Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes

Malinverno, Alberto; Briggs, Victoria A.

doi:10.1190/1.1778243

Cited by 259 publications

(221 citation statements)

References 25 publications

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“…This allows us to take into account also the uncertainty on the geomagnetic reversal timescale used to time finite rotations. Similarly, the uncertainty of each model is parameterized within the model itself 19 (hierarchical approach) to account for our ignorance on the noise magnitude, and thus on how close to the data a given model should be in order for the latter to be considered a faithful realization of the true temporal trends. As Euler vectors may change position or angular velocity independently, the sole constraint we impose on the ensemble consists of requiring latitude and longitude to change simultaneously, but independently from the residual angle.…”

Section: Trans-dimensional Hierarchical Bayesian Formulationmentioning

confidence: 99%

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Reconstructing plate-motion changes in the presence of finite-rotations noise

2012

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understanding lithospheric plate motions is of paramount importance to geodynamicists. much effort is going into kinematic reconstructions featuring progressively finer temporal resolution. However, the challenge of precisely identifying ocean-floor magnetic lineations, and uncertainties in geomagnetic reversal timescales result in substantial finite-rotations noise. unless some type of temporal smoothing is applied, the scenario arising at the native temporal resolution is puzzling, as plate motions vary erratically and significantly over short periods ( < 1 myr). This undermines our ability to make geodynamic inferences, as the rates at which forces need to be built upon plates to explain these kinematics far exceed the most optimistic estimates. Here we show that the largest kinematic changes reconstructed across the Atlantic, Indian and south Pacific ridges arise from data noise. We overcome this limitation using a trans-dimensional hierarchical Bayesian framework. We find that plate-motion changes occur on timescales no shorter than a few million years, yielding simpler kinematic patterns and more plausible dynamics.

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Section: Trans-dimensional Hierarchical Bayesian Formulationmentioning

confidence: 99%

“…Here, we tackle noise in finite rotations by using a trans-dimensional hierarchical Bayesian framework [17][18][19][20][21] (Methods). We find that changes in the temporal trends of plate motions occur on timescales no shorter than a few million years, yielding simpler kinematic patterns and more plausible dynamics.…”

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confidence: 99%

Reconstructing plate-motion changes in the presence of finite-rotations noise

2012

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“…MCMC is generally cast in a Bayesian framework and is widely used in geophysical inversion (Mosegaard and Tarantola, 1995;Stoffa, 1995, 1996;Curtis and Lomax, 2001;Mosegaard and Sambridge, 2002;Sambridge and Mosegaard, 2002;Malinverno and Briggs, 2004;Malinverno and Leaney, 2005) and particularly in seismic inversion (Godfrey et al, 1980;Mosegaard et al, 1997;Eidsvik et al, 2004;Hong and Sen, 2009;van der Burg et al, 2009;Martin et al, 2012;Chen and Glinsky, 2014).…”

Section: Brief Overview Of Conventional Algorithmsmentioning

confidence: 99%

“…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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“…Thus, the error levels are distributed uniformly on a logarithmic scale between these bounds. Estimating the measurement errors amounts to hierarchical Bayesian inference (e.g., Bodin et al, 2012;Malinverno and Briggs, 2004).…”

Section: Model Parameterizationmentioning

confidence: 99%

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Lochbühler

Breen

Detwiler

et al. 2014

Journal of Applied Geophysics

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Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO 2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship.

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Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes

Cited by 259 publications

References 25 publications

Reconstructing plate-motion changes in the presence of finite-rotations noise

Reconstructing plate-motion changes in the presence of finite-rotations noise

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

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

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