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.     

Illumination of the shadow zone in a two-channel oceanic waveguide with a fine structure of sound speed inhomogeneities

The experimental data on the sound field structure, which were obtained by emitting a continuous pseudonoise signal (a midfrequency of 3.2 kHz) in a two-channel oceanic waveguide, are compared with the calculations performed by the wave program with allowance for the fine structure of the sound speed inhomogeneities. A considerable increase in the intensity of the sound field with a definite angular spectrum is observed in the upper channel in the first shadow zone, and, in the experiment, the increase begins nearer to the sound source than predicted by the wave and ray calculations for a smooth sound speed profile. These features of the field structure are explained by the illumination of the shadow zone by the regular scattering of signals from highly anisotropic fine-structure inhomogeneities of the sound speed profile, which are clearly pronounced in the region of the given oceanic experiment.     

Spectral-energy characteristics of sound fields scattered by fine-structured inhomogeneities of sound velocity into the geometrical shadow zone

In analyzing experimental results obtained with explosive sources in the tropical zone of the Indian Ocean, a good agreement was obtained for spectral-energy characteristics of signals observed in the first geometrical shadow zone with computer calculations of the sound field scattered by fine structure inhomogeneities of the fractal type. From the comparison of the results of calculating the frequency characteristics of sound fields in the shadow zone by the wave code and by the method combining ray acoustics with the wave theory of sound scattering, it was found that both methods are appropriate for describing the real processes of scattering and propagation of sound in the ocean with fine-structured stratification and that these methods can be used for solving inverse problems.     

Formation Mechanisms for the Spectral Characteristis of Low-Frequency Reverberations and Predictive Estimates

The paper considers the problem of monostatic scattering of low-frequency sound waves by nearsurface volumetric inhomogeneities under conditions of intense wind waves. We calculate the expected shape of the scattered signal spectrum taking into account the distribution of the volumetric inhomogeneities over the surface and their quasiperiodic motion in three-dimensional space under the action of wind waves. For deep-ocean conditions, a carrier frequency of 228 Hz, and a pulse duration longer than 100 s, we compare the experimental data on the shape of the reverberation spectrum with theoretical estimates. We compare the spectral levels of subsurface scattering with similar data on sound scattering directly on the wind-roughed surface.     

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.     

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.     

Regional variability of the phenomenon of sound penetration into shadow zones in the ocean with fine-structure stratification

The regional variability of the phenomenon of the shadow zone insonification in the ocean is manifested in the variability of the main parameters of the sound signals that penetrate into these zones because of the scattering by the fine-structure inhomogeneities of the refractive index. The intensity of the phenomenon is governed by a combination of the vertical distribution of intensity of the fine-structure inhomogeneities and the caustics that exist in the insonified domains, along with the caustic intensity and position, both of which depend on the mean sound speed profile and on the geometry of the experiment. For the chosen typical regions of the ocean, the characteristics of the fine structure are systematized, and the phenomenon under study is analyzed. The results obtained offer a justified approach to solving inverse problems and a way to perform practical-purpose studies aimed at improving the ultimate performance of underwater observation and monitoring systems.     

On the low-frequency sound scattering in a moving microinhomogeneous medium

The Rayleigh law that governs low-frequency sound attenuation due to the scattering by inhomogeneities in a microinhomogeneous medium is generalized to the case of particles moving in a flow or falling under gravity. Corrections to the scattering’s cross section that adjust the Rayleigh law to the case of a potential flow around inhomogeneities are calculated. It is shown that, when microinhomogeneities are moving in a viscous medium, the characteristics of discrete scatterers may considerably deviate from the Rayleigh law. Based on the data on the velocity and size distribution of falling drops of water in air, refinements are proposed for the laws of low-frequency sound scattering by rain.     

Long-range sound propagation in the shallow-water part of the Sea of Okhotsk

Experimental data on the long-range propagation of explosion-generated sound signals in the shallow-water northern part of the Sea of Okhotsk are analyzed. The propagation conditions in this region are characterized by a fully-developed underwater sound channel that captures the rays crossing the channel axis at angles lower than 3°. The experimental data reveal a small increase in the duration of the sound signal in proportion to the range with the proportionality factor lower than 0.00025 s/km. The frequency dependence of attenuation exhibits a pronounced minimum whose position on the frequency axis is close to the critical frequency of the first “water” mode (about 160 Hz). The increase in the attenuation coefficient at lower frequencies is confirmed by the field calculations performed with the wave-field computer code and is explained by the sound energy loss in the bottom sediments. At frequencies higher than 200 Hz, as in the Baltic Sea, the most probable reason for the attenuation to exceed the absorption in sea water is sound scattering by internal waves.     

Sound scattering by random fractal inhomogeneities in the ocean

Sound scattering by random volume inhomogeneities (fluctuations of the refraction index in a medium) with an arbitrary anisotropy is considered using the small perturbation method (Born’s approximation). Surfaces (boundaries) of the inhomogeneities are deemed to be fractal ones: the energy spectra of the refraction index fluctuations follow the power law with a nonintegral exponent. Formulas are obtained for the volume scattering coefficient. Frequency and angular dependences of the scattering coefficient and their relations to the fractal dimension of inhomogeneities with different kinds of anisotropy and different sizes (on the sound wavelength scale) are presented. The fractal dimension of the inhomogeneities is estimated.     

Single scattering of waves by random strong anisotropic inhomogeneities

Research is carried out into scattering of waves by random strong anisotropic inhomogeneities when the inhomogeneities are in the distant zone according to one (transverse) scale and at the same time they are in the near zone according to another (longitudinal) scale. To analyse the formulas of the single scattering the stationary phase method in the longitudinal coordinate integral is used. It is shown that the angle sensitivity of strong anisotropic scattering, unlike weak anisotropic scattering, strongly depends on the longitudinal statistical homogeneity of the medium.     

The angular dependence of the coefficient of sound reflection from anisotropic volume inhomogeneities of the ocean

The small perturbation method is used to consider the scattering of sound by random volume inhomogeneities of the ocean. The inhomogeneities are assumed to be horizontally anisotropic with their horizontal dimensions far exceeding the vertical ones. Expressions are obtained for the angular dependence of the scattering coefficient. Vertical and horizontal sections of the scattering pattern are presented, and the angular widths of its maxima are analytically estimated.     

Low-frequency bottom reverberation in shallow-water ocean regions

A phenomenological model of long-range reverberation in a shallow sea is developed to describe the statistical characteristics and interference of the sound field scattered by bottom inhomogeneities. Experimental data on the scattering of low-frequency sound by the sea bottom are presented for a shallow-water region of the Barents Sea. The results of a numerical simulation of the low-frequency bottom reverberation in a multimode waveguide are described. The simulation is based on experimentally measured values of backscattering strength.     

Modeling of bottom backscattering from three-dimensional volume inhomogeneities and comparisons with experimental data

In this paper, backscattering from 3D volume inhomogeneities in the seabed is modeled and the results compared with experimental data at 250-650 Hz. The experiment was part of the Acoustic Reverberation Special Research Program (ARSRP) and the data were obtained in a sediment pond on the western flank of the Mid-Atlantic Ridge. A volume scattering model based on first-order perturbation theory is developed incorporating contributions from both sound speed and density fluctuations. With the propagators, i.e., the Green's functions, handled accurately through numerical wave number integration and random fluctuations generated effectively by a new scheme modified from the spectral method, the model is capable of simulating monostatic, backscattered fields in the frequency domain as well as in the time domain owing to 3D volumetric sediment inhomogeneities. The model compares favorably and consistently with the ARSRP backscattering data over the entire frequency band, with the fluctuations of sound speed and density in two irregular sediment layers, identified from the data analysis, described by a power-law type of power spectrum.     

Mean field of a low-frequency sound wave propagating in a fluctuating ocean

Statistical characteristics of low-frequency sound waves propagating over long distances in a fluctuating ocean are important for many practical problems. In this paper, using the theory of multiple scattering, the mean field of a low-frequency sound wave was analytically calculated. In these calculations, the ratio of the sound wavelength and the scale of random inhomogeneities can be arbitrary. Furthermore, the correlation function of inhomogeneities is expressed in terms of a modal spectrum (e.g., internal waves modes). The obtained mean sound field is expressed as a sum of normal modes that attenuate exponentially. It is shown that the extinction coefficients of the modes are linearly related to the spectrum of random inhomogeneities in the ocean. Measurements of the extinction coefficients can therefore be used for retrieving this spectrum. The mean sound field is calculated for both 3D and 2D geometries of sound propagation. The results obtained can be used to study the range of applicability of the 2D propagation model.     

Caustics and volume prereverberation in a surface oceanic waveguide

A kinematic model of volume prereverberation caused by sound scattering from different types of inhomogeneities in the caustic zones of a surface oceanic waveguide is considered. Numerical estimates are presented for the prereverberation time as a function of range, number of ray cycles, and width of the scattering diagram.     

Sound scattering from small compact inhomogeneities in a sea waveguide: The inverse problem

An approach based on the redistribution of acoustic energy between waveguide modes is used to state the inverse problem of sound scattering from small compact inhomogeneities in a shallow-water waveguide. Numerical results are presented.     

Multiple small-angle scattering—A review

Small-angle scattering (SAS) is a powerful experimental technique in condensed matter physics for studying structural features of inhomogeneities of colloidal dimensions. So far the technique has been largely exploited to study thin samples for which the single scattering approximation, for the radiation-matrix interaction, holds good. The single scattering approximation is invalid when the thickness of the sample exceeds the scattering mean free path. This situation calls for a guideline to analyse the scattering data having significant contribution from multiple scattering. Since multiple scattering broadens the scattering profile, the beam broadening nature of multiple scattering can also be exploited, by making the sample suitably thick, to study large size inhomogeneities which are otherwise inaccessible to a small-angle scattering set up because of its resolution constraints. The present article presents a review and extension of the theoretical basis for analysing multiple scattering data from the point of view of a recent formalism on multiple small-angle scattering. The formalism is valid for both monodisperse and polydisperse scattering media characterized by the presence of large size inhomogeneities in the matrix. It is shown that multiple scattering from a polydisperse sample can be described by a system of coupled integrodifferential equation. However, multiple scattering from a monodisperse sample can be described by a Fokker-Planck type of equation. These equations have been analysed with an emphasis laid on the nature of the structural information pertaining to the inhomogeneities which is extractable from the multiple scattering profile. When the linear dimension of inhomogeneities becomes comparable to the scattering mean free path of the radiation in the sample, the statistical nature of the medium becomes pronounced. The statistical nature of the medium modulates the scattering profile. The modulation effect could be broadening or narrowing of the profile depending upon the nature of the inhomogeneities and their population distribution. The limiting regimes of validity and the implications of various approximations, frequently used to analyse the scattering data, have been indicated.     

Scattering of sound in a moving viscous microinhomogeneous medium at large Reynolds numbers

A generalization of the Rayleigh law of a low-frequency sound attenuation in a microinhomogeneous medium to the case of scattering particles moving in a viscous liquid at a large Reynolds numbers is proposed. It is shown that, under these conditions, the attenuation may be independent of the scattering by the moving particles themselves but be only determined by the flow caused by these particles, the maximum attenuation being observed in the direction across the particle motion. The corresponding corrections proportional to the first power of the hydrodynamic Mach number are compared with the corrections lying at the basis of the modified Rayleigh law, which was proposed earlier for the potential flow of an ideal liquid around inhomogeneities, and also with the laws of scattering in a moving viscous microinhomogeneous medium at a small Reynolds numbers. As an example of the operation of the generalized law, characteristics of the sound scattering by rain are refined.     

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.