A Backscatter Model for a Dense Discrete Medium: Analysis and Numerical Results

In this article, a backscatter theory for an electrically dense medium is presented. The random medium is modeled by a layer of randomly distributed dielectric spherical scatterers, bounded on top and bottom by a rough surface. The phase matrix for the discrete spherical scatterers is evaluated using the dense medium phase and amplitude correction (DM-PACT) method (Chuah et al., 1996) so that it can be used for a dense medium (such as snow and sea-ice). This phase matrix differs from the conventional one in that both amplitude and phase corrections for the close-spacing effect are considered. The rough surface is modeled using the integral equation method (IEM) (Fung, 1994). The problem is formulated by using radiative transfer theory. The integrodifferential equations are solved using an iterative method. Explicit expressions up to second-order solutions are given. Based on these solutions, terms resulting from three major scattering mechanisms, namely, direct surface, surface–volume, and volume scattering terms, can be identified. The volume interactions include both direct volume and volume–volume interactions. Using this model, dense medium effect and relative contributions of the three major scattering mechanisms are investigated. The study of relative contributions of the various scattering mechanisms is important to indicate the conditions under which a simple incoherent theory, where backscatter returns are obtained by direct addition of volume and direct surface terms, is acceptable. Comparisons are also made with measurements in the laboratory and in the field.