A T-matrix approach to wave propagation and scattering in layered environments with rough interfaces

Abstract

Wave propagation and interactions at the interfaces of multi-layered media can be described in terms of transition matrix coefficients, or T- matrixes, taken from solutions for a plane wave transformation, reflection, scattering, and transmission, at an interface between two homogeneous half- spaces. These solutions can be found separately for each interface of the layered system and each combination of adjacent media. Then scattering amplitudes or the T-matrix of the whole multi-layered system can be obtained using an iterative procedure that starts from a simple case of two half-spaces at the basement of the system. A quite similar iterative procedure is frequently used for calculating the reflection coefficient of compressional plane waves for a multi-layered fluid system with flat interfaces using the reflection coefficients of each interface. In this paper, we show that a similar, but a more general T-matrix approach, can be developed to include interface roughness, different types of media and waves, for instance fluid, elastic or poroelastic layers, compressional and shear waves (vertically and horizontally polarized). As an example, scattering from a rough elastic layer is considered. An explicit first-order expression for the scattering strength is obtained and it’s applications to remote sensing of sea ice layer are discussed. [Work supported by ONR.]