Extracting the Green's function from measurements of the energy flux

Existing methods for Green's function extraction give the Green's function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green's function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green's function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green's function can be retrieved from measurement of the flux of scattered particles through a closed surface.     

Time reversal of ocean noise

It has recently been shown [Roux et al., "Extracting coherent wave fronts from acoustic ambient noise in the ocean," J. Acoust. Soc. Am. 116, 1995-2003 (2004)] that the time-averaged correlation of ocean noise between two points yields a deterministic waveguide arrival structure embedded in the time-domain Green's function. By performing a set of these correlations between a vertical receive array and a single receiver, transfer functions necessary for time reversal can be extracted from ocean noise. Theory and simulation demonstrate this process and data of opportunity from the North Pacific Acoustic Laboratory experiment confirm the expected performance of a noise-based time reversal mirror.     

The effect of ocean wave on the vertical spatial correlation of ocean ambient noise

The effect of the correlation function of noise sources derived from the ocean wave spectrum on the vertical spatial correlation of ocean ambient noise is investigated. The spatial correlation models of ocean ambient noise usually assume that the surface noise sources are uncorrelated. This assumption can be used to explain some physical phenomena, but it is not consistent with the real situation. Considering the relation between the ocean wave motion and the ambient noise generated by wind, the spectrum of ocean wave is introduced to calculate the vertical correlation of ocean ambient noise as the correlation function of noise sources by using the Kuperman-Ingenito(K/I) noise model. The comparison of the simulations and the experimental data shows that the simulations of vertical correlation of ambient noise have some differences with the experimental data by assuming the noise sources are uncorrelated and the simulations of vertical correlation of ambient noise have a good agreement with the experimental data by using the correlation function of noise sources derived from the ocean wave spectrum under the situation of high wind speed.     

海面波浪对海洋环境噪声垂直空间相关性的影响

研究了由海浪谱导得的噪声源的相关函数对海洋环境噪声垂直空间相关性的影响。常用的海洋环境噪声空间相关性模型一般假设海面噪声源是非相关的,这种假设可以解释一些物理现象,但是与真实情况并不符合。考虑到风成噪声与海浪运动的相关性,引入海浪谱,得到噪声源的相关函数,利用Kuperman-Ingenito (K/I)噪声模型,计算海洋环境噪声的垂直相关性。通过仿真结果与实验数据对比可以看出,在高风速下,假设噪声源不相关时计算得到的噪声场垂直相关性与实验结果相差较大,而利用由海浪谱导得的噪声源的相关函数计算得到的噪声场的垂直相关性与实验结果符合较好。      

A passive inverse filter for Green's function retrieval

Passive methods for the recovery of Green's functions from ambient noise require strong hypotheses, including isotropic distribution of the noise sources. Very often, this distribution is nonisotropic, which introduces bias in the Green's function reconstruction. To minimize this bias, a spatiotemporal inverse filter is proposed. The method is tested on a directive noise field computed from an experimental active seismic data set. The results indicate that the passive inverse filter allows the manipulation of the spatiotemporal degrees of freedom of a complex wave field, and it can efficiently compensate for the noise wavefield directivity.     

Green's functions for a volume source in an elastic half-space

Green's functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed. First, the Green's function is expanded with respect to eigenmodes that correspond to Rayleigh waves. While bulk waves are thus ignored, this approximation is valid on the surface far from the source, where the Rayleigh wave modes dominate. The second approach employs an angular spectrum that accounts for the bulk waves and yields a solution that may be separated into two terms. One is associated with bulk waves, the other with Rayleigh waves. The latter is proved to be identical to the Green's function obtained following the first approach. The Green's function obtained via angular spectrum decomposition is analyzed numerically in the time domain for different burial depths and distances to the receiver, and for parameters relevant to seismo-acoustic detection of land mines and other buried objects.     

表面声道对深海风成噪声垂直空间特性的影响规律

水下风成噪声的垂直空间特性包括噪声垂直方向性和垂直相关性,研究海洋环境对其影响规律对提升声呐性能、增加海洋环境参数反演的准确性具有重要意义.本文利用Pekeris割线下的简正波理论描述噪声的传播过程,研究了深海环境下存在表面声道时,表面声道以下噪声垂直空间特性的变化规律及其原因.研究表明,在临界深度以上,表面声道的存在导致噪声垂直方向性在水平凹槽边缘靠近海底方向上的峰值升高,噪声垂直相关性随垂直距离增加先后周期地向正相干和负相干方向偏移;在临界深度以下,表面声道的存在导致水平方向上的噪声能量增强,噪声垂直相关性整体向正相干方向偏移.当表面声道的参数变化时,表面声道的厚度变化对噪声垂直空间特性影响较大,而表面声道内的声速梯度变化对噪声垂直空间特性几乎没有影响.结合各类简正波的变化分析表明,存在表面声道时,噪声源激发的折射简正波阶数增加,强度增强,是表面声道引起噪声垂直空间特性变化的主要原因.     

Green's function estimation using secondary sources in a shallow water environment

This work provides a new way to measure the Green's function between two points in an acoustic channel without emitting a pulse by any of the two points. The Green's function between A and B is obtained from a set of secondary sources in the guide by averaging either the correlation or the convolution of the signals received in A and B. A theoretical approach based on mode propagation in a monochromatic regime is presented. Results are then extended to the time domain. Estimation of the Green's function is performed numerically in a range-independent and a range-dependent environment. Application to discreet acoustic communications is discussed.     

Recovering the acoustic Green's function from ambient noise cross correlation in an inhomogeneous moving medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.     

Fluctuations in diffuse field-field correlations and the emergence of the Green's function in open systems

Recent intense interest in diffuse field correlation functions, with applications to passive imaging in underwater acoustics and seismology, has raised questions about the degree with which a retrieved waveform can be expected to conform to the Green's function, and in particular the degree with which a ray arrival may be discerned. On considering a simple scalar wave model consisting of fields with distributed random sources, the difffuse field-field correlation function R is defined as a sum of correlation integrals, one for each of the many distinct distributed sources. It is then shown that this ensemble of fields has a correlation function with expectation (R) equal to the Green's function. This model also lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green's function. The model predicts that such conformation is strongest at low frequencies. Ray arrivals are detectable if sufficient data have been collected, but the amount of data needed scales in three dimensions with the square of the source-receiver separation, and the square of the frequency. Applications to seismology are discussed.     

Spatial coherence and cross correlation of three-dimensional ambient noise fields in the ocean

Ambient acoustic noise fields in the ocean are generally three dimensional in that they exhibit vertical and horizontal directivity. A model of spatially homogeneous noise is introduced in which the directionality is treated as separable, that is, the overall directionality of the field is the product of the individual directivities in the horizontal and vertical. A uni-modal von Mises circular distribution from directional statistics is taken to represent the noise in the horizontal, whilst the vertical component is consistent with a surface distribution of vertical dipoles. An analysis of the coherence and cross correlation of the noise at two horizontally aligned sensors is developed. The coherence function involves a single integral over finite limits, whilst the cross-correlation function, derived on the assumption that the noise has been pre-whitened, is given by an integral with limits that depend on the correlation delay time. Although the cross-correlation function does not exhibit delta functions that could be identified with the Green's function for propagation between the two sensors in the field, it does drop abruptly to zero at numerical time delays equal to the travel time between the sensors. Hence the noise could be used to recover the sound speed in the medium.     

Using cross correlations of turbulent flow-induced ambient vibrations to estimate the structural impulse response. Application to structural health monitoring

It has been demonstrated theoretically and experimentally that an estimate of the impulse response (or Green's function) between two receivers can be obtained from the cross correlation of diffuse wave fields at these two receivers in various environments and frequency ranges: ultrasonics, civil engineering, underwater acoustics, and seismology. This result provides a means for structural monitoring using ambient structure-borne noise only, without the use of active sources. This paper presents experimental results obtained from flow-induced random vibration data recorded by pairs of accelerometers mounted within a flat plate or hydrofoil in the test section of the U.S. Navy's William B. Morgan Large Cavitation Channel. The experiments were conducted at high Reynolds number (Re > 50 million) with the primary excitation source being turbulent boundary layer pressure fluctuations on the upper and lower surfaces of the plate or foil. Identical deterministic time signatures emerge from the noise cross-correlation function computed via robust and simple processing of noise measured on different days by a pair of passive sensors. These time signatures are used to determine and/or monitor the structural response of the test models from a few hundred to a few thousand Hertz.     

利用矢量海洋环境噪声提取声场格林函数

考虑到矢量水听器在垂直方向上具有8字形指向性,能够有效抑制远方非平稳噪声源的干扰,提出了一种矢量环境噪声相关函数(NCF)提取声场时域格林函数(TDGF)的方法。基于简正波理论建立了声压和垂直振速垂直相关性模型。在此基础上,给出了声压和垂直振速相关函数提取声场纵向格林函数的过程.数值仿真对比和实验数据分析表明,相对于声压提取方法,垂直振速提取方法能够有效消除直达波前出现的亮纹与亮区干扰。此外,对于同等时间长度噪声序列,声压提取方法只提取到直达波路径,而垂直振速提取方法还提取到了我们更为关心的海底反射路径。利用直达波与海底反射波到达时延差估计的海深与实测海深吻合较好。      

水下目标对幅度高斯相关海面环境噪声场扰动特性的研究

理论探讨了水下目标受海面环境噪声场激发产生的散射场对海洋环境噪声场的扰动特性,基于幅度高斯型相关海面噪声源模型,利用任意声源分布声场的积分表达式和单极子源半无限空间格林函数的球面波展开式,获得了刚性球目标在海面单极子和偶极子源海洋环境噪声“照射”下的直达噪声场、散射噪声场、总噪声场,以及二接收点直达、散射和总噪声协方差的理论表达式,表明总噪声场除了和目标阻抗特性、接收点的方向有关外,还受到海面噪声源相关特性,以及直达与散射噪声场之间干涉的较大影响。数值计算结果给出较近距离范围内,刚球目标声学可见度约为4~5dB,并指出在海洋环境噪声场中,刚球目标散射的方向特性明显不同于平面波入射。      

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.     

Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

利用环境噪声互相关实现散射体无源成像

最近研究表明利用环境噪声的互相关可以恢复两点之间的时域格林函数(声脉冲响应),这一原理在文献中被称为格林函数恢复。基于此原理,通过对多个传声器所接收的环境噪声进行互相关处理,获取与散射体相关联的散射波的到达时延信息,结合最小二乘反演算法和改进克希霍夫移位算法,分别获得道路交通噪声场中石柱以及海浪噪声场中塑料桶的空间位置,且其估计结果与实际测量相一致。实验结果表明将环境噪声作为探测信号进行散射体无源成像是可行的。这为设计室内无源声监测系统以及通过海洋环境噪声实现对水中静默目标成像提供了新思路和有益参考。      

Emergence of the acoustic Green's function from thermal noise

The fluctuation-dissipation theorem is used to show how acoustic Green's functions corresponding to sound propagation in opposite directions between any two given points can be extracted from time series of thermal noise recorded at these points. The result applies to arbitrarily inhomogeneous, moving or motionless fluids with time-independent parameters, and demonstrates that the two-point correlation function of thermal noise contains as much information about the environment as can be obtained acoustically by placing transceivers at the two points.     

Unified Green's function retrieval by cross correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green's function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green's function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in "remote sensing without a source."