Search

Theoretically, the empirical Green's function between a pair of receivers can be extracted from the cross correlation of the received diffuse noise. The diffuse noise condition rarely is met in the ocean and directional sources may bias the Green's function. Here matrix-based spatial filters are used for removing unwanted contributions in the cross correlations. Two methods are used for solving the matrix filter design problem. First a matrix least-square problem is solved with a low-rank approximation of the pseudo-inverse, here, derived for linear and planar arrays. Second, a convex optimization approach is used to solve the design problem reformulated with ad hoc constraints. The spatial filter is applied to real-data cross correlations of elements from a linear array to attenuate the contribution of a discrete interferer. In the case of a planar array and simulated data, a spatial filter enables a passive upgoing/downgoing wavefield separation along with an efficient rejection of horizontally propagating noise. The impact of array size and frequency band on the filtered cross correlations is discussed.

The challenge of a deep-water oil leak is that a significant quantity of oil remains in the water column and possibly changes properties. There is a need to quantify the oil settled within the water column and determine its physical properties to assist in the oil recovery. There are currently no methods to map acoustically submerged oil in the sea. In this paper, high-frequency acoustic methods are proposed to localize the oil polluted area and characterize the parameters of its spatial covariance, i.e., variance and correlation. A model is implemented to study the underlying mechanisms of backscattering due to spatial heterogeneity of the medium and predict backscattering returns. An algorithm for synthetically generating stationary, Gaussian random fields is introduced which provides great flexibility in implementing the physical model of an inhomogeneous field with spatial covariance. A method for inference of spatial covariance parameters is proposed to describe the scattering field in terms of its second-order statistics from the backscattered returns. The results indicate that high-frequency acoustic methods not only are suitable for large-scale detection of oil contamination in the water column but also allow inference of the spatial covariance parameters resulting in a statistical description of the oil field.

Sequential Bayesian methods such as particle filters have been used to track a moving source in an unknown and space/time-evolving ocean environment. These methods treat both the source and the ocean parameters as non-stationary unknown random variables and track them via the multivariate posterior probability density function. Particle filters are numerical methods that can operate on nonlinear systems with non-Gaussian probability density functions. Particle smoothers are a natural extension to these filters. A smoother is appropriate in applications where data before and after the time of interest are readily available. Both past and "future" measurements are exploited in smoothers, whereas filters just use past measurements. Geoacoustic and source tracking is performed here using two smoother algorithms, the forward-backward smoother and the two-filter smoother. Smoothing is demonstrated on experimental data from both the SWellEx-96 and SW06 experiments where the parameter uncertainty is reduced relative to just filtering alone.

A typical geoacoustic inversion procedure involves powerful source transmissions received on a large-aperture receiver array. A more practical approach is to use a single moving source and/or receiver in a low signal to noise ratio (SNR) setting. This paper uses single-receiver, broadband, frequency coherent matched-field inversion and exploits coherently repeated transmissions to improve estimation of the geoacoustic parameters. The long observation time creates a synthetic aperture due to relative source-receiver motion. This approach is illustrated by studying the transmission of multiple linear frequency modulated (LFM) pulses which results in a multi-tonal comb spectrum that is Doppler sensitive. To correlate well with the measured field across a receiver trajectory and to incorporate transmission from a source trajectory, waveguide Doppler and normal mode theory is applied. The method is demonstrated with low SNR, 100-900 Hz LFM pulse data from the Shallow Water 2006 experiment.

Cross-correlations of diffuse noise fields can be used to extract environmental information. The influence of directional sources (usually ships) often results in a bias of the travel time estimates obtained from the cross-correlations. Using an array of sensors, insights from random matrix theory on the behavior of the eigenvalues of the sample covariance matrix (SCM) in an isotropic noise field are used to isolate the diffuse noise component from the directional sources. A sequential hypothesis testing of the eigenvalues of the SCM reveals eigenvalues dominated by loud sources that are statistical outliers for the assumed diffuse noise model. Travel times obtained from cross-correlations using only the diffuse noise component (i.e., by discarding or attenuating the outliers) converge to the predicted travel times based on the known array sensor spacing and measured sound speed at the site and are stable temporally (i.e., unbiased estimates). Data from the Shallow Water 2006 experiment demonstrates the effectiveness of this approach and that the signal-to-noise ratio builds up as the square root of time, as predicted by theory.

It is well known that observations of the spatial sample covariance matrix (SCM, also called the cross-spectral matrix) reveal that the ordered noise eigenvalues of the SCM decay steadily, but common models predict equal noise eigenvalues. Random matrix theory (RMT) is used to derive and discuss properties of the eigenvalue spectrum of the data SCM for linear arrays, with an application to ocean acoustic data. Noise on the array is considered either incoherent or propagating acoustic noise that is coherent across the array. Using conventional three-dimensional or two-dimensional isotropic noise models with full or snapshot-deficient observations, realizations of the SCM eigenvalues are explained using RMT. Deep-water towed-array data are analyzed and it is shown that the eigenvalues of the SCM compare well with theory. It is demonstrated how RMT can be applied to study eigenvalue spectrum estimation as dependent on array properties (element spacing to wavelength ratio) and data sampling (snapshots). Apart from explaining the observed noise eigenvalue spectrum, the improved model of the eigenvalue spectrum has important applications in array signal processing.

Environmental parameters can have large spatial and temporal variability in shelfbreak regions. The capability of sequential Bayesian filters in tracking this variation is investigated. Particle filtering (PF) is used to extract the environmental parameters and their uncertainties. The method tracks the environment with fewer particles relative to conventional geoacoustic inversion methods using successive independent inversions. As an example, data from the Shallow Water 2006 Experiment are processed. The PF approach first is used to track the source and the environment with little spatial variation just northwest of the shelfbreak. Then the strongly range-dependent shelfbreak region is analyzed and the PF results are compared to previous geoacoustic inversion studies from the region., (© 2012 Acoustical Society of America)

Seabed interface depths and fathometer amplitudes are tracked for an unknown and changing number of sub-bottom reflectors. This is achieved by incorporating conventional and adaptive fathometer processors into sequential Monte Carlo methods for a moving vertical line array. Sediment layering information and time-varying fathometer response amplitudes are tracked by using a multiple model particle filter with an uncertain number of reflectors. Results are compared to a classical particle filter where the number of reflectors is considered to be known. Reflector tracking is demonstrated for both conventional and adaptive processing applied to the drifting array data from the Boundary 2003 experiment. The layering information is successfully tracked by the multiple model particle filter even for noisy fathometer outputs., (© 2012 Acoustical Society of America.)

The passive fathometer algorithm was applied to data from two drifting array experiments in the Mediterranean, Boundary 2003 and 2004. The passive fathometer response was computed with correlation times from 0.34 to 90 s and, for correlation times less than a few seconds, the observed signal-to-noise ratio (SNR) agrees with a 1D model of SNR of the passive fathometer response in an ideal waveguide. In the 2004 experiment, the fathometer response showed the array depth varied periodically with an amplitude of 1 m and a period of 7 s consistent with wave driven motion of the array. This introduced a destructive interference, which prevents the SNR growing with increasing correlation time. A peak-tracking algorithm applied to the fathometer response of experimental data was used to remove this motion allowing the coherent passive fathometer response to be averaged over several minutes without destructive interference. Multirate adaptive beamforming, using 90 s correlation time to form adaptive steer vectors which were applied to 0.34 s data snapshots, increases the SNR of the passive fathometer response., (© 2011 Acoustical Society of America)

This paper discusses the effects of frequency selection on source localization and geoacoustic inversion methods that use frequency coherent objective functions. Matched-field processors based on frequency-coherent objective functions often have rapidly fluctuating range ambiguity surfaces. Insufficient sampling in frequency domain results in range aliasing terms that affect geoacoustic inversion. Range aliasing and its effects on source localization and environmental parameter inversion are demonstrated on data collected during the MAPEX2000 experiment. Guidance for frequency selection to avoid range aliasing is provided., (© 2011 Acoustical Society of America)

A model is presented for the complete passive fathometer response to ocean surface noise, interfering discrete noise sources, and locally uncorrelated noise in an ideal waveguide. The leading order term of the ocean surface noise contribution produces the cross-correlation of vertical multipaths and yields the depth of sub-bottom reflectors. Discrete noise incident on the array via multipaths give multiple peaks in the fathometer response. These peaks may obscure the sub-bottom reflections but can be attenuated with use of minimum variance distortionless response (MVDR) steering vectors. The seabed critical angle introduces discontinuities in the spatial distribution of distant surface noise and may introduce spurious peaks in the passive fathometer response. These peaks can be attenuated by beamforming within a bandwidth limited by the array geometry and critical angle.

Sensors are becoming ubiquitous and can be combined in arrays for source localization purposes. If classical conventional beamforming is used, then random arrays have poor beampatterns. By pre-computing sensor weights, these beampatterns can be improved significantly. The problem is formulated in the frequency domain as a desired look direction, a frequency-independent transition region, and the power minimized in a rejection-region. Using this formulation, the frequency-dependent sensor weights can be obtained using convex optimization. Since the weights are data independent they can be pre-computed, the beamforming has similar computational complexity as conventional beamforming. The approach is demonstrated for real 2D arrays.

Geoacoustic inversion using fluctuating signal observations can be challenging. The origin of these fluctuations needs to be understood so the signals can be used appropriately. A set of experiments [Tang et al., Oceanogr. 20(4), 156-167 (2007)] was carried out in shallow water near the New Jersey shelf break in summer 2006. Significant fluctuations in the direct path and surface-reflected arrivals of short-range chirp transmissions (1.1-2.9 kHz) were observed on a vertical line array. This paper explains the origin of these signal fluctuations through analysis of the arrival amplitudes. It is shown that the strong thermocline combined with an oscillating source motion due to ocean surface waves results in the signal fluctuations.

A particle filtering (PF) approach is presented for performing sequential geoacoustic inversion of a complex ocean acoustic environment using a moving acoustic source. This approach treats both the environmental parameters [e.g., water column sound speed profile (SSP), water depth, sediment and bottom parameters] at the source location and the source parameters (e.g., source depth, range and speed) as unknown random variables that evolve as the source moves. This allows real-time updating of the environment and accurate tracking of the moving source. As a sequential Monte Carlo technique that operates on nonlinear systems with non-Gaussian probability densities, the PF is an ideal algorithm to perform tracking of environmental and source parameters, and their uncertainties via the evolving posterior probability densities. The approach is demonstrated on both simulated data in a shallow water environment with a sloping bottom and experimental data collected during the SWellEx-96 experiment.

Recently, a technique has been developed to image seabed layers using the ocean ambient noise field as the sound source. This so called passive fathometer technique exploits the naturally occurring acoustic sounds generated on the sea-surface, primarily from breaking waves. The method is based on the cross-correlation of noise from the ocean surface with its echo from the seabed, which recovers travel times to significant seabed reflectors. To limit averaging time and make this practical, beamforming is used with a vertical array of hydrophones to reduce interference from horizontally propagating noise. The initial development used conventional beamforming, but significant improvements have been realized using adaptive techniques. In this paper, adaptive methods for this process are described and applied to several data sets to demonstrate improvements possible as compared to conventional processing.

Green's function approximation via ocean noise cross-correlation, referred to here as ocean acoustic interferometry, has been demonstrated experimentally for passive noise sources. Active sources offer the advantages of higher frequencies, controllability, and continuous monitoring. Experimental ocean acoustic interferometry is described here for two active source configurations: a source lowered vertically and one towed horizontally. Results are compared and contrasted with cross-correlations of passive noise. The results, in particular, differences between the empirical Green's function estimates and simulated Green's functions, are explained with reference to theory and simulations. Approximation of direct paths is shown to be consistently good for each source configuration. Secondary (surface reflection) paths are shown to be more accurate for hydrophones with a greater horizontal separation.

A statistical estimation of source location incorporating uncertainty in ocean environmental model parameters is derived using a Bayesian approach. From a previous geoacoustic inversion, a posterior probability distribution of the environmental parameters that reflects uncertainty in the ocean environment is obtained. This geoacoustic uncertainty then is mapped into uncertainty in the acoustic pressure field and is propagated through the Bartlett matched-field processor for source localization. Using data from the ASIAEX 2001 East China Sea experiment, the estimated source location and variability over time are compared with the known source positions.

Approximation of Green's functions through cross-correlation of acoustic signals in the ocean, a method referred to as ocean acoustic interferometry, is potentially useful for estimating parameters in the ocean environment. Travel times of the main propagation paths between hydrophone pairs were estimated from interferometry of ocean noise data that were collected on three L-shaped arrays off the New Jersey coast while Tropical Storm Ernesto passed nearby. Examination of the individual noise spectra and their mutual coherence reveals that the coherently propagating noise is dominated by signals of less than 100 Hz. Several time and frequency noise normalization techniques were applied to the low frequency data in order to determine the effectiveness of each technique for ocean acoustic applications. Travel times corresponding to the envelope peaks of the noise cross-correlation time derivatives of data were extracted from all three arrays, and are shown to be in agreement with the expected direct, surface-reflected, and surface-bottom-reflected interarray hydrophone travel times. The extracted Green's function depends on the propagating noise. The Green's function paths that propagate horizontally are extracted from long distance shipping noise, and during the storm the more vertical paths are extracted from breaking waves.

This paper incorporates tracking techniques such as the extended Kalman, unscented Kalman, and particle (PF) filters into geoacoustic inversion problems. This enables spatial and temporal tracking of environmental parameters and their underlying probability densities, making geoacoustic tracking a natural extension to geoacoustic inversion techniques. Water column and seabed properties are tracked in simulation for both vertical (VLA) and horizontal (HLA) line arrays using the three tracking filters. Filter performances are compared in terms of filter efficiencies using the posterior Cramer-Rao lower bound. Tracking capabilities of the geoacoustic filters under slowly and quickly changing environments are studied in terms of divergence statistics. Geoacoustic tracking can provide continuously environmental estimates and their uncertainties using only a fraction of the computational power of classical geoacoustic inversion schemes. Interfilter comparison show that while a high-particle-number PF outperforms the Kalman filters, there are many cases where all three filters perform equally well depending on the inversion configuration (such as the HLA versus VLA and frequency) and the tracked parameters.

A practical application of noise cross-correlation for the diagnosis of a multichannel ocean hydrophone array is derived. Acoustic data were recorded on a horizontal line array on the New Jersey Shelf while Tropical Storm Ernesto passed through. Results obtained from active source measurements reveal that signals from several hydrophones, which were recorded on certain channels before the storm, are recorded on different channels after the storm. Noise cross-correlation of data recorded during the storm show when, and in what manner, these changes took place.

This paper presents travel time geoacoustic inversion of broadband data collected on a vertical line array at short range of 230 m during the Shallow Water 2006 experiments. A ray-tracing method combined with a hybrid optimization algorithm that utilizes differential evolution and downhill simplex was used for the inversion of sediment properties. The ocean sound speed profile and geometric parameters were inverted prior to the sea bottom properties to account for the temporally variable ocean environment. The sediment sound speed and thickness estimates are consistent with in situ measurements and matched-field inversion results of longer-range data from the experiment.

Land-based seismic observations of double frequency (DF) microseisms generated during tropical storms Ernesto and Florence are dominated by signals in the 0.15-0.5 Hz band. In contrast, data from sea floor hydrophones in shallow water (70 m depth, 130 km off the New Jersey coast) show dominant signals in the ocean gravity-wave frequency band, 0.02-0.18 Hz, and low amplitudes from 0.18 to 0.3 Hz, suggesting significant opposing wave components necessary for DF microseism generation were negligible at the site. Florence produced large waves over deep water while Ernesto only generated waves in coastal regions, yet both storms produced similar spectra. This suggests near-coastal shallow water as the dominant region for observed microseism generation.

The effect of ocean sound speed uncertainty on matched-field geoacoustic inversion is investigated using data from the SW06 experiment along a nearly range-independent bathymetric track. Significant sound speed differences were observed at the source and receiving array and several environmental parameterizations were investigated for the inversion including representing the ocean sound speed at both source and receivers with empirical orthogonal function (EOF) coefficients. A genetic algorithm-based global optimization method was applied to the candidate environmental models. Then, a Bayesian inversion technique was used to quantify uncertainty in the environmental parameters for the best environmental model, which included an EOF description of the ocean sound speed.

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

Geoacoustic inversion estimates environmental parameters from measured acoustic fields (e.g., received on a towed array). The inversion results have some uncertainty due to noise in the data and modeling errors. Based on the posterior probability density of environmental parameters obtained from inversion, a statistical estimation of transmission loss (TL) can be performed and a credibility level envelope or uncertainty band for the TL generated. This uncertainty band accounts for the inherent variability of the environment not usually contained in sonar performance prediction model inputs. The approach follows [Gerstoft et al. IEEE J. Ocean. Eng. 31, 299-307 (2006)] and is demonstrated with data obtained from the MAPEX2000 experiment conducted by the NATO Undersea Research Center using a towed array and a moored source in the Mediterranean Sea in November 2000. Based on the geoacoustic inversion results, the TL and its variability are estimated and compared with the measured TL.

Ocean acoustic interferometry refers to an approach whereby signals recorded from a line of sources are used to infer the Green's function between two receivers. An approximation of the time domain Green's function is obtained by summing, over all source positions (stacking), the cross-correlations between the receivers. Within this paper a stationary phase argument is used to describe the relationship between the stacked cross-correlations from a line of vertical sources, located in the same vertical plane as two receivers, and the Green's function between the receivers. Theory and simulations demonstrate the approach and are in agreement with those of a modal based approach presented by others. Results indicate that the stacked cross-correlations can be directly related to the shaded Green's function, so long as the modal continuum of any sediment layers is negligible.

Quantifying uncertainty for parameter estimates obtained from matched-field geoacoustic inversions using a Bayesian approach requires estimation of the uncertainties in the data due to ambient noise as well as modeling errors. In this study, the variance parameter of the Gaussian error model, hereafter called error variance, is assumed to describe the data uncertainty. In practice, this parameter is not known a priori, and choosing a particular value is often difficult. Hence, to account for the uncertainty in error variance, several methods are introduced for implementing both the full and empirical Bayesian approaches. A full Bayesian approach that permits uncertainty of the error variance to propagate through the parameter estimation processes is a natural way of incorporating the uncertainty of error variance. Due to the large number of unknown parameters in the full Bayesian uncertainty analysis, an alternative, the empirical Bayesian approach, is developed, in which the posterior distributions of model parameters are conditioned on a point estimate of the error variance. Comparisons between the full and empirical Bayesian inferences of model parameters are presented using both synthetic and experimental data.

A time domain geoacoustic inversion method using ship noise received on a towed horizontal array is presented. The received signal, containing ship noise as a source of opportunity, is time-reversed and then back-propagated to the vicinity of the ship. The back-propagated signal is correlated with the modeled signal which is expected to peak at the ship's location in case of a good match for the environment. This match is utilized for the geoacoustic parameter inversion. The objective function for this optimization problem is thus defined as the normalized power focused in an area around the source position, using a matched impulse response filter. A hybrid use of global and local search algorithms, i.e., GA and Powell's method is applied to the optimization problem. Applications of the proposed inversion method to MAPEX 2000 noise experiment conducted north of the island of Elba show promising results, and it is shown that the time domain inversion takes advantage of dominant frequencies of the source signature automatically.