Approximation of spherical wave reflection coefficient from rough sea surface

In underwater applications, acoustic scattering from the sea surface must be considered in any system that utilizes surface-reflected acoustic energy. In this paper, we obtain spherical wave reflection coefficient approximately by expansion of a spherical wave into plane waves and using the method of stationary phase. The obtained spherical wave reflection coefficient depends on various parameters such as frequency and incidence angle of the spherical wave, the length of the path that connects the source to the receiver, and the root-mean-square (RMS) displacement of the rough sea surface. We verify that the spherical wave reflection coefficient approaches to the plane wave reflection coefficient in far field approximation. Finally, the statistical distribution of the spherical wave reflection coefficient is obtained considering statistical characteristics of the source and receiver positions.