Source terms acting only in a single point are described by the Dirac function

1. z z h y x x SPICE receiver line 17 km 6 km 6 km 15 km 15 km z z y h x x 4 sec 8 sec 12 sec Simulation of Seismic Wave Propagation due to Finite Source Rupture Models Using an Arbitrarily High Order Discontinuous Galerkin Method on Unstructured Tetrahedral Meshes M. Käser1), M. Dumbser1), P.M. Mai2), J. de la Puente3); 1) DICA, Università di Trento; 2) Institut f. Geophysik, ETH Zürich; 3) Geophysik, LMU München S13A-0177 The DG-Method Point Sources Numerical Examples Convergence Tests • The 3-D elastic wave equation in velocity-stress formulation gives the hyperbolic system • with the vector of unknowns given as • The numerical solution can be approximated by • a linear combination of polynomial basis functions • after the transformation to the unit tetrahedron. • Multiplying the governing equation by a test function the integration over a tetrahedron gives • Advantages of ADER-DG on tetrahedrons: • mesh flexibility w.r.t. complex geometries • precomputation of mass and stiffness matrices • mass matrix is diagonal • stiffness matrices are very sparse • boundary conditions treated by numerical fluxes • very local character due • to extremely compact • neighbourhood • suitable for parallelisation • due to few communication Source terms acting only in a single point are described by the Dirac function and the source time function SpT(t). The space-time integral of the source term gives where the basis function Fk can be evaluated at any location inside a tetrahedral element. • SCEC benchmark LOH4 • layer over halfspace • with finite rupture plane • analytic slip rate function • reference solutions of five • different codes available • Mesh decomposition • done with graph • partitioner • METIS ADER-DG achieves extremely high accuracy with increasing approximation order. Rupture Plane in a Linearly Varying Medium Tetrahedral mesh spacing is direct proportional to P-wave velocity Finite Source Models The point source assuption is applicable to every subfault of a finite source rupture model. Comparisons of synthetic seismograms obtained by ADER-DG and the SCEC reference codes • Comparison with analytic seismograms • ADER-DG 4th order in space and time on 928 750 tetrahedrons • mesh spacing 1000 m - 4000 m Station 10 Station 8 The orientation and shape of the finite rupture plane w.r.t. the tetrahedral mesh is arbitrary. Station 5 Station 2 Improvement due to increasing order 3-D visualization of the vertical velocity component of the elastic wave field • Simulation parameters: • adapted mesh spacing by tetrahedrons with edge • lengths between 350 m - 3000 m • number of elements 249 338 • 3rd order approximation in space and time • 16 processors • 6 hours CPU time • Incorporation of all subfault contributions: • approximation of source terms by high order • polynomial representation • high order space-time integration over each • tetrahedral element Contact: Martin Käser, DICA, Università di Trento, Via Mesiano 77, I-38050 Trento, martin.kaeser@ing.unitn.it