Trans-dimensional inversion for seafloor properties for three mud depocenters on the New England shelf under dynamical oceanographic conditionsa).

This paper presents inversion results for three datasets collected on three spatially separated mud depocenters (hereafter called mud ponds) during the 2022 Seabed Characterization Experiment (SBCEX). The data considered here represent modal time-frequency (TF) dispersion as estimated from a single hydrophone. Inversion is performed using a trans-dimensional (trans-D) Bayesian inference method that jointly estimates water-column and seabed properties along with associated uncertainties. This enables successful estimation of the seafloor properties, consistent with in situ acoustic core measurements, even when the water column is dynamical and mostly unknown. A quantitative analysis is performed to (1) compare results with previous modal TF trans-D studies for one mud pond but under different oceanographic condition, and (2) inter-compare the new SBCEX22 results for the three mud ponds. Overall, the estimated mud geoacoustic properties show no significant temporal variability. Further, no significant spatial variability is found between two of the mud ponds while the estimated geoacoustic properties of the third are different. Two hypotheses, considered to be equally likely, are explored to explain this apparent spatial variability: it may be the result of actual differences in the mud properties, or the mud properties may be similar but the inversion results are driven by difference in data information content.

Depth and frequency dependence of geoacoustic properties on the New England Mud Patch from reflection coefficient inversiona).

Muddy sediments cover significant portions of continental shelves, but their physical properties remain poorly understood compared to sandy sediments. This paper presents a generally applicable model for sediment-column structure and variability on the New England Mud Patch (NEMP), based on trans-dimensional Bayesian inversion of wide-angle, broadband reflection-coefficient data in this work and in two previously published reflection-coefficient inversions at different sites on the NEMP. The data considered here include higher frequencies and larger bandwidth and cover lower reflection grazing angles than the previous studies, hence, resulting in geoacoustic profiles with significantly better structural resolution and smaller uncertainties. The general sediment-column structure model includes an upper mud layer in which sediment properties change slightly with depth due to near-surface processes, an intermediate mud layer with nearly uniform properties, and a geoacoustic transition layer where properties change rapidly with depth (porosity decreases and sound speed, density, and attenuation increase) due to increasing sand content in the mud above a sand layer. Over the full frequency band considered in the new and two previous data sets (400-3125 Hz), there is no significant sound-speed dispersion in the mud, and attenuation follows an approximately linear frequency dependence.

Joint trans-dimensional inversion for water-column sound speed and seabed geoacoustic models.

This letter considers joint estimation of the water-column sound-speed profile (SSP) and seabed geoacoustic model through Bayesian inversion of ocean-acoustic data. The inversion is formulated in terms of separate trans-dimensional models for the water column (as an unknown number of nodes of a piecewise-continuous SSP) and seabed (as an unknown number of uniform layers) to intrinsically parameterize each according to the information content of the data. The inversion estimates marginal posterior probability profiles, quantifying the resolution of water-column and seabed structure. To validate the proposed method, modal-dispersion data from the New England Mud Patch, collected using hand-deployable systems, are considered.

Hamilton's geoacoustic model.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

On compressional wave attenuation in muddy marine sediments.

A method for measuring in situ compressional wave attenuation exploiting the spectral decay of reflection coefficient Bragg resonances is applied to fine-grained sediments in the New England Mud Patch. Measurements of layer-averaged attenuation in a 10.3 m mud layer yield 0.04 {0.03, 0.055} dB/m/kHz (braces indicate outer bounds); the attenuation is twice as large at a site with 3.2 m mud thickness. It is shown that both results are heavily influenced by a ∼1 m sand-mud transition interval created by geological and biological processes that mix sand (at the base of the mud) into the mud. Informed by the observations, it appears that the spatial dependence of mud layer attenuation across the New England Mud Patch can be predicted by accounting for the transition interval via simple scaling. Further, the ubiquity of the processes that form the transition interval suggests that the scaling may be applied to any muddy continental shelf. In principle, attenuation predictions in littoral environments could be substantively improved with a modest amount of geologic and biologic information.

Ship source level estimation and uncertainty quantification in shallow water via Bayesian marginalization.

This paper applies a non-linear Bayesian marginalization approach to ship spectral source level estimation in shallow water with unknown seabed properties and uncertain source depth. The algorithm integrates the posterior probability density over seabed models sampled via trans-dimensional Bayesian matched-field inversion and over depths/ranges of multiple point sources (representing different noise-generating components of a large ship) via Metropolis-Hastings sampling. Source levels and uncertainty are derived from marginal distributions for source strength. The approach is applied to radiated noise due to a container ship recorded on a bottom-moored horizontal array in shallow water. The average uncertainty is 3.8 dB/Hz for tonal frequencies.

Geoacoustic inversion of the acoustic-pressure vertical phase gradient from a single vector sensor.

A vector sensor can provide measurements of ocean acoustic fields in terms of the acoustic pressure and three-dimensional particle velocity, providing potentially highly-informative data for applications such as geoacoustic inversion. This paper applies nonlinear Bayesian inversion to vector sensor data to estimate seabed geoacoustic properties and uncertainties in South China Sea. Linear-frequency-modulated source transmissions, recorded as acoustic pressure and vertical particle velocity, are processed to estimate the vertical phase gradient of acoustic pressure at multiple frequencies as the inversion data. An advantage of this type of data is that it can be modeled without knowledge of the source spectrum, allowing inversion with an unknown source and a single sensor. Geoacoustic inversion of phase-gradient data is carried out and compared to inversion of the vertical acoustic impedance, another type of vector-sensor data, independent of the source spectrum, which has been considered previously. Model selection for the optimal number of seabed sediment layers is carried out using Bayesian information criterion, and parameter estimates, uncertainties, and correlations are calculated using delayed-rejection adaptive Metropolis-Hastings sampling. Results indicate a three-layer seabed model (including the semi-infinite basement), with properties in agreement with independent measurements including a high-resolution seismic profile and surficial sediment type from a core.

Cataloging fish sounds in the wild using combined acoustic and video recordings.

Although many fish are soniferous, few of their sounds have been identified, making passive acoustic monitoring (PAM) ineffective. To start addressing this issue, a portable 6-hydrophone array combined with a video camera was assembled to catalog fish sounds in the wild. Sounds are detected automatically in the acoustic recordings and localized in three dimensions using time-difference of arrivals and linearized inversion. Localizations are then combined with the video to identify the species producing the sounds. Uncertainty analyses show that fish are localized near the array with uncertainties < 50 cm. The proposed system was deployed off Cape Cod, MA and used to identify sounds produced by tautog (Tautoga onitis), demonstrating that the methodology can be used to build up a catalog of fish sounds that could be used for PAM and fisheries management.

Bowhead whale localization using time-difference-of-arrival data from asynchronous recorders.

This paper estimates bowhead whale locations and uncertainties using nonlinear Bayesian inversion of the time-difference-of-arrival (TDOA) of low-frequency whale calls recorded on onmi-directional asynchronous recorders in the shallow waters of the northeastern Chukchi Sea, Alaska. A Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by 0.5-9.2 km, was deployed for several months over which time their clocks drifted out of synchronization. Hundreds of recorded whale calls are manually associated between recorders. The TDOA between hydrophone pairs are calculated from filtered waveform cross correlations and depend on the whale locations, hydrophone locations, relative recorder clock offsets, and effective waveguide sound speed. A nonlinear Bayesian inversion estimates all of these parameters and their uncertainties as well as data error statistics. The problem is highly nonlinear and a linearized inversion did not produce physically realistic results. Whale location uncertainties from nonlinear inversion can be low enough to allow accurate tracking of migrating whales that vocalize repeatedly over several minutes. Estimates of clock drift rates are obtained from inversions of TDOA data over two weeks and agree with corresponding estimates obtained from long-time averaged ambient noise cross correlations. The inversion is suitable for application to large data sets of manually or automatically detected whale calls.

Bowhead whale localization using asynchronous hydrophones in the Chukchi Sea.

This paper estimates bowhead whale locations and uncertainties using non-linear Bayesian inversion of their modally-dispersed calls recorded on asynchronous recorders in the Chukchi Sea, Alaska. Bowhead calls were recorded on a cluster of 7 asynchronous ocean-bottom hydrophones that were separated by 0.5-9.2 km. A warping time-frequency analysis is used to extract relative mode arrival times as a function of frequency for nine frequency-modulated whale calls that dispersed in the shallow water environment. Each call was recorded on multiple hydrophones and the mode arrival times are inverted for: the whale location in the horizontal plane, source instantaneous frequency (IF), water sound-speed profile, seabed geoacoustic parameters, relative recorder clock drifts, and residual error standard deviations, all with estimated uncertainties. A simulation study shows that accurate prior environmental knowledge is not required for accurate localization as long as the inversion treats the environment as unknown. Joint inversion of multiple recorded calls is shown to substantially reduce uncertainties in location, source IF, and relative clock drift. Whale location uncertainties are estimated to be 30-160 m and relative clock drift uncertainties are 3-26 ms.

Joint inversion for transponder localization and sound-speed profile temporal variation in high-precision acoustic surveys.

This letter develops a Bayesian inversion for localizing underwater acoustic transponders using a surface ship which compensates for sound-speed profile (SSP) temporal variation during the survey. The method is based on dividing observed acoustic travel-time data into time segments and including depth-independent SSP variations for each segment as additional unknown parameters to approximate the SSP temporal variation. SSP variations are estimated jointly with transponder locations, rather than calculated separately as in existing two-step inversions. Simulation and sea-trial results show this localization/SSP joint inversion performs better than two-step inversion in terms of localization accuracy, agreement with measured SSP variations, and computational efficiency.

Bayesian source localization with uncertain Green's function in an uncertain shallow water ocean.

Matched-field acoustic source localization is a challenging task when environmental properties of the oceanic waveguide are not precisely known. Errors in the assumed environment (mismatch) can cause severe degradations in localization performance. This paper develops a Bayesian approach to improve robustness to environmental mismatch by considering the waveguide Green's function to be an uncertain random vector whose probability density accounts for environmental uncertainty. The posterior probability density is integrated over the Green's function probability density to obtain a joint marginal probability distribution for source range and depth, accounting for environmental uncertainty and quantifying localization uncertainty. Because brute-force integration in high dimensions can be costly, an efficient method is developed in which the multi-dimensional Green's function integration is approximated by one-dimensional integration over a suitably defined correlation measure. An approach to approximate the Green's function covariance matrix, which represents the environmental mismatch, is developed based on modal analysis. Examples are presented to illustrate the method and Monte-Carlo simulations are carried out to evaluate its performance relative to other methods. The proposed method gives efficient, reliable source localization and uncertainties with improved robustness toward environmental mismatch.

Geoacoustic inversion for the seabed transition layer using a Bernstein polynomial model.

This paper develops an inversion method for the seabed transition layer at the water-sediment interface, often found in muddy sediments, which provides density and sound-speed profiles that were previously not resolvable. The resolution improvements are achieved by introducing a parametrization that captures general depth-dependent gradients in geoacoustic parameters with a small number of parameters. In particular, the gradients are represented by a sum of Bernstein basis functions, weighted by unknown coefficients. Compared to previous forms found in the literature, the Bernstein-based parametrization can represent a wider range of depth-dependent geoacoustic profiles using fewer parameters which leads to reduced uncertainty and improved resolution. In addition, the Bernstein basis is the most stable polynomial representation in that small perturbations to the unknown coefficients result in small, localized perturbations to the geoacoustic profile, thereby providing an efficient exploration of the parameter space using Markov-chain methods in nonlinear inversion. Geoacoustic profiles at four mud sites on the Malta Plateau are studied with the proposed approach. Results show exceptional resolution of density profiles, estimated with low uncertainty and clear sensitivity to sediment features of centimeter scale.

Efficient localization and spectral estimation of an unknown number of ocean acoustic sources using a graphics processing unit.

This paper develops a matched-field approach to localization and spectral estimation of an unknown number of ocean acoustic sources employing massively parallel implementation on a graphics processing unit (GPU) for real-time efficiency. A Bayesian formulation is developed in which the locations and complex spectra of multiple sources and noise variances are considered unknown random variables, and the Bayesian information criterion is minimized to estimate these parameters, as well as the number of sources present. Optimization is carried out using simulated annealing and includes steps that attempt to add/delete sources to/from the model. Closed-form maximum-likelihood (ML) solutions for source spectra and noise variances in terms of the source locations allow these parameters to be sampled implicitly, substantially reducing the dimensionality of the inversion. Source sampling, addition, and deletion are based on joint conditional probability distributions for source range and depth, which incorporate the ML spectral estimates. Computing these conditionals requires solving a very large number of systems of equations, which is carried out in parallel on a GPU, improving efficiency by 2 orders of magnitude. Simulated examples illustrate localizations and spectral estimation for a large number of sources (up to eight), and investigate mitigation of environmental mismatch via efficient multiple-frequency inversion.

Fast computation of seabed spherical-wave reflection coefficients in geoacoustic inversion.

This paper develops a fast numerical approach to computing spherical-wave reflection coefficients (SWRCs) for layered seabeds, which provides substantial savings in computation time when used as the forward model for geoacoustic inversion of broadband seabed reflectivity data. The approach exploits the Sommerfeld-integral representation of SWRCs as the Hankel transform of a function proportional to the plane-wave reflection coefficient (PWRC), and applies Levin integration to the rapidly oscillating integrand cast as the product of a (pre-computed) media-independent matrix and a vector involving PWRCs at a sparse sampling of integration angles. Compared to conventional Simpson's rule integration for computation of the SWRC, the Levin integration yields speed-up factors of an order of magnitude or more. Further, it results in reduced memory requirements for storage of pre-computed quantities, a desirable property when a graphics processing unit (GPU) is used for parallel computation of SWRCs. The paper applies trans-dimensional Bayesian inversion to investigate the impact of forward modeling in terms of PWRCs and SWRCs on the estimation of geoacoustic parameters and uncertainties. Model comparisons are quantified in simulated- and measured-data inversions by comparing the estimated geoacoustic parameters to the true parameters or core measurements, respectively, and by calculating the deviance information criterion for model selection.

Linearized two-hydrophone localization of a pulsed acoustic source in the presence of refraction: Theory and simulations.

This paper develops an efficient three-dimensional localization method for transient acoustic sources, with uncertainty estimation, based on time differences between direct and surface-reflected arrivals at two hydrophones. The localization method accounts for refraction caused by a depth-dependent sound-speed profile using a ray-theoretic approach for calculating eigenray travel times and partial derivatives. Further, the method provides localization error estimates accounting for uncertainties of the arrival times and hydrophone locations, as well as for depth-dependent uncertainties in the sound-speed profile. In the first of two steps, source depth and range to each hydrophone are estimated using an iterative, linearized Gauss-Markov inversion scheme. In the second step, the estimated source ranges are combined with the hydrophone locations to obtain the source location in the horizontal. Localization performance is analyzed in a simulation study, and the linearized localization estimates and uncertainties are validated by comparison with a fully nonlinear (but numerically intensive) Markov-chain Monte Carlo inversion.

Discrimination between discrete and continuum scattering from the sub-seafloor.

There is growing evidence that seabed scattering is often dominated by heterogeneities within the sediment volume as opposed to seafloor roughness. From a theoretical viewpoint, sediment volume heterogeneities can be described either by a fluctuation continuum or by discrete particles. In at-sea experiments, heterogeneity characteristics generally are not known a priori. Thus, an uninformed model selection is generally made, i.e., the researcher must arbitrarily select either a discrete or continuum model. It is shown here that it is possible to (acoustically) discriminate between continuum and discrete heterogeneities in some instances. For example, when the spectral exponent γ3>4, the volume scattering cannot be described by discrete particles. Conversely, when γ3≤2, the heterogeneities likely arise from discrete particles. Furthermore, in the range 2<γ3≤4 it is sometimes possible to discriminate via physical bounds on the parameter values. The ability to so discriminate is important, because there are few tools for measuring small scale, O(10(-2) to 10(1)) m, sediment heterogeneities over large areas. Therefore, discriminating discrete vs continuum heterogeneities via acoustic remote sensing may lead to improved observations and concomitant increased understanding of the marine benthic environment.

Bayesian environmental inversion of airgun modal dispersion using a single hydrophone in the Chukchi Sea.

This paper presents estimated water-column and seabed parameters and uncertainties for a shallow-water site in the Chukchi Sea, Alaska, from trans-dimensional Bayesian inversion of the dispersion of water-column acoustic modes. Pulse waveforms were recorded at a single ocean-bottom hydrophone from a small, ship-towed airgun array during a seismic survey. A warping dispersion time-frequency analysis is used to extract relative mode arrival times as a function of frequency for source-receiver ranges of 3 and 4 km which are inverted for the water sound-speed profile (SSP) and subbottom geoacoustic properties. The SSP is modeled using an unknown number of sound-speed/depth nodes. The subbottom is modeled using an unknown number of homogeneous layers with unknown thickness, sound speed, and density, overlying a halfspace. A reversible-jump Markov-chain Monte Carlo algorithm samples the model parameterization in terms of the number of water-column nodes and subbottom interfaces that can be resolved by the data. The estimated SSP agrees well with a measured profile, and seafloor sound speed is consistent with an independent headwave arrival-time analysis. Environmental properties are required to model sound propagation in the Chukchi Sea for estimating sound exposure levels and environmental research associated with marine mammal localization.

High-resolution bottom-loss estimation using the ambient-noise vertical coherence function.

The seabed reflection loss (shortly "bottom loss") is an important quantity for predicting transmission loss in the ocean. A recent passive technique for estimating the bottom loss as a function of frequency and grazing angle exploits marine ambient noise (originating at the surface from breaking waves, wind, and rain) as an acoustic source. Conventional beamforming of the noise field at a vertical line array of hydrophones is a fundamental step in this technique, and the beamformer resolution in grazing angle affects the quality of the estimated bottom loss. Implementation of this technique with short arrays can be hindered by their inherently poor angular resolution. This paper presents a derivation of the bottom reflection coefficient from the ambient-noise spatial coherence function, and a technique based on this derivation for obtaining higher angular resolution bottom-loss estimates. The technique, which exploits the (approximate) spatial stationarity of the ambient-noise spatial coherence function, is demonstrated on both simulated and experimental data.

Estimating seabed scattering mechanisms via Bayesian model selection.

A quantitative inversion procedure is developed and applied to determine the dominant scattering mechanism (surface roughness and/or volume scattering) from seabed scattering-strength data. The classification system is based on trans-dimensional Bayesian inversion with the deviance information criterion used to select the dominant scattering mechanism. Scattering is modeled using first-order perturbation theory as due to one of three mechanisms: Interface scattering from a rough seafloor, volume scattering from a heterogeneous sediment layer, or mixed scattering combining both interface and volume scattering. The classification system is applied to six simulated test cases where it correctly identifies the true dominant scattering mechanism as having greater support from the data in five cases; the remaining case is indecisive. The approach is also applied to measured backscatter-strength data where volume scattering is determined as the dominant scattering mechanism. Comparison of inversion results with core data indicates the method yields both a reasonable volume heterogeneity size distribution and a good estimate of the sub-bottom depths at which scatterers occur.