Low-grazing angle scattering from rough surfaces in a duct formed by a linear-square refractive index profile

The problem of rough surface scattering and propagation over rough terrain in a ducting environment has been receiving considerable attention in the l iterature. One popular method of modeling this problem is the parabolic wav e equation (PWE) method. An alternative method is the boundary integral equ ation (BIE) method. The implementation of the BIE in inhomogeneous media (d ucting environments) is not straightforward, however, since the Green's fun ction for such a medium is not usually known. In this paper, a closed-form approximation of the Green's function for a two-dimensional (2-D) ducting e nvironment formed by a linear-square refractive index profile is derived us ing asymptotic techniques. This Green's function greatly facilitates the us e of the BIE approach to study low-grazing angle (LGA) rough surface scatte ring and propagation over rough surfaces in the aforementioned ducting envi ronment. This paper demonstrates how the BIE method can model the combined effects of surface roughness and medium inhomogeneity in a very rigorous fa shion. Furthermore, it illustrates its capability of accurately predicting scattering In all directions including backscattering. The boundary integra l equation of interest is solved via the method of ordered multiple interac tions (MOMI), which eliminates the requirements of matrix storage and inver sion and, hence, allows the application of the BIE method to very long roug h surfaces.