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.     

Diffraction of sound pulses on an elastic spherical shell submerged in an oceanic waveguide

The paper is devoted to simulating an acoustic field scattered by an elastic spherical shell placed in a waveguide with a fluid attenuating bottom. The emitted signal is a wideband pulse with a Gaussian envelope. The normal wave method is used in the frequency domain for calculating the field of a point source in a free waveguide and the shell scattering coefficients. Movement of the receiver along a vertical straight line located behind the shell makes it possible to obtain a “three-dimensional” image of the field scattered by the shell. In this representation, the horizontal axis is time; the vertical axis is the submersion depth of the receiver; the intensity shows the amplitude of the received signal. Such three-dimensional structures make it possible to analyze the dependence of the complex diffraction structure of the acoustic field on receiver depth. In the considered numerical example, a thin, elastic, spherical shell is located near the attenuating fluid bottom.     

The complex equivalent source method for sound propagation over an impedance plane

The sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane. Originally, such an approach for representing the half-space Green's function was described by Sommerfeld at the beginning of the last century, in order to treat half-space problems of heat conduction. However, the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances. The singular part of the line integral can be transformed into a Hankel function, which shows that surface waves are contained in the whole solution. Unfortunately, this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence. The main idea of the present method is to use also a superposition of equivalent point sources, but to allow that these sources can be located at complex source points. The corresponding form of the half-space Green's function is suitable for both masslike and springlike surface impedances, and can be used as a cornerstone for a boundary element method.     

浅海波导中目标散射的边界元方法

提出了一种计算三维散射体在声速剖面随深度变化、距离无关浅海波导中散射声场的数值方法波导边界元方法。当散射体不十分靠近波导界面因而边界多次散射可以忽略时,在边界元计算中可以用自由场格林函数近似波导格林函数。应用镜像法和球波函数加法定理推导了理想波导中球体散射声场的解析解,用来验证波导边界元方法的计算精度,证明该数值方法是准确的。对浅海波导中水下潜器散射声场数值模拟的结果表明,浅海波导海面、海底界面反射、声速剖面等对目标散射声场的幅值和方向性都有很大的影响。      

Cancellation of spurious arrivals in Green's function retrieval of multiple scattered waves

The Green's function for wave propagation can be extracted by cross-correlating field fluctuations excited on a closed surface that surrounds the employed receivers. This study treats an acoustic multiple scattering medium with discrete scatterers and shows that for a given source the cross-correlation of waves propagating along most combinations of scattering paths gives unphysical arrivals. Because theory predicts that the true Green's function is retrieved, such unphysical arrivals must cancel after integration over all sources. This cancellation occurs because the scattering amplitude of each scatterer satisfies the generalized optical theorem. The cross-correlation of scattered waves with themselves does not lead to the correct retrieval of scattered waves, because the cross-terms between the direct and scattered waves is essential.     

Subcritical scattering from buried elastic shells

Buried objects have been largely undetectable by traditional high-frequency sonars due to their insignificant bottom penetration. Further, even a high grazing angle sonar approach is vastly limited by the coverage rate dictated by the finite water depth, making the detection and classification of buried objects using low frequency, subcritical sonar an interesting alternative. On the other hand, such a concept would require classification clues different from the traditional high-resolution imaging and shadows to maintain low false alarm rates. A potential alternative, even for buried targets, is classification based on the acoustic signatures of man-made elastic targets. However, the elastic responses of buried and proud targets are significantly different. The objective of this work is to identify, analyze, and explain some of the effects of the sediment and the proximity of the seabed interface on the scattering of sound from completely and partially buried elastic shells. The analysis was performed using focused array processing of data from the GOATS98 experiment carried out jointly by MIT and SACLANTCEN, and a new hybrid modeling capability combining a virtual source-or wave-field superposition-approach with an exact spectral integral representation of the Green's functions for a stratified ocean waveguide, incorporating all multiple scattering between the object and the seabed. Among the principal results is the demonstration of the significant role of structural circumferential waves in converting incident, evanescent waves into backscattered body waves, emanating to the receivers at supercritical grazing angles, in effect making the target appear closer to the sonar than predicted by traditional ray theory.     

A new bistatic model for electromagnetic scattering from randomly rough surfaces

In this paper we propose a bistatic model for electromagnetic scattering from a Gaussian rough surface with small to moderate heights. It is based on the integral equation formulation where the spectral representations of the Green's function and its gradient are in complete forms, a general approach similar to those used in the advanced integral equation model (AIEM) and the integral equation model for second-order multiple scattering (IEM2M). Yet this new model can be regarded as an extension to these two models on two accounts: first it has made fewer and less restrictive assumptions in evaluating the complementary scattering coefficient for single scattering, and second it contains a more rigorous analysis by the inclusion of the error function related terms for the cross- and complementary scattering coefficients, which stems from the absolute phase term in the spectral representation of the Green's function. It is expected that our result for the complementary scattering coefficient is more accurate and more general, even when the effect of the error function related terms is neglected. As a result, the proposed model is expected to have wider applicability with a better accuracy. Numerical simulations are provided to demonstrate the validity of the proposed model.     

A representation for Green's function retrieval by multidimensional deconvolution

Green's function retrieval by crosscorrelation may suffer from irregularities in the source distribution, asymmetric illumination, intrinsic losses, etc. Multidimensional deconvolution (MDD) may overcome these limitations. A unified representation for Green's function retrieval by MDD is proposed. From this representation, it follows that the traditional crosscorrelation method gives a Green's function of which the source is smeared in space and time. This smearing is quantified by a space-time point-spread function (PSF), which can be retrieved from measurements at an array of receivers. MDD removes this PSF and thus deblurs and deghosts the source of the Green's function obtained by correlation.     

浅海波导中目标散射的简正波-Kirchhoff近似混合方法

提出了计算浅海波导中复杂目标散射的数值方法:简正波-Kirchhoff近似混合方法。通过把目标散射的Kirchhoff近似方法和简正波声传播模型相结合,可对大尺寸复杂目标在浅海波导中的散射声场进行计算。以浅海波导中刚性球体散射的解析解为标准解验证了本方法,说明简正波-Kirchhoff近似混合方法是有一定计算精度的工程预报方法。数值计算Pekeris浅海波导中球体目标散射声场在深度-频率平面和距离-频率平面上的二维干涉结构及其与自由空间中的差异。进而通过FFT获得目标时域回波随深度的分布图,分析浅海波导中目标姿态、声速剖面对Benchmark潜艇目标散射的影响。      

Efficient calculation of two-dimensional periodic and waveguide acoustic Green's functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.     

水下掩埋目标的散射声场计算与实验

水下掩埋目标声散射问题是识别和探测掩埋目标的理论基础, 是声散射研究领域的热点问题. 本文基于射线声学推导了掩埋情况下目标声散射计算的格林函数近似式, 并在此基础上进一步给出了相应的远场积分公式. 在有限元方法的基础上, 将推导得到的公式写入有限元仿真软件, 对软件功能进行拓展, 构建二维轴对称目标的声散射模型, 并计算掩埋情况下弹性实心球在不同条件下的目标强度, 获得了其散射声场随频率、掩埋深度、沙层吸收系数等参数的变化规律. 开展实心球的自由空间和浅掩埋条件下水池声散射实验, 利用共振隔离技术处理实验数据, 提取目标声散射的纯弹性共振特征进行分析, 结果表明可将其用于掩埋目标识别和探测. 最后利用总散射声场与理论计算结果进行对比, 验证了理论仿真的正确性.     

Passive fathometer processing

Ocean acoustic noise can be processed efficiently to extract Green's function information between two receivers. By using noise array-processing techniques, it has been demonstrated that a passive array can be used as a fathometer [Siderius, et al., J. Acoust. Soc. Am. 120, 1315-1323 (2006)]. Here, this approach is derived in both frequency and time domains and the output corresponds to the reflection sequence. From this reflection sequence, it is possible to extract seabed layering. In the ocean waveguide, most of the energy is horizontally propagating, whereas the bottom information is contained in the vertically propagating noise. Extracting the seabed information requires a dense array, since the resolution of the bottom layer is about half the array spacing. If velocity sensors are used instead of pressure sensors, the array spacing requirement can be relaxed and simulations show that just one vertical velocity sensor is sufficient.     

Arrival-time structure of the time-averaged ambient noise cross-correlation function in an oceanic waveguide

Coherent deterministic arrival times can be extracted from the derivative of the time-averaged ambient noise cross-correlation function between two receivers. These coherent arrival times are related to those of the time-domain Green's function between these two receivers and have been observed experimentally in various environments and frequency range of interest (e.g., in ultrasonics, seismology, or underwater acoustics). This nonintuitive result can be demonstrated based on a simple time-domain image formulation of the noise cross-correlation function, for a uniform distribution of noise sources in a Pekeris waveguide. This image formulation determines the influence of the noise-source distribution (in range and depth) as well as the dependence on the receiver bandwidth for the arrival-time structure of the derivative of the cross-correlation function. These results are compared with previously derived formulations of the ambient noise cross-correlation function. Practical implications of these results for sea experiments are also discussed.     

楔形理想波导中球体散射的镜像方法

应用镜像原理和球波函数加法公式,把楔形理想波导中球体的散射声场等效为无界空间中多球体散射声场,镜像解析解与边界元数值结果相同,可以作为边界随水平距离变化波导中目标散射数值方法的标准解。比较无界空间和楔形理想波导中球体散射声场空间分布特征,结果表明:楔形理想波导中球体的散射声场在水平和倾斜边界反射;散射声场沿楔形理想波导下坡方向的衰减在相同的水平距离下小于无界空间的情况,散射声场在楔形理想波导上坡的空间分布受到限制。     

Application of acoustic feedback to target detection in a waveguide: experimental demonstration at the ultrasonic scale

People are familiar with the acoustic feedback phenomenon, which results in a loud sound that is heard when a musician plays an electric instrument directly into a speaker. Acoustic feedback occurs when a source and a receiver are connected both acoustically through the propagation medium and electrically through an amplifier, such that the amplified received signal is continuously re-emitted by the source. The acoustic feedback can be initiated from a continuous sine wave. When the emitter and the receiver are in phase, resonance is obtained, which appears to be highly sensitive to any fluctuation of the propagation medium. Another procedure consists in initiating the acoustic feedback from a continuous loop of ambient noise. It then generates an unstable self-sustained feedback oscillator (SFO) that is tested here as a method for monitoring temperature fluctuations of a shallow-water oceanic environment. The goal of the present study is to reproduce and study the SFO at the laboratory scale in an ultrasonic waveguide. The experimental results demonstrate the potential applications of the SFO for the detection of a target in the framework of the acoustic-barrier problem in shallow-water acoustics.     

多孔硅通道型光波导的制备及传输损耗的测量

利用多孔硅在阳极腐蚀过程中外加的光照度与孔隙率的对应关系,提出了一种利用光照控制多孔硅折射率的方法制备通道型光波导技术.对制备出的多孔硅波导损耗进行了分析.由于多孔硅波导层中孔状结使得波导端面较为粗糙,耦合损耗大是多孔硅光波导传输损耗测量中遇到的的问题,对此采用了一种非破坏性的简便的优化端面耦合传输损耗测量方法,可以实现入射光束与波导的完全耦合,消除了因光波与波导中导波模式间失配引起的损耗.较精确的测量出实验中制备的通道型多孔硅光波导的传输损耗为16.2dBcm,波导端面的散射损耗为3.6dB.     

Evaluation of the integrals of target/seabed scattering using the method of complex images

In this paper the integrals which arise in target/seabed scattering problems are examined. These are the integrals which express the propagation of a spherical harmonic term in a fluid above or below a half-space and the integrals which compute the conversion coefficients of outgoing spherical harmonics into incident spherical harmonics after a seabed reflection. A very efficient and accurate method of computing these integrals, using the method of complex images, is derived. Numerical comparisons with the exact integral expressions show the accuracy of this approach.     

非线性内波存在下的浅海远程混响模型

研究了浅海非线性内波对远程混响场的影响。通过分析非线性内波活动引起声源到海底散射元以及散射元到接收点之间的声传播变化,给出了非线性内波引起远程混响强度变化的表示,建立了非线性内波存在下的浅海远程混响模型,数值计算了非线性内波运动引起远程混响强度的变化。理论和数值计算表明,非线性内波的活动能够引起远程混响强度的变化,在某些情况下会导致远程混响强度增强。通过讨论非线性内波引声简正波的耦合效应,给出了其引起远程混响强度增强的原因。      

Parameter study of sound propagation between city canyons with a coupled FDTD-PE model

A parameter study is performed for the case of two-dimensional sound propagation from a (source) city canyon to a nearby, identical (receiver) city canyon. Focus was on sound pressure levels, relative to the free field, in the shielded canyon. An accurate and efficient coupled FDTD-PE model was applied, exploiting symmetry of the source and receiver canyon. With the proposed calculation method, simulations were necessary in only half the sound propagation domain. The shielding in the receiver canyon in case of a coherent line source was compared to the shielding by an incoherent line source, by means of sound propagation calculations in a number of 2D cross-sections through source and receiver. It was found that the shielding is rather insensitive to the width-height ratio of the canyons. The presence of diffusely reflecting façades and balconies lead to an important increase in shielding compared to flat façades. Rigid façades yield significantly lower shielding compared to partly reflecting façades. Effects of a moving atmosphere were modeled in detail. Shielding decreases significantly in case of downwind sound propagation when comparing to sound propagation in a non-moving atmosphere. Refraction is the most important effect in the latter. In case of upwind sound propagation, turbulent scattering plays an important role and the shielding is similar to the one of a non-moving atmosphere for the parameters used in this paper. The combination of effects, as is shown by some examples, is in general not a simple addition of the separate effects.     

Single frequency sound propagation in flat waveguides with locally reactive impedance boundaries

A coherent image source method is presented for evaluating single frequency sound propagation from a point source in a flat waveguide with two infinite and parallel locally reactive boundaries. The method starts from formulating reflections of the spherical sound radiation into integrals of plane wave expansion, and the analytical evaluation of the integrals is simplified by introducing a physically plausible assumption that wave front shapes remain the same before and after each reflection on a reflective boundary. The proposed model can determine coherently the sound fields at arbitrary receiver locations in a flat waveguide, even when one boundary is highly sound absorptive. Being compared with the classical wave theory and the existing coherent ray-based methods, it is shown that the proposed method provides considerable accuracy and advantages to predict sound propagation in flat waveguides with a sound absorptive ceiling and a reflective floor over a broad frequency range, particularly at large distances from the source where the existing methods are problematic.