Sound propagation and scattering in media with random inhomogeneities of sound speed, density and medium velocity

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

Sound propagation and scattering in media with random inhomogeneities of sound speed,density and medium velocity

Abstract

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

On the feasibility of normal wave selection in a shallow-water waveguide

Long-range propagation of low-frequency narrowband sound signals in the near-bottom acoustic channel with random inhomogeneities caused by internal waves and a rough bottom is investigated in the framework of numerical and field experiments. The feasibility of selecting the signal components corresponding to different normal waves is analyzed. The problem of selecting such components is considered for signals of long duration exceeding the characteristic time of the stationary state of the channel.     

Stochastic differential equation analysis for sound scattering by random internal waves in the ocean

The scattering of a weakly divergent narrow sound beam by random inhomogeneities of a fluctuating ocean is considered in the coupled-mode approximation. The random index of sound refraction is described using the Garrett-Munk internal wave spectrum. The problem is solved using the stochastic differential equations for the first-and second-order statistical moments of the acoustic field. The equations are formulated according to the cumulant expansion method. The existence of weakly divergent narrow sound beams in long-range sound propagation was one of the last discoveries of L.M. Brekhovskikh, to which he attached much importance. The concentration of sound into narrow beams away from the axis of the underwater sound channel was first observed experimentally and then explained by Brekhovskikh and his former students Goncharov, Kurtepov, and Petukhov. In the present paper, the scattered field intensity of a sound beam is calculated for different frequencies and source depths. Analytical expressions are obtained for the coefficients of the differential equation. The intermode energy transfer that accompanies the long-range propagation of a weakly divergent sound beam is analyzed. A comparison with the conventionally used Monte Carlo simulation in the parabolic equation approximation is performed.     

Computer modeling of sound fields in the ocean with fine-structured inhomogeneities

The results of a computer modeling of sound propagation in the ocean with fine-structured inhomogeneities are presented. The modeling was performed using a wave code based on the wide-angle approximation, which allows one to estimate the effects of sound field perturbations. These effects include the insonification of the geometric shadow zones and the abnormal attenuation of low-frequency sound in the course of its propagation in an oceanic waveguide. Calculations clearly demonstrate that the fine-structured inhomogeneities of the sound velocity considerably affect the sound propagation in the ocean.     

The contribution of a lateral wave in simulating low-frequency sound fields in an irregular waveguide with a liquid 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.     

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.     

Experimental and theoretical study of the vertical coherence of the sound field in a shallow sea

The combined effect of multiple scattering by random inhomogeneities of a waveguide and bottomcaused sound absorption is known to be a fundamental factor that governs the formation of the sound field in a shallow sea [1, 2]. A number of publications [2–6] present statistical analyses of the fluctuation phenomena that accompany the sound propagation in shallow sea regions. In these publications, most attention is paid to studying the evolution of the intensities of normal waves under the effect of scattering by the random field of internal waves. It is shown that in natural conditions, in addition to the inhomogeneities of the water column, one should take into account the irregular boundaries of the sound channel, which can also affect the correlation characteristics of the sound field. In this paper, we present experimental data on the vertical coherence of the sound field on a fixed path in the Barents Sea. We also compare the experimental data with theoretical calculations based on a model of sound scattering by the rough sea surface.     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

Underwater acoustic scattering from a radially layered cylindrical obstacle in a 3D ocean waveguide

A solution based on coupled mode expansions is presented for the 3D problem of acoustic scattering from a radially layered penetrable cylindrical obstacle in a shallow-water plane-horizontal waveguide. Each cylindrical ring is characterized by a general, vertical sound speed and density profile (ssdp), the ocean environment around the obstacle can be also considered horizontally stratified with a depth-arbitrary ssdp, and the bottom is assumed to be rigid. The total acoustic field generated by an harmonic point source is represented as a normal-mode series expansion. The expansion coefficients are calculated exploiting the matching conditions at the cylindrical interfaces, which results in an infinite linear system. The system is appropriately truncated and numerically solved by using a recursive relation, which involves the unknown coefficients of two successive rings. Results concerning the transmission loss outside and inside obstacles consisting of three cylindrical rings are given for a typical depth-dependent ocean sound-speed profile. The presented solution can serve as a benchmark solution to the general problem of 3D acoustic scattering from axisymmetric inhomogeneities in ocean waveguides at low frequencies.     

Long-range sound propagation in the central region of the Baltic Sea

The data obtained from a set of experiments on the long-range, low-frequency (<5 kHz) sound propagation in the central region of the Baltic Sea are analyzed. The experiments were carried out in the summer season, with a fully developed underwater sound channel. Experimental data on the sound attenuation are presented. A significant excess of the attenuation coefficients over the predicted absorption coefficients is obtained. The quantitative estimates indicate that the sound scattering by internal waves is the most probable mechanism responsible for the observed excessive sound attenuation. The frequency dependence of the attenuation coefficient exhibits a minimum whose position on the frequency axis at the beginning of the summer season noticeably differs from that at the end of summer. The analysis of the propagation conditions allows one to relate the position of this minimum to the critical frequency of the water modes. In addition to the intensity parameters of the sound field, the formation of the time structure of explosion-generated signals propagating in the Baltic underwater sound channel is considered for the case of the sound propagation along the 360-km path crossing the Gotland Hollow. The specific role of the bottom waves in the time structure formation at short distances from the sound source is demonstrated.     

Study of the mechanism for broadening of the spectrum of a low-frequency reverberation signal for sound scattering by near-surface inhomogeneities under conditions of intense wind waves

The paper considers the problem of backscattering of sound waves by near-surface volumetric inhomogeneities under conditions of intense wind waves. We calculate the expected share of the scattered signal spectrum based on the given wind-wave intensity and the depth distribution of volumetric inhomogeneities. For deep ocean conditions in the frequency range of 500–1000 Hz for a pulse duration of 10 s, we measure the levels and shape of the reverberation spectrum for time delays from 20 to 100 s. Comparison of the measured and calculated reverberation spectra has shown their good coincidence.     

On the possibility of using acoustic reverberation for remote sensing of ocean dynamics

The two-point correlation function of diffuse noise fields produced by distributed random sound sources carries useful information on the medium of sound propagation. Such information can be used for performing passive acoustic tomography of the ocean. In a number of cases that are important for practice, the noise field in the ocean is predominated by contributions of individual point sources. Here, a theoretical study is presented on the possibility of determining the sound speed and current velocity in the water column by the correlation processing of reverberation signals measured by two vertical receiving arrays. In other words, we study the possibility of replacing the diffuse noise produced by a great number of delta-correlated sources by waves generated by a localized source and scattered at the rough surface and bottom of the ocean for sensing the medium. The correlation function of scattered waves is calculated by using the method of small perturbations. It is shown that the correlation processing of the scattered waves offers an opportunity of measuring the acoustic nonreciprocity and reconstructing the field of sound speed in the fluid, without using any acoustiLc transceivers.     

High-frequency solitons in media with induced scattering from damped low-frequency waves with nonuniform dispersion and nonlinearity

The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrödinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.     

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.     

Sound scattering by spatially localized inhomogeneities in a shallow-water waveguide in the presence of internal waves

A method is developed for solving the problem of sound scattering by concentrated inhomogeneities in a waveguide of small depth in the presence of internal waves (IW) typical of an oceanic shelf. The sound field fluctuations related to the motion of a model scatterer (a soft spheroid) and to the propagation of the IW are calculated and analyzed. It is shown that the field of internal waves considerably affects the scattered sound field even when the source-receiver and source-scatterer distances are relatively small (about several kilometers). This effect depends not only on the amplitude of the IW, but on their propagation direction as well.     

三维绝热简正波-抛物方程理论及应用

复杂海域通常存在环境参数的水平变化,这会导致声波在传播过程中发生水平折射,呈现出三维效应.利用绝热简正波-抛物方程理论进行三维声场建模,在垂直方向上使用标准简正波模型KRAKEN求解本征值和本征函数,水平方向上使用宽角抛物方程模型RAM求解简正波幅度.该模型物理意义清晰,计算效率高,但由于忽略了各号简正波之间的耦合,只适用于环境参数水平变化缓慢的问题.使用该模型分析了内波环境和大陆架楔形波导中的声波水平折射现象,结果表明,声波的水平折射将水平平面分为不同区域,每个区域内的声场结构明显不同.此外,声强在水平平面内的分布与声源频率和简正波号数有关,这种依赖关系是导致声信号频谱变化、波形畸变以及声场时空扰动的主要原因.     

Sound attenuation on an ocean shelf at short ranges from a source in the presence of surface waves

The effect of surface roughness on the attenuation of low-frequency acoustic waves on a shallow ocean shelf is analyzed using numerical simulation. We focus here on transmission loss during propagation at short (less than 50 water layer depths) ranges from the sound source. The effect is considered both for a soft and hard bottom, when the sound velocity in the bottom is, respectively, lower or higher than the sound velocity in seawater. It is shown that to correctly predict losses at a short range in the presence of a rough upper boundary, it is necessary to take into account the interaction of both propagation and leaky modes. In the case of a hard bottom compared to a low-velocity one, the effect of surface roughness on propagation turned out to be the most pronounced.     

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.