COHERENT FIELD AND SPECULAR REFLECTION AT GRAZING-INCIDENCE ON A ROUGH-SURFACE

The coherent component of the field scattered at grazing angles from a slightly rough pressure release surface is found. This is valid for multiple scattering and is based upon the parabolic integral equation method. Also examined are the scattering of planes waves under the method and in particular, the effect of truncating the boundary integral. It is shown that the coherent field remains invariant when the source and receiver are displaced vertically by equal and opposite distances, as was found numerically in a previous paper. In general, this can be shown to hold because the coherent field due to any plane wave is specular; however, under the parabolic equation method reflection is not specular, and thus the result is of particular interest. Reflection coefficients are given in closed form for several surface statistics, valid asymptotically at large distances.