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Strebelle, Sebastien

doi:10.1023/a:1014009426274

Cited by 1,202 publications

(192 citation statements)

References 15 publications

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“…Multi-Gaussian models are used extensively, but they are poor descriptions of many geological settings. There are many approaches to create more geologically realistic conceptual models , for example, multiple-point statistics (MPS) ( Strebelle, 2002 ).…”

Section: Discussionmentioning

confidence: 99%

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Brunetti

Linde

Vrugt

2017

Advances in Water Resources

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a b s t r a c tGeophysical data can help to discriminate among multiple competing subsurface hypotheses (conceptual models). Here, we explore the merits of Bayesian model selection in hydrogeophysics using crosshole ground-penetrating radar data from the South Oyster Bacterial Transport Site in Virginia, USA. Implementation of Bayesian model selection requires computation of the marginal likelihood of the measured data, or evidence, for each conceptual model being used. In this paper, we compare three different evidence estimators, including (1) the brute force Monte Carlo method, (2) the Laplace-Metropolis method, and (3) the numerical integration method proposed by Volpi et al. (2016). The three types of subsurface models that we consider differ in their treatment of the porosity distribution and use (a) horizontal layering with fixed layer thicknesses, (b) vertical layering with fixed layer thicknesses and (c) a multi-Gaussian field. Our results demonstrate that all three estimators provide equivalent results in low parameter dimensions, yet in higher dimensions the brute force Monte Carlo method is inefficient. The isotropic multi-Gaussian model is most supported by the travel time data with Bayes factors that are larger than 10 100 compared to conceptual models that assume horizontal or vertical layering of the porosity field.

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Section: Discussionmentioning

confidence: 99%

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Brunetti

Linde

Vrugt

2017

Advances in Water Resources

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“…The training image is scanned by a template that jointly considers spatial variability among a number of (more than two) pixel values in the image to obtain a joint probability distribution that holds information about these spatial correlations. The model parameter values are subsequently sequentially simulated from conditional probabilities on the basis of the jointly considered pixel values (e.g., Strebelle, 2002). The algorithm originally suggested by Guardiano and Srivastava (1993) was, however, computationally unfeasible.…”

Section: Methodsmentioning

confidence: 99%

“…This provides a means of using complex a priori statistical models that allow reproduction of geologically plausible structures, such as channels and tortuosity. Such complex patterns (i.e., spatial autocorrelation) can be learned from so-called training images and reproduced by simulation algorithms based on multiple-point statistics (e.g., Strebelle, 2002). Multiple-point algorithms offer the flexibility of simulating realizations with high entropy (e.g., Gaussian distributions) as well as low entropy (i.e., a few facies) structures or a combination of both (Journel and Zhang, 2006).…”

Section: Introductionmentioning

confidence: 99%

“…Initially, the theoretical background for this inversion strategy is outlined. Subsequently, the theory is applied to a tomographic crosshole GPR full-waveform inverse problem in which the a priori information is inferred (i.e., learned) from a training image and realized through the geostatistical algorithm Single Normal equation SIMulation (Snesim) (Strebelle, 2002). Full-waveform data traces are often contaminated by noise and are, in addition, subject to uncertainties related to inadequacies in the data simulation algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

2012

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We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework for a full-waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included. At the same time we show how temporally and/or spatially correlated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional methods do. Moreover, an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates. The latter may be a key challenge when considering field experiments, which will not be addressed here.

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“…Conventional geostatistical methods (e.g., kriging) use the two-point variogram (or covariance) to describe spatial structures; recently the three-point variogram has been advocated [Strebelle, 2002;Krishnan and Journel, 2003;Journel and Zhang, 2006;Feyen and Caers, 2006]. An alternate geostatistical method, one that does not use a variogram, uses transition probability and Markov chains (TP/MC) to describe spatial structures of categorical data [e.g., Carle andFogg, 1996, 1997;Fogg et al, 1998;Carle, 1999;Weissmann et al, 1999;Li et al, 1999;Ritzi, 2000;Elfeki and Dekking, 2001;Lu and Zhang, 2002;Park et al, 2004;Dai et al, 2005;Sivakumar et al, 2005;Maji et al, 2006;Zhang et al, 2006;Li, 2007aLi, , 2007bLee et al, 2007;Dai et al, 2007;Sun et al, 2008].…”

Section: Introductionmentioning

confidence: 99%

A Markov chain model for characterizing medium heterogeneity and sediment layering structure

Khaleel

2008

Water Resources Research

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[1] By leveraging use of ''soft'' data (e.g., initial moisture content, q i ), this study applies the transition probability (TP) based Markov chain (MC) model to sediment textural classes for characterizing the medium heterogeneity and sediment layering structure. The TP/MC method is evaluated by simulating the vadose zone moisture movement at a field site, where the stratigraphy consists of imperfectly stratified soil layers. Soil heterogeneity is characterized via spatial variability of the geometry of soil textural classes. When the q i measurements, which carry signature about medium heterogeneity and stratigraphy, are not included in the TP/MC model, it is not possible to identify the horizontal TP. The q i measurements, when transformed into soil classes, are necessary in mapping the soil layering structure prevalent at the site. The soil hydraulic parameters for each soil class are treated deterministically and are estimated on the basis of core samples. To evaluate uncertainty in characterizing geometry of the soil classes, multiple conditional realizations of the soil classes are generated. A Monte Carlo simulation shows that the simulated mean moisture contents agree well with corresponding field observations. The observed splitting of the moisture plume in a coarse sand layer that is sandwiched between two fine-textured layers, the southeastward movement of the plume during the redistribution period, and the near-zero fluid flux below the bottom fine layer are adequately simulated. Spatial variability of the field-measured moisture content is sufficiently captured by the 95% confidence intervals calculated from the Monte Carlo simulations. Investigating the effect of data conditioning on the simulated results shows that a reduction of conditioning data does not necessarily deteriorate simulation results if other conditioning data exist within the mean length of the soil classes. The TP/MC method is flexible so that other types of site characterization data (e.g., geophysical data) can be incorporated as they become available.Citation: Ye, M., and R. Khaleel (2008), A Markov chain model for characterizing medium heterogeneity and sediment layering structure, Water Resour. Res., 44, W09427,

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Untitled

Cited by 1,202 publications

References 15 publications

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Bayesian model selection in hydrogeophysics: Application to conceptual subsurface models of the South Oyster Bacterial Transport Site, Virginia, USA

Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

A Markov chain model for characterizing medium heterogeneity and sediment layering structure

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