Flexible Coupling in Joint Inversions: A Bayesian Structure Decoupling Algorithm

Agostinetti, Nicola Piana; Bodin, Thomas

doi:10.1029/2018jb016079

Cited by 20 publications

(12 citation statements)

References 56 publications

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“…Hence, each geophysical data set reveals partial information of the unique true model. Despite disparities in the material parameters that the different methods are sensitive to (e.g., electromagnetic data to conductivity, seismic data to velocity, magnetic data to permeability and gravity data to density), models for different material parameters can often be expected to have geometrical similarity (Gallardo and Meju 2004;Linde et al 2006Linde et al , 2008Gallardo and Meju 2011;Brown et al 2012;Zhou et al 2014;Wiik et al 2015;Takam Takougang et al 2015;Le et al 2016;Yan et al 2017b;Giraud et al 2019;Ogunbo et al 2018;Agostinetti and Bodin 2018;Wang et al 2018b) or can be related by some determined or stochastic petrophysical relationship (Moorkamp et al 2007(Moorkamp et al , 2011; Moorkamp 2017; Haber and Holtzman Gazit 2013). Thus, joint inversion of multiple geophysical data sets can significantly reduce uncertainty and improve resolution of the resulting models, i.e.…”

Section: Uncertainty and Resolution Analyses Of Models Inverted From mentioning

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: Uncertainty and Resolution Analyses Of Models Inverted From mentioning

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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“…Usually, this is done by introducing a scale factor that multiplies C d and which can be estimated through maximum likelihood (Mecklenbrauker & Gerstoft 2000;Dosso & Wilmut 2006;Sambridge 2013;Ray et al 2016) or through Hierarchical Bayes methods (Bodin et al 2012;Malinverno & Briggs 2004;Agostinetti et al 2015). In the case of joint inversion, there is usually a different scale factor applied to each data set separately (Agostinetti & Bodin 2018). Under the Hierarchical Bayes approach, these scale factors are hyperparameters inverted for, allowing the data and hyperparameters to select the optimal contribution for each data set.…”

Section: Bayesian Joint Inversion Frameworkmentioning

confidence: 99%

“…In the latter case, the two separate models must be made to 'communicate' in some manner, often through the use of cross gradients or a statistical or analytic relationship between the different physical quantities. More recently, Agostinetti & Bodin (2018) develop a method to permit the two models to share structure only where allowed by the data. In this study, both data sets inform subsurface electrical resistivity, so we will focus our attention on the first approach.…”

Section: Introductionmentioning

confidence: 99%

“…Bayesian sampling-based inverse methods are readily adaptable to a joint inversion framework, which will be discussed in detail in the following section. Jardani et al (2010) inverted synthetic seismic and seismo-electric data for reservoir properties in a 1-D layered model; Rosas-Carbajal et al (2013) inverted synthetic radio frequency MT and electrical resistivity tomography (ERT) data for 2-D electrical resistivity models; Rabben et al (2008) estimated subsurface elastic parameters from synthetic PP and PS reflection coefficients; Bodin et al (2012) recovered estimates of 1-D shear wave velocity profiles from measured surface wave dispersion (SWD) and receiver function (RF) data, while Agostinetti & Bodin (2018) invert electrical resistivity and shear wave velocity. Of the foregoing, all but Bodin et al (2012) and Agostinetti & Bodin (2018) use a fixed-dimensional MCMC sampler.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian joint inversion of controlled source electromagnetic and magnetotelluric data to image freshwater aquifer offshore New Jersey

Blatter

Key

Ray

et al. 2019

Geophysical Journal International

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SUMMARY Joint inversion of multiple electromagnetic data sets, such as controlled source electromagnetic and magnetotelluric data, has the potential to significantly reduce uncertainty in the inverted electrical resistivity when the two data sets contain complementary information about the subsurface. However, evaluating quantitatively the model uncertainty reduction is made difficult by the fact that conventional inversion methods—using gradients and model regularization—typically produce just one model, with no associated estimate of model parameter uncertainty. Bayesian inverse methods can provide quantitative estimates of inverted model parameter uncertainty by generating an ensemble of models, sampled proportional to data fit. The resulting posterior distribution represents a combination of a priori assumptions about the model parameters and information contained in field data. Bayesian inversion is therefore able to quantify the impact of jointly inverting multiple data sets by using the statistical information contained in the posterior distribution. We illustrate, for synthetic data generated from a simple 1-D model, the shape of parameter space compatible with controlled source electromagnetic and magnetotelluric data, separately and jointly. We also demonstrate that when data sets contain complementary information about the model, the region of parameter space compatible with the joint data set is less than or equal to the intersection of the regions compatible with the individual data sets. We adapt a trans-dimensional Markov chain Monte Carlo algorithm for jointly inverting multiple electromagnetic data sets for 1-D earth models and apply it to surface-towed controlled source electromagnetic and magnetotelluric data collected offshore New Jersey, USA, to evaluate the extent of a low salinity aquifer within the continental shelf. Our inversion results identify a region of high resistivity of varying depth and thickness in the upper 500 m of the continental shelf, corroborating results from a previous study that used regularized, gradient-based inversion methods. We evaluate the joint model parameter uncertainty in comparison to the uncertainty obtained from the individual data sets and demonstrate quantitatively that joint inversion offers reduced uncertainty. In addition, we show how the Bayesian model ensemble can subsequently be used to derive uncertainty estimates of pore water salinity within the low salinity aquifer.

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“…Jardani et al (2010) inverted synthetic seismic and seismo-electric data for reservoir properties in a 1D layered model; Rosas-Carbajal et al (2013) inverted synthetic radio frequency MT and electrical resistivity tomography (ERT) data for 2D electrical resistivity models; Rabben et al (2008) estimated subsurface elastic parameters from synthetic PP and PS reflection coefficients; Bodin et al (2012) recovered estimates of 1D shear wave velocity profiles from measured surface wave dispersion (SWD) and receiver function (RF) data, while Agostinetti and Bodin (2018) invert electrical resistivity and shear wave velocity. Of the foregoing, all but Bodin et al (2012) and Agostinetti and Bodin (2018) use a fixed-dimensional MCMC sampler. We have used the trans-D method, where both the unknown geophysical quantities (earth conductivity) as well the number of such quantities are sampled, thus solving to a large extent the "appropriate model" selection problem.…”

Section: Joint Inversionmentioning

confidence: 99%

Bayesian joint inversion of controlled source electromagnetic and magnetotelluric data to infer presence of a freshwater aquifer offshore New Jersey

Blatter

Key

Ray

et al. 2019

ASEG Extended Abstracts

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Flexible Coupling in Joint Inversions: A Bayesian Structure Decoupling Algorithm

Cited by 20 publications

References 56 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

Bayesian joint inversion of controlled source electromagnetic and magnetotelluric data to image freshwater aquifer offshore New Jersey

Bayesian joint inversion of controlled source electromagnetic and magnetotelluric data to infer presence of a freshwater aquifer offshore New Jersey

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