Bayesian Markov‐Chain‐Monte‐Carlo Inversion of Time‐Lapse Crosshole GPR Data to Characterize the Vadose Zone at the Arrenaes Site, Denmark

Scholer, Marie; Irving, James; Looms, Majken C.; Nielsen, Lars; Holliger, Klaus

doi:10.2136/vzj2011.0153

Cited by 27 publications

(25 citation statements)

References 44 publications

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“…Formulating the inverse problem in a probabilistic framework, Bayesian methods can be used to accurately estimate the unknown parameters and associated uncertainties. As a very popular Bayesian method, Markov chain Monte Carlo (MCMC) requires repeated evaluations of the governing equations to generate posterior parameter samples (Scholer et al, 2012; Zhang et al, 2015; Shi et al, 2014). If the numerical solver is computationally demanding, the computational cost of MCMC simulation will be prohibitive.…”

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confidence: 99%

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Gao

Zhang

Liu

et al. 2019

Vadose Zone Journal

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Core Ideas The adaptive GP‐based MCMC was efficient to estimate hydraulic parameters in soils. Accuracy of the estimated parameters was verified by simulating experimental results. These simulations revealed a significant effect of layered structure on soil water flow. Modeling water movement in heterogeneous soils, e.g., layered soils, is an essential but challenging task that requires accurate estimation of multiple sets of soil hydraulic parameters. Markov chain Monte Carlo (MCMC) is a popular but computationally expensive method for parameter estimation. An adaptive Gaussian process (GP)‐based MCMC method proposed in our previous work presents significant computational efficiency. Nevertheless, its performance was evaluated only for synthetic numerical cases and has not been experimentally validated. Furthermore, its applicability in estimating hydraulic parameters of layered soils is still unknown. In this study, we systematically evaluated the performance of the GP‐based MCMC method in estimating the layered soil hydraulic parameters through a water infiltration experiment. It was shown that the proposed method could provide reliable estimations that were very close to those given by the original‐model‐based MCMC but at a much lower computational cost. The simulated soil water dynamics using the estimated parameters revealed a significant effect of layered heterogeneity on water flow. The lower layer(s) with higher water suction may cause persistent unsaturated status of the upper layer(s) during infiltration.

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confidence: 99%

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Gao

Zhang

Liu

et al. 2019

Vadose Zone Journal

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“…Our results are comparable to the recent Bayesian hydraulic parameter inversions of Scholer et al . []. Specifically, these studies also investigated layered profiles and showed very similar orders of magnitude in the overall parametric uncertainty as well as similar effects of conditioning, but using water contents estimated from ground penetrating radar measurements instead of moisture content data obtained from TDR.…”

Section: Resultsmentioning

confidence: 92%

“…Specifically, these studies also investigated layered profiles and showed very similar orders of magnitude in the overall parametric uncertainty as well as similar effects of conditioning, but using water contents estimated from ground penetrating radar measurements instead of moisture content data obtained from TDR. However, our results are obtained with a validated likelihood function rather than an assumption of independent and identically distributed Gaussian residuals [ Scholer et al ., ].…”

Section: Resultsmentioning

confidence: 99%

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Bayesian inversion of Mualem‐van Genuchten parameters in a multilayer soil profile: A data‐driven, assumption‐free likelihood function

Over

Wollschläger

Osorio-Murillo

et al. 2015

Water Resources Research

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This paper introduces a hierarchical simulation and modeling framework that allows for inference and validation of the likelihood function in Bayesian inversion of vadose zone hydraulic properties. The likelihood function or its analogs (objective functions and likelihood measures) are commonly assumed to be multivariate Gaussian in form; however, this assumption is not possible to verify without a hierarchical simulation and modeling framework. In this paper, we present the necessary statistical mechanisms for utilizing the hierarchical framework. We apply the hierarchical framework to the inversion of the vadose zone hydraulic properties within a multilayer soil profile conditioned on moisture content observations collected in the uppermost four layers. The key result of our work is that the goodness-of-fit validated likelihood function form provides empirical justification for the assumption of multivariate Gaussian likelihood functions in past and future inversions at similar sites. As an alternative, the likelihood function need not be assumed to follow a parametric statistical distribution and can be computed directly using nonparametric methods. The nonparametric methods are considerably more computationally demanding, and to demonstrate this approach, we present a smaller dimension synthetic case study of evaporation from a soil column. The main drawback of our work is the increased computational expense of the inversion.

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“…Such methods can be formulated using either a measure theoretic or random variable approach, the first being the most formal and axiomatic definition of probability and preferred by theoreticians, and the latter more easy and practical to use and therefore favored by practitioners. Among these methods, Bayesian inference coupled with Markov chain Monte Carlo (MCMC) simulation has found widespread application and use in GPR inversion [6,[13][14][15][16][17][18][19][20]. This approach results in a posterior parameter distribution and quantifies the uncertainty in the modeling results emerging from the model, observed data, likelihood function and prior distribution.…”

Section: Introductionmentioning

confidence: 99%

Underground structure defect detection and reconstruction using crosshole GPR and Bayesian waveform inversion

Qin

Xie

Vrugt

et al. 2016

Automation in Construction

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A B S T R A C TCrosshole ground-penetrating radar (GPR) is a widely used measurement technique to help inspect the structural integrity of man-made underground structures, yet the resulting waveform and travel-time data can be difficult, complex and challenging to interpret. Here, we introduce the elements of a Bayesian inversion method for analyzing crosshole GPR data to guide detection of defects (weakness zones) in underground concrete structures. This framework uses as main building blocks the two-dimensional finite-difference time-domain (FDTD) simulator, the discrete cosine transform (DCT) method, and the DREAM (ZS) algorithm to reconstruct the relative permittivity field of an underground concrete structure from full-waveform GPR inversion. The FDTD simulator solves numerically Maxwell's equations in the time and space domain of the crosshole GPR experiment and simulates iteratively the electromagnetic (EM) waveforms. The DCT algorithm transforms the Cartesian parameterization to the frequency domain and reduces drastically the dimensionality of the parameter space by retaining only the low-frequency DCT-coefficients. Markov chain Monte Carlo (MCMC) simulation with the DREAM (ZS) algorithm is used to estimate the posterior distribution of the DCT-coefficients. The usefulness and applicability of the FDTD−DCT−DREAM (ZS) framework is demonstrated on a synthetic test example involving a unit square concrete structure with a small defect. Our results demonstrate that the proposed method successfully detects and locates defects in concrete structures. The inversion results appear rather insensitive to the noise level of the measured GPR waveforms, and the amount of data used (number of receiving antenna positions), as long as a sufficient number of measurements is available. The more DCT-coefficients that are used to characterize the concrete structure, the more accurate the results, yet the larger the posterior uncertainty of the reconstructed permittivity fields.

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Bayesian Markov‐Chain‐Monte‐Carlo Inversion of Time‐Lapse Crosshole GPR Data to Characterize the Vadose Zone at the Arrenaes Site, Denmark

Cited by 27 publications

References 44 publications

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Bayesian inversion of Mualem‐van Genuchten parameters in a multilayer soil profile: A data‐driven, assumption‐free likelihood function

Underground structure defect detection and reconstruction using crosshole GPR and Bayesian waveform inversion

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