Wave propagation in a random medium layer with rough boundaries

Wave propagation in random media, and scattering from rough surfaces have been studied extensively during the past few decades. However, the combined problem of propagation in random media with rough boundaries has not been well investigated. Yet there are many situations where there is a need for models involving random media and rough boundaries. To address this people have used hybrid approaches that directly add procedures from random media and rough surface scattering theories. Another popularly used approach for this problem is the radiative transfer theory. In contrast to these we present in this paper a unified approach which treats volumetric scattering and surface scattering on an equal footing. For illustration, we choose the following model. The permittivity of the random medium layer has a deterministic part and a randomly fluctuating part. The rough boundaries are parallel planes on the average. All random fluctuations of the problem are zero-mean stationary processes independent of each other. A point source excites waves in the random medium layer and we are interested in the propagation characteristics of waves in the layer.