Gavin Steininger

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.

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.

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.].

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.

Efficient trans-dimensional Bayesian inversion for geoacoustic profile estimation

This paper considers sampling efficiency of trans-dimensional (trans-D) Bayesian inversion based on the reversible-jump Markov-chain Monte Carlo (rjMCMC) algorithm, with application to seabed acoustic reflectivity inversion. Trans-D inversion is applied to sample the posterior probability density over geoacoustic parameters for an unknown number of seabed layers, providing profile estimates with uncertainties that include the uncertainty in the model parameterization. However, the approach is computationally intensive. The efficiency of rjMCMC sampling is largely determined by the proposal schemes applied to perturb existing parameters and to assign values for parameters added to the model. Several proposal schemes are examined, some of which appear new for trans-D geoacoustic inversion. Perturbations of existing parameters are considered in a principal-component space based on an eigen-decomposition of the unit-lag parameter covariance matrix (computed from successive models along the Markov chain, a diminishing adaptation). The relative efficiency of proposing new parameters from the prior versus a Gaussian distribution focused near existing values is considered. Parallel tempering, which employs a sequence of interacting Markov chains with successively relaxed likelihoods, is also considered to increase the acceptance rate of new layers. The relative efficiency of various proposal schemes is compared through repeated inversions with a pragmatic convergence criterion.

Geoacoustic inversion via trans-dimensional sampling over seabed and error models

This paper develops an efficient Bayesian sampling approach to geoacoustic scattering and reflection inversion based on trans-dimensional (trans-D) sampling over both the seabed model (number of sediment layers) and error model (autoregressive order to represent residual correlation). Sampling is carried out using a population of interacting Markov chains employing a range of sampling temperatures (parallel tempering). The approach is applied to both simulated and measured data. The advantages of trans-D autoregressive model sampling over alternative methods of error model selection is explored in terms of the reduction in posterior uncertainty of geoacoustic parameters and evaluation of residual correlation. The seabed is modeled as a stack of homogeneous fluid sediment layers overlying an elastic basement. Including elastic (shear) parameters in the basement makes this layer distinct from the overlying sediment layers and requires a novel formulation of the partition prior distribution for trans-D sampl...

Bayesian inversion of seabed scattering data.

Reverberation modeling and sonar performance predictions in shallow water require good estimates of seabed scattering and reflection as well as an understanding of scattering processes in a particular region. This talk considers the ability to resolve scattering parameters (e.g., scattering strength and roughness) and geoacoustic parameters (layer thicknesses, sound speed, density, and attenuation) using Bayesian inversion and a forward model based on first‐order perturbation scattering theory and multilayer reflection coefficients. Results are considered in terms of marginal posterior probability distributions, which quantify the effective data information content to resolve scattering/geoacoustic parameters. Inversions are applied to synthetic data and to direct‐path scattering measurements from shallow‐water test beds. These measurements probe the seabed on an intermediate spatial scale (patch‐size radius of ∼500 m for both reflection and scattering), which reduces the effects of ocean variability (ass...

Measurement of diffuse sound reflection from an impedance surfaces using one microphone by bayesian inversion.

This paper discusses the use of inverse methods to find the absorption and diffusion characteristics of surfaces. An impedance surface in an anechoic chamber is excited by a pure tone source above it. The steady‐state sound level is measured at n points above the impedance surface. The distribution of the n steady‐state sound‐pressure levels is assumed to be Gaussian. The set of mean or predicted values for this distribution is generated by finding the modulus of a modified Sommerfeld boundary element solution to the Helmholtz equation. The modification is to add multiple diffusely reflected waves each of which is additionally attenuated by a distribution that is proportional to sin(2θ)×G(θ)Dθ×H(φ)Dφ, where G(θ) is the piecewise function [G(θ)=θ/θSpec, θ⩽θSpec, and [(π/2)−θ]/[(π/2)−θ]Spec otherwise] and H(φ)=|(1−φ)/π|. The system of equations is then optimized for the specific impedance of the surface, the normal diffusion coefficient, and the azimuth diffusion coefficient (Z, Dθ, and Dφ) using Bayesian i...

Model selection using Bayesian samples: An introduction to the deviance information criterion

This paper presents the deviance information criterion (DIC) as a metric for model selection based on Bayesian sampling approaches, with examples from seabed geoacoustic and/or scattering inversion. The DIC uses all samples of a distribution to approximate Bayesian evidence, unlike more common measures such as the Bayesian information criterion, which only use point estimates. The DIC uses distribution samples to approximate Bayesian evidence, unlike more common measures such as the Bayesian information criterion based on point estimates. Hence the DIC is more appropriate for non-linear Bayesian inversions utilizing posterior sampling. Two examples are considered: determining the dominant seabed scattering mechanism (interface and/or volume scattering), and choosing between seabed profile parameterizations based on smooth gradients (polynomial splines) or discontinuous homogeneous layers. In both cases, the DIC is applied to trans-dimensional inversions of simulated and measured data, utilizing reversible...

Objective identification of the dominant seabed scattering mechanism

This paper develops and applies a quantitative inversion procedure for scattering-strength data to determine the dominant scattering mechanism (surface and/or volume scattering) and to estimate the relevant scattering parameters and their uncertainties. 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 from the Malta Plateau where volume scattering is...