A random matrix approach to long range acoustic propagation in the ocean.

Abstract

Low frequency sound propagates in the ocean within a wave guide, formed by the confining effects of temperature, salinity, and pressure on the sound speed. Within the wave guide, sound scatters due to range dependent sound speed oscillations from internal waves. These weak perturbations in the sound speed serve to randomize the acoustic signal so that the structure formed by the time series of arrivals at the receivers (i.e., the timefront) contains only minimal average information about the propagation through the action of a generalized central limit theorem. This study characterizes this information by the parameters of a statistical ensemble model for the propagation. The propagation is described by the evolution of a unitary propagation matrix, whose elements are the complex probability amplitudes for modal transitions during the propagation. The ensemble model is constructed from a product of unitary random matrices utilizing complex Gaussian random variables with minimal information about the propagation to 50 km stored in a matrix of variances and a vector of mean phases. A comparison of the properties of the average intensity timefront resulting from this ensemble model is made with those from the simulated propagations for several ranges. [This work was supported by ONR and NSF.]