Source localization in shallow water in the presence of sensorlocation uncertainty

The problem of source localization in shallow water in the presence of sensor location uncertainty is considered. The Cramer-Rao Bound is used to carry out a feasibility study for the joint source and sensor location problem when the multipath propagation channel is modeled as a known, deterministic waveguide. Unlike the free-space propagation channel, the boundedness of the shallow-water waveguide along its vertical axis provides the key to joint determination of the source and sensor location parameters. It is seen that, when a set of intuitive identifiability conditions are satisfied, numerical examples indicate that, for the scenarios considered, the resulting loss in accuracy with which the source location can be estimated due to sensor location uncertainty may be tolerable     

Experimental matched-field localization results using a short vertical array and mid-frequency signals in shallow water

Traditionally, matched-field processing (MFP) has been used to localize low-frequency sources (e.g., <300 Hz) from their acoustic signals received on long vertical arrays. However, some sources emit acoustic signals of much higher frequency. Applying MFP to signals in the mid-frequency range (e.g., 1-4 kHz) is a very challenging problem because MFP's sensitivity to environmental parameter mismatch becomes more severe with increasing frequency. Robust MFP techniques are required to process signals in the mid-frequency range. As a practical issue, short vertical arrays are more convenient to work with than are long vertical arrays; they are easier to deploy and are less prone to large amounts of deformation. However, short vertical arrays undersample the water column, which can result in severely degraded MFP performance. In this paper, we present experimental data results for this nonconventional paradigm. Using the environmentally robust broad-band L/sub /spl infin//-norm estimator, MFP results are given using shallow-water experimental data. This data consisted of broad-band signals in the 3-4-kHz band collected on an eight-element 2.13-m vertical array. These results serve to demonstrate that good localization performance can be attained for this difficult problem. Guidelines on the appropriate use of ray and normal-mode propagation models are also presented.     

Acoustic backscattering from a sandy seabed

Acoustic backscattering from a sandy seabed was measured at a frequency of 5.5 kHz at a wide range of grazing angles. The measurement system used was the University of Miami's sonar tower, consisting of an omni-directional broadband source and two 16-channel hydrophone receiver arrays. A volume scattering model, which combines a fluid model with reflection/transmission coefficients derived from the Biot theory, is used. This model allows energy penetration into the bottom, calculations of the volume scattering at all grazing angles, and the frequency dependence of the sound speed in the water-saturated sediment. In the model, rather than assume sound-speed correlation length in sedimentary volume, core data were used to assimilate a 3-D fluctuation spectrum of the density. The numerical results showed excellent agreement with the measurement at lower grazing angles. We concluded that the interface roughness scattering was dominant at lower grazing angles, while the volume scattering is dominant at higher grazing angles at the sandy site. The border of the dominance of the interface and volume scattering was the so-called critical angle at this frequency. The frequency dependence of sound speeds is also discussed.     

Acoustic inversion of bottom reflectivity and bottom sound-speedprofile

This paper applies a full-field technique to invert bottom sound profile and bottom reflectivity from simulated acoustic data in a shallow water environment. Bottom sound-speed profile and bottom reflectivity have been traditionally estimated using seismic reflection/refraction techniques when acoustic ray paths and travel time can be identified and measured from the data. However, in shallow water, the many multipaths due to bottom reflection/refraction make such identification and measurement rather difficult. A full-field inversion technique is presented here that uses a broad-band source and a vertical array for bottom sound-speed and reflectivity inversion. The technique is a modified matched field inversion technique referred to as matched beam processing. Matched beam processing uses conventional beamforming processing to transform the field data into the beam domain and correlate that with the replica field also in the beam domain. This allows the analysis to track the acoustic field as a function of incident/reflected angle and minimize contamination or mismatch due to sidelobe leakage     

Inversion for Time-Evolving Sound-Speed Field in a Shallow Ocean by Ensemble Kalman Filtering

In the context of the recent Maritime Rapid Environmental Assessment/Blue Planet 2007 sea trial (MREA/BP07), this paper presents a range-resolving tomography method based on ensemble Kalman filtering of full-field acoustic measurements, dedicated to the monitoring of environmental parameters in coastal waters. The inverse problem is formulated in a state–space form wherein the time-varying sound-speed field (SSF) is assumed to follow a random walk with known statistics and the acoustic measurements are a nonlinear function of the SSF and the bottom properties. The state–space form enables a straightforward implementation of a nonlinear Kalman filter, leading to a data assimilation problem. Surface measurements augment the measurement vector to constrain the range-dependent structure of the SSF. Realistic scenarios of vertical slice shallow-water tomography experiments are simulated with an oceanic model, based on the MREA/BP07 experiment. Prior geoacoustic inversion on the same location gives the bottom acoustic properties that are input to the propagation model. Simulation results show that the proposed scheme enables the continuous tracking of the range-dependent SSF parameters and their associated uncertainties assimilating new measurements each hour. It is shown that ensemble methods are required to properly manage the nonlinearity of the model. The problem of the sensitivity to the vertical array (VA) configuration is also addressed.      

Internal wave spectrum in shallow water: measurement and comparisonwith the Garrett-Munk model

The covariance matrix of sound-speed variations is determined from yo-yo CTD data collected during the SWARM 95 experiment at a fixed station. The data covered approximately 2 h and were collected during a period when nonlinear solitary internal waves were absent or negligible. The method of empirical orthogonal functions (EOF) is applied to the sound-speed covariance matrix assuming that the internal wave modes are uncorrelated. The first five eigenvectors are found to agree well with the theoretically modeled eigenfunctions based on the measured buoyancy frequency and the internal wave eigenmode equation. The mode amplitudes for the first five modes are estimated from the corresponding eigenvalues. They agree with the Garrett-Munk model if j*=1 is used instead of j*=3. A second method is used to deduce the mode amplitudes and mode frequency spectra by projecting the sound-speed variation (as a function of time) onto the theoretical mode depth functions. The mode amplitudes estimated with this method are in agreement with the EOF results. A modified Garrett-Munk model is proposed to fit the frequency spectrum of linear internal waves in shallow water     

Horizontal refraction modal tomography of the ocean with modeinteractions

The acoustical tomography scheme for inferring a three-dimensional sound-speed field within some area based on the measurements of horizontal refraction angles is reviewed. The numerical simulations made so far were based on the assumption of the adiabaticity of low-frequency mode propagation. In this paper, an inversion scheme is presented that accounts for the acoustic mode interaction. We found that, generally, the interaction weakly affects the horizontal refraction angle, and it can be accounted for by iterations. Numerical simulations for the case of an Atlantic “meddy” corresponding to a strong double channel stratification are presented. Only three iterations were required to retrieve the exact strong sound-speed-field inhomogeneity within an area of 500 km×500 km     

Effects of seabed properties on acoustic wave fields in a seismo-acoustic ocean waveguide

Acoustic wave fields in an ocean waveguide with a sediment layer having continuously varying density and sound speed overlying an elastic subbottom are considered in this analysis. The objective of this study is to investigate the effects of seabed acoustic properties, including the density and sound speed of the sediment layer and subbottom, on the characteristics of the wave fields. Examination of the reflection coefficient, wavenumber spectrum, and noise intensity of the sound field through numerical analysis has shown that the variation in the acoustic properties in the sediment layer is an important factor in determining the reflected or noise sound fields. In particular, the sediment thickness-to-wavelength ratio and the types of variation of acoustic properties inside the layer give rise to many characteristics that potentially allow for acoustic inversion of the seabed properties. With regard to the wave-field components in a shallow-water environment, the various types of waves existing in a seismo-acoustic waveguide have been illustrated. The results indicate that the effects of the sediment properties on the wavenumber spectrum are primarily on the continuous and evanescent regimes of the wave field. The noise intensity generated by distributive random monopoles at various depths, together with the effect of refractive sound-speed distribution in the water column, has been obtained and analyzed.     

Acoustic tomography at basin scales and clock errors

A basin-scale acoustic tomography simulation is carried out for the northeast Pacific Ocean to determine the accuracy with which time must be kept at the sources when clocks at the receivers are accurate. A sequential Kalman filter is used to estimate sound-speed fluctuations and clock errors. Sound-speed fluctuations in the simulated ocean are estimated from an eddy-resolving hydrodynamic model of the Pacific forced by realistic wind fields at daily resolution from 1981-1993. The model output resembles features associated with El Nino and the Southern Oscillation, as well as many other features of the ocean's circulation. Using a Rossby-wave resolving acoustic array of four fixed sources and twenty drifting receivers, the authors find that the percentage of the modeled ocean's sound-speed variance accounted for with tomography is 92% at 400-km resolution, regardless of the accuracy of the clocks. Clocks which drift up to hundreds of seconds of error or more for a year do not degrade tomographic images of the model ocean. Tomographic reconstructions of the sound-speed field are insensitive to clock error primarily because of the wide variety of distances between the receivers from each source. Every receiver “sees” the same clock error from each source, regardless of section length, but the sound-speed fluctuations in the modeled ocean cannot yield travel times which lead to systematic changes in travel time that are independent of section length. The Kalman filter is thus able to map the sound-speed field accurately in the presence of large errors at the source's clocks     

Refraction of Sound in a Horizontally Inhomogeneous, Time-Dependent Ocean

Measurements of the three-dimensional (3-D) structure of a sound-speed field in the ocean with the spatial and temporal resolution required for prediction of acoustic fields are extremely demanding in terms of experimental assets, and they are rarely available in practice. In this study, a simple analytic technique is developed within the ray approximation to quantify the uncertainty in acoustic travel time and propagation direction that results from an incomplete knowledge or purely statistical characterization of sound-speed variability in the horizontal plane. Variation of frequency of an acoustic wave emitted by a narrowband source due to a temporal variation of environmental parameters is considered for deterministic and random media. In a random medium with locally statistically homogeneous, time-dependent 3-D fluctuations of the sound speed, calculation of the signal frequency and bearing angle variances as well as the travel-time bias due to horizontal refraction is approximately reduced to integration of respective statistical parameters of the environmental fluctuations along a ray in a background, range-dependent, deterministic medium. The technique is applied to acoustic transmissions in a coastal ocean, where tidally generated nonlinear internal waves are the prevailing source of sound-speed fluctuations, and in a deep ocean, where the fluctuations are primarily due to spatially diffuse internal waves with the Garrett–Munk spectrum. The significance of 3-D and four-dimensional (4-D) acoustic effects in deep and shallow water is discussed.     

Generating interface waves using a freely falling, instrumentedsource

In recent years, interface waves such as the Scholte wave have become important tools in the study of the geoacoustic properties of near-bottom seafloor sediments. Traditionally, these waves have been generated by explosive or pneumatic sources deployed at or near the seafloor and monitored by ocean-bottom seismographs or geophone arrays. While these sources generate the requisite interface waves, they also produce higher frequency compressional waves in the water and sediment that tend to contaminate the surface wave and make inversion of the data difficult in the near field. In this paper, a new source consisting of a freely falling projectile instrumented with an accelerometer is described. When the projectile impacts the bottom, the exact time history of the vertical force applied to the sediment is known and therefore may be convolved with the transfer function of a sediment geoacoustic model to produce accurate synthetic seismograms. Moreover, the vertical force applied to the seafloor is very efficient in generating surface wave motion while producing very little compressional wave energy so that the near-field signals are much more easily analyzed. An example of the use of the new source is presented including inversion of the received signals to obtain shear-wave velocity and attenuation as a function of depth in the near bottom sediments at a shallow-water site     

Environmental Effects of Waveguide Uncertainty on Coherent Aspects of Propagation, Scattering, and Reverberation

The robustness of the coherence of waveguide propagation to environmental uncertainty becomes an important consideration for systems that seek to exploit coherence for gain. Examples include matched field processing for passive localization and time reversal mirrors (TRMs) for active systems. Here, efficient normal mode representations of midfrequency time-domain propagation using the narrowband and adiabatic approximations are used to explore the deterioration of coherent active system predictability and performance in the presence sound-speed perturbations in the water column. Results show that for TRMs the reverberation level at the focal range is increased, and the scattering from an illuminated object is reduced for ensembles over oceanographic uncertainty. Results are obtained analytically as formal averages and are believed to represent a lower limit on the deterioration of TRM performance in the presence of environmental uncertainty for shallow-water waveguides.     

Deep-water acoustic coherence at long ranges: theoreticalprediction and effects on large-array signal processing

This paper presents results of combined consideration of sound coherence and array signal processing in long-range deep-water environments. Theoretical evaluation of the acoustic signal mutual coherence function (MCF) of space for a given sound-speed profile and particular scattering mechanism is provided. The predictions of the MCF are employed as input data to investigate the coherence-induced effects on the horizontal and vertical array gains associated with linear and quadratic beamformers with emphasis on the optimal ones. A method of the radiation transport equation is developed to calculate the MCF of the multimode signal under the assumption that internal waves or surface wind waves are the main source of long-range acoustic fluctuations in a deep-water channel. Basic formulations of the array weight vectors and small signal deflection are then exploited to examine optimal linear and quadratic processors in comparison with plane-wave beamformers. For vertical arrays, particular attention is paid also to evaluation of the ambient modal noise factor. The numerical simulations are carried out for range-independent environments from the Northwest Pacific for a sound frequency of 250 Hz and distances up to 1000 km. It was shown distinctly that both signal coherence degradation and modal noise affect large-array gain, and these effects are substantially dependent on the processing technique used. Rough surface sound scattering was determined to cause the most significant effects     

Signal variability in shallow-water sound channels

Coherence of broad-band acoustic waves for mid-to-high frequencies (0.6-18 kHz) is obtained for a very shallow-water (15-m-deep) waveguide over a wide band of environmental conditions and for a source-receiver range of 387 m. Temporal behavior is sampled at two different rates: one that resolves at fractions of a second over intermittent periods of 40 s and another that resolves at 10 min over periods of several days. Spatial behavior is sampled in the vertical by hydrophones with spacings of the order of meters. The effect of environmental variability on coherence, in particular, soundspeed fluctuations in the water column and wind-induced modulations of the air-sea interface, is noted as a function of acoustic frequency and ray path. Analysis of the acoustic fluctuations over short time scales more accurately resolves the temporal decorrelation of the received signal due to sea surface waves. The vertical sampling of the received signal permits an analysis of arrival-angle fluctuations. The dependence of coherence on the number of surface bounces is studied by comparing arrivals that have zero, one, two, and three surface bounces     

Preliminary analysis of the applicability of adiabatic modes to inverting synthetic acoustic data in shallow water over a sloping sea floor

The May 2001 Geoacoustic Inversion Techniques Workshop provided synthetic transmission loss (TL) data for four cases with range-dependent shallow-water all-liquid environments. In two of these cases ("0" and "1"), the sea floor has constant slope and the geoacoustic model (GAM) is range independent. Cost functions have been computed using a new adiabatic-mode TL algorithm (which uses an exact velocity boundary condition at the sloping sea floor), as one parameter in the GAM is varied. Two frequencies (80 and 220 Hz) were selected. In case 0, the sea-floor slope is 0.0183 and the GAM comprises an inhomogeneous layer over a basement. The sea-floor sound-speed was selected as the variable parameter. The resulting cost minima at 80 and 220 Hz are displaced from the actual sound speed by 2.3 and 3.4 m/s, respectively. In case 1, the sea-floor slope is 0.012 and the GAM comprises one homogenous layer, five inhomogeneous layers, and a basement. The selected parameter was the sound-speed in the homogeneous layer. The corresponding cost minima are displaced by -1.2 and +1.1 m/s. The relative values of these four errors indicate that mode coupling increases with sea-floor slope and that there may be a dependence on frequency at the greater slope.     

Estimating climatic temperature change in the ocean with syntheticacoustic apertures

An acoustic tomography simulation is carried out in the eastern North Pacific ocean to assess whether climate trends are better detected and mapped with mobile or fixed receivers. In both cases, acoustic signals from two stationary sources are transmitted to ten receivers. Natural variability of the sound-speed field is simulated with the Naval Research Laboratory (NRL) layered-ocean model. A sequential Kalman-Bucy filter is used to estimate the sound speed field, where the a priori error covariance matrix of the parameters is estimated from the NRL model. A spatially homogeneous climate trend is added to the NRL fluctuations of sound speed, but the trend is not parameterized in the Kalman filter. Acoustic travel times are computed between the sources and receivers by combining sound speeds from the NRL model with those from the unparameterized climate trend. The effects of the unparameterized climate trend are projected onto parameters which eventually drift beyond acceptable limits. At that time, the unparameterized trend is detected. Mobile and fixed receivers detect the trend at about the same time. At detection time, however, maps from fixed receivers are less accurate because some of the unparameterized climate trend is projected onto tile spatially varying harmonics of the sound-speed field. With mobile receivers, the synthetic apertures suppress the projection onto these harmonics. Instead, the unparametrized trend is correctly projected onto the spatially homogeneous portion of the parameterized sound-speed field     

Multimegameter-range acoustic data obtained by bottom-mountedhydrophone arrays for measurement of ocean temperature

Acoustic signals transmitted from the ATOC source on Pioneer Seamount off the coast of California have been received at various sites around the Pacific Basin since January 1996. We describe data obtained using bottom-mounted receivers, including US Navy Sound Surveillance System arrays, at ranges up to 5 Mm from the Pioneer Seamount source. Stable identifiable ray arrivals are observed in several cases, but some receiving arrays are not well suited to detecting the direct ray arrivals. At 5-Mm range, travel-time variations at tidal frequencies (about 50 ms peak to peak) agree well with predicted values, providing verification of the acoustic measurements as well as the tidal model. On the longest and northernmost acoustic paths, the time series of resolved ray travel times show an annual cycle peak-to-peak variation of about 1 s and other fluctuations caused by natural oceanic variability. An annual cycle is not evident in travel times from shorter acoustic paths in the eastern Pacific, though only one realization of the annual cycle is available. The low-pass-filtered travel times are estimated to an accuracy of about 10 ms. This travel-time uncertainty corresponds to errors in range- and depth-averaged temperature of only a few millidegrees, while the annual peak-to-peak variation in temperature averaged horizontally over the acoustic path and vertically over the upper 1 km of ocean is up to 0.5°C     

Statistics of broad-band bottom reverberation predictions in shallow-water waveguides

A new coherent reverberation model developed at the Naval Research Laboratory, Washington, DC, and the Supreme Allied Commander Atlantic Undersea Research Centre, La Spezia, Italy, is exercised in the 17-750-Hz band to estimate the degree of non-Rayleighness of shallow-water reverberation envelopes as a function of waveguide multipath, system bandwidth, directivity, and frequency. Findings suggest that reverberation from diffuse, but non-Gaussian, scatterer distributions is significantly more Rayleigh for multipath environments than for equivalent environments excited by a single or small number of modes or for broadside receiver array processing that extracts narrow angles of reception. These findings suggest that the problem of non-Rayleigh reverberation in shallow-water waveguides can be ameliorated through the use of tuned ensonification and reception schemes, which retain high probabilities of detection while reducing the associated probability of false alarm.     

Nonlinear effects at the initial stage of tsunami-wave development

An analytical solution to shallow-water nonlinear equations determining the height of tsunami waves leaving the source is obtained. The initial water-level displacement in the source and the distribution of particle velocities are set. The numerical solution showed that analytical estimates fit well with source characteristics varying in a broad range, even if the waves produced by the source collapse.     

Reverberation-derived shallow-water bottom scattering strength

Determinations of acoustic scattering strength for sand bottoms have been made at several different shallow-water areas under downward refracting sound propagation conditions in the frequency decade below 1 kHz. The measurements have been made using explosive sources detonated at mid-water depth and bottom-mounted vertical and horizontal hydrophone line arrays as receivers. The ubiquitous presence of multipaths in shallow water prevents a direct-path scattering geometry, and scattering strength must be extracted from the full reverberation field, which complicates the determination of bottom grazing angle dependence of scattering. The major focus of this paper has been the variation of scattering strength with frequency (integrated over participating bottom angles), though estimates of the angular dependence of scattering strength have been made using the vertical receiving array. Typically the integrated scattering strength for sand bottoms reported (and elsewhere) are found to decrease below 1 kHz and in some instances to exhibit a minimum in the several hundred hertz range. Sand bottom scattering strengths below 1 kHz are significantly lower than those predicted by the Mackenzie formula and the limited angular dependence determinations have been found to be consistent with Lambert's law