Scattering of sound by an elastic spherical shell immersed in a waveguide with a fluid bottom

The paper is devoted to modeling an acoustic field scattered by an elastic spherical shell. The shell is immersed in a waveguide with a fluid attenuating bottom. Modal analysis is applied to calculations of both the point source field in a free waveguide and the scattering coefficients of the shell. The occurring integrals along a branch cut are expressed via the probability integral. Cases are analyzed when the source frequency differs from the critical frequencies of normal waves and when it coincides with one of them. The method is applied to estimate the effect of the field scattered by a thin elastic shell filled with air with transmission loss of the total acoustic field with distance and its depth distribution.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.     

Characteristics of the diffraction of acoustic waves in stratified sound channels

The results of calculations performed in the framework of the approximate approach developed by the authors are presented for the diffraction of sound waves by a stiff spheroid in an acoustic waveguide. The scattered sound field is analyzed as a function of the following parameters of the problem: the spheroid dimensions, its position relative to the sound source and the receiver, the vertical profile of sound velocity in the waveguide, and the acoustic parameters of the waveguide bottom.     

Sound wave scattering by a spherical scatterer located near an ice surface

An echo signal is simulated, which is reflected from a spherical scatterer located near an ice surface. The homogeneous water medium in which the scatterer is located is assumed semi-infinite. For the scattering coefficients of the sphere, asymptotic formulas are obtained by the saddle point method, which can be used for sufficiently large distances between the source emitting a spherical wave and the scatterer. For the occurring branch cut integrals using the steepest descent method, asymptotic expressions are also obtained. Numerical results are obtained for an acoustically rigid sphere and an ice sphere. The density of the ice medium and speed of longitudinal waves in it coincide with the analogous parameters of the ice cover. In a wide frequency range of 8–12 kHz, echo signals are compared that have been calculated for two models of media: a water half-space bordering an ice half-space and an ice-covered homogeneous waveguide with a fluid bottom under the assumption that the source placed in the water layer is directional. It is shown that in a large distance interval between the source and the spherical scatterer, the half-space model sufficiently accurately describes the echo signal while substantially reducing calculation time (by approximately a factor of 10 for the waveguide with a depth of 200 m and a sandy bottom considered in the paper).     

Interaction of a spherical acoustic wave with an elastic spherical shell

The interaction of a spherical acoustic wave with an elastic spherical shell is treated analytically. The solution includes the coupling between the acoustic sound field and vibration of the shell with any degree of fluid loading. The formulation for the far-field acoustic pressure is derived in terms of natural spherical wave functions, the properties of the acoustic medium, and the material constants of the shell. The far acoustic field is computed for a thin aluminum shell and several sound source locations over a large range of ka, where k is the wavenumber, and a is the shell radius. It is shown that the acoustic pressure depends significantly on whether the shell is in air or is submerged in water, particularly when the sound source is very near the surface. In air, the sound field of the shell is nearly identical to that of a rigid sphere but, in water, the shell is more compliant, which results in a damped radiation field that is characterized by vibrational resonances throughout the range of frequencies considered. As the sound sources is moved further away from the surface, however, this resonance response decreases very rapidly, and the sound field corresponds more closely to that of the shell in air.     

水中分层弹性球壳高频时域回波的声学编码研究

针对水下集群目标及敌我目标识别的难题,该文提出了一种基于水中分层弹性球壳高频时域回波的声学编码原理及方法。推导了水中4层弹性球壳目标散射声压的简正级数解,并与有限元结果进行了对比验证。通过构造高频主动声呐的探测脉冲信号,与4层弹性球壳声传递函数的简正级数解做卷积运算,获得了目标的时域回波脉冲序列。研究了分层弹性球壳的厚度、各层材料属性、排布顺序等对时域回波特征的影响规律,提出了基于时域回波特征的声学编码方法。研究表明：利用水中分层弹性球壳目标高频时域回波特征能够实现声学编码,回波结构稳定,且不受限于探测方向。通过携带或安装这种分层弹性球壳结构,有望识别水下航行体/悬浮体等目标。该文的研究对水下目标的主动探测身份识别及导航等具有一定的参考价值。     

基于联合波叠加法的浅海信道下圆柱壳声辐射研究

针对浅海信道下弹性结构声辐射预报尚无高效可靠的研究方法,提出了一种浅海信道下弹性结构声辐射快速预报的联合波叠加法.该方法结合了浅海信道传输函数、多物理场耦合数值计算法和波叠加法理论,运用该方法可对浅海信道下弹性结构辐射声场进行快速预报.经数值法和解析解法验证后,从信道下辐射源、环境影响和辐射声场测量的角度研究分析了浅海信道下弹性圆柱壳的声辐射特性,阐释了进行浅海信道下结构声辐射研究的必要性.研究结果表明,仅在低频浅海信道下弹性结构可近似等效为点源,信道上下边界对声场产生显著的耦合影响,高频段的空间声场指向性分布尤为明显,垂直线列阵进行信道下结构辐射声功率测量时,测量结果受到信道环境边界和潜深的影响较大.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Formation of a weakly diverging caustic beam in an underwater sound channel open to the bottom

The paper studies the patterns manifesting themselves in the formation and propagation of caustic and weakly diverging beams using the geometric acoustic approximation and mode theory applied to the simplest model of an underwater sound channel open to the bottom in the form of the bilinear dependence of the square of the refractive index on depth. It is established that when a vertical array emitting a tonal sound signal is located at a certain critical depth, the multimode caustic beam which forms near the reference ray horizontally departing from its center and which predominates in intensity is simultaneously the most weakly diverging beam. It is shown that the reference ray of such a weakly diverging caustic beam corresponds to the smoothest minimum for the dependence of the length of the ray cycle on their angle of departure from the center of the array and to the depth level of revolution at the critical depth characteristic of the given oceanic waveguide.     

Modeling of High-Frequency Acoustic Fields Scattered by Bodies in Refractive Waveguides

We study the structure of the high-frequency field scattered by a body (observed object) in a refractive plane-layered waveguide with a curved bottom. The solution of the problem allows one to analyze the possibilities of development of acoustic tomography systems with finite numbers of acoustic sources and receivers located in a limited observation region.     

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.     

Forward scatter target strength extraction in a marine environment (L)

A 48 m rail with a moving receiver was used to measure forward scattering from a spherical shell lying on the bottom in the Gulf of Mexico. The target was mid-way between the source and rail, on a line from the source bisecting the rail. The major obstacle to the measurement of forward scattering is the much stronger source signal which overlaps the scattered signal in space and time. Here, forward scattered target strength is obtained by processing the received signals using a wavenumber filter to remove the incident wave. The result compares favorably to that obtained from numerical predictions.     

Simulation of the lower boundary of an acoustic waveguide

The paper discusses simulation of the lower boundary of an acoustic waveguide. The applicability and relationship of rigid bottom and fluid half-space models are studied as a function of the bottom sediment parameters. The influence of bottom losses on the sound field characteristics in a waveguide is studied. Examples of numerical simulation are given.

     

Vector-scalar noise fields formed by an excited sea surface

Vector-scalar noise fields in a waveguide were studied using computer simulation. A stochastic model of dynamic acoustic noise was used in the calculations. Noise field parameters on a single vector-scalar module and spatial correlation functions on vector-scalar arrays in a homogeneous waveguide were analyzed. Calculations were performed for vertically and horizontally located arrays. It was shown that the vector-scalar noise field characteristics depend on the bottom parameters and the state of the ocean surface due to the wind force. The calculation results can be used to predict the characteristics of detection and direction finding of signal sources for vector-scalar arrays working in a waveguide against the background of sea noise.     

Numerical modeling of the wave field in seismic profiling of the seafloor

The seismoacoustic field produced by an omnidirectional sound source located near the bottom of a shallow-water sea is numerically modeled at frequencies lower than 100 Hz. The main types of waves that are excited and scattered in the fluid and the layered bottom medium are represented in the form of wave hodographs on the distance-arrival time plane. A possibility to solve some problems of acoustic tomography of the bottom is demonstrated, in particular, the problem of determining the thickness of the bottom sediment layers and the velocities of the longitudinal and transverse waves propagating in them. By varying the elastic parameters of the layered bottom model, typical changes in the wave field are analyzed and the possibility to predict the presence of oil-saturated layers in the seafloor is established.     

Spatial attenuation of different sound field components in a water layer and shallow-water sediments

The paper presents the results of an experimental study of spatial attenuation of low-frequency vector-scalar sound fields in shallow water. The experiments employed a towed pneumatic cannon and spatially separated four-component vector-scalar receiver modules. Narrowband analysis of received signals made it possible to estimate the attenuation coefficients of the first three modes in the frequency of range of 26–182 Hz and calculate the frequency dependences of the sound absorption coefficients in the upper part of bottom sediments. We analyze the experimental and calculated (using acoustic calibration of the waveguide) laws of the drop in sound pressure and orthogonal vector projections of the oscillation velocity. It is shown that the vertical projection of the oscillation velocity vector decreases significantly faster than the sound pressure field.     

Spectral and modal formulations for the Doppler-shifted field scattered by an object moving in a stratified medium

Spectral and normal mode formulations for the three-dimensional field scattered by an object moving in a stratified medium are derived using full-field wave theory. The derivations are based on Green's theorem for the time-domain scalar wave equation and account for Doppler effects induced by target motion as well as source and receiver motion. The formulations are valid when multiple scattering between the object and waveguide boundaries can be neglected, and the scattered field can be expressed as a linear function of the object's plane wave scattering function. The advantage of the spectral formulation is that it incorporates the entire wave number spectrum, including evanescent waves, and therefore can potentially be used at much closer ranges to the target than the modal formulation. The normal mode formulation is more computationally efficient but is limited to longer ranges. For a monochromatic source that excites N incident modes in the waveguide, there will be roughly N2 distinct harmonic components in the scattered field. The Doppler shifts in the scattered field are highly dependent upon the waveguide environment, target shape, and measurement geometry. The Doppler effects are illustrated through a number of canonical examples.     

Modal Doppler theory of an arbitrarily accelerating continuous-wave source applied to mode extraction in the oceanic waveguide

A Doppler-based method for using a moving narrow-band source to extract the modes of acoustic propagation in a range-independent shallow ocean waveguide over a partial-water-column spanning vertical line array (VLA) is introduced. Because the modal components propagate at distinct frequencies in the case of uniform radial source motion, the modal depth functions may be isolated and extracted from a frequency decomposition of the field. Because Doppler broadening due to radial source accelerations degrades the effectiveness of the extraction method, the method incorporates a technique to compensate for Doppler broadening. As the basis for the compensation technique, a theory is introduced for describing the VLA field from an accelerating cw source. By connecting the range of the source at the time a signal feature is emitted (the retarded time) to the range of the source at the time the signal feature arrives at the receiver (the contemporary time), the theory incorporates the Doppler effects associated with the finite group velocities of the modal components. The mode extraction method and compensation technique are applied to simulation and ocean data.