Ray dynamics in long-range deep ocean sound propagation

Recent results relating to ray dynamics in ocean acoustics are reviewed. Attention is focused on long-range propagation in deep ocean environments. For this class of problems, the ray equations may be simplified by making use of a one-way formulation in which the range variable appears as the independent (timelike) variable. Topics discussed include integrable and nonintegrable ray systems, action-angle variables, nonlinear resonances and the KAM theorem, ray chaos, Lyapunov exponents, predictability, nondegeneracy violation, ray intensity statistics, semiclassical breakdown, wave chaos, and the connection between ray chaos and mode coupling. The Hamiltonian structure of the ray equations plays an important role in all of these topics.     

The Ray-Wave correspondence and the suppression of chaos in long-range sound propagation in the ocean

The long-range sound propagation in a horizontally inhomogeneous underwater sound channel is considered. It is shown that the vertical oscillations of inhomogeneity affect the near-axis rays in a resonant way and destroy their stability. As a consequence, the near-axis rays exhibit a chaotic behavior. The ray chaos manifests itself as intensification of interaction between adjacent low-order modes. In this case, a great number of strongly coupled modes appear, and the field structure near the channel axis becomes diffusive. However, as the signal frequency decreases, the inhomogeneity oscillations in depth lead to decoupling of adjacent modes and, hence, to suppression of chaos. As a result, the field structure near the channel axis becomes regular, which is confirmed by numerical simulation.     

Wave chaos and mode-medium resonances at long-range sound propagation in the ocean

We study how the chaotic ray motion manifests itself at a finite wavelength at long-range sound propagation in the ocean. The problem is investigated using a model of an underwater acoustic waveguide with a periodic range dependence. It is assumed that the sound propagation is governed by the parabolic equation, similar to the Schrodinger equation. When investigating the sound energy distribution in the time-depth plane, it has been found that the coexistence of chaotic and regular rays can cause a "focusing" of acoustic energy within a small temporal interval. It has been shown that this effect is a manifestation of the so-called stickiness, that is, the presence of such parts of the chaotic trajectory where the latter exhibit an almost regular behavior. Another issue considered in this paper is the range variation of the modal structure of the wave field. In a numerical simulation, it has been shown that the energy distribution over normal modes exhibits surprising periodicity. This occurs even for a mode formed by contributions from predominantly chaotic rays. The phenomenon is interpreted from the viewpoint of mode-medium resonance. For some modes, the following effect has been observed. Although an initially excited mode due to scattering at the inhomogeneity breaks up into a group of modes its amplitude at some range points almost restores the starting value. At these ranges, almost all acoustic energy gathers again in the initial mode and the coarse-grained Wigner function concentrates within a comparatively small area of the phase plane.     

On the stability of long-range sound propagation through a structured ocean.

Several acoustic experiments show a surprising degree of stability in wave fronts propagating over multi-megameter ranges through the ocean's sound channel despite the presence of random-like, sound-speed fluctuations. Previous works have pointed out the existence of chaos in simplified ray models incorporating structure inspired by the true ocean environment. A "predictability horizon" has been introduced beyond which stable wavefronts cease to exist and point-wise, detailed comparisons between even the most sophisticated models and experiment may be limited for fundamental reasons. By applying one of the simplified models it is found that, for finite ranges, the fluctuations of the ray stabilities are very broad and consistent with log-normal densities. A fraction of the ray density retains a much more stable character than the typical ray. This may be one of several possible mechanisms leading to greater than anticipated sound-field stability. The log-normal ray stability density may underlie the recent, experimentally determined, log-normal density of wave-field intensities [Colosi et al., J. Acoust. Soc. Am. 105, 3202-3218 (1999)].     

深海表面层声速剖面变化对声传播的影响

在我国部分海域，表面声速常常在较短的时间内从弱正梯度变为弱负梯度，这将对表面附近的声传播产生巨大影响。本文通过数值模拟的方法，讨论了表面层声速梯度变化对声传播的影响，同时解释了某次海上实验出现的异常现象：在同一地点同一航向，前后两天海况相同，水文相差不大，第一天的实验可以在50km之外接收到信号，而第二天只能在30km处才能收到信号。     

Broadband sound propagation in shallow water and geoacoustic inversion

Part of an experiment to test a measurement package in a shallow water region in the Gulf of Mexico was designed to gather broadband acoustic data suitable for inversion to estimate seabed geoacoustic parameters. Continuous wave tow acoustic signals at multiple frequencies and broadband impulsive source signals were recorded on a horizontal line array in a high-noise environment. Simulated annealing with a normal mode forward propagation model is utilized to invert for a geoacoustic representation of the seabed. Several inversions are made from different data samples of two light bulb implosions, the measured sound speed profiles at the HLA and at the positions of the light bulb deployments, and for two different cost functions. The different cost functions, measured sound speed profiles, and measured time series result in different inverted geoacoustic profiles from which transmission loss is generated for comparison with measurements. On the basis of physical consistency and from the comparison of the transmission loss and time series, a best estimate geoacoustic profile is selected and compared to those obtained from previously reported inversions. Uncertainties in the sound speed profile are shown to affect the uncertainties of the estimated seabed parameters.     

Numerical modeling of sound propagation in an inhomogeneous waveguide with absorption

Computation of the acoustic field in vertically and horizontally inhomogeneous waveguides with allowance for absorption is considered. The method of normal waves and the parabolic equation method are used as alternative approaches to the problem. The efficiency of the algorithms suggested is demonstrated by a test example of sound propagation in a wedge with the acoustic velocity depending on the depth.State University, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 1–2, pp. 134–138, January–February, 1995.     

Investigation of long-range sound propagation in surface ducts

Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze the features of surface-duct propagation in this paper. Firstly, according to the Lloyd-mirror theory, a shallow point source generates directional lobes, whose grazing angles are determined by the source depth and frequency. By assuming a part of the first lobe to be just trapped in the surface duct, a method to calculate the minimum cutoff frequency （MCF） is obtained. The presented method is source depth dependent and thus is helpful for determining the working depth for sonar. Secondly, it is found that under certain environments there exists a layer of low transmission loss （TL） in the surface duct, whose thickness is related to the source geometry and can be calculated by the Lloyd-mirror method. The receiver should be placed in this layer to minimize the TL. Finally, the arrival angle on a vertical linear array （VLA） in the surface duct is analyzed based on normal mode theory, which provides a priori knowledge of the beam direction of passive sonar.     

海洋内波对水下声场的影响

海洋内波是海水内部的波动之一,它与海洋表面的海浪运动有着非常不同的物理特征。海洋内波会引起海水温度剖面发生剧烈的波动,这种波动具有很强的方向性和时变性,对水下声传播影响巨大,并展现出一些很奇特的声波导效应(包括二维波导效应和三维波导效应),给水下目标的探测与定位以及水声通信等带来严重影响。海洋内波对声场的影响研究涉及到海洋动力学和水声学两个学科领域,文章重点介绍海洋内波对声场影响研究领域的相关进展,并对内波环境下典型声波导现象进行了讨论,最后对该领域未来的发展进行了总结和展望。     

Effect of a sloping bottom on sound propagation

Acoustical Physics - The paper presents the results of field measurements of acoustic fields generated in autumn hydrological conditions of the Sea of Japan shelf by a TON-320Hz autonomous signal...     

Methods for measuring bistatic characteristics of sound scattering by the ocean bottom and surface

It is very interesting to measure the bistatic characteristics of sound scattering by the ocean bottom and surface for the development of present-day hydrolocation net-centric schemes. Possible methods for measuring scattering bistatic characteristics are evaluated. The angular characteristics of reverberation related to illumination of a water area by active linearly frequency-modulated signals are studied using linear passive arrays to test a measuring scheme in a shallow water area with a depth of ~20 m in the 1–3 kHz frequency range. The bistatic sound-scattering characteristics in the water area are calculated based on the measurements. The obtained characteristics are compared with the known data on the backscattering of sound.     

Sound wave propagation in a vertically inhomogeneous ocean

Propagation of sound waves generated by a time dependent acoustic source in a vertically inhomogeneous ocean is considered. The effect of the solid bottom is included so that both the longitudinal and shear waves can be excited inside the bottom. The possibility of exciting a lateral shear wave by the acoustic source is also discussed. Although the results presented here are formal and general, physical interpretations have been offered whenever possible.     

Features of sound propagation in the ocean with fine-structure inhomogeneities

We analyze the results of an experiment using an explosive sound source in the tropical part of the Indian Ocean. We consider the time structure of sound signals in geometric shadow zones to a distance of 270 km and the scheme of how the sound field in the shadow zone is formed by rays reflected from horizontally extended fine-structured sound velocity layers. From the results of calculation using a wave program that realizes the method of psuedodifferential parabolic equations, we analyze the influence of signal scattering by fine-structure sound velocity inhomogeneities on the sound field distribution in a waveguide. We show that the field formed by spots of light in each of the shadow zones is generated by a regular field and propagates in parallel to it, taking energy from the regular zone in the near field and in each subsequent convergence zone. This mechanism causes an additional decrease in the field in illuminated zones, which can be interpreted as additional attenuation of the regular sound field.     

The WKBZ mode approach to sound propagation in range-independent ocean channels

I.IntroductionThenorma1-modeapproachcangiveanexactso1utiontotheacousticfie1dinastratifiedmedium,soitisoftenusedtocomparewithotherapproximatemethodssuchasraytheory,parabo1icequationl'](PE)methodandGaussianbeam[21approach,andtakenasacriteriontochecktheaccuracyofapproximatemeth0dsl3J.Themodeapproachmayalsobeextendedtorange-dcpendente..i,onmentsl4.5l.Thoughtherearemanynumerica1propagationcodesbasedonthemodeapproachI'],theconventionalmodeapproachisawkwardtoapplyt0'higherfrequencya-ndbroadbandprop…     

Simulation of low-frequency sound propagation in an irregular shallow-water waveguide with a fluid bottom

A further development of a previously proposed approach to calculating the sound field in an arbitrarily irregular ocean is presented. The approach is based on solving the first-order causal mode equations, which are equivalent to the boundary-value problem for acoustic wave equations in terms of the cross-section method. For the mode functions depending on the horizontal coordinate, additional terms are introduced in the cross-section equations to allow for the multilayer structure of the medium. A numerical solution to the causal equations is sought using the fundamental matrix equation. For the modes of the discrete spectrum and two fixed low frequencies, calculations are performed for an irregular two-layer waveguide model with fluid sediments, which is close to the actual conditions of low-frequency sound propagation in the coastal zone of the oceanic shelf. The calculated propagation loss curves are used as an example for comparison with results that can be obtained for the given waveguide model with the use of adiabatic and one-way propagation approximations.     

Computer modeling of sound propagation in the ocean with fractal inhomogeneities

The wave-field computer code based on the wide-angle parabolic equation is modified and adapted to the problems of sound scattering in a medium with anisotropic inhomogeneities of fractal type. To verify the computer code, a model numerical experiment on determining the angular dependence of the scattered sound field is performed for different anisotropy coefficients of the sound speed inhomogeneities. The comparison of the computed data with the theoretical dependences shows their rather good agreement and indicates that the computer code can be applied to calculations of sound propagation in the ocean with fine-structure inhomogeneities possessing fractal properties.     

Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional (3D) coupled-mode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the 3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Padé approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.