Regional wave propagation using the discontinuous Galerkin method

S Wenk,H Igel,C Pelties,M Käser

doi:10.5194/se-4-43-2013

Abstract

Abstract. We present an application of the discontinuous Galerkin (DG) method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER) Riemann problem. This ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily implemented in the computational domain. The ADER-DG method is benchmarked for the accurate radiation of elastic waves excited by an explosive and a shear dislocation source. We compare real data measurements with synthetics of the 2009 L'Aquila event (central Italy). We take advantage of the geometrical flexibility of the approach to generate a European model composed of the 3-D EPcrust model, combined with the depth-dependent ak135 velocity model in the upper mantle. The results confirm the applicability of the ADER-DG method for regional scale earthquake simulations, which provides an alternative to existing methodologies.

Highlights

To understand the influence of 3-D Earth structure on regional seismic wave propagation, numerical algorithms are required that accurately simulate ground motions towards high frequencies using today’s computing architectures
We present an application of the discontinuous Galerkin (DG) method to regional scale earthquake simulations up to periods of 20 s, offering considerable flexibility to accurately take into account 3-D Earth models in the meshing part of the workflow
In SeisSol a constant value for each material parameter is averaged over all vertices in one single tetrahedral element, whereas in SpecFEM material values are evaluated at each GLL point within a hexahedron, leading to a higher sampling of the PREM background model

Summary

Introduction

To understand the influence of 3-D Earth structure on regional seismic wave propagation (continental scale), numerical algorithms are required that accurately simulate ground motions towards high frequencies using today’s computing architectures. The schemes have to flexibly handle complicated geological formations, such as the structure of subduction and rifting zones, the shape of mantle plumes, the topography of elastic discontinuities, and the heterogeneities of continental crust. We present an application of the discontinuous Galerkin (DG) method to regional scale earthquake simulations up to periods of 20 s, offering considerable flexibility to accurately take into account 3-D Earth models in the meshing part of the workflow. The FD method approximates solutions to the wave equation on a structured grid, applying low-order (e.g., Virieux, 1984), and later high-order (e.g., Bayliss et al, 1986) numerical operators in 3-D, in order to improve the accuracy and computational efficiency. Due to restrictions in the geometrical flexibility of standard FD methods, applying structured grids with regular grid spacing, approaches which make use of variable grids have been introduced (Pitarka, 1999; Ely et al, 2008; Kristek et al, 2010; Kozdon et al, 2012)

Results

Discussion

Conclusion