The mean Green's dyadic for a half-space random medium - A nonlinear approximation

The vector problem of a source embedded in a half space random medium is considered, and a zeroth-order solution for the mean Green's dyadic in the nonlinear approximation is derived. This is accomplished through application of a two-variable expansion method to obtain a perturbation solution of the Dyson equation for the mean Green's dyadic. The final results of the dyadic are given in closed form as a corrected effective propagation constant. It is noted that these results show a significant difference from those of the one-dimensional problem considered by Tsang and Kong (1976). Whereas the scalar solution gives different effective propagation constants for the component waves in the Green's function, the vector solution derived contains only a single propagation constant for all of the components in the Green's dyadic.