1 DICA, Università di Trento; 2 Institut f. Geophysik, ETH Zürich The Discontinuous Galerkin Method for 3-D Elastic Wave Propagation and Kinematic Sources SPICE M. Käser1, M. Dumbser1, P.M. Mai2 1 DICA, Università di Trento; 2 Institut f. Geophysik, ETH Zürich The DG-Method The Semi-Discrete Scheme Numerical Example Considering the 3-D elastic wave equation in velocity-stress formulation leads to the hyper-bolic system of the form where the vector of unknowns is given by The numerical solution Qh of this system can be approximated inside a tetrahedron by the linear combination of time-independent poly-nomial basis functions and time-dependent degrees of freedom, i.e. For a 3rd order scheme, the 10 basis functions are given as: Multiplying the governing equation by a test function and integrating over a tetrahedron gives Transformation from a physical tetrahedron into the reference tetrahedron improves the computational efficiency as integrations can be pre-computed analytically, such as: The resulting scheme is then given through: The time integration can be carried out by using a classical Runge-Kutta method or the new ADER approach automatically leading to the same order of approximation in space and time. Code validation through wave excitation by finite source rupture models using a layered medium and a set of well distri- buted stations and their reference seismograms. Point Sources Source terms acting only in a point can be described by the Dirac Delta distribution, where , and a source time function: The space-time integral of the source term gives where the test function Fk can be evaluated at any point location inside a tetrahedron of the compu-tational domain. Mesh parameters: Average edge length on surface: 1000m Average edge length on base: 4000m Total number of tetrahedrons: 928 750 Synthetic Seismograms A comparison of the reference seismograms and the DG synthetics. Higher order provides drastic improvement. Finite Source Rupture Models The point source assumption can be applied to every subfault of a finite source rupture model z z y h x x 3-D visualization of the elastic wave field showing the vertical velocity component w 4 sec 8 sec 12 sec Contact: Martin Käser, DICA, Università di Trento, Via Mesiano 77, I-38050 Trento, martin.kaeser@ing.unitn.it