Statistical description of chaotic rays in a deep water acoustic waveguide

Abstract

This paper analyzes the chaotic ray dynamics at multimegater ranges in a deep water environment with internal-wave-induced fluctuations of the sound speed. The behavior of acoustic ray paths is investigated using the Hamiltonian formalism expressed in terms of action-angle variables. It is shown that the range dependence of the action variable of chaotic ray can be approximated by a random Wiener process. On the basis of this result an approximate statistical description of the chaotic ray structure is derived. Distributions of coordinates, momenta (grazing angles), and actions of sound rays are evaluated. This statistical approach is used for studying ray travel times, that is, arrival times of sound pulses coming to the receiver through different ray paths. The spread of travel times for a bundle of rays with close starting parameters and the influence of sound speed fluctuations on the timefront representing ray arrivals in the time-depth plane are examined. Estimates for the widening and bias of the timefront segment caused by the fluctuations are obtained.