Higher Moment Estimation for Shallow-Water Reverberation Prediction

The modeling of the higher moments of shallow-water reverberation is addressed for problems where non-Rayleigh reverberation is caused by scattering from rough boundaries with chi-squared height distributions. Expressions for the first and third spatial moments of chi-squared height-distributed roughness are derived for exponential correlation functions corresponding to von-Karman second-order spectra. The trispectra for these roughness distributions are also derived, and differences are highlighted between these results and the results that are obtained for the limiting case of Gaussian height-distributed higher order spectra. A normal mode model for propagation to and from these scatterers is combined with first-order perturbation theory to compute the higher moments of the reverberation pressure envelope in a 2-D shallow-water waveguide as a function of time, correlation length scale, and non-Gaussianity as parameterized by the degrees of freedom (dof) of the chi-squared distribution. Results show that the non-Rayleighness of shallow-water reverberation with non-Gaussian chi-squared roughness is controlled by both the degree of non-Gaussianity and the ratio of the ensonified scatterer patch size to the correlation length scale. In shallow-water waveguides, the size of the ensonified patch increases with time, due to multipath effects. It is shown that this effect causes a trend towards Rayleighness in the reverberation pressure envelope. It is also shown that when the correlation length scale of the scatterers is much greater than the size of the ensonified patch, the effects of multipath time spread on the reverberation statistics is much reduced, and non-Rayleighness can persist.