A. L. Virovlyansky

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.

Focusing of a sound beam in an underwater waveguide using a vertical antenna

We propose a method for calculating the amplitude-phase distributions of signals on the elements of an emitting antenna for generating narrow wave beams and field focusing at given points of the waveguide. The efficiency of the method is confirmed by the data of a field experiment conducted in Lake Ladoga.

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°.

Joint statistical moments of mode amplitudes at different frequencies in a random acoustic waveguide

This paper considers an approximate ray-based analytical approach for evaluating the joint statistical moments of mode amplitudes in an acoustic waveguide with large-scale sound speed fluctuations. Explicit analytic expressions for the statistical moments are derived from an approximate analytical solution of the mode-coupling equations. The analytic solution allows one to deduce a scaling law establishing the connection between amplitudes of modes with the same ratio of the mode number to frequency. The applicability of the ray-based approach for evaluating the joint statistical moments of modes amplitudes including the moments at different frequencies is demonstrated using the Monte Carlo simulation of sound fields in a model of the underwater acoustic waveguide in a deep ocean. Numerical simulation also shows different manifestations of the scaling law. In particular, it is shown how this law manifests itself in the acoustic energy distribution between normal modes, in the jump-like range variations of statistical moments, and in the shape of the correlation function between amplitudes of different modes at different frequencies.

Focusing of sound pulses using the time reversal technique on 100-km paths in a deep sea

Numerical and analytical studies are performed on how unstable fluctuations of the parameters of the medium in a deep sea affect the focusing of sound pulses using the time reversal method. The simplest situation, when point sources and receivers are used for emission and reception, is considered. Pulse propagation in the direct and backward directions is numerically simulated by the parabolic equation method. Calculations are performed for sound signals with frequencies of several tens of hertz. It is shown that, in the presence of sound velocity fluctuations caused by random internal waves, noticeable attenuation of the field amplitude at the center of the focal spot can be observed beginning from distances of 200 to 400 km. As the central frequency of the pulsed signal increases, the effect of nonstationarity of the perturbation on the focusing is amplified. This phenomenon is explained qualitatively and quantitatively in the geometrical optics approximation.

Observation of Stable Sound Field Components in Lake Ladoga

The paper presents the results of processing measurement data on the spatiotemporal structures of sound fields in Lake Ladoga. Measurements were taken with an extended vertical receiver array. The aim of processing was to isolate the field components that were stable with respect to small variations in the waveguide parameters. Since a model of the medium is inevitably inaccurate, such components can be predicted with greater accuracy than the total field. In terms of the ray approach, a stable component is generated by a beam of rays propagating over close trajectories. The discussed experiment analyzed sound fields excited by a point source that emitted wideband pulses, as well as the fields of wave beams excited by the emitting vertical array at fixed frequencies. In both cases, the processing results showed that the isolated stable components, as expected, coincide substantially better with the prediction of theoretical calculation (by the wide angle parabolic equation method) than with the total wave field.

Minimal size of the focal spot when focusing a field in a waveguide using a vertical array

The paper considers the problem of using a vertical array to focus a monochromatic field in the vicinity of a given point of an underwater sound channel. The solution to the problem is discussed, which has been obtained with a limitation on the initial grazing angles of the emitted waves. The limitation is introduced to increase the stability of the solution to the influence of random perturbations of the sound velocity field. Then, the radiated field represents a wave beam propagating along a reference ray that connects the center of the array and the focusing point. In the geometric optics approximation, analytic estimates of the smallest possible dimensions of the focal spot are obtained. A simplified version of the formula is obtained for the vertical scale of the spot convenient for rough express estimates and comparison of the focusing properties of waveguides with different sound velocity profiles.