A Random Matrix Approach to Long Range Acoustic Propagation in the Ocean
Hegewisch, Katherine Christina
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Low frequency sound propagates in the ocean within awave guide, formed by the confining effects oftemperature, salinity and pressure on the sound speed.This wave guide enables long range acoustic propagation upwards of 3000 km.Within the wave guide, sound scatters due to range dependent sound speedoscillations 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 propagationthrough the action of a generalized central limit theorem. The goal of this study is to characterize this remaining 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 $50$ kmstored 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. The results of this study suggest that a random matrix model is an appropriate model for characterizing the information contained in the acoustic timefronts at long ranges.