A high-order Discontinuous Galerkin method for the seismic wave propagation

We are interested in the simulation of P-SV seismic wave propagation by a high-order Discontinuous Galerkin method based on centered fluxes at the interfaces combined with a leap-frog time-integration. This non-diffusive method, previously developed for the Maxwell equations (4,9,20), is particularly well adapted to complex topographies and fault discontinuities in the medium. We prove that the scheme is stable under a CFL type condition and that a discrete energy is preserved on an infinite domain. Convergence properties and efficiency of themethod are studied through numerical simulations in two and three dimensions of space. Resume. Nous nous interessonsa la propagation d'ondes sismiques de types P et SV par une methode de Galerkin Discontinue d'ordreeleve basee sur des flux centres aux interfaces combinesa un schema saute-mouton en temps. Cette methode non-dissipative, precedemment developpee pour lesequations de Maxwell (4, 9, 20), est particulierement bien adapteea des milieux presentant une topographie complexe ou contenant des failles. On prouve la stabilite du schema sous une condition de type CFL ainsi que la conservation d'une energie discrete dans un domaine infini. L'efficacite de la methode est illustree par des simulations numeriques en deux et trois dimensions d'espace.