques with cubic elements as in traditional flat free-surface simulations.