Probability distribution of acoustic scattering from slightly rough sea surface

• The Probability Density Function (PDF) of the acoustic wave scattered from rough sea surface is calculated.
• The integral existing in the calculated PDF is approximated using the method of stationary phase.
• The calculated PDF is compared with some commonly used distribution.
• The amplitude of the surface scattered wave is not Rayleigh-distributed in some cases.

This paper focuses on statistical characterization of acoustic scattering from slightly rough sea surface with small Rayleigh parameter. Infinite random rough sea surface is irradiated with a plane wave single-frequency source and the field scattered by this surface is calculated by the Method of Small Perturbation (MSP). Then, Probability Density Function (PDF) of the scattered wave is calculated. The calculated PDF is compared with some commonly used distribution. For real cases, due to directivity of the sound source, only a certain part of the rough sea surface is insonified. The PDF of the scattered wave is also found in this case. To find the PDF of the scattered pressure amplitude it is necessary to solve numerical integrals. When the distance between the reference point and the insonified surface is much greater than the wavelength of the incident wave, obtaining a numerical solution to these integrals is impractical. To avoid this problem, we propose in this paper, to calculate the integrals approximately by using the method of stationary phase. In all cases, the calculated distribution for amplitude of the scattered wave is compared with the distribution proposed in the literature.