Reflection, by a Two-dimensional Ocean Surface, of Plane Sound Waves Coming from the Water Side

Problems involving the reflection of radiation by random rough surfaces arise in a number applications. We shall be interested primarily in an acoustic plane wave impinging on the surface from the water side. The acoustic pressure changes vanish at the surface. We use an expansion in polynomials of Guassian functionals. The method can be extended to more general situations involving more than one medium with irregular separating surfaces and three dimensional surfaces. We treat here a two-dimensional rough surface. By means of the Wiener-Hermite (W-H) expansion, we represent stochastic field functions using the (assumed) Gaussian reflecting surface as the basic element, to three terms. Multiple reflection effects are visible, even for these low order terms in the expansion. Such reflections can be expected to greatly enchance backscatter at grazing incidence.