A multiscale medium approximation method for the propagation P-waves in highly heterogeneous geophysical media

Approximating the solution of Helmholtz problems is a tricky task, especially at high frequency. Indeed, because of the numerical dispersion, it is mandatory to increase the number of discretization points per wavelength for higher frequencies. Using high degree polynomial shape functions on a coarse mesh is an interesting approach because it contributes to reduce such numerical dispersion as compared to linear functions set on a fine mesh. While this solution is very efficient for wave propagation in homogeneous media, it is not obvious how the variations of the medium inside a cell have to be taken into account. Recently the Multiscale Medium Approximation method (MMAm) has been proposed to overcome this difficulty. High-order shape functions are used with a coarse mesh to reduce dispersion and hence, the pollution effect. Then, the key idea is to introduce a multiscale approximation of the medium to take into account fine scale heterogeneities on the coarse mesh. This approach has proven to be efficient on academic test cases and a convergence theory has been developed. In this work, we further validate the MMAm by demonstrating its efficiency on geophysical benchmarks. Highly heterogeneous media, Seismic wave propagation, Time-harmonic modelling, High-order methods, Mulsticale methods, Finite element methods