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The very low-frequency noise from merchant ships provides a good broadband sound source to study the deep layers of the seabed. The nested striations that characterize ship time-frequency spectrograms contain unique acoustic features corresponding to where the waveguide invariant β becomes infinite. In this dataset, these features occur at frequencies between 20 and 80 Hz, where pairs of modal group velocities become equal. The goal of this study is to identify these β = ∞ frequencies in ship noise spectrograms and use them to perform statistical inference for the deep layer sound speeds and thicknesses in the New England Mudpatch for a larger number of ships and acoustic arrays over a larger geographical region than previously studied. Marginal probability distributions of the data indicate that using singular points for a feature-based inversion yields an estimate of the sound speed and a limiting value for the thickness of the first deep layer. Heterogeneity is examined by correlating spatial variability of the deep layer sound speeds with ship tracks. [ABSTRACT FROM AUTHOR]

The coherent recombination of a direct and seabed reflected path is sensitive to the geophysical properties of the seabed. The concept of feature-based inversion is used in the analysis of acoustic data collected on a vertical line array (VLA) on the New England continental shelf break in about 200 m of water. The analysis approach for the measurements is based on a ray approach in which a direct and bottom reflected path is recombined, resulting in constructive and destructive interference of the acoustic amplitudes with frequency. The acoustic features have the form of prominent nulls of the measured received levels as a function of frequency as a broadband (500–4500 Hz) source passes the closest point of approach to the VLA. The viscous grain shearing (VGS) model is employed to parameterize a two-layer seabed model. The most likely seabed is a sand sediment with a porosity of about 0.42. There is a possibility of a thin (less than 0.5 m) surface layer having a slightly higher porosity between 0.45 and 0.50. Using the estimates for the VGS parameters inferred from the short-range frequency features, a normal mode model is used to predict the received acoustic levels over larger range scales. [ABSTRACT FROM AUTHOR]

An ocean acoustics experiment in 2017 near a shipping lane on the New England continental shelf in about 75 m of water provided an opportunity to evaluate a methodology to extract source signatures of merchant ships in a bottom-limited environment. The data of interest are the received acoustic levels during approximately 20 min time intervals centered at the closest position of approach (CPA) time for each channel on two 16-element vertical line arrays. At the CPA ranges, the received levels exhibit a frequency-dependent peak and null structure, which possesses information about the geophysical properties of the seabed, such as the porosity and sediment thickness, and the characterization of the source, such as an effective source depth. The modeled seabed is represented by two sediment layers, parameterized with the viscous grain shearing (VGS) model, which satisfies causality, over a fixed deep layered structure. Inferred estimates of the implicit source levels require averaging an error function over the full 20 min time intervals. Within the 200–700 Hz band, the Wales–Heitmeyer model captures the inferred frequency dependence of the source levels. [ABSTRACT FROM AUTHOR]

Acoustic data were recorded on two vertical line arrays (VLAs) deployed in the New England Mud Patch during the Seabed Characterization Experiment 2017 in about 75 m of water. The sound recorded during the passage of merchant ships permits identification of singular points for the waveguide invariant β for mode pairs (1 , n) : β 1 , n , for n = 2 , 3 , 4 , 5 , in the 15–80 Hz band. Using prior geophysical information and an acoustic data sample from the merchant ship KALAMATA, a geoacoustic model M of the seabed was developed. Then, using data samples from other merchant ships, a feature-ensemble maximum entropy method is employed to infer the statistical properties of geoacoustic parameter values for the sound speeds in a surface mud layer and a deep sand layer. Technical challenges include a sparsity of observed singular points, the unique identification of mode pairs for an observed singular point, and the deviation of the waveguide from horizontal stratification. A geoacoustic model M is developed that reproduced the observed β ≈ − 1 for f < 20 Hz and mode cutoff features at about 15 Hz. The statistical low-frequency inference of the singular point structure from multiple ships provides evidence of an angle of intromission at the water sediment interface with an average sound speed ratio of about 0.986 and an average sound speed for the deeper sand layer of about 1775 m/s. [ABSTRACT FROM AUTHOR]

Two residual networks are implemented to perform regression for the source localization and environment classification using a moving mid-frequency source, recorded during the Seabed Characterization Experiment in 2017. The first model implements only the classification for inferring the seabed type, and the second model uses regression to estimate the source localization parameters. The training is performed using synthetic data generated by the ORCA normal mode model. The architectures are tested on both the measured field and simulated data with variations in the sound speed profile and seabed mismatch. Additionally, nine data augmentation techniques are implemented to study their effect on the network predictions. The metrics used to quantify the network performance are the root mean square error for regression and accuracy for seabed classification. The models report consistent results for the source localization estimation and accuracy above 65% in the worst-case scenario for the seabed classification. From the data augmentation study, the results show that the more complex transformations, such as time warping, time masking, frequency masking, and a combination of these techniques, yield significant improvement of the results using both the simulated and measured data. [ABSTRACT FROM AUTHOR]

An examination of the received spectrogram levels of about twenty merchant ship recordings on two vertical line arrays deployed on the New England continental shelf during the Seabed Characterization Experiment 2017 has identified an acoustic feature that can be attributed to the group velocities of modes 1 and 2 being equal at a frequency f = F. The observation of such a feature is a result of β n m (2 π F) = ∞ , where βnm is the waveguide invariant for modes n and m. For the New England Mudpatch, the average value of F is about 24.5 Hz. An effective seabed model is inferred from a feature inversion method that has a deep sediment layer which lies between 190 m and 290 m beneath the seafloor with sound speeds on the order of 1810 m/s. This effective sediment model appears to be consistent with a previous seismic survey on the New England shelf that identified a deep low speed layer about 250 m beneath the water sediment interface. [ABSTRACT FROM AUTHOR]

While source localization and seabed classification are often approached separately, the convolutional neural networks (CNNs) in this paper simultaneously predict seabed type, source depth and speed, and the closest point of approach. Different CNN architectures are applied to mid-frequency tonal levels from a moving source recorded on a 16-channel vertical line array (VLA). After training each CNN on synthetic data, a statistical representation of predictions on test cases is presented. The performance of a single regression-based CNN is compared to a multitask CNN in which regression is used for the source parameters and classification for the seabed type. The impact of water sound speed profile and seabed variations on the predictions is evaluated using simulated test cases. Environmental mismatch between the training and testing data has a negative impact on source depth estimates, while the remaining labels are estimated tolerably well but with a bias towards shorter ranges. Similar results are found for data measured on two VLAs during Seabed Characterization Experiment 2017. This work shows the superiority of multitask learning and the potential for using a CNN to localize an acoustic source and detect the surficial seabed properties from mid-frequency sounds. [ABSTRACT FROM AUTHOR]

The received acoustic field generated by a single passage of a research vessel on the New Jersey continental shelf is employed to infer probability distributions for the parameter values representing the frequency dependence of the seabed attenuation and the source levels of the ship. The statistical inference approach employed in the analysis is a maximum entropy methodology. The average value of the error function, needed to uniquely specify a conditional posterior probability distribution, is estimated with data samples from time periods in which the ship-receiver geometry is dominated by either the stern or bow aspect. The existence of ambiguities between the source levels and the environmental parameter values motivates an attempt to partially decouple these parameter values. The main result is the demonstration that parameter values for the attenuation (a and the frequency exponent), the sediment sound speed, and the source levels can be resolved through a model space reduction technique. The results of this multi-step statistical inference developed for ship radiated noise is then tested by processing towed source data over the same bandwidth and source track to estimate continuous wave source levels that were measured independently with a reference hydrophone on the tow body. [ABSTRACT FROM AUTHOR]

Addressed is the physics of sound propagation through a shallow water waveguide whose seabed has a random rough surface. The basic coupled integral equations for the modal amplitudes can be split into forward and backward going coupled integral equations. Numerical solutions of the coupled equations are obtained for multiple roughness realizations from which ensemble averages can be obtained for the modal intensities and cross-mode coherence as a function of range. Sample calculations illustrate some of the basic characteristics of the average cross-mode coherence and intensity with and without seabed attenuation and for different source depths on range scales of 1500 acoustic wavelengths. [ABSTRACT FROM AUTHOR]

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. [ABSTRACT FROM AUTHOR]

In an acoustic waveguide spatial inhomogeneities couple the forward and backward propagating modal amplitudes. To address the nature of such coupling the integral equation for the range-dependent modal amplitudes is decomposed into components that satisfy the asymptotic boundary conditions of the free Green's function operator. An equivalent set of equations is obtained by eliminating the components that become the asymptotically backward propagating channels to leave a set of integral equations that describe only the components that become asymptotically the forward propagating channels. The elimination of the components that become asymptotically the backward propagating channels is done at the expense of introducing a nonlocal effective coupling operator. The nonlocal operator contains all the effects of the asymptotically backward propagating field on the asymptotically forward propagating field. An expansion of the effective coupling operator allows an investigation of the importance of the coupling and provides a systematic approach to add correction terms to the forward only equation. Idealistic underwater waveguides with various degrees of inhomogeneities are used to illustrate the main features of the convergence characteristics for the expansion. [ABSTRACT FROM AUTHOR]

The debate on the sound speed dispersion and the frequency dependence of sound attenuation in seabottoms has persisted for decades, mainly due to the lack of sufficient experimental data in the low-frequency (LF) to high-frequency speed/attenuation transition band. This paper analyzes and summarizes a set of LF measurements in shallow water that have resulted in the identification of nonlinear frequency dependence of sound attenuation in the effective media of sandy seabottoms. The long-range acoustic measurements were conducted at 20 locations in different coastal zones around the world. The seabed attenuations, inverted from different acoustic field measurements and characteristics, exhibit similar magnitude and nonlinear frequency dependence below 1000 Hz. The resulting effective sound attenuation can be expressed by α(dB/m)=(0.37±0.01)(f/1000)(1.80±0.02) for 50–1000 Hz. The corresponding average sound speed ratio at the bottom-water interface in the 50–600 Hz range is 1.061±0.009. Both the LF-field-derived sound speed and attenuation can be well described by the Biot–Stoll model with parameters that are consistent with either theoretical considerations or experimental measurements. A combination of the LF-field-inverted data with the SAX99, SAX04, and other high-frequency measurements offers a reference broadband data set in the 50–400 000 Hz range for sonar prediction and sediment acoustics modeling. [ABSTRACT FROM AUTHOR]

Acoustic time series data were collected in a shallow, hard bottom lake environment located in central Texas using both short range (2 m) implosive data, obtained with the source and a single hydrophone located near mid-depth in the waveguide, along with longer range implosive and explosive data from a near surface source to a bottom mounted hydrophone. Matched field inversions using simulated annealing were performed with a ray trace plus complex plane wave reflection coefficient forward propagation model that was validated in previous work. Isolating bottom interacting paths to perform the inversions is shown to be essential to reduce parameter uncertainties in the hard bottom environment and enables a systematic approach to the inversions which establishes the number of layers needed to represent the lake environment. Measured transmission loss data from a towed source were compared through a RMS error analysis to modeled transmission loss, constructed with the parameters from inversions of data from several source types, to further establish the validity of the inversion approach for this environment. Geoacoustic parameters obtained by inversions of short range, low frequency impulsive data are used to predict transmission loss at longer ranges and higher frequencies. The range dependence of the global minimum is discussed. [ABSTRACT FROM AUTHOR]

Sound propagation in a wedge-shaped environment with a penetrable bottom is simulated with broadband adiabatic mode, coupled mode, and parabolic equation model computations. Simulated results are compared to measured data taken in a tank experiment by Tindle et al. The coupled mode formalism is shown to predict, in agreement with that experiment, that modal wave fronts in penetrable wedges are approximately circular arcs centered at the apex of the wedge for a source near the apex. It is also shown that for wedge angles up to 6°, the received waveforms are well approximated by the adiabatic waveforms time-shifted by a depth-dependent interval to account for the curvature of the modal wave fronts. A small deviation from circularity in the modal wave fronts is possibly observed in the 6° case. [ABSTRACT FROM AUTHOR]

A new, efficient, versatile ray-based model is presented that performs geoacoustic inversions in range-dependent ocean waveguides faster than alternative forward models for which the computation time becomes extremely long, especially for broadband inversions. The water propagation is approximately separated from the seabed interaction using predetermined bathymetry and a possibly range-dependent water sound speed profile. The geometrical optics approximation is used to calculate eigenrays between sources and receivers, including bottom reflecting paths. Modeled broadband pressure fields are obtained by computing the plane wave reflection coefficient at specific angles and frequencies and by then linking this result with the bottom reflected eigenrays. Each perturbation of the seabed requires a recalculation of the plane wave reflection coefficient, but not a recalculation of the eigenrays, resulting in a highly efficient method. Range-independent problems are treated as a limiting case of the approach. The method is first described and then demonstrated with a few simple range-independent theoretical models. The versatility of addressing range-dependence in the bottom seabed is demonstrated with a simulated data set. Finally, the new model is applied to inversion from a measured data set, taken with impulsive sources, for both range-independent and range-dependent continental shelf environments. [ABSTRACT FROM AUTHOR]

A two-way integral equation coupled mode method is applied to a continental shelf ocean waveguide proposed for a special session devoted to range-dependent acoustic modeling at the 141st meeting of the Acoustical Society of America. The coupled mode solution includes both sediment trapped and continuum modes. The continuum is approximated by a finite number of leaky modes but neglects the branch cut contribution. Mode coupling matrix elements and the range evolution of the modal amplitudes show the nature of the mode coupling. Transmission loss versus range at 100 Hz predicted by the integral equation approach is compared to the transmission loss predicted by a wide angle parabolic equation method. While there is very good agreement, one observes small differences that can be interpreted as backscattering predicted by the integral equation solution. © 2003 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Part of an experiment to test a measurement package in a shallow water region in the Gulf of Mexico was designed to gather broadband acoustic data suitable for inversion to estimate seabed geoacoustic parameters. Continuous wave tow acoustic signals at multiple frequencies and broadband impulsive source signals were recorded on a horizontal line array in a high-noise environment. Simulated annealing with a normal mode forward propagation model is utilized to invert for a geoacoustic representation of the seabed. Several inversions are made from different data samples of two light bulb implosions, the measured sound speed profiles at the HLA and at the positions of the light bulb deployments, and for two different cost functions. The different cost functions, measured sound speed profiles, and measured time series result in different inverted geoacoustic profiles from which transmission loss is generated for comparison with measurements. On the basis of physical consistency and from the comparison of the transmission loss and time series, a best estimate geoacoustic profile is selected and compared to those obtained from previously reported inversions. Uncertainties in the sound speed profile are shown to affect the uncertainties of the estimated seabed parameters. [ABSTRACT FROM AUTHOR]

A two-way coupled mode approach based on an integral equation formalism is applied to sound propagation through internal wave fields defined at the 1999 Shallow Water Acoustics Modeling Workshop. Solutions of the coupled equations are obtained using a powerful approach originally introduced in nuclear theory and also used to solve simple nonseparable problems in underwater acoustics. The basic integral equations are slightly modified to permit a Lanczos expansion to form a solution. The solution of the original set of integral equations is then easily recovered from the solution of the modified equations. Two important aspects of the integral equation method are revealed. First, the Lanczos expansion converges faster than a Born expansion of the original integral equations. Second, even when the Born expansion diverges due to strong mode coupling, the Lanczos expansion converges. It is shown that the internal wave problems examined are essentially one-way propagation problems because one observes good agreement between the coupled mode solutions and those provided by an energy-conserving parabolic equation algorithm. In the Workshop examples, at both 25 and 250 Hz, significantly greater coupling between modes occurs in the linear internal wave field case than the nonlinear soliton case. [ABSTRACT FROM AUTHOR]

An optimization approach is used to estimate waveguide parameters for selected test cases of the Geoacoustic Benchmark Inversion Workshop held in Vancouver, June 1997. The approach uses multiple acoustic data samples to decouple the original N-dimensional problem into several smaller-dimensional problems. A nonlinear least squares approach is used to estimate parameters in each subset. The estimation of parameters in each subset proceeds until convergence is reached. Predicted values are in good agreement with the true values, which suggests that the decoupling of waveguide parameters allows a nonlinear least squares approach to be an effective tool in the inversion of ocean waveguide parameters. [ABSTRACT FROM AUTHOR]

A new application of the Galerkin technique to the calculation of the normal modes that are used to describe underwater acoustic propagation is presented. This expansion approximation method (EAM) is especially relevant for broadband normal mode calculations in which normal mode eigenvalues, depth functions, and attenuations are needed. The EAM is used to construct approximate normal mode eigenvalues and depth functions for some frequency from eigenvalues and depth functions previously calculated at another, higher frequency. The EAM approach for broadband underwater acoustic propagation calculations is evaluated in comparison with an exact normal mode model calculation of impulse responses and other broadband results. © 1995 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Data from a moving source received by three horizontally separated bottomed sensors in a shallow water environment are analyzed using a broadband matched-field approach to source localization. The water depth was approximately 150 m, and the low bottom loss in the area results in low spatial coherence of the broadband field. The modeled acoustic fields are constructed via a ray model. Localizations are made in the x-y plane. In a large search area the time evolution of the ambiguity surfaces produced from the data agree fairly well with simulated surfaces. Ambiguity surfaces are generated successively at intervals of about 1.6 s in small search areas with a fine spatial grid to test the possibility of tracking a source. Results of the source tracking are presented. The analysis also considers the effects of the sea floor on localization in the context of spatial coherence. [ABSTRACT FROM AUTHOR]

A method is presented for the solution of coupled-mode equations for sound propagation in a range-dependent waveguide. By following a new approach recently introduced in nuclear theory, the coupled-mode equations are modified and then solved using the Lanczos method. Calculations are made for isovelocity waveguides with rigid bell-shaped bathymetries having large slopes. Convergence properties and computer CPU times are examined as a function of the dimension of the coupled-mode equations and the nature of the coupling. The efficiency of the approach is shown to increase as the dimension of the coupled-mode equations increases. [ABSTRACT FROM AUTHOR]

Two complementary methods are proposed for exact numerical calculations of the acoustic field scattered by a rigid sphere in an isovelocity fluid layer overlying a horizontally stratified medium. These two methods are based on the partial wave and Fourier expansions of the medium Green's function. It is shown that the method based on the partial wave expansion is useful for clarifying the physical nature of the approximation involved in the method proposed by Ingenito some time ago [F. Ingenito, J. Acoust. Soc. Am. 82, 2051 (1987)]. It is in fact shown that the Ingenito approximation is equivalent to replace the exact medium Green's function by that of the free-field Green's function in obtaining boundary values of the field on the surface of the target. Numerical studies are performed and it is demonstrated that the exact results obtained by using the presently proposed methods are largely different from those obtained by using Ingenito's approximation. In addition more complex cases are examined where the target is nonspherical and the waveguide is bottom limited as is commonly found in shallow water ocean waveguides. The sensitivity of the scattered field to various types of geoacoustic profiles when the target is near the sea floor is also considered. [ABSTRACT FROM AUTHOR]

A method for localizing a broadband moving source using the signals received on a horizontal planar array is presented. The method involves finding the constant-velocity, straight-line source track that generates the least error between measured and modeled correlation traces over a period of time. Measured correlation traces are obtained by cross-correlating multiple pairs of received time series. Simulated correlation time delays are obtained using a ray model that includes the effects of refraction on the ray arrival times. A nonlinear optimization routine is used to obtain the best match in measured and simulated time delays over time and receiver pair. The main problem in shallow water is to identify which multipath pairs produce the correlation traces observed in the measured data. An approach for overcoming this problem that involves testing multiple hypotheses concerning the multipath pairs will be presented. An example application of the method to a shallow water dataset with three bottom-mounted receivers in a triangular configuration is presented. In order to validate the localization, the measured correlagram is compared with a correlagram produced by a broadband normal mode model using the derived source track. [Work supported by the Office of Naval Research (Code 322).] [ABSTRACT FROM AUTHOR]

A new fast and efficient acoustic propagation model is introduced which solves the coupled-mode differential equations in underwater acoustics for range-dependent, fluid-layered, ocean environments. The coupled range equations are first modified and then solved using the Lanczos method, an approach recently introduced in nuclear theory. This method has been successfully applied to the description of the nuclear response of heavy atomic nuclei in the giant resonance region of the energy excitation spectrum [T. Udagawa and B. T. Kim, Phys. Rev. C 40, 2271-2275 (1989)], as well as, other physical processes in low to medium energy in nuclear theory. The efficiency of this method permits the solution of coupled mode equations with large dimensions. The eigenvalues and depth-dependent mode functions are quickly obtained using an Airy function approach, which allows the range-dependent mode-coupling matrices to be evaluated analytically. The validity of the model is demonstrated, and example calculations are presented. [This work is supported by the Office of Naval Research (ONR 4530) Project RO35K01.] [ABSTRACT FROM AUTHOR]

A new algorithm for calculating the normal modes that are used to describe underwater acoustic propagation is presented. The algorithm is especially relevant for broadband normal mode calculations in which normal mode eigenvalues, depth functions, and attenuations are needed. The new algorithm uses an expansion technique to construct normal mode eigenvalues and depth functions for some frequency from eigenvalues and depth functions previously calculated at another, higher frequency. Comparisons of the estimated eigenvalues, depth functions, and attenuations with exact results are presented for several shallow water environments. A broadband propagation model that uses normal mode sets calculated with the new algorithm has been developed. Transmission loss and impulse responses based on estimated and exact normal mode sets are compared. [This work was supported by the Office of Naval Research through Block RL3B and Block CS3A.] [ABSTRACT FROM AUTHOR]

On the New Jersey continental shelf ambient sound levels were recorded during tropical storm Ernesto that produced wind speeds up to 40 knots in early September 2006. The seabed at the position of the acoustic measurements can be approximately described as coarse sand. Differences between the ambient noise levels for the New Jersey shelf measurements and deep water reference measurements are modeled using both normal mode and ray methods. The analysis is consistent with a nonlinear frequency dependent seabed attenuation for the New Jersey site.

Acoustic measurements were made on a sand ridge on the New Jersey continental shelf. Data collected on two L arrays separated by 20 km from a single multi-frequency tow suggest small horizontal environmental variability. Values for the sound speed structure of the seabed are extracted by first applying a geo-acoustic inversion method to broadband and narrowband acoustic data from short-range sources. Then, a parabolic equation algorithm is used to properly include the bathymetry and sub-bottom layering. Finally, the frequency dependence of the seabed attenuation is inferred by optimizing the model fit to long-range transmission loss data in the 50-3000 Hz band.