Model‐uncertainty quantification in seismic tomography: method and applications

Osypov, Konstantin; Yang, Yi; Fournier, A.; Иванова, Н. Л.; Bachrach, Ran; Yarman, Can Evren; You, Yu; Nichols, David M.; Woodward, Marta

doi:10.1111/1365-2478.12058

Cited by 70 publications

(14 citation statements)

References 69 publications

(95 reference statements)

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“…Therefore, it has the capability of speeding up the model analysis for large-scale 2D and 3D problems. Currently, the LSQR technique is widely adopted in the linear seismic tomography problem (Zhang and McMechan 1995;Yao et al 1999;Tryggvason et al 2002;Vasco et al 2003;Osypov et al 2013;Chen and Xie 2017). Until now, the LSQR technique has not been widely used in 2D and 3D geo-electromagnetic induction problems.…”

Section: Partial or Truncated Svd Analysismentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, mostsquares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important Extended author information available on the last page of the article applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitation...

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Section: Partial or Truncated Svd Analysismentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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“…The final stage of the project involved uncertainty analysis using Bayesian estimation based on eigenvector decomposition of the tomographic resolution matrices (Osypov et al 2013). Figure 7 shows the corridor of 200 model realizations of the main fault plane, with an instance of the standard deviations of a point termination of the Kvitnos horizon against the fault.…”

Section: Uncertainty Analysismentioning

confidence: 99%

Risk Reduction on the Ivory Prospect via Geologically Constrained Non-parametric Inversion and Bayesian Uncertainty Estimation on a Fault-bounded Reservoir

Raffle¹,

Earnshaw²,

Fruehn³

et al. 2017

Proceedings

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“…The knowledge of any object can be subdivided into what we know we know and what we know we do not know (Ma, 2011;Osypov et al, 2013). The goal of the uncertainty quantification is to answer what we know we do not know.…”

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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Model‐uncertainty quantification in seismic tomography: method and applications

Cited by 70 publications

References 69 publications

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Risk Reduction on the Ivory Prospect via Geologically Constrained Non-parametric Inversion and Bayesian Uncertainty Estimation on a Fault-bounded Reservoir

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

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