Une méthode Galerkin discontinue d'ordre élevé pour la propagation d'ondes sismiques en milieu viscoélastique

Abstract : We present a high-order discontinuous Galerkin method for the simulation of P-SV seismic wave propagation in heterogeneous media and two dimensions of space. The first-order velocity-stress system is obtained by assuming that the medium is linear, isotropic and viscoelastic, thus considering intrinsic attenuation. The associated stress-strain relation in the time domain being a convolution, which is numerically intractable, we consider the rheology of a generalized Maxwell body replacing the convolution by differential equations. This results in a velocity-stress system which contains additional equations for the anelastic functions including the strain history of the material. Our numerical method, suitable for complex triangular unstructured meshes, is based on a centered numerical flux and a leap-frog time-discretization. The extension to high order in space is realized by Lagrange polynomial functions, defined locally in each element. The inversion of a global mass matrix is avoided since an explicit scheme in time is used and because of the local nature of the discontinuous Galerkin formulation. The method is validated through numerical simulations including comparisons with a finite difference scheme.
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Fabien Peyrusse, Nathalie Glinsky, Céline Gélis, Stephane Lanteri. Une méthode Galerkin discontinue d'ordre élevé pour la propagation d'ondes sismiques en milieu viscoélastique. [Rapport de recherche] RR-8242, INRIA. 2013. ⟨hal-00789682⟩

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