Mean wave solution: bounded medium—discrete scatterers

Abstract

Multiple scattering technique has been employed in order to derive an eqaution for the mean wave which is propagating in a one dimensional half space random medium containing randomly distributed discrete scatterers with nonuniform background. The equation of the mean field is in the form of Dyson equation. Small and large scale variables have been defined, and the two variable expansion technique has been used in order to obtain the zero order solution to the mean field. In this solution it is assumed that the interparticulate spacing over the size of the particle is small compared to unity (sparse distribution of scatterers). In contrast to the one dimensional continuous random medium, only one effective propagation constant has been found. The zero order solution to the mean field can be used in order to derive the radiative transfer equation from the correlation equation, thus eliminating the gap between the multiple scattering and radiative transfer theory.