Stochastic differential equation analysis for ocean acoustic energy scattering by internal waves

Abstract

Stochastic coupled mode theory is used to study acoustical scattering of a narrow-angle, low-frequency acoustical beam. Random index of refraction perturbation fields are described using the Garrett-Munk internal wave spectrum. The stochastic differential equations for the first- and second-order statistical moments of the acoustical field are derived using the Markov approach similar to Dozier, Tappert, and Chernov theories. The main objective of the research is to account for cross-mode correlations and to show that the method can be used for a calculation of the detailed structure of the mean acoustic field intensity distribution. For this purpose a narrow finite-frequency beam was taken as an example, and the intensity of the scattering field was calculated as a function of frequency and sound source depth. The coefficients of the matrix differential equation were obtained analytically, and an efficient numerical computation was obtained. Comparisons to Monte Carlo simulation show that the method can be used for detailed statistical sound field analysis in long-range propagation.