Quantifying uncertainty in geoacoustic inversion. I. A fast Gibbs sampler approach

This paper describes a Bayesian approach to matched-field inversion (MFI) of ocean acoustic data for seabed geoacoustic properties. In a Bayesian formulation, the unknown environmental and experimental parameters are considered random variables constrained by noisy data and prior information, and the goal is to interpret the multi-dimensional posterior probability density (PPD). The PPD is typically characterized in terms of point estimates, marginal distributions, and posterior correlations (or joint statistics). Computing these requires numerical optimization and integration of the PPD, which are carried out efficiently here using adaptive hybrid optimization and Metropolis-Hastings sampling in principal-component space, respectively. Likelihood and misfit functions for multi-frequency MFI with incomplete source spectral information are derived based on the assumption of complex Gaussiandistributed data errors with covariance matrices estimated from residual analysis; posterior statistical tests are applied to validate these estimates and assumptions. Model selection is carried out by applying the Bayesian information criterion to determine the simplest seabed parameterization consistent with the resolving power of the data. Bayesian MFI is illustrated for shallow-water acoustic data measured in the Mediterranean Sea.

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“…Integration can be carried out using Markov-chain Monte Carlo importance sampling methods, such as fast Gibbs sampling [2].…”

Section: J = {(Mi -M )(Mj -Mj)p(m | D)dmmentioning

confidence: 99%

Bayesian matched-field geoacoustic inversion

Dosso

Dettmer

2011

Inverse Problems

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“…The uncertainty in geophysical inverse problems was estimated by various stochastic inversion algorithms, such as MCMC (Liu and Stock, 1993;Malinverno and Briggs, 2004;Chen and Dickens, 2009;Gunning et al, 2010;Kwon and Snieder, 2011), SA (Dosso, 2002;Dosso and Nielsen, 2002;Bhattacharya et al, 2003;Roy et al, 2005;Varela et al, 2006), PSO (Fernández-Martínez et al, 2012;Rumpf and Tronicke, 2015), and rjMCMC Reading and Gallagher, 2013;Dadi, 2014;Galetti et al, 2015;Dadi et al, 2015).…”

Section: Uncertainty Estimationmentioning

confidence: 99%

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

Zhu

Gibson

2016

SEG Technical Program Expanded Abstracts 2016

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We use a transdimensional inversion algorithm, reversible jump MCMC (rjMCMC), in the seismic waveform inversion of post-stack and prestack data to characterize reservoir properties such as seismic wave velocity, density as well as impedance and then estimate uncertainty. Each seismic trace is inverted independently based on a layered earth model. The model dimensionality is defined as the number of the layers multiplied with the number of model parameters per layer. The rjMCMC is able to infer the number of model parameters from data itself by allowing it to vary in the iterative inversion process, converge to proper parameterization and prevent underparameterization and overparameterization. We also use rjMCMC to enhance uncertainty estimation since it can transdimensionally sample different model spaces of different dimensionalities and can prevent a biased sampling in only one space which may have a different dimensionality than that of the true model space. An ensemble of solutions from difference spaces can statistically reduce the bias for parameter estimation and uncertainty quantification. Inversion uncertainty is comprised of property uncertainty and location uncertainty. Our study revealed that the inversion uncertainty is correlated with the discontinuity of property in such a way that 1) a smaller discontinuity will induce a lower uncertainty in property at the discontinuity but also a higher uncertainty of the location of that discontinuity and 2) a larger discontinuity will induce a higher uncertainty in property at the discontinuity but also a higher ''certainty'' of the location of that discontinuity. Therefore, there is a trade-off between the property uncertainty and the location uncertainty. To our surprise, there is a lot of hidden information in the uncertainty result that we can actually take advantage of due to this trade-off effect. On the basis of our study ii using rjMCMC, we propose to use the inversion uncertainty as a novel attribute in an optimistic way to characterize the magnitude and the location of subsurface discontinuities and reflectors. important it is to estimate the uncertainty, and I used another method for two years but it turned out that method was unsuccessful for solving my research problems because it couldn't answer the question for uncertainty assessment. This is one of the biggest mistakes that I have ever made because I wasn't aware of the importance of my advisor's words and questions. Indeed, research is not always successful and smooth and I did encounter failures, but I didn't give up.

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“…Bayesian methods as implemented in geophysics and ocean acoustics [11][12][13] compute the PPD by developing the likelihood function followed by an application of Bayes' rule. In such applications, the statistics of E n are a requirement to derive a likelihood function.…”

Section: A Maximum Entropymentioning

confidence: 99%

Maximum entropy inference of seabed attenuation parameters using ship radiated broadband noise

Knobles

2015

The Journal of the Acoustical Society of America

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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 (α 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.

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Quantifying uncertainty in geoacoustic inversion. I. A fast Gibbs sampler approach

Cited by 202 publications

References 27 publications

Bayesian matched-field geoacoustic inversion

Bayesian matched-field geoacoustic inversion

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

Maximum entropy inference of seabed attenuation parameters using ship radiated broadband noise

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