Theoretical expressions are derived for the sound scattered at a time-dependent rough surface. The calculations are made for a Gaussian shaded source transducer and point receiver. The Helmholtz theorem and Fresnel approximation are used. The rough surface is assumed to be a traveling wave and to have a traveling wave packet type of correlation function. The coherent component of the signal is the product of the Fourier transformation of the surface distribution function and the smooth surface reflection signal. Comparison of theory and experiment shows the coherent component to be sensitive to the non-Gaussian character of the wind-blown water waves. The incoherent components and the temporal correlation function of the scattered sound are given
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