Coupled Wideangle Wave Approximations

Abstract

In this paper we analyze wave propagation in three-dimensional random media. We consider a source with limited spatial and temporal support that generates spherically diverging waves. The waves propagate in a random medium whose fluctuations have small amplitude and correlation radius larger than the typical wavelength but smaller than the propagation distance. In a regime of separation of scales we prove that the wave is modified in two ways by the interaction with the random medium: first, its time profile is affected by a deterministic diffusive and dispersive convolution; second, the wave fronts are affected by random perturbations that can be described in terms of a Gaussian process whose amplitude is of the order of the wavelength and whose correlation radius is of the order of the correlation radius of the medium. Both effects depend on the two-point statistics of the random medium.