A. Yu. Kazarova

Statistical description of chaotic rays in a deep water acoustic waveguide.

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.

Ray-based description of normal modes in a deep ocean acoustic waveguide

Modal structure of the wave field in a deep ocean environment with sound speed fluctuations induced by random internal waves is considered. An approximate analytical description of the modal structure at megameter ranges is derived by combining two known results: (i) relations expressing mode amplitudes through parameters of ray paths and (ii) stochastic ray theory. For a monochromatic wave field, a simple analytical estimate has been obtained for a coarse-grained distribution of acoustic energy between normal modes. Significant attention has been paid to the investigation of the mode pulses, that is, sound pulses carried by individual modes. Analytical estimates for the spread of mode pulse and bias of its mean travel time in the presence of internal waves are derived.

Focusing of a field in a hydroacoustic waveguide into a given depth interval

We propose and test in a field experiment a method that uses an emitting vertical array to focus a field to a given depth interval in a vertical section of an underwater sound channel at the observation distance. The amplitude-phase distribution of signals at the array elements is found by solving the variational problem of maximizing the ratio of mean sound field intensities inside and outside the chosen area of the section. The introduction of an additional restriction on the range of allowable grazing angles of excited waves has made it possible to obtain a solution in the form of a wave beam propagating without bottom reflections. Such solutions can be used for field focusing without information on the bottom parameters.

Reconstruction of the average ocean temperature from the measured travel times of sound pulses

An approximate formula expressing the variations of ray travel times in terms of range-averaged characteristics of temperature inhomogeneities is derived. This formula essentially reduces the underdetermination of the inverse problem, which appears in the reconstruction of climatic variations of the average ocean temperature from acoustic measurement data. The efficiency of the suggested approach is confirmed by numerical simulations.

Focusing of a wave beam in an underwater sound channel

The use of a vertical radiating antenna array for generation of a wave beam propagating in an underwater sound channel along the reference ray trajectory is discussed. The method for selecting the starting field in the antenna aperture for maximum compression of a beam in the specified vicinity of the reference ray is proposed. The estimates showing up to what distances a beam can propagate while remaining narrow as compared to the range of depths between the rotation horizons have been obtained. The problem concerning the distances from the antenna array at which a beam can still be effectively focused in the vicinity of the selected reference ray point is investigated.

Experiment on estimating the coordinates of an emitter on the Black Sea shelf

The paper presents the results of an experiment, conducted in Sukhumi Bay, on estimating the depth of a wideband emitter and its distance to a vertical reception array moored close to shore. The coordinates of the emitter were reconstructed from acoustic measurement data. The solution to the formulated problem was complicated by the absence of reliable information on the bottom relief and bottom parameters. It is demonstrated that under such conditions, matched field processing can be applied to estimate the coordinates of the emitter. For this, when solving the inverse problem, the components of signals without bottom reflection were used as the input parameters.

Ray-based description of shadow zone arrivals

Field experiments and numerical simulation show that due to scattering from internal-wave-induced sound speed perturbations, the sound energy at megameter ranges penetrates well below the unperturbed timefront, i.e., into the geometric shadow. Shadow zone arrivals form continuations of cusps of the timefront. In the present paper, this effect is analyzed using a stochastic ray theory derived for statistical description of chaotic rays. Probability density functions for parameters of perturbed rays, including those penetrating into the shadow zone, are evaluated analytically. This made it possible to derive analytical estimates for a vertical extent of shadow zone arrivals and for a coarse-grained distribution of sound energy in the shadow zone. It is shown that the lengths of cusp extensions into the shadow zone grow with range r as r(1/2). A known estimate for the spread of timefront segments in the presence of internal waves is applied for obtaining a criterion of nonoverlapping of the cusp continuations. These results are derived for steep rays whose grazing angles at the sound channel axis exceed 5°.

Estimation of distortions in the sound field propagating through mesoscale inhomogeneities

Hamiltonian formalism is used to analyze the effect of the mesoscale inhomogeneities of the ocean medium on the ray structure of the sound field. It is shown that the distortions of the structure of the sound field can be successfully estimated by a function that links the values of the canonical variables of the ray action before and after crossing the inhomogeneity. That function is calculated with the use of the standard ray code. Sound propagation through the synoptic eddy and frontal zone is considered.

The possibility of using a vertical array for estimating the delays of sound pulses at multimegameter ranges

The majority of schemes used for acoustic monitoring of temperature fields in the ocean are based on measuring the variations of the so-called ray arrival times, i.e., the travel times of sound pulses along different ray trajectories connecting a source and a receiver. The solution of the inverse problem is considerably hindered by the fact that, in the case of signal detection by a point receiver, it is possible to resolve only the sound pulses propagating along steep rays. To a large extent, this is caused by the phenomenon of ray chaos, which is fully developed at distances of about one thousand of kilometers. The present study shows that the use of a vertical receiving array provides an opportunity to loosen this restriction. An appropriate space-time processing procedure is proposed. The procedure is based on the characteristics of ray arrival distribution in the time-depth plane that remain stable even under the conditions of ray chaos.

Ray Description of the Field of a Distributed Source in a Waveguide

A procedure is proposed for constructing the ray description of the field of a distributed source on a long track. It consists in the generalization of the known transformation relating the mode and ray representations of the field of a point source in a waveguide. The result is used to study the structure of a wave beam emitted by a vertical array. An example of a beam for which a simple analytical description can be obtained not only at long ranges, but also near the source, is considered. The spread of the beam with distance is analyzed.