Introduction

The propagation of waves through heterogeneous media occurs in many forms, including acoustic, electromagnetic, and elastic. As these waves propagate, the wave front is altered because of spatial variations in properties. The result of the interaction with the medium is that the incident energy is dispersed in many directions – the input energy is said to be scattered. If the scattering is strong and one waits long enough, the signal received will become complex because of multiple scattering effects. Understanding this process is necessary for locating an object within a scattering medium and/or for quantifying the properties of the medium itself. The focus here is on the use of diagrams than can aid in analysis of the multiple scattering process.

Multiple scattering has been discussed by theorists since the time of Rayleigh (1892, 1945). Systems with distributions of discrete inclusions (scatterers) in a homogeneous background were studied by Foldy (1945), Lax (1951, 1952), Waterman and Truell (1961), and Twersky (1977) in terms of assumed exact descriptions of scattering by isolated inclusions. This approach may be contrasted with a model of the heterogeneous medium as having continuously varying properties. This approach entails stochastic operator theory and includes the work of Karal and Keller (1964), Frisch (1968), McCoy (1981), Stanke and Kino (1984), and Hirsekorn (1988). Both approaches seek the wave speed and attenuation of an ensemble average field, although the connection to measurements in a single sample is not always obvious.