Signal travel times along chaotic rays in long-range sound propagation in the ocean

Abstract

Numerical calculations show that, in the presence of weak fluctuations of sound velocity, ray trajectories in underwater acoustic waveguides exhibit a chaotic behavior. According to the findings of the late 1990s, under the chaotic conditions, the travel times of sound pulses along trajectories connecting the source and receiver form compact clusters. Each cluster is formed by the rays that have the same sign of their launch angles at the source and the same number of turning points. The cluster center is close to the arrival time of an unperturbed ray with a similar topology. The paper presents a quantitative description of this phenomenon. The ray structure of the field is analyzed using the Hamiltonian formalism in terms of the action-angle canonical variables. The width of the cluster and its shift with respect to the unperturbed ray arrival are estimated. The results of the study explain (from the point of view of geometrical optics) the presence of stable maxima in the initial part of a pulse signal, which are observed in the field and in numerical experiments on the long-range sound propagation in the ocean.