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.

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.

Sound speed gradients in mud.

Various methods have been used to estimate sound speed profiles in mud at the New England Mud Patch. Some of these methods show large sound speed gradients of order 10 s-1. New measurements of the seabed reflection coefficient exhibit an angle of intromission over three octaves in frequency; these data constrain the range of possible sound speed gradient values. The data indicate that sound speed gradients must be quite weak, i.e., much smaller than |10 s-1|. This conclusion is supported by core data which indicate nearly constant porosity in most of the mud layer.

Fast computation of time-domain scattering by an inhomogeneous stratified seafloor.

Marine sediment properties exhibit fluctuations on a very wide range of scales in all three spatial dimensions. These fluctuations lead to scattering of acoustic waves. Seabed scattering models that treat such fluctuations are reasonably well developed under the plane-wave assumption. A recent model, called TDSS (time domain model for seafloor scattering), accurately treats the important point-source-point-receiver geometry for generally stratified fluid sediments-important because this is the geometry employed in many seabed scattering measurements. The computational cost associated with this model is very high and scales roughly with the product of mean source-receiver height above the basement to the fifth power and both bandwidth and wavenumber to the second power. Thus, modeling deep ocean scattering from a near sea surface source and receiver is prohibitive at frequencies above a few tens of hertz. A computational approach was developed based on Levin's method of oscillatory integration, which is orders of magnitude faster than standard numerical integration techniques and makes deep ocean seabed scattering computations practical up to many kilohertz. This approach was demonstrated to agree with the narrowband sonar equation in several simple environments in the limit of small bandwidths, but the TDSS model is expected to be valid for a much wider range of environments.

Sediment interval velocities from a monostatic multibeam sonar.

Interval velocities for marine sediments are generally obtained from source-receiver separations at various offsets. A method is described for estimating interval velocities using a monostatic configuration. Testing is performed using simulated data from rough layered seabeds and interval velocity is estimated within less than 1% of the true value. Monostatic multibeam data from the Gulf of Lion are also presented which exhibit many characteristics similar to the simulated data. The method applied to the measured data yield an interval velocity of 1569 m/s in an 18 m sediment layer. This accords with nearby independent data from cores and wide-angle reflection analysis.

Roughness influence on multibeam-subbottom-profiler specular echoes and roughness parameter inversion.

Integral solutions for wave scattering over slightly rough surfaces generally include the source and receiver directivity. In this paper, it is shown that integrating the point source, point receiver solution over the source and receiver apertures leads to solutions with a clear physical interpretation. The scintillation, time-of-arrival, and direction-of-arrival spatial covariances of the specular echo are derived for a multibeam-subbottom-profiler configuration and result in surface integrals that can be evaluated numerically. In addition, algebraic expressions are obtained for the variances when the roughness has a Gaussian autocorrelation function and the source and receiver arrays have Gaussian apodization functions. Variances obtained from a numerical evaluation of the surface integrals compare well with estimates from a realistic three-dimensional numerical experiment. A simple inversion scheme is used to extract the roughness parameters from the numerical experiment signals.

Seafloor sound-speed profile characterization with non-parallel layering by the image source method: Application to CLUTTER'09 campaign data.

The image source method was originally developed to estimate sediment sound speed as a function of depth assuming plane-layered sediments. Recently, the technique was extended to treat dipping, i.e., non-parallel layers and was tested using synthetic data. Here, the technique is applied to measured reflection data with dipping layers and mud volcanoes. The data were collected with an autonomous underwater vehicle towing a source (1600-3500 Hz) and a horizontal array of hydrophones. Data were collected every 3 m criss-crossing an area about 1 km(2). The results provide a combination of two-dimensional sections of the sediment sound-speeds plotted in a three-dimensional picture.

Relative velocity measurement from the spectral phase of a match-filtered linear frequency modulated pulse.

Linear frequency modulated signals are commonly used to perform underwater acoustic measurements since they can achieve high signal-to-noise ratios with relatively low source levels. However, such signals present a drawback if the source or receiver or target is moving. The Doppler effect affects signal amplitude, delay, and resolution. To perform a correct match filtering that includes the Doppler shift requires prior knowledge of the relative velocity. In this paper, the relative velocity is extracted directly from the Doppler cross-power spectrum. More precisely, the quadratic coefficient of the Doppler cross-power-spectrum phase is proportional to the relative velocity. The proposed method achieves velocity estimates that compare favorably with Global Positioning System ground truth and the ambiguity method.

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.

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.

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.

A trans-dimensional polynomial-spline parameterization for gradient-based geoacoustic inversion.

This paper presents a polynomial spline-based parameterization for trans-dimensional geoacoustic inversion. The parameterization is demonstrated for both simulated and measured data and shown to be an effective method of representing sediment geoacoustic profiles dominated by gradients, as typically occur, for example, in muddy seabeds. Specifically, the spline parameterization is compared using the deviance information criterion (DIC) to the standard stack-of-homogeneous layers parameterization for the inversion of bottom-loss data measured at a muddy seabed experiment site on the Malta Plateau. The DIC is an information criterion that is well suited to trans-D Bayesian inversion and is introduced to geoacoustics in this paper. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile and provides smaller overall uncertainties in geoacoustic parameters. In addition, the spline parameterization is found to be more parsimonious, and hence preferred, according to the DIC. The trans-dimensional polynomial spline approach is general, and applicable to any inverse problem for gradient-based profiles. [Work supported by ONR.].

Seabed roughness parameters from joint backscatter and reflection inversion at the Malta Plateau.

This paper presents estimates of seabed roughness and geoacoustic parameters and uncertainties on the Malta Plateau, Mediterranean Sea, by joint Bayesian inversion of mono-static backscatter and spherical wave reflection-coefficient data. The data are modeled using homogeneous fluid sediment layers overlying an elastic basement. The scattering model assumes a randomly rough water-sediment interface with a von Karman roughness power spectrum. Scattering and reflection data are inverted simultaneously using a population of interacting Markov chains to sample roughness and geoacoustic parameters as well as residual error parameters. Trans-dimensional sampling is applied to treat the number of sediment layers and the order (zeroth or first) of an autoregressive error model (to represent potential residual correlation) as unknowns. Results are considered in terms of marginal posterior probability profiles and distributions, which quantify the effective data information content to resolve scattering/geoacoustic structure. Results indicate well-defined scattering (roughness) parameters in good agreement with existing measurements, and a multi-layer sediment profile over a high-speed (elastic) basement, consistent with independent knowledge of sand layers over limestone.

Mid frequency shallow water fine-grained sediment attenuation measurements.

Attenuation is perhaps the most difficult sediment acoustic property to measure, but arguably one of the most important for predicting passive and active sonar performance. Measurement techniques can be separated into "direct" measurements (e.g., via sediment probes, sediment cores, and laboratory studies on "ideal" sediments) which are typically at high frequencies, O(10(4)-10(5)) Hz, and "indirect" measurements where attenuation is inferred from long-range propagation or reflection data, generally O(10(2)-10(3)) Hz. A frequency gap in measurements exists in the 600-4000 Hz band and also a general acknowledgement that much of the historical measurements on fine-grained sediments have been biased due to a non-negligible silt and sand component. A shallow water measurement technique using long range reverberation is critically explored. An approximate solution derived using energy flux theory shows that the reverberation is very sensitive to depth-integrated attenuation in a fine-grained sediment layer and separable from most other unknown geoacoustic parameters. Simulation using Bayesian methods confirms the theory. Reverberation measurements across a 10 m fine-grained sediment layer yield an attenuation of 0.009 dB/m/kHz with 95% confidence bounds of 0.006-0.013 dB/m/kHz. This is among the lowest values for sediment attenuation reported in shallow water.

Trans-dimensional joint inversion of seabed scattering and reflection data.

This paper examines joint inversion of acoustic scattering and reflection data to resolve seabed interface roughness parameters (spectral strength, exponent, and cutoff) and geoacoustic profiles. Trans-dimensional (trans-D) Bayesian sampling is applied with both the number of sediment layers and the order (zeroth or first) of auto-regressive parameters in the error model treated as unknowns. A prior distribution that allows fluid sediment layers over an elastic basement in a trans-D inversion is derived and implemented. Three cases are considered: Scattering-only inversion, joint scattering and reflection inversion, and joint inversion with the trans-D auto-regressive error model. Including reflection data improves the resolution of scattering and geoacoustic parameters. The trans-D auto-regressive model further improves scattering resolution and correctly differentiates between strongly and weakly correlated residual errors.

In situ sediment dispersion estimates in the presence of discrete layers and gradients.

One of the difficulties in validating sediment models has been the lack of reliable low frequency dispersion measurements. A reflection method is presented that yields in situ dispersion without sediment disturbance over a broad range of frequencies and can explicitly disentangle frequency-dependent effects of vertical structure, e.g., layers and gradients. Measurements on the outer shelf from 300 to 3000 Hz show that dispersion is a strong function of depth in the sediment column. The depth and frequency-dependent results generally agree well with independent measurements on core data. Cohesive sediments in the upper few meters exhibit a nearly frequency-independent sound speed and a nearly linear frequency dependence of attenuation. In the lower part of the sediment column the sediments are more granular: the lowest layer exhibits an attenuation with a peak frequency at 1100 Hz, where its dependence below and above trends to f(2) and f(1/2), respectively. While Biot theory predicts this dependence, its underlying physical explanation, fluid flow through interstitial pores, does not seem plausible for this sediment due to the unreasonable permeability value required. Viscous grain shearing theory also predicts this dependence, but it is not known whether the parameter values are reasonable.

Parallel tempering for strongly nonlinear geoacoustic inversion.

This paper applies parallel tempering within a Bayesian formulation for strongly nonlinear geoacoustic inverse problems. Bayesian geoacoustic inversion consists of sampling the posterior probability density (PPD) of seabed parameters to estimate integral properties, such as marginal probability distributions, based on ocean acoustic data and prior information. This sampling is usually carried out using the Markov-chain Monte Carlo method of Metropolis-Hastings sampling. However, standard sampling methods can be very inefficient for strongly nonlinear problems involving multi-modal PPDs with the potential to miss important regions of the parameter space and to significantly underestimate parameter uncertainties. Parallel tempering achieves efficient/effective sampling of challenging parameter spaces with the ability to transition freely between multiple PPD modes by running parallel Markov chains at a series of increasing sampling temperatures with probabilistic interchanges between chains. The approach is illustrated for inversion of (simulated) acoustic reverberation data for which the PPD is highly multi-modal. While Metropolis-Hastings sampling gives poor results even with very large sample sizes, parallel tempering provides efficient, convergent sampling of the PPD. Methods to enhance the efficiency of parallel tempering are also considered.

Evidence for a common scale O(0.1) m that controls seabed scattering and reverberation in shallow water.

Analysis of the spectral content of long-range reverberation yields two observations. First, there is a remarkably similar scale, O(0.1) m, between three diverse continental shelf regions. This is surprising given the complexity and diversity of geologic processes. Second, there is strong evidence that the scale is associated with heterogeneities within the sediment. Thus, sediment volume scattering, not interface scattering, controls long-range reverberation from a few hundred hertz to several kilohertz. This is also unexpected given that at long ranges the vertical grazing angles are less than the critical angle, and hence the penetration of the acoustic field into the sub-bottom is expected to be modest. The consistency of the scale, O(0.1) m, suggests an underlying feature or mechanism that is consistent across many ostensibly diverse geological settings. Neither the feature nor mechanism is known at this time.