Multiscale Medium Approximation: Application to Geophysical Benchmarks

High order finite element methods are very efficient to approximate the solution of wave propagation problems in the high frequency regime when the propagation medium is homogeneous. Unfortunately, theses methods fail to handle small-scale heterogeneities if the mesh is not properly constrained. In geophysical applications, constraining the mesh to the size of small-scale heterogeneities might be unaffordable so that high order finite element methods can not be applied directly. We propose to overcome this limitation by considering a multiscale strategy, which makes it possible to take into account small-scale heterogeneities on coarse meshes. Our multiscale procedure is equivalent to a quadrature-like formula. It thus corresponds to a pre-processing step in the computations which can be easily parallelized. Hence, the overhead of our multiscale technique is negligible. We validate the accuracy and the efficiency of our methodology on 2D and 3D geophysical benchmarks.