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.     

Methods for calculating low-frequency surface reverberation at known sea roughness characteristics

The problem of estimating the parameters of a reverberation signal generated due to scattering of acoustic waves on a rough surface is considered for a bistatic localization scheme using the example of tone and tone-pulse signals. Relatively simple calculation schemes that make it possible to recalculate three-dimensional space-time roughness spectra into angular-frequency reverberation characteristics and determine the positions of the surface regions that mainly contribute to the integral reverberation level are found. A reverberation spectrum is calculated for the wind waves typical for shallow-water closed basins, and the positions of the scattering regions forming the components of this spectrum are determined.     

The influence of random drift of resonance-scattering harmonics on the frequency spectrum of surface acoustic reverberation in the ocean

We propose a modified model for the frequency spectrum of surface reverberation with allowance for random drift of Bragg resonance harmonics due to long wind-generated waves. The dependence of this effect on the parameters of large-scale surface waves is analyzed. Analytical expressions for the reverberation frequency spectrum are obtained for both narrow-band and wideband sounding signals. It is shown that for matched filtering of wideband signals, the considered effect leads to an increase in the effective pulse reverberation volume. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 1, pp. 20–30, January 2007.     

Calculation of the reverberation spectrum for Doppler-based sonar

For monostatic sonar using long pulsed tone signals, the problem of evaluating the spectrum of reverberation due to sound wave scattering by a rough sea surface is solved. Relatively simple computational schemes are proposed, which make it possible (i) to transform the three-dimensional spectra of surface waves to the frequency-angular characteristics of reverberation and (ii) to choose the optimal operating frequency band for a Doppler sonar from the point of view of reverberation. For typical wind wave characteristics measured in shallow water areas, the spectral levels of reverberation are estimated in the frequency band of acoustic signals within 0.4?C2 kHz.     

Reverberation of Wideband Signals in Shallow Water when Using Sound Focusing

Within the framework of the normal mode approximation, expressions are obtained for calculating bottom reverberation signals recorded by a horizontal array in an inhomogeneous shallow-water waveguide in a wide frequency band. These expressions can be used to simulate bottom-scattered signals both for a monostatic and bistatic geometry, as well as in the case when sound focusing is applied. The constructed model is used to numerically study the structure of bottom reverberation in a waveguide with different parameters and characteristics of the receiver and source systems. The considered bottom inhomogeneities are the slope of the bottom, change in thermocline depth, and wind waves. The study demonstrates the promise of using sound focusing as time reversal using a single receiver–transmitter element to enhance the reverberation signal arriving from a given bottom area.     

Bulk plasma waves in a randomly inhomogeneous conductor

The modification of the spectrum and damping of bulk plasma waves due to three-dimensional random inhomogeneities of the density of a degenerate electron gas in a conductor have been investigated using the averaged Green??s function method. The dependences of the frequency and damping of the averaged plasma waves, as well as the position ?? _m and width ???? of the peak of the imaginary part of the Fourier trans-form of the averaged Green??s function, on the wave vector k have been determined in the self-consistent approximation, which makes it possible to take into account multiple scattering of plasma waves by inhomogeneities. It has been found that, in the long-wavelength region of the spectrum, the decrease revealed in the frequency of the plasma waves is caused by the inhomogeneities, which agrees qualitatively with the behavior of the position of the peak ?? _m . In the range of large values of the correlation length of inhomogeneities and small values of k, the damping of the plasma waves tends to zero, whereas the width of the peak ???? remains finite, which is due to the nonuniform broadening. A comparison with the data of numerical calculations has been performed.     

Effects of the mixture of one-and three-dimensional inhomogeneities on the wave spectrum of superlattices

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on the dimensionality of inhomogeneities modulating the period of the superlattice are studied. The cases of one-and three-dimensional modulations, as well as modulation by a mixture of inhomogeneities of both of these dimensionalities, are considered. The correlation function of the superlattice K(r) has the form of a product of the same periodic function and a decreasing function that is significantly different for these different cases. The decreasing part of the correlation function for the mixture of inhomogeneities of different dimensionalities has the form of a product of the decreasing parts of the correlation functions of the components of the mixture. This leads to the nonadditivity of the contributions of the components of different dimensionalities to the resulting modification of the parameters of the wave spectrum that are due to the inhomogeneities (the damping of waves for the mixture of these components is smaller than the sum of the dampings of the components, the maximum gap in the spectrum corresponds to the simultaneous presence of both components of the mixture, not only of the three-dimensional inhomogeneities).     

Uniform integral representation for the fluctuating field propagating through the multi-scale media

A uniform integral representation for the wave field propagating through the statistically homogeneous multi-scale medium was obtained. It is shown that the considered expression for the field contains the limiting cases for both the Born’s approximation for the single-scattered field and a phase approximation of geometric optics method. Hybrid method formulae for calculation of the fluctuation field, taking into account the effect of backscattering enhancement can be obtained from the investigated integral representation, provided that the spectrum of inhomogeneities can be represented as a sum of two uncorrelated components: small-scale and large-scale. The paper contains the numerical simulation results of the effect of average intensity enhancement of the backscattered field in the medium containing both large- and small-scale irregularities. Unlike the hybrid method of calculation, the proposed approach does not require explicit separation of the inhomogeneities spectrum into two uncorrelated components and allows investigating the effect of the average intensity enhancement of the backscattered field in a more general situation. In particular, numerical calculations have shown that the effect of enhancement of the backscattered signal may occur in the study of the high-latitude ionosphere by method of incoherent scattering of radio waves.     

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.     

Improving sound diffusion in a reverberation tank using a randomly fluctuating surface

Underwater reverberation environments that satisfy the conditions of uniformity and isotropy of the diffuse field can be used to measure the acoustic characteristics of underwater targets. This study combines two practical indicators — the standard deviation of the absolute sound pressure field (to indicate uniformity) and the analysis of the wavenumber spectrum in the spherical harmonics domain (to indicate isotropy) — for an accurate evaluation of the diffusion of the sound field in a reverberation tank. A method is proposed that can improve the narrow-band diffusion of the sound field by employing a randomly fluctuating surface. An acoustic experiment was performed in a reverberation water tank (1.2 m×1 m×0.8 m), where a randomly fluctuating surface was generated by making waves. The experimental results show that as the wave motion contributes effectively to the random reflection of sound rays in all directions, the uniformity and isotropy are improved significantly when the surface is fluctuating randomly. This work helps to ensure accurate measurements of the characteristics of underwater targets in reverberation tanks.     

Electromagnetic waves with a negative group velocity in a randomly inhomogeneous Josephson junction

Electromagnetic waves in a randomly inhomogeneous Josephson junction have been investigated by the averaged Green’s function method for a nonmonotonic decay of the correlations of inhomogeneities. Modifications of the spectrum and the decay of these excitations caused by spatial fluctuations of the critical current of the Josephson junction have been studied. The regions of the values of the frequency, the wave number, and the stochastic parameters of the medium, at which the waves have a negative group velocity, have been determined.     

Effects of cross correlations between exchange and magnetic-anisotropy inhomogeneities on the spectrum and damping of spin waves

Effects of cross correlations between inhomogeneities of the exchange and magnetic-anisotropy parameters on the spectrum and damping of spin waves in a ferromagnet are investigated. One- and three-dimensional inhomogeneities are considered. It is demonstrated that the positive cross correlations lead to an increase in the modification of the dispersion law and the damping of spin waves. The negative cross correlations result in the opposite effects: a decrease in the modification of the dispersion law and a decrease in the damping of spin waves. A comparison of the specific features revealed in this work and the results of targeted experimental investigations of modifications of the dispersion laws and damping in inhomogeneous magnets would make it possible to determine the contribution of the cross correlations to the formation of the stochastically inhomogeneous ground state in amorphous magnetic alloys.     

Spectral integral representations of monostatic backscattering from three-dimensional distributions of sediment volume inhomogeneities

A theory is developed for generating short time, monostatic reverberation realizations caused by three-dimensionally distributed volume inhomogeneities in stratified media. A wave number integral approach to treating the propagation to and from the scatterers, combined with a two-dimensional spectral representation of the azimuthally averaged scatterer realizations and a novel numerical implementation, combine to yield an efficient, high fidelity reverberation simulator for predicting monostatic backscatter from horizontally stratified sediments.     

Scroll-wave dynamics in the presence of ionic and conduction inhomogeneities in an anatomically realistic mathematical model for the pig heart

Nonlinear waves of the reaction–diffusion (RD) type occur in many biophysical systems, including the heart, where they initiate cardiac contraction. Such waves can form vortices called scroll waves, which result in the onset of life-threatening cardiac arrhythmias. The dynamics of scroll waves is affected by the presence of inhomogeneities, which, in a very general way, can be of (i) ionic type; i.e., they affect the reaction part, or (ii) conduction type, i.e., they affect the diffusion part of an RD-equation. We demonstrate, for the first time, by using a state-of-the-art, anatomically realistic model of the pig heart, how differences in the geometrical and biophysical nature of such inhomogeneities can influence scroll-wave dynamics in different ways. Our study reveals that conduction-type inhomogeneities become increasingly important at small length scales, i.e., in the case of multiple, randomly distributed, obstacles in space at the cellular scale (0.2–0.4 mm). Such configurations can lead to scroll-wave break up. In contrast, ionic inhomogeneities affect scroll-wave dynamics significantly at large length scales, when these inhomogeneities are localized in space at the tissue level (5–10 mm). In such configurations, these inhomogeneities can attract scroll waves, by pinning them to the heterogeneity, or lead to scroll-wave breakup.     

修正的混响多普勒扩展非对称统计模型

运动声源探测低速目标时,混响谱呈现的非对称性导致正负速度目标的回波具有不同的信混比,需要准确估计双边谱的扩展程度来分别设计检测策略,而传统的对称模型不能描述这种非对称性。基于双边指数分布对称模型,修正的非对称统计模型可用来描述由平台运动、海面运动等引起的混响谱非对称扩展现象。文中推导了非对称模型的数学表达式,并阐述了模型各参数的物理意义。运动声呐平台的湖试实验分析结果验证了该模型对平台在不同速度运动时引起的非对称混响谱都有较高的拟合度,证明混响谱负向多普勒扩展程度随平台运动速度提高而加剧,且非对称模型参数具有量化描述混响谱非对称扩展程度的能力。      

Surface reverberation at sound field focusing in shallow water

A numerical experiment is carried out to study the long-range surface reverberation in the presence of intense surface waves for the case of using vertical transmitting arrays providing sound field focusing at different depths. To focus the field, a phase conjugation of acoustic waves from a probe source positioned at the focusing point is used. It is demonstrated that surface waves considerably affect the focusing quality at a distance of several tens of kilometers from the transmitting array. This prevents the efficient suppression of long-range reverberation by increasing the focusing depth.     

On fractal structure of large-scale electron-density inhomogeneities of traveling disturbances in the midlatitude ionosphere

We present the results of studies of the multifractal structure of slow (of duration τ ≈ 10 s) fluctuations of the received-signal amplitudes in special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2004–2006. It is shown, in particular, that the method of multifractal analysis of amplitude records of the received signals yields information on the spectrum of large-scale ionospheric inhomogeneities, which is inaccessible for the classical method of radio scintillations. From the results of measurements with the use of multifractal processing of experimental data, we found that large-scale (tens of kilometers) quasiregular electron-density inhomogeneities of traveling ionospheric disturbances (TIDs) have a power-law spectrum. It is exactly the power-law form of the spatial spectrum of large-scale inhomogeneities of TIDs that can be the reason for the observed multifractal structure of the intermittency of slow fluctuations of the received-signal amplitudes. However, under conditions of a developed small-scale turbulence of TIDs, the observed multifractal structure of the received signals is, as a rule, stipulated by the spatial inhomogeneity of the variance of the integral electron-density fluctuations of small-scale inhomogeneities on scales comparable with the sizes of large-scale inhomogeneities of TIDs. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 3, pp. 191–198, March 2008.     

Reverberation time measurements in non-diffuse acoustic field by the modal reverberation time

The increasing presence of low frequency sources and the lack of acoustic standard measurement procedures make the extension of reverberation time measurements to frequencies below 100 Hz necessary. In typical ordinary rooms with volumes between 30 m³ and 200 m³ the sound field is non-diffuse at such low frequencies, entailing inhomogeneities in space and frequency domains. Presence of standing waves is also the main cause of bad quality of listening in terms of clarity and rumble effects. Since standard measurements according to ISO 3382 fail to achieve accurate and precise values in third octave bands due to non-linear decays caused by room modes, a new approach based on reverberation time measurements of single resonant frequencies (the modal reverberation time) has been introduced. From background theory, due to the intrinsic relation between modal decays and half bandwidth of resonant frequencies, two measurement methods have been proposed together with proper measurement procedures: a direct method based on interrupted source signal method, and an indirect method based on half bandwidth measurements. With microphones placed at corners of rectangular rooms in order to detect all modes and maximize SNRs, different source signals were tested. Anti-resonant sine waves and sweep signal turned out to be the most suitable for direct and indirect measurement methods respectively. From spatial measurements in an empty rectangular test room, comparison between direct and indirect methods showed good and significant agreements. This is the first experimental validation of the relation between resonant half bandwidth and modal reverberation time. Furthermore, comparisons between means and standard deviations of modal reverberation times and standard reverberation times in third octave bands confirm the inadequacy of standard procedure to get accurate and precise values at low frequencies with respect to the modal approach. Modal reverberation time measurements applied to furnished ordinary rooms confirm previous results in the limit of modal sound field: for highly damped modes due to furniture or acoustic treatment, the indirect method is not applicable due to strong suppression of modes and the consequent deviation of the acoustic field from a non-diffuse condition to a damped modal condition, while standard reverberation times align with direct method values. In the future, further investigations will be necessary in different rooms to improve uncertainty evaluation.     

双基地冰-水界面混响强度的理论预报

针对北极冰层冰水界面具有小尺度粗糙界面的情况,给出由冰层造成的混响平均强度的理论预报公式。首先将北极冰层等效为具有粗糙界面的弹性介质,并且采用小粗糙度微扰理论在精细拟合粗糙度谱的基础上,建立粗糙冰层的三维散射强度模型,然后建立三维双基地声呐几何模型确定有效散射区域,最后给出双基地冰下混响平均强度的估算公式,并在所拟合的粗糙度谱的情况下,利用该预报公式计算双基地声呐配置参数和海冰物理及声学特性对冰下混响强度的影响算例。数值仿真表明该公式能够估算出北极冰下双基地声呐产生的混响平均强度,并且分析出了时延、基线长度等声呐配置参数和冰层声速比、密度比等海冰物理参数会对混响强度造成的影响。声呐的配置参数主要影响散射的有效面积,海冰的物理参数则影响着冰层的散射强度。其中,冰层声速比不仅影响混响强度的大小,还会影响混响强度随时间的衰减速度。      

Effect of random hydrodynamic inhomogeneities on low frequency sound propagation loss in shallow water

Low frequency (100–500 Hz) sound propagation loss on the US Atlantic continental shelf and in the Barents Sea in the presence of stochastic surface waves, and for the US Atlantic shelf also in the presence of internal waves, is studied for the range of up to 150 km by means of numerical simulations. Qualitative difference between sound propagation loss behavior on the US Atlantic shelf and in the Barents Sea is demonstrated for summertime conditions even without random inhomogeneities. It is shown that whereas internal waves have a weak effect on propagation loss, surface waves result in its considerable increase in both areas under wintertime conditions with a wind speed of more than 9 m/s.