Range of Validity of the Rayleigh Hypothesis for Sound Wave Scattering From a Periodic Seafloor

In this paper, sound scattering at a water/sediment periodic interface is modeled by an integral equation method to investigate the range of validity of the Rayleigh hypothesis. Due to the periodicity of surface, coupled integral equations are simplified by introducing the quasi-periodic Green´s function, which can be evaluated with a relatively small number of terms of the spectral series. By comparing the scattering amplitudes obtained from the integral equation method and the method based on the Rayleigh hypothesis, the range of validity of the Rayleigh hypothesis is determined. For a given wavenumber κ of the periodic surface, the maximum surface amplitude hmax beyond which the Rayleigh hypothesis is invalid decreases with frequency of incident waves. For the grazing angle θ = 90^°, h_max is larger than h_c=0.448/κ (the upper limit of surface amplitude determined by the criterion of the Rayleigh hypothesis) in the frequency range 2.5-40 kHz. However, for a small grazing angle, such as, θ = 35^°, h_max is observed to be smaller than h_c for the large surface period Λ at frequency 40 kHz.