Integral Expression of Sea-surface Scattering Filed and Behaivour of Fresnel Zone

Sound wave scattering from the rough sea surface is studied. The sea surface was discretized using a step function to compute sound scattering. Wavenumber integration of the sound field is then applied to the sound wave scattering from a pressure-release infinitesimal segment of the step function representing displacements of the rough sea surface. The scattering mechanism accommodated here is a specular reflection of the sound wave from the sea surface, where the reflection coefficient is equal to −1. Despite this simplicity, not only is the computed reflection coefficient with surface roughness in excellent agreement with the theoretical value for a Rayleigh parameter of less than 3, but the statistical properties of the scattering-wave amplitude obey the Nakagami-Rice distribution. Our solution for the scattering fields works well, and we conclude that a random displacement of the sea surface can create the random phase of the sound wave signal. In addition, we confirm that the coherent component is due to the contribution of the 1st Fresnel zone. Our model and numerical experiments revealed the essence of coherent/incoherent scattering components. The difference between the forward and the back scattering is also discussed.