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This study provides an argument cautioning against the use of adaptive-beamforming (ABF) techniques in conjunction with a known method for estimating the bottom reflection loss from natural marine ambient noise. This application of ABF has been investigated in the past with rather inconsistent results. Furthermore, no formal proof that ABF algorithms do indeed provide an estimate of the bottom reflection loss is available. This study moves from a recent derivation of the relationship between the bottom reflection coefficient and the Fourier transform of the marine-noise spatial coherence function. The circumstances under which the beamforming operation approximates a discrete Fourier transform (DFT) of the spatial coherence function estimated from array data are analyzed. It is shown that, under certain conditions, conventional beamforming is equivalent to directly computing the DFT of the coherence function, as long as some subtle details are properly taken into account. Furthermore, it is shown that ABF cannot be guaranteed, in general, to perform this operation, and therefore provide an estimate of the bottom reflection coefficient. The conclusions are demonstrated on simulated and measured data.

The acoustic performance of passive or active panel structures is usually tested in sound transmission loss facilities. A reverberant sending room, equipped with one or a number of independent sound sources, is used to generate a diffuse sound field excitation which acts as a disturbance source on the structure under investigation. The spatial correlation and coherence of such a synthesized non-ideal diffuse-sound-field excitation, however, might deviate significantly from the ideal case. This has consequences for the operation of an active feedforward control system which heavily relies on the acquisition of coherent disturbance source information. This work, therefore, evaluates the spatial correlation and coherence of ideal and non-ideal diffuse sound fields and considers the implications on the performance of a feedforward control system. The system under consideration is an aircraft-typical double panel system, equipped with an active sidewall panel (lining), which is realized in a transmission loss facility. Experimental results for different numbers of sound sources in the reverberation room are compared to simulation results of a comparable generic double panel system excited by an ideal diffuse sound field. It is shown that the number of statistically independent noise sources acting on the primary structure of the double panel system depends not only on the type of diffuse sound field but also on the sample lengths of the processed signals. The experimental results show that the number of reference sensors required for a defined control performance exhibits an inverse relationship to control filter length.

Filtered Delay Multiply and Sum (F-DMAS) is an ultrasound beamforming technique derived from microwave imaging, which exploits the spatial autocorrelation of the receive aperture to improve the quality of images. Being based on the spatial coherence of backscattered echoes, it reconstructs a pulse-echo beam with lower sidelobes and a narrower main lobe as compared to standard Delay and Sum (DAS). Thanks to this, F-DMAS can be effectively employed in high frame-rate (HFR) ultrasound imaging, where higher acquisition rates come together with more artifacts, lower contrast and worse spatial resolution. This presentation will provide an overview of the most recent applications of F-DMAS in HFR imaging, e.g., with multi-line transmission and plane-wave techniques. Results of simulations, phantom experiments and in vivo scans, particularly of cardiac imaging, show that F-DMAS represents an effective solution to improve image quality, suppress artifacts and increase the frame-rate at the same time. Moreover, two alternative methods, developed starting from the F-DMAS formulation, will be shown as they further enhance the image quality in HFR imaging.

Ultrasound Short Lag Spatial Coherence (SLSC) imaging exploits the spatial coherence (SC) of backscattered echoes to suppress acoustic clutter and to significantly improve image contrast, particularly in difficult-to-image patients. Multi-line transmission (MLT) imaging simultaneously transmits multiple beams to increase frame rates. We hypothesize that the combination of SLSC and MLT has the potential to enhance detectability of coherent structures within a tissue background. Sector images of a 14G biopsy needle inserted within ex vivo bovine meat were acquired after implementing single-line transmission (SLT) and MLT with 4, 6, 8 and 16 simultaneous beams. The SLSC algorithm was applied to the acquired data. Results show that MLT SLSC images have a visibly darker background than SLT SLSC images, which is caused by the rapid decorrelation of the SC at short lags with MLT. This decorrelation is caused by inter-beam crosstalk interferences and can be leveraged to enhance the coherence of highly reflective targets within a tissue background, causing an increase in needle contrast from about 25 dB with SLT to ∼44 dB with 16-MLT. These results support our hypothesis that the decorrelation caused by crosstalk improves visualization of highly coherent targets within tissue, with promising applications to biopsy needle localization.

Correlation sonar systems, such as correlation velocity logs and synthetic aperture sonar micronavigation, can estimate platform motion using measurements of the spatial coherence of seafloor scattering. During the course of operation, the spatial coherence measurements made by these systems will fluctuate about their average values. A variety of factors, including noise sources, changing environmental properties, and statistical estimation error can all contribute to the variability in these measurements. This presentation will introduce models that can be used to predict the variability in measurements of spatial coherence. These models will be compared with field measurements of spatial coherence collected at normal incidence to the bottom of Seneca Lake. Finally, the application of these models will be discussed as they relate to the design of arrays and signal processing algorithms for correlation sonar systems. (The authors want to acknowledge the financial support for this work by Lockheed Martin Rotary and Mission Systems.)Correlation sonar systems, such as correlation velocity logs and synthetic aperture sonar micronavigation, can estimate platform motion using measurements of the spatial coherence of seafloor scattering. During the course of operation, the spatial coherence measurements made by these systems will fluctuate about their average values. A variety of factors, including noise sources, changing environmental properties, and statistical estimation error can all contribute to the variability in these measurements. This presentation will introduce models that can be used to predict the variability in measurements of spatial coherence. These models will be compared with field measurements of spatial coherence collected at normal incidence to the bottom of Seneca Lake. Finally, the application of these models will be discussed as they relate to the design of arrays and signal processing algorithms for correlation sonar systems. (The authors want to acknowledge the financial support for this work by Lockheed Martin R...

This paper reviews selected previous work in photoacoustic imaging conducted at the Institute of Cancer Research or with collaborators and considers directions for future research. For flexible introduction as an additional mode to clinical freehand ultrasound scanning, a multispectral epiphotoacoustic system was built by adapting a Zonare z.oneUltra™. Early clinical findings from photoacoustic imaging of breast tumours were consistent with contrast MRI although also provided evidence that photoacoustic image interpretation and penetration were limited by clutter generated by photoacoustic emissions from regions at or near the skin surface. Schemes for improving photoacoustic signal-to-clutter ratio were therefore explored. These have included deformation compensated averaging, spatial coherence processing, photoacoustic contrast agents, and localised vibration tagging (LOVIT). LOVIT (implemented using acoustic radiation force) was particularly successful, tripling penetration depth in breast-mimicking phantoms. It has also been implemented on a Verasonics™ platform and extended using a 3 + 3 interleaved comb-push method, which further reduces the clutter and improves the frame rate. Multidimensional and other extensions to LOVIT remain possible. Meanwhile, work at other institutions has explored various propagation model-based schemes. Most of the clutter reduction methods are complementary in nature, and a combined approach therefore represents a worthwhile direction for the future work.

Sparse arrays reduce the number of redundant measurements for lags on an array in comparison to fully populated arrays. For ideal measurements, where spatial stationarity is maintained and measurement error is minimal, the performance of such arrays can be shown to be similar to that of a uniform array of the same length with appropriate processing techniques. However, for complex environments with limited spatial coherence or noisy measurements, array sparsity can impact performance. We construct a simple model that relates the relative positions of redundant measurements and channel coherence length to the variance of covariance function estimates, determine a set of lag measurement weightings that minimize said variance for a given set of redundant lag positions, determine a set of conditions on which a uniform weighting is optimal, and demonstrate that regularly spaced lag repetitions optimally sample a spatially varying covariance function.

Matched-field processing is a method for inversion of the acoustic field utilizing its spatial coherence. In this work, a matched-field processor is introduced that incorporates the spatial coherence of the acoustic field not only at a single frequency but across frequencies as well. The new processor is suitable for multitonal sources and does not require knowledge of the source spectrum which is typically unavailable in passive estimation problems. A performance evaluation on source localization under low signal-to-noise ratios shows that the new processor is significantly superior, under certain circumstances, to the conventional incoherent Bartlett processor especially in cases involving receiver arrays with a small number of phones.

An analytical model is developed for the vertical coherence of the ambient noise field generated by a plane of sources at a finite depth beneath the ocean surface. To clarify the effects of source depth on the noise field, the relatively simple case of a semi-infinite ocean with an isovelocity profile is considered. The expression derived for the coherence is exact; it depends on the source depth explicitly, and it includes the homogeneous and inhomogeneous components of the field. When the sources are shallow, that is, the source depth is much less than a wavelength and the source–image pairs act as dipoles, the coherence is an oscillatory function of frequency, consistent with an earlier theory of noise coherence in deep water. With deeper sources, the dipole description fails and the coherence function becomes approximately independent of frequency. This change of character suggests that the spatial structure of the noise field at depth in the ocean could be inverted to yield information on the acoustic properties of the bubble sources associated with breaking surface waves.

A new array processing system that performs high‐resolution imaging in turbulent ocean media is introduced. It exploits information contained in higher‐order spatial spectra and images to a resolution which is limited by the array aperture rather than the medium. Precise a priori knowledge of the turbulence’s spatial coherence structure is not needed. Furthermore, the signal processing is straightforward to implement, the system is self‐calibrating, and the computational demands are reasonable. Initial tests of the imager have been conducted and several representative examples are presented. It is found that precise bispectrum estimates are required for good image quality. Since this requires large data sets, in essence this algorithm trades data requirements for resolution. In addition, the direction of arrival information, contained in phase terms that are processed with the bispectrum, is lost in the averaging process. Nevertheless, the system provides very good quality images, even in severe environments.

The Array Gain(AG) is a metric to assess the performance of an array and is dependent on the configuration of array, frequency, as well as on the directionality of noise. In this study, AG is calculated based on the spatial coherence between sensor elements in directional noise environment for a given array shape. The estimated AG is then compared with AG derived from the sea going data based on the signal to noise ratio. The results are presented and discussed.

As a complement to experimental efforts in seismics and acoustics to infer geo-acoustic properties of the propagation environment from the second order statistics of ambient noise measurements, a set of exact, explicit, closed form expressions for the cross-spectral density and spatial coherence of diffuse random wave fields is presented. Taken together, the expressions are well suited for modeling broadband, diffuse wave coherence in realistic scenarios involving directive, ambient noise from local (i.e., volume) and distant (i.e., plane wave) source features in an open, dispersive, attenuating medium.

Though referred to as noise, the ambient ocean soundscape carries valuable information about the physical ocean environment. To study this information, Kuperman and Ingenito introduced a model for spatial coherence in a depth stratified ocean arising from the vertically directive diffuse acoustic noise produced by bubbles distributed throughout the surface. Here the model is adapted to incorporate horizontal directivity as well, making it possible to include additional noise contributions from directive features such as storms, biologics, shipping, and wave breaking. As an analytic approach, the model can serve as a computationally light complement to existing methods.

Mid-frequency (12 kHz) acoustic scattering from the sea surface is analyzed with regard to surface wave shape inversion and receiver array characteristics. The forward scattered data is from the Surface Processes and Communications Experiment (SPACE08). Multipath arrivals representing surface, bottom-surface, and surface-bottom paths are distinguishable, implying that knowledge of the surface is known approximately 1/3, 1/2, and 2/3 the distance between source and receiver. Surface wave shape inversion at those ranges are presented in a variety of environmental conditions and compared to other calculable statistics such as vertical and horizontal array correlation length. The relationship between temporal fluctuations in the intensity of the surface reflected multi-path and array spatial coherence is investigated. To what extent receiver array statistics related to acoustic focusing follows environmental conditions such as wind speed and sea state are considered.

In this work, a two-stage multi-rank solution for passive ranging is presented for acoustic sensing systems using multi-module towed hydrophone arrays operating in underwater environments subject to spatial coherence loss. The first stage of processing consists of adaptive beam-forming on the individual modular array level to improve the signal-to-noise ratio and at the same time to adaptively reduce the data dimensionality. The second stage of multi-rank filtering exploits the possible spatial coherence existing across the spatially distributed modular arrays to further improve the accuracy of passive ranging. The proposed solution reduces to either the well-known non-coherent solution under no spatial coherence, or the fully coherent solution under perfect spatial coherence. For large distributed arrays, the asymptotic approximation of the proposed solution has a simple beam-space interpretation. We conclude with a discussion of the estimator when the spatial coherence is unknown and its implications for the passive ranging system performance.

Humans exploit environmental regularities in sounds to perceptually bind acoustic energy occurring simultaneously at different frequencies. Such abilities influence vowel perception in speech and timbre perception in music. Other animals solve similar binding problems in the recognition of species-specific acoustic signals. Moreover, they commonly do so using auditory systems that differ in notable ways from that of mammals. This study of two treefrog species investigated temporal and spatial coherence as cues that promote grouping of two spectral bands emphasized in their acoustic signals. In two-alternative choice tests, females preferred temporally and spatially coherent calls over alternatives in which the onsets/offsets of the two bands were time-shifted by more than 25 ms or in which the two bands were spatially separated by 7.5° or more. These results, which suggest temporal coherence and spatial coherence promote across-frequency auditory grouping, are notable given differences in how the two spec...

The detection performance of single vector sensors and vector sensor line arrays is degraded by nonacoustic self‐noise and spatial coherence of the noise between vector sensor components. Results based on optimizing the directivity index for a single vector sensor show that the particle motion channels should always be included in the processing for optimal detection, regardless of self‐noise level, assuming these levels are properly taken into account. The vector properties of acoustic intensity can be used to estimate the levels of nonacoustic noise in ocean measurements. Application of conventional, minimum variance distortionless response, and white‐noise‐constrained adaptive beamforming methods with ocean acoustic data collected by a vector sensor illustrates increase in spatial resolution but corresponding decrease in beamformer output and introduction of bias with increasing beamformer adaptivity. Expressions for the spatial coherence of all pairs of vector sensor components in homogeneous, isotrop...

Little experimental data have been reported in the literature about spatial coherence of low‐frequency sound waves propagating over megameter ranges in the ocean. In 1998–1999, the North Pacific Acoustic Laboratory (NPAL) carried out a comprehensive low‐frequency long range sound propagation experiment with the use of the receiving billboard acoustic array. By signal‐processing of the NPAL data, we calculated spatial coherence of the broadband acoustic signals (with 75 Hz carrier) after their propagation of about four thousand km in North Pacific. The results obtained are presented in this paper. First, the horizontal coherence of the NPAL signals is discussed. The results show that the horizontal coherence radius varies in the range 500–1000 m. This value is in a good agreement with predictions of a 3D modal theory of low‐frequency long‐range sound propagation in a fluctuating ocean. Secondly, the vertical coherence of the NPAL signals is presented. After averaging over several days of the experiment, the vertical coherence reveals non‐monotonic dependence on the distance between hydrophones. Finally, the horizontal‐vertical coherence is studied. This coherence rapidly degrades with the increase of vertical separation between hydrophones. [Work supported by ONR.]

Multireference partial field decomposition (PFD) can be used to generate coherent holograms for scan-based near-field acoustical holography measurements. PFD is successful when the reference array completely senses all independent subsources, but meeting this requirement is not straightforward when the number of subsources and their locations are ambiguous (such as in aeroacoustic sources). A figure of merit based on spatial coherence lengths, called references per coherence length (RPLc), is a useful metric to guide inter-reference spacing in the array design so that the source is spanned. Coherence length is defined as the axial distance over which the ordinary coherence drops from unity to some desired value. Numerical experiments involving an extended, partially correlated source show that sufficiency of the reference array for different source conditions may be simply expressed in terms of RPLc. For sources of varying spatial coherence and over a large range of frequencies, one reference per coherenc...

Averaged transmission characteristics for underwater sound channels, using energy flux descriptions, were independently introduced and developed by Leonid Brekhovskikh [Sov. Phys.-Acoust. 11, 126-134 (1965)], David Weston [J. Sound Vib. 18, 271-287(1971)], and Preston Smith [J. Acoust. Soc. Am. 50, 332-336 (1971)]. While most attention in these studies was focused on elucidating averaged transmission loss in range dependent environments, Preston, in particular, also examined the application of energy flux techniques to other statistical characterizations of multipath environments, including channel impulse response and spatial coherence. Preston’s incisive physical insight resulted in channel statistical characterizations that were simple to apply, but notably effective for signal processing and sonar studies. My purpose in this talk will be to trace the development of statistical characterizations of multipath channels based on energy flux notions, and to sketch some specific applications of these ideas,...

Broadband noise correlation methods for the passive extraction of information about the point-to-point propagation of waves between distant sensor locations have received considerable attention in the literature. This talk addresses the rate at which the wave coherence accumulates to overcome stochastic random fluctuations in a spatially correlated random wave field. It is shown that the expected magnitude of the random uncertainty associated with a single realization of the sample cross-correlation function depends on the total power incident on the sensors. This notion is applied to quantify the emergence rate of the coherence between correlated beams in the ocean waveguide. The point-to-point build-up rate is compared to the gain achieved through the application of directional filters over multi-sensor line arrays. Various array geometry scenarios of experimental interest are considered. These results are straight forwardly extendable to other environments such as seismics, helioseismics, and nondestru...

Vertical spatial coherence for shallow water propagation at frequencies 1–10 kHz is studied as function of range (50 to 5000 m), as part of the Shallow‐Water 2006 program that took place off the coast of New Jersey in August 2006 in waters 80 m deep. An acoustic source was deployed from the R/V Knorr at depths 30 and 40 m and signals were recorded on a moored receiving system consisting of two 1.4 m long vertical line arrays (VLA) centered at depths 25 and 50 m. At all ranges, spatial coherence, Γ (normalized spatial correlation), is locally stationary and depends on element vertical separation d up to the maximum kd (59) afforded by the VLA, where k is acoustic wave number. For range normalized by depth, r*, less than about 10, Γ is oscillatory, with non‐zero imaginary part, reflecting the inclusion of multipaths for which no single path dominates. For r* greater than 10, Γ tends to exhibit a monotonic decay with kd and the imaginary part vanishes reflecting symmetry about 0 deg vertical arrival angle. T...

Wide area sonar system, such as OAWRS (ocean acoustics waveguide remote sensing), can instantaneously image large shoals of fish spanning tens of kilometers from long ranges in an ocean waveguide. An analytic and numerical model is developed for the spatial and temporal coherence of the scattered field from a large group of fish in a shallow water waveguide. The temporal coherence of the received signal depends on both the temporal coherence of the random waveguide through the medium Green’s function and the correlation time scale for fish group distribution. The spatial coherence of the received signal depends on both the spatial correlation scale of the random waveguide inhomogeneities and that for the imaged fish group distribution. The temporal and spatial correlation scale for the fish group distribution are determined from experimental data acquired in the Gulf of Maine during the 2006 Ocean Acoustics Waveguide Remote Sensing (OAWRS) Experiment. The effect of temporal and spatial coherence of the sc...

Spatial and temporal coherence of acoustic field has very important effects on applications of underwater acoustics. In this paper, recent experimental results of low‐frequency signal coherence in shallow water are presented. For signals with low frequencies of 100∼500Hz in shallow water, the vertical correlation has no distinct depth dependence, but it has obvious range dependence. The horizontal correlation length is greater than 40 wavelengths, the temporal correlation length is greater than 510s at frequency of 475Hz and greater than 1800s at frequency of 150Hz. These experimental results show that low‐frequency acoustic field has strong spatial coherence and temporal stability in shallow water. [Work supported by the National Natural Science Foundation of China under Grant No.10734100]

Scattering from small, random inhomogeneities in the ground (such as rocks and voids) diminishes the spatial coherence of seismic waves, much as turbulence in the atmosphere diminishes spatial coherence of propagating sound waves. In this paper, modeling of seismic spatial coherence for surface waves propagating over short distances (roughly 50 m to 1 km) and at relatively high frequencies (greater than approximately 1 Hz) is considered. The random inhomogeneities are distributed broadly in size and are described with a quasi‐wavelet (QW) model. For simplicity, we consider propagation of a 2‐D scalar wavefield. Scattering from an individual QW is first calculated using a single‐scattering approximation. Then, the contributions from all randomly placed QWs, including all size classes, are cross‐correlated to find the spatial coherence of the total wavefield. As an example, we consider modeling of seismic coherence at a site in the Mojave Desert with random basaltic inhomogeneities surrounded by sand. The i...

Ambient noise propagates through the ocean in much the same way as sound from a man‐made source. The noise is a stochastic phenomenon, but some of its statistical measures, for instance, the spatial coherence, may be influenced by the environment in a systematic and stable manner. Such statistical measures may then be inverted to obtain information on the environment. In particular, over the continental shelf, where water depths are less than 200 m, the nature of the seabed has a significant effect on the vertical coherence, or, equivalently, vertical directionality, of the noise in the water column. This suggests that simple measurements of the vertical coherence of the noise, taken with just two hydrophones in the water column, may be inverted to yield the geoacoustic parameters of the bottom. An essential element of such an inversion procedure is an ambient noise model which includes a geoacoustic model of the sediment. In the presentation, a noise inversion model based on spatial coherence will be described. Examples of inversions for the bottom properties, obtained from real data taken at shallow‐water sites in the northern and southern hemispheres, will be presented. [Research supported by ONR.]

Predictions of transverse horizontal spatial coherence from path integral theory are compared with measurements for two ranges between 2000 and 3000 km. The measurements derive from a low-frequency (75 Hz) bottom-mounted source at depth 810 m near Kauai that transmitted m-sequence signals over several years to two bottom-mounted horizontal line arrays in the North Pacific. In this paper we consider the early arriving portion of the deep acoustic field at these arrays. Horizontal coherence length estimates, on the order of 400 m, show good agreement with lengths calculated from theory. These lengths correspond to about 1° in horizontal arrival angle variability using a simple, extended, spatially incoherent source model. Estimates of scintillation index, log-amplitude variance, and decibel intensity variance indicate that the fields were partially saturated. There was no significant seasonal variability in these measures. The scintillation index predictions agree quite well with the dataset estimates; nevertheless, the scattering regime predictions (fully saturated) vary from the regime classification (partially saturated) inferred from observation. This contradictory result suggests that a fuller characterization of scattering regime metrics may be required.

The development and application of high resolution acoustic systems by Holliday and Greenlaw has played a key role in demonstrating that zooplankton could can form highly concentrated layers ranging in thickness from a few decimeters to a few meters. These thin layers are remarkable in that they persist longer and have higher spatial coherence than multi‐meter thick patches that can be sampled by nets and conventional acoustics. These results are inconsistent with the classical theory that thicker patches are more persistent and thus more important. Simultaneous measurements of temporal and spatial changes in the finescale physical, optical, chemical structure have provided important insights into the mechanisms controlling not only the dynamics of thin zooplankton layers but also their impacts on marine ecosystems and the transmission of sound in the ocean. [Work supported by grants from the ONR Biology and Chemistry program.]

A system for high‐speed calculation of tissue elastic properties using a clinical ultrasonic imaging system will be presented. The hypothesis driving this development is that real‐time feedback of elasticity images is essential in obtaining high‐quality data (consecutive images with high spatial coherence). Extensive experience with laboratory fixtures and off‐line processing of elasticity data showed that problems occurring in data acquisition often resulted in poor elasticity image quality. The delay in observing the resulting images, due to off‐line processing, resulted in slow progress in developing experimental techniques and signal processing strategies. When high‐quality data were obtained, high contrast‐to‐noise images were available. Initial experience with real‐time freehand elasticity imaging shows that images with similar high contrast to noise can be obtained. Results in volunteer patients have shown that high‐quality elasticity images are easily obtained in vivo for a variety of breast patho...

Due to the existence of relatively smooth local extrema in the dependencies of ray‐cycle lengths on initial path angles, different kinds of weakly diverging bundles (WDB) of rays can arise in refractive oceanic waveguides. As Brekhovskikh et al. have shown [Acoust. J. (in Russian) 36, 5, 824–831 (1990)], such bundles transporting high‐level acoustic intensity can be interesting with respect to these applications in ocean acoustic tomography (OAT). Conditions for the existence of WDB for piecewise linear approximations of sound velocity profiles are formulated in this work. Based on these results, the possibilities for the existence of WDB for different regions of the world’s oceans are discussed. Important for tomographical application, the coherence of WDB is investigated under assumptions that the acoustic signals are emitted by noise sources with limited lengths of spatial coherence and the oceanic environment is randomly inhomogeneous in spatial coherence, as described by a Gaussian distribution. Nume...

In this presentation, effects of small random fluctuations on the spatial coherence of the sound field in shallow water with multilayered sediments will be examined. These fluctuations occur within the water volume and the sediment layers as well as at the layer interfaces. Most previous work has dealt with either range‐independent or weakly range‐dependent environments with random variabilities. However, strong range dependence often occurs in sound‐speed profiles and at layer interfaces. For example, the region of the ACT III experimental series in the Straits of Korea shows range variability arising from sloping bathymetry and a coastal front. Consequently, spatial coherence for range‐dependent waveguides with small random fluctuations will be treated. Numerical simulations of the coherence function will be presented. Results will be compared with coherence lengths of the field extracted from ACT III data.

As part of ONR’s high‐frequency initiative, a field experiment to determine the temporal and spatial coherence of acoustic fluctuations induced by propagation through a fully developed turbulent flow has been planned in collaboration with several other research groups for late September 1994. Narrow‐band measurements (67‐kHz coded signals) will be taken in Cordova Channel, British Columbia, where strong, semidiurnal tidal flows (up to 1.0 m/s) create fully developed turbulence (Reynolds number ≊107), and strong mixing prevents stratification (bulk Richardson number ≊0.02). Prior experiments have established the turbulent nature of the flow and examined the horizontal arrival angle and intensity fluctuations with time. In the present experiment, a new compact acoustic array, consisting of 128 hydrophones in an elliptical configuration, is being adapted to monitor the acoustic arrivals in the vertical and horizontal, with finer spatial resolution than has previously been obtained. Amplitude and phase data w...

The formation of a passive synthetic aperture in a nonisotropic ocean is a complex problem that includes two main areas of investigation. The first one, which is discussed in another study, is related to the limitations imposed by the temporal and spatial coherence properties of the underwater medium on the size of an effective synthetic aperture. The second area of investigation is related to the development of an algorithm that will synthesize coherently the successive spatial information of a small moving line array into an extended aperture. The synthetic aperture techniques, that have been discussed in the open literature, however, have not been fully tested with experimental results including many targets. The present study is concerned with an experimental attempt in forming a long (i.e., 100 λ) synthetic aperture in an ocean where the spatial and temporal coherence properties of the acoustic field are known. For a multitarget environment, results indicated that an optimum synthetic aperture proces...

This paper shows a successful modeling of some full‐scale low‐frequency acoustic measurements in shallow water. Match between model‐ and stable‐measured Doppler spectra by means of an inverse‐problem approach made estimation of geoacoustic and source parameters possible. Spatial coherence has been measured. Significant parts of the loss of spatial coherence are modeled and explained. A simple method has been formulated making it possible under certain conditions to estimate the spatial coherence function using a single hydrophone and a moving source. Finally, spatial mode filtering has been demonstrated using a horizontal array.

An expression for the spatial coherence in a semicircular noise field is obtained which involves the function J0(x) and a single integral that can be evaluated by Gaussian quadrature. The semicircular noise model is motivated by an idealized representation of ship traffic plying a well‐defined sea lane. The model coherence is characterized by a marked dependence on sensor orientation relative to the sea lane. An extension of the single lane model to the case of multiple parallel lanes yields a coherence expression which involves the weighted sum of J0(x) and the previously derived coherence function for a single lane. For this general situation the weighting factors depend on the relative power distribution among the lanes. Model calculations show good qualitative agreement with coherence estimates for d/λ≤1 which were computed from acoustic data for sensor orientations both parallel and perpendicular to known shipping lanes.

Clay and Medwin [J. Acoust. Soc. Am. 47, 1419–1429 (1970)] performed an experiment in which they measured the spatial coherence of signals scattered from a wind‐driven surface in a water tank. The coherence values were obtained by cross‐correlating signals received at two hydrophones and were presented as a function of receiver separation. In this paper, a comparison is provided between these measured values and values predicted using (1) a technique based on Eckart theory [C. S. Clay, J. Geophys. Res. 71, 2037–2046 (1966)] and (2) the facet‐ ensemble method [W. A. Kinney et al., J. Acoust. Soc. Am. 73, 183–194 (1983)]. The former technique is presented by way of a review and provides an approximate single‐valued estimate of coherence independent of receiver separation. The facet‐ensemble method, on the other hand, provides precise estimates that are fully dependent on geometry. Agreement between the method and the experiment is good.

Measurements were made of the fluctuations in amplitude and spatial coherence of acoustic wavefronts transmitted through the deep ocean at two frequencies concurrently, 114 and 400 Hz. The signals were generated by a ship‐suspended souce at 1000‐ft depth and received over two ranges, 130 and 145 nmi, on a string of five bottomed receivers laid horizontally on a deep‐water slope at about 5000‐ft depth. The receiver spacing varied from 500–2500 ft. Amplitude fluctuations were found to differ significantly at receiver separations of 500 ft and appeared unrelated at separations of 2000 ft or more. For multipath transmission, unlike single‐path transmission, the relative phase fluctuations between given receiver pairs were not proportional to frequency, and phase coherence at a given receiver separation was generally less than for single‐path transmission. Coherence at 145 nmi was almost as good as for single path, presumably because ray‐tracing predicts a dominant path and because the phase measurements were ...

Reverberation from the ocean surface, bottom, and volume is discussed in the context of the point scatterer model, with uniform spatial distributions. It is shown that, for sufficiently narrow beamwidths or bandwidths, the covariance factors into a product of spatial and temporal covariances. The spatial covariance is shown to vanish for separations larger than the horizontal width of the transmitting array. This prediction is found to be in reasonable agreement with the experimental results of Wilson and Frazer and with our own sea surface reverberation data reported here.

A problem in underwater passive listening is to detect a possible noise source in a given direction when background noise and other sources are present. It is assumed that the signal to be detected is perfectly coherent spatially. If the correlation matrix of the outputs of the sensors without the signal is known, it is possible to compute both an estimation and a detection test for the signal. When this matrix is unknown, which is the case in passive listening, an estimation of the signal can be obtained by an adaptive antenna thanks to the perfect coherence hypothesis. But in order to find a detection test, the shape of the spatial coherence matrix of the background noise must be known. Then the spectral density of this noise can be estimated even in the presence of the signal and of other coherent sources. A detection test using this estimation and the output of the adaptive antenna is proposed. Theoretical asymptotic results and simulations are presented.

A new method for treating the problem of infrasonic‐noise spatial coherence with relation to a noise‐reducing array design is developed. The behavior of this coherence at Penas, Bolivia (4000 m above sea level), is investigated. The optimum spacing between sampling inlets for that particular location seems to be approximately 12 m at this preliminary stage of the work. The noise recorded with a two‐inlet noise‐reducing array at a 12‐m separation was 40% less than that using only one inlet.

This paper describes experiments performed to determine some of the spatial characteristics of reverberation signals as encountered in pulsed echo‐ranging sonar systems. A sonar system operating at 112 kHz was set up in a tank and used to obtain reverberation signals from smooth sand surfaces (particle sizes≪λ). Backscattered signals for small grazing angles (4°–12°) and narrow beamwidths (8°, 15°, and 22°) were recorded. Spatial correlations of the reverberation fluctuations were plotted for various spatial translations of the transducers relative to the scattering surface. The correlations of the fluctuations became small for lateral displacements (displacements normal to transducer axis) on the order of a wavelength and longitudinal displacements (displacements parallel to transducer axis) on the order of a pulselength. Further analyses of the recorded signals indicated that the average reverberation pressure diminished as a function of range as r−2.7 for one grade of sand and as r−21 for another grade...

Biot and Tolstoy [J. Acoust. Soc. Am. 29, 381–391 (1957)] have devised solutions appropriate to a point explosive source for diffraction and reflection from a single wedge of arbitrary angle. Medwin and Novarini [J. Acoust Soc. Am. Suppl. 1 67, S67 (1980)] have used these solutions to model backscattering from the ocean surface. A model similar to that of Medwin and Novarini is discussed here wherein the solutions are used to predict the spatial coherence of energy scattered in the forward direction by a rough rigid ocean bottom. This model includes diffraction and reflection along with shadowing and has the potential for including bottom topographic characteristics explicitly or in a statistical form. The bottom is approximated by a collection of wedges (and troughs) each of arbitrary angle. The signal at a receiver is then taken as a sum of solutions for individual wedges and troughs. Finally, spatial coherence is determined using signals synthesized for two receiver points. The strengths and weaknesses...

Sonobuoy arrays located over the Mid‐Atlantic Ridge have been used to measure the spatial coherence of sound radiated from sea quakes. These measurements were made with array elements separated by several kilometers and tracked to an accuracy of 20 m. Spatial coherence, defined as the normalized, cross‐power spectral density, has been found to be as high as 0.7 at 14 Hz, to be typically about 0.5 between 16 and 60 Hz, and to drop sharply to zero above 60 Hz. Short‐range events, distinguished by time delays of the order of 0.1 sec across the array and by a rapid onset of the pulse, are presumed to leave the bottom at sharp angles. These events are significantly more coherent than long‐range events that have little time delay across the aperture and whose onset is smeared out in time. Long‐range events are presumed to exit from the bottom at shallow angles. Significant processing gain is possible using high‐resolution spectral analysis. Improvements over the conventional delay and sum processor of as much a...

An exact solution for the field from a cw point source in an ideal wedge exists in the form of normal modes where the mode coefficients contain the entire range and cross‐range dependence. This model is proposed as a benchmark 3‐D solution. For the case when the wedge angle is a submultiple of π the solution has been implemented on a VAX 11/750, and results are available for the following: (a) the complete complex field throughout the wedge including the vicinity of the source; (b) individual mode coefficients (amplitude and phase); (c) transmission loss as a function of position; and (d) the spatial coherence of the field. The model is suitable for a general sensitivity analysis.

In this modeling study subsurface layering effects on the spatial coherence of bottom‐interacting sound were investigated. The ocean bottom was modeled as alternating layers of clay and clayey silt. A silty clay bottom was used as a control. Complex reflection coefficients were calculated using a plane‐wave multilayer model [G. J. Fryer, J. Acoust. Soc. Am. 63, 35–42 (1978)]. Using a frequency averaging technique, estimates of the spatial coherence were obtained as a function of grazing angle for fixed sensor separation. The results indicated that subsurface layering can seriously degrade the spatial coherence at frequencies above 100–200 Hz. The spatial coherence is considerably less affected by subsurface layering at very shallow grazing angles (10° or less) or very steep grazing angles (75° or greater). [Work supported by NORDA.]

An important parameter in the use of the surface acoustic method for sound power measurement or sound power accounting of sources is a knowledge of the behavior of the spatial coherence or incoherence of the surface motion viewed as an acoustic source. If the machine surface can be treated as a collection of incoherent sources with some scale determined by a correlation length then considerable simplification in the power measurements may result. Measurement of the coherence of surface vibrations on a large machine are discussed with a view toward establishing a correlation length and hence the determination of the number of measurement points.

Passive‐synthetic apertures [W. Carey and N. Yen, J. Acoust. Soc. Am. Suppl. 1 75, S62 (1984)] were formed with experimental towed hydrophone data in a sound channel that supported RR and RSR transmission. These apertures were formed with lengths up to 95λ with coherent temporal processing gains approaching 0.75 of theoretical. These results and those of previous investigators [R. Fitzgerald, J. Acoust. Soc. Am. 60, 752–753 (1976); R. Williams, J. Acoust. Soc. Am. 60, 60–73 (1976)] indicate that synthetic apertures can be formed by the coherent summation of the phase‐corrected summation of either hydrophone or subaperture beams over successive time samples when the synthetic aperture length is less than the spatial coherence length and the processing time is less than the temporal coherence length. The evaluation of synthetic apertures requires comparisons with conventional and other high‐resolution techniques. Comparisons between conventional array processing and high‐resolution techniques [maximum entro...

In a recent paper [W. A. Kinney, C. S. Clay, and G. A. Sandness, J. Acoust. Soc. Am., in press], the authors showed agreement between acoustic intensity values measured in a water‐tank scattering experiment and values predicted using the facet‐ensemble method. Medwin and Clay [J. Acoust. Soc. Am. 47, 1419–1429 (1970)] performed a laboratory experiment in which they measured the spatial correlation of underwater acoustic signals scattered from a wind‐driven surface (the rms height was 0.19 cm) as a function of the separation between two receivers (0 to 40 cm). A comparison is provided here between coherence values obtained in the experiment and values predicted using the facet‐ensemble method. The coherence values are given for 60‐, 100‐, and 160‐kHz signals scattered in the specular direction at a grazing angle of 35° (the propagation distance was 420 cm). The measured coherence was dependent upon both Doppler shift and the bandwidth of the correlator, and this dependence was included in the predictions. ...