On the two-point cross-correlation function of anisotropic, spatially homogeneous ambient noise in the ocean and its relationship to the Green's function

It is well established that the free-space Green's function can be recovered from the two-point cross-correlation function of a random noise field if the noise is white and isotropic. Ambient noise in the ocean rarely satisfies either of these conditions. However, a non-uniform spectrum could be pre-whitened by the application of a suitable filter but anisotropy cannot be so readily eliminated. To investigate the effects of vertical anisotropy, three azimuthally uniform, spatially homogeneous noise fields are analyzed, two of which are idealized, while the third is representative of ambient noise in the deep ocean. In each case, the coherence function, the cross-correlation function, and the derivative of the latter with respect to the correlation delay, are derived for vertical and horizontal alignments of the sensor pair. With vertical sensors, any step-function discontinuity in the directional density function is mapped into a delta function at an appropriate time delay in the derivative (with respect to time delay) of the cross-correlation function. No such mapping occurs with horizontal sensors. In this case, only horizontally traveling noise can generate delta functions in the derivative of the cross-correlation function, and these always appear at the retarded time on either side of the origin.     

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.     

利用自相关函数和双耳自相关函数分析对交通噪声特征参量的提取~

对实地双通道测量获得的道路交通噪声和铁路噪声信号样本进行了自相关函数和双耳自相关函数(Interaural CrossCorrelation Function)的分析。进而通过对噪声样本时间因子和空间因子的相关性分析、主成分分析和主观评价实验,得到了3个铁路噪声源特征参量物理因子和4个道路交通噪声源特征参量物理因子。发现与传统的声压级测量相比,表征声音信号时间特性和空间特性的这7个物理量可以更全面、准确地表征交通噪声的特性。在对道路噪声进行测量或分析时,掌握与声源视觉宽度和音调感相对应的物理因子以及双耳时延和初始能量,就可获悉与人的主观评价相一致的道路交通噪声特征信息;对铁路噪声而言,掌握与声源视觉宽度相对应的物理因子以及双耳时延和声音的重复性特征,就可以得到与入主观评价相一致的铁路噪声特征信息。综合道路噪声特征参量和铁路噪声特征参量可以发现,双耳时延和与声源视觉宽度相对应的物理因子是与人的主观反应最为一致的主成分指标,说明噪声中决定人的评价的最主要的因素是代表空间特征的信号因子。      

Associated relaxation time and intensity correlation function of a bistable system driven by cross-correlation additive and multiplicative coloured noise sources

The associated relaxation time and the intensity correlation function of a bistable system driven by an additive and a multiplicative coloured noise with coloured cross-correlation are investigated. Using the Novikov theorem and the projection operator method, the analytic expressions of the stationary probability distribution P_st(x), the relaxation time T_c, and the normalized correlation function C(s) of the system are obtained. The effects of the noise intensity, the cross-correlation strength λ and the cross-correlation time τ are discussed. By numerical computation, it is found that the cross-correlation strength |λ| and the quantum noise intensity D decrease the relaxation of the system from unstable points. The cross-correlation time τ delays relaxation of the system from unstable points. The cross-correlation strength λ and the cross-correlation time τ can alter the effects of the pump noise intensity Q. Thus, the relaxation time T_c is a stochastic resonant phenomenon, and distribution curves exhibit a single-maximum structure.     

Coherence and interference in diffuse noise: on the information and statistics associated with spatial wave correlations in directional noise fields

Broadband noise correlation methods for the passive extraction of information about the propagation of waves between distant sensor locations have received considerable attention in the literature. For the case of an isotropic ambient field distribution, there is a well-defined relationship between the expectation value of the wave coherence over the sensors and point-to-point wave propagation. Experimental applications, however, must contend with ambient field anisotropy as well as the performance limitations associated with stochastic fluctuations. This paper explores the influence of ambient field directionality on both (1) the connection between the measured wave coherence and sensor-to-sensor propagation and on (2) the rate at which measurements stochastically converge to the expectation value of the underlying wave coherence. Due to diffraction, the relationship between the measured wave coherence and sensor-to-sensor propagation is shown to be robust to even highly directional ambient field features. While the fluctuations of a stochastic system are generally known to depend on bandwidth and measurement duration, the rate of stochastic convergence depends additionally on the cross-spectral power density (coherent power) relative to the power-spectral density (total incident power). Practical experimental implications of these results are discussed.     

Cross-correlation in band-limited ocean ambient noise fields

Observations of ambient noise in the ocean are generally band limited, because of the natural spectral shape of the noise or the restricted bandwidth of the detection system. Either way, the noise may be regarded as white noise to which a band-limiting filter has been applied. An analysis of the two-point cross-correlation function of such filtered noise is presented for two cases, isotropic and surface-generated noise. The most pronounced effects occur with high-pass and bandpass filters when the low-frequency cut-off falls well above the first few zeros in the coherence function. In this situation, the sensor separation is very many times the longest acoustic wavelength (associated with the lowest frequency) in the passband. The filtering then produces sharp pulses at correlation delays equal to the numerical value of the acoustic travel time between the sensors. Although these pulses are narrow, they have a finite width, within which a fine structure appears in the form of multiple rapid oscillations, due to the differentiating action of the filter. The number of such oscillations increases as the low-frequency roll-off of the filter becomes steeper. This fine structure is evident in several recently published experimental determinations of the cross-correlation function of band-limited ocean ambient noise.     

孤子内波导致海洋环境噪声垂直指向性异常分析

依据近场波数积分、远场耦合简正波相结合的二维噪声场模型,侧重理论研究孤子内波所在扇区,环境噪声垂直阵响应的变化,分析了某些孤子内波情形下垂直阵环境噪声水平凹槽变深这一异常现象的原因:孤子内波离垂直阵较近时,远离内波的海面噪声源多,其激发的简正波能量由低号耦合到高号,在垂直阵处高号简正波能量对环境噪声场贡献增大,导致环境噪声水平凹槽加深;对于大尺度、多波包孤子内波,其范围相对较大,内波所在区的局部简正波本征值和本征函数产生的变化影响显著,使低号简正波衰减变快,而高号衰减慢,导致接收阵处高号简正波能量增加,低号简正波变弱,这样,无论孤子内波群靠近或离接收阵远,都将使垂直阵环境噪声水平凹槽加深。      

Temporal coherence of acoustic rays and modes using the path integral approach

Acoustic propagation can be described by rays and normal modes. Applying the path integral to refractive rays in three dimensional space, Dashen et al. [J. Acoust. Soc. Am. 77, 1716-1722 (1985)] derived the mutual coherence function of the acoustic field. For shallow water where sound interacts with boundaries, the acoustic field can be described by vertical modes and horizontal rays. Applying the path integral to the horizontal rays, one obtains the mutual coherence function of the normal modes. This paper applies this formulation to the derivation of the temporal coherence function of individual modes and also that of the acoustic field in the presence of linear internal waves. The effects of mode coupling due to internal waves on temporal coherence loss are illustrated with numerical calculations.     

岛礁海域海洋环境噪声垂直分布和垂直指向性

依据岛礁海域复杂海底地形、海试期间航船分布和实测风速数据,应用射线声传播理论,建立岛礁海域海洋环境噪声三维模型。在海试岛礁海域深海声道条件下,采用射线3D算法,仿真计算了32元垂直测量阵所处265~885 m负声速梯度深度范围内1 kHz风关和50 Hz远处航船海洋环境噪声级垂直分布,以及50 Hz航船海洋环境噪声垂直指向性,并与实测分析进行比较。结果表明,仿真结果与海试实测数据一致性良好。在本例海底起伏、接收点周边存在众多岛礁和海底山的三维环境中,1 kHz风关海洋环境噪声级随深度分布较近于均匀;西南方向较远处航道区海域海底较平坦,航道区至接收阵为缓斜坡海底,50 Hz远处航船海洋环境噪声级随深度有所增加,其噪声垂直指向性无明显水平凹槽。文中建立的岛礁海域海洋环境噪声三维模型,可较好地表征本例岛礁复杂地形海底起伏海域的风关和航船海洋环境噪声级的垂直分布、及航船环境噪声的垂直指向性,实测和仿真的岛礁海域海洋环境噪声相关数据,可供实际应用及相关研究参考。      

Forward scattering from the sea surface and the van Cittert-Zernike theorem

The van Cittert-Zernike theorem is used to generate models for the spatial coherence of a sound field that has been forward scattered from the sea surface. The theorem relates the spatial coherence of an observed wave field to the distant source intensity distribution associated with this field. In this case, the sea surface upon ensonification is taken to be the source, and the sea-surface bistatic cross section corrected for transmission loss is taken as a surrogate for the source intensity distribution. Improvements in methodology for generating an estimate of the 2D autocorrelation function for sea surface waveheight variation, necessary to compute the bistatic cross section, are documented in the Appendix. Upon invoking certain approximations, simple expressions for the characteristic length scales of vertical, horizontal, and horizontal-longitudinal coherence, are derived from the theorem. The three coherence length scales identify a coherence volume for the spatial coherence of a sound field arriving via the surface bounce channel. Models for spatial coherence derived from the van Cittert-Zernike theorem without these approximations compare reasonably well with measurements of complex vertical coherence made at 8 kHz and 20 kHz in the East China Sea as part of the 2001 ASIAEX field program. In terms of the ASIAEX field geometries and sea-surface conditions, at frequency of 20 kHz the coherence volume is a vertical layer 0.5 m thick by 3 m in each of the two horizontal dimensions; at 8 kHz these dimensions increase by a factor of 2.5, representing the ratio of the two frequencies.     

Geoacoustic inversion of ambient noise: a simple method

The vertical directionality of ambient noise is strongly influenced by seabed reflections. Therefore, potentially, geoacoustic parameters can be inferred by inversion of the noise. In this approach, using vertical array measurements, the reflection loss is found directly by comparing the upward- with the downward-going noise. Theory suggests that this simple ratio is, in fact, the power reflection coefficient-potentially a function of angle and frequency. Modeling and parameter searching are minimized, and the method does not require a detailed knowledge of the noise source distribution. The approach can handle stratified environments and is believed to tolerate range dependence. Experimental data from five sites, four in the Mediterranean, one on the New Jersey Shelf, are described. Most of the Mediterranean sites had temporally varying noise directionality, yet yielded the same reflection properties, as one would hope. One site was visited in conditions of very low surface noise. This paper concentrates on an experimental demonstration of the feasibility of the method and data quality issues rather than automatic search techniques for geoacoustic parameters.     

The use of low-frequency noise in passive tomography of the ocean

A possible design of the mode tomography of the ocean with the use of a scheme requiring no expensive low-frequency radiators is considered. The design is based on the widely discussed method of estimating the Green’s function from the cross-coherence function of noise field received in a great number of observation points. The relationship between the Green’s function and the noise coherence function is derived from the Helmholtz-Kirchhoff integral. The use of the vertical multielement arrays composed of vector receivers is suggested to decrease the duration of noise signal accumulation required for a reliable determination of the Green’s function. The solution of the tomographic problem is based on the determination of the mode structure of acoustic field from the eigenvectors and eigenvalues of the cross-coherence matrix of the received noise field.     

Passive structural health monitoring of a high-speed naval ship from ambient vibrations

Previous studies have used the cross-correlation of ambient vibrations (CAV) technique to estimate the impulse response (or Green's function) between passive sensors for passive imaging purposes in various engineering applications. The technique (CAV) relies on extracting deterministic coherent time signatures from the noise cross-correlation function computed between passive sensors, without the use of controlled active sources. Provided that the ambient structure-borne noise field remains stable, these resulting coherent waveforms obtained from CAV can then be used for structural monitoring even if they differ from the actual impulse response between the passive sensors. This article presents experimental CAV results using low-frequency random vibration data (<50 Hz) collected on an all-aluminum naval vessel (the HSV-2 Swift) operating at high speed (up to 40 knots) during high sea states. The primary excitation sources were strong wave impact loadings and rotating machinery vibrations. The consistency of the CAV results is established by extracting similar coherent arrivals from ambient vibrations between the pairs of strain gages, symmetrically located across the ship's centerline. The influence of the ship's operating conditions on the stability of the peak coherent arrival time, during the 7 days trial, is also discussed.     

互相关自适应加权的医学超声成像算法研究

根据超声成像系统的超声回波信号互相关性,提出互相关自适应加权超声成像算法.该算法根据散射点回波信号之间的空间相关性设置加权系数,对不同位置的散射点进行自适应加权成像,从而降低了成像系统的旁瓣,抑制了相关性较差的噪声.通过Field II仿真的点目标和吸声斑目标处理结果表明该方法成像的横向和纵向分辨率高,成像速度快.相对于延时叠加(DAS)算法,该算法对散射点成像可提高对比度16 dB,对于吸声斑成像可提高对比度0.85 dB.最后采用完备数据集进行实验,结果表明该算法成像分辨率优于DAS算法,对比度提高了17 dB.     

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加.     

Multipath maximums in the correlation function of a wideband noise signal produced by a sea object: Noise immunity of their extraction

The noise immunity of the procedures used for extracting the local maximums of the autocorrelation and cross-correlation functions of a wideband noise signal produced by a sea object is studied. The autocorrelation and cross-correlation functions refer to the outputs of one or two spatial channels formed by a hydroacoustic array in the vertical plane. The limiting cases of low and high signal-to-noise ratios are considered. The noise immunity of extracting the maximums of the correlation function is compared with the noise immunity of the signal detection.     

Cross-correlation coefficient of field emission flicker noise from potassium submonolayers on tungsten

In a field emission tube with two probe-holes the cross-correlation coefficient of current fluctuations from potassium submonolayers on tungsten has been measured. The cross-correlation coefficient depends on the probe-hole positions, i.e. on the substrate structure, and increases with emitter temperature and with potassium coverage; it is zero at the minimum of the noise power accompanying the work function minimum. These measurements seem to show for the first time the existence of spatial correlation in adsorbate submonolayers.     

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。      

利用海洋环境噪声直接提取海底反射系数

提出了一种利用海洋环境噪声直接(非迭代)提取海底反射系数的方法,基于海洋环境噪声垂直相关函数与方向密度函数的相似性,结合海洋环境噪声射线理论,由两个垂直排列的水听器实现海底反射系数的被动获取.方法适应性的仿真分析说明较高海况下且近场无航船干扰的海洋环境噪声数据有利于方法的实现;对于两层海底,海洋环境噪声垂直相干函数经高...     

Intensity Correlation Function of a Single-Mode Laser Driven by Two Colored Noises with Colored Cross-Correlation

By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. Moreover, we find that there is a minimum Tmin in the curve of the intensity correlation time versus the pump noise intensity, and the depth and position of Train strongly depend on the quantum noise self-correlation time T2 and cross-correlation time T3.