Normal-mode statistics of sound scattering by a rough elastic boundary in underwater wave-guide in a full coupled mode approach, including back-scattering

The underwater sound scattering by rough sea surface, ice, or rough elastic bottom is studied. The effects of scattering from a rough elastic boundary are included in a coupled mode propagation model by the analytical equation for solid-state layer impedance. A full two-way coupled mode solution was used to derive the stochastic differential equations for the second order statistics in a Markov approximation for a transport theory. The coupled mode matrix was approximated by a linear function of one random parameter such as ice-thickness or the surface perturbation. A one parameter Gaussian model has a form of a two-way differential stochastic equation for the correlation of normal mode coefficients. The derived equation relates the correlation matrix of mode coefficients (for both directions) with the correlation function of the rough boundary and the power spectrum of the its slopes. The theory gives a solution for sound attenuation and horizontal coherence over long-range propagation along random inter...