Accurate and efficient numerical methods to simulate dynamic earthquake rupture and wave propagation in complex media and complex fault geometries are needed to address fundamental questions in earthquake dynamics, to integrate seismic and geodetic data into emerging approaches for dynamic source inversion, and to generate realistic physics-based earthquake scenarios for hazard assessment. Modeling of spontaneous earthquake rupture and seismic wave propagation by a high-order discontinuous Galerkin (DG) method combined with an arbitrarily high-order derivatives (ADER) time integration method was introduced in two dimensions by de la Puente et al. (2009). The ADER-DG method enables high accuracy in space and time and discretization by unstructured meshes. Here we extend this method to three-dimensional dynamic rupture problems. The high geometrical flexibility provided by the usage of tetrahedral elements and the lack of spurious mesh reflections in the ADER-DG method allows the refinement of the mesh close to the fault to model the rupture dynamics adequately while concentrating computational resources only where needed. Moreover, ADER-DG does not generate spurious high-frequency perturbations on the fault and hence does not require artificial Kelvin-Voigt damping. We verify our three-dimensional implementation by comparing results of the SCEC TPV3 test problem with two well-established numerical methods, finite differences, and spectral boundary integral. Furthermore, a convergence study is presented to demonstrate the systematic consistency of the method. To illustrate the capabilities of the high-order accurate ADER-DG scheme on unstructured meshes, we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes curved faults, fault branches, and surface topography. Copyright 2012 by the American Geophysical Union.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors thank the DFG (Deutsche Forschungsgemeinschaft),as the work was supported through the EmmyNoether-Programm (KA 2281/2-1). J.-P. A. was partially funded by NSF(grant EAR-0944288) and by the Southern California Earthquake Center(funded by NSF Cooperative Agreement EAR-0106924 and USGS CooperativeAgreement 02HQAG0008). The DFM data used for comparison wereprovided by Luis A. Dalguer and the SBIEM solutions where producedwith the code of Eric M. Dunham (MDSBI: Multidimensional spectralboundary integral, version 3.9.10, 2008, available at http://pangea.stanford.edu/~edunham/codes/codes.html). Furthermore, we thank Luis A. Dalguerand Alan Schiemenz for very helpful and fruitful discussions. Cristóbal E.Castro gave valuable comments and advice on the solution of the Riemannproblem and the parallelization. We also thank M. Mai for providing computationalresources as many parallel tests, the convergence test, and theSCEC benchmark have been computed on the BlueGene/P Shaheen ofthe King Abdullah University of Science and Technology, Saudi Arabia.This paper is SCEC contribution 1526 and Caltech Seismological Lab contribution10067. The reviews and comments by J.-P. Vilotte, S. M. Day,and the Associate Editor are appreciated and helped us to improve themanuscript.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.