Perfectly Matched Layers equations for 3D acoustic wave propagation in heterogeneous media

This work is dedicated to the analysis of Berenger PML method applied to the 3D linearized Euler equations without advection terms, with variable wave velocity and acoustic impedance. It is an extension of a previous work presented in a 2D context [8]. The 3D linearized Euler equations are used to simulate propagation of acoustic waves beneath the subsurface. We propose an analysis of these equations in a general heterogeneous context, based on a priori error estimates. Following the method introduced by Métral and Vacus [9], we derive an augmented system from the original one, involving the primitive unknowns and their first order spatial derivatives. We define a symetrizer for this augmented system. This allows to compute energy estimates in the three following cases: the Cauchy problem, the half-space problem with a non homogeneous Dirichlet boundary condition and finally the transmission problem between two half-spaces separated by an impedance discontinuity. Introduction Geophysicists are interested in the modeling of seismic wave propagation beneath the subsurface. To this purpose, for instance in seismic imaging, they can be led to use acoustic wave propagation model. In this context, wave propagation is described by the following equation ∂ttp(x, t)− c(x)I(x)div ( c(x) I(x) ∇p(x, t) )