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

Steininger, Gavin; Holland, Charles W.; Dosso, Stan E.; Dettmer, Jan

doi:10.1121/1.4817833

Cited by 17 publications

(9 citation statements)

References 37 publications

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“…Here we assume Gaussian data errors and quantify error correlations by an autoregressive process of order 1 (AR1), for details, see Dettmer et al [] and Steininger et al []. In this case, the likelihood function can be written as

L ((), m) = \frac{1}{\sqrt{{((), 2 π)}^{normalN}} σ^{N}} normale normalx normalp ([], - \frac{1}{2 σ^{2}} {|((), d^{normalo normalb normals} - boldd ((), m) - boldd ((), a))|}^{2}),

where d ( a ) are AR (1) predictions that account for correlated errors, and a is the model vector containing the autoregressive parameters.…”

Section: Inversion Methodsmentioning

confidence: 99%

Bayesian inference for ultralow velocity zones in the Earth's lowermost mantle: Complex ULVZ beneath the east of the Philippines

2014

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Ultralow velocity zones (ULVZs) are small-scale structures with a sharp decrease in S and P wave velocity, and an increase in the density on the top of the Earth's core-mantle boundary. The ratio of S and P wave velocity reduction and density anomaly are important to understanding whether ULVZs consist of partial melt or chemically distinct material. However, existing methods such as forward waveform modeling that utilize 1-D and 2-D Earth-structure models face challenges when trying to uniquely quantify ULVZ properties because of inherent nonuniqueness and nonlinearity. This paper develops a Bayesian inversion for ULVZ parameters and uncertainties with rigorous noise treatment to address these challenges. The posterior probability density of the ULVZ parameters (the solution to the inverse problem) is sampled by the Metropolis-Hastings algorithm. To improve sampling efficiency, parallel tempering is applied by simulating a sequence of tempered Markov chains in parallel and allowing information exchange between chains. First, the Bayesian inversion is applied to simulated noisy data for a realistic ULVZ model. Then, measured data sampling the lowermost mantle under the Philippine Sea are considered. Cluster analysis and visual waveform inspection suggest that two distinct classes of ScP (S waves converted to, and reflected as, P waves) waves exist in this region. The distinct waves likely correspond to lateral variability in the lowermost mantle properties in a NE-SW direction. For the NE area, Bayesian model selection identifies a two-layer model with a gradual density increase as a function of depth as optimal. This complex ULVZ structure can be due to the percolation of iron-enriched, molten material in the lowermost mantle. The results for the SW area are more difficult to interpret, which may be due to the limited number of data available (too few waveforms to appropriately reduce noise) and/or complex 2-D and 3-D structures that cannot be explained properly by the 1-D models required by our inversion approach. In particular, the complex waveforms require highly layered 1-D models to fit the data. These models appear physically unreasonable and suggest that the SW region cannot be explained by 1-D structure.

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L ((), m) = \frac{1}{\sqrt{{((), 2 π)}^{normalN}} σ^{N}} normale normalx normalp ([], - \frac{1}{2 σ^{2}} {|((), d^{normalo normalb normals} - boldd ((), m) - boldd ((), a))|}^{2}),

where d ( a ) are AR (1) predictions that account for correlated errors, and a is the model vector containing the autoregressive parameters.…”

Section: Inversion Methodsmentioning

confidence: 99%

Bayesian inference for ultralow velocity zones in the Earth's lowermost mantle: Complex ULVZ beneath the east of the Philippines

2014

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“…For parameterizations based on discrete homogeneous layers, this amounts to an unknown number of layers. 10,12,16,20 For the new spline parameterization developed here, this amounts to an unknown number of spline nodes for each geoacoustic property. In either case, adopting too few parameters (layers or nodes) can lead to under-fitting the data, biasing parameter estimates, and under-estimating parameter uncertainties.…”

Section: Bayesian Inversionmentioning

confidence: 99%

“…32 Both BL (Refs. [33][34][35] and reflection coefficients 16,36 have been applied in geoacoustic inversion. The choice to use BL instead of jRj is made here because BL is more sensitive to the small reflection amplitudes near the angle of intromission for low sound speed sediments.…”

Section: Forward Modelmentioning

confidence: 99%

“…The change in variance is included since reflectioncoefficient or BL errors are commonly observed to change structure near the critical or intromission angle. 16 For multi-layer media the critical/intromission angle is not well defined so it is approximated by a cut-off angle h c , which is treated as an unknown and sampled in the inversion. Errors (e) for data at angles below h c have a variance of S 2 L and errors above h c have a variance of S 2 H .…”

Section: Forward Modelmentioning

confidence: 99%

“…[2][3][4][5][6][7][8] In particular, trans-D Bayesian inversion provides an effective, automated approach to model selection (e.g., determining the number of sediment layers consistent with the resolving power of the data), such that the parameter estimate uncertainties account for model selection uncertainties. [9][10][11][12][13][14][15][16] As the concept of model parsimony is linked to the choice of model parameterization type, the posterior uncertainty of parameter estimates are still affected by a priori parameterization selection decisions. This work highlights the importance of model parameterization in Bayesian inversion a) Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Steininger

Dosso

Holland

et al. 2014

The Journal of the Acoustical Society of America

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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.].

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Efficient trans-dimensional Bayesian inversion for geoacoustic profile estimation

et al. 2014

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This paper considers the efficiency of trans-dimensional (trans-D) Bayesian inversion based on reversible-jump Markov-chain Monte Carlo (rjMCMC) sampling, with application to geophysical inverse problems for a depthdependent earth or seabed model of an unknown number of layers (seabed acoustic reflectivity inversion is the specific example). Trans-D inversion is applied to sample the posterior probability density over geoacoustic/geophysical parameters for a variable number of 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 which are applied to generate perturbed values for existing parameters and new values for parameters assigned to layers added to the model. Several proposal schemes are considered here, some of which appear new for trans-D geophysical 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 examined. Parallel tempering, which employs a sequence of interacting Markov chains in which the likelihood function is successively relaxed, is also considered as a means 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.

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

Cited by 17 publications

References 37 publications

Bayesian inference for ultralow velocity zones in the Earth's lowermost mantle: Complex ULVZ beneath the east of the Philippines

Bayesian inference for ultralow velocity zones in the Earth's lowermost mantle: Complex ULVZ beneath the east of the Philippines

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

Efficient trans-dimensional Bayesian inversion for geoacoustic profile estimation

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