Abstract
A general asymptotic theory of scattering by a moving rough surface is presented. The theory is valid for a slowly varying refractive index, and for ocean-surface wave heights that are small compared with the acoustic wavelength and the ocean-surface correlation length. In contrast with the Kirchhoff or physical optics approximation, this theory is valid when the acoustic wavelength and ocean-surface correlation length are of the same order. The ocean surface is described as a sum of gravity waves of varying frequency progressing in different directions. It is demonstrated that, to a given order of approximation in the asymptotic theory, the average energy associated with signal sideband rays is precisely accounted for by a reduction of intensity of the reflected carrier. Wave number diagrams are introduced which are extremely useful for depicting the directions of the incident and scatteres rays at the surface, demonstrating the effect of varying surface-wave and acoustic frequency, and demonstrating the frequency cutoff of the sideband power spectrum. The phenomenon of Bragg resonance at glancing incidence of the carrier is also easily depicted. The theory can accomodate the effects of ray focusing, both in the carrier and sidebands, through the use of uniformly valid asymptotic expansions which account for the presence of caustics. Subject Classification: [43]30.40, [43]30.20, [43]30.25, [43]30.30.
Published Version
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