High frequency attenuation of elastic waves transmitted at an angle through a randomly-fluctuating horizontally-layered slab

This paper is concerned with the modeling of elastic waves travelling at small incidence angles through a randomly-fluctuating horizontally-layered slab, in regimes where the wavelength is small compared to the thickness of the slab. The wave propagation problem is reset in a frame following the coherent front, which propagates in a homogenized medium. This homogenized medium is anisotropic because of the layering, and the equations obtained account explicitly for the coupling of quasi-P and quasi-S waves. The resulting model is governed by a set of coupled stochastic ordinary differential equations that can be approximated numerically very efficiently, and yields in particular estimates of the transmission and reflections coefficients of the slab. The latter compare favorably to the coefficients obtained in a full scale numerical simulation of the (micro-scale) wave equation, for a fraction of the cost.