Spectral Domain Methods For Scattering In Random Media

Abstract

Scattering problems in randomly irregular media are generally analyzed by using the parabolic wave equation when the random medium is continuous or the Foldy-Lax-Twersky formalism when the medium consists of discrete scatterers. In the former, moment equations can be derived by assuming (1) small local perturbations (the Markov approximation), (2) narrow-angle scatter, and 69) negligible backscatter. For discrete tenuous media, approximations involving the relation between the local effective fields and the average fields permit the derivation of moment equations that apply under similar conditions. This paper describes a spectral-domain method for computing the first-and second-order moments of scattered wavefields that can be applied to both discrete and continuous media as long as the local perturbations are small. The method fully accommodates multiple forward and backward scattering, and it makes minimal restrictions on angular extent. The scattering is characterized by incremental forward and backward scattering functions that can be computed from the constitutive properties of the medium or the particle scattering functions. The application of the method to scalar wavefields in continuous media is described in Rino The extension of the spectral-domain method to vector wavefields in discrete media is straightforward. General solutions for the coherent wavefield are obtained and compared to known results, which are recovered when the backscatter terms or the cross-polarization terms are neglected. The extensions of the theory to second-order moments give new insights into backscatter enhancements by showing that they depend on the correlation between scattered waves propagating in the forward and backward directions.