Geochemical characterization using geophysical data and Markov Chain Monte Carlo methods: A case study at the South Oyster bacterial transport site in Virginia

Chen, Jinsong; Hubbard, Susan S.; Rubin, Yoram; Murray, Christopher J L; Roden, Eric E.; Majer, Ernest L.

doi:10.1029/2003wr002883

Cited by 41 publications

(46 citation statements)

References 49 publications

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“…This is followed by our development of a Bayesian model to invert SIP data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods (Gilks et al, 1996). MCMC methods are effective methods for drawing samples from complex and high-dimensional joint probability distribution functions and have been increasingly used to invert complex geophysical data (Bosch, 1999;Buland and Omre, 2003;Gunning and Glinsky, 2004;Chen et al, 2004Chen et al, , 2006. Our goal is to develop an inversion approach that is insensitive to initial values and that provides sufficient uncertainty information on the estimation when we invert SIP data for parameters in a multiple Cole-Cole model.…”

Section: Introductionmentioning

confidence: 99%

A comparison between Gauss-Newton and Markov-chain Monte Carlo–based methods for inverting spectral induced-polarization data for Cole-Cole parameters

2008

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We develop a Bayesian model to invert spectral induced polarization (SIP) data for ColeCole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive global information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.3

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Section: Introductionmentioning

confidence: 99%

A comparison between Gauss-Newton and Markov-chain Monte Carlo–based methods for inverting spectral induced-polarization data for Cole-Cole parameters

2008

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“…A few applications of MCMC approaches to spatial processes have been presented in the literature. For example, Chen et al [2004] presented an application of a Gibbs sampler for estimating the spatial distribution of iron concentrations using GPR tomographic data and borehole lithofacies logs. A Gibbs sampler is an approach that relies on sequentially sampling the marginal distribution of individual random variables.…”

Section: Mcmc Methods In Hydrologymentioning

confidence: 99%

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

Michalak

2008

Water Resources Research

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[1] Interpolation and inverse modeling problems are ubiquitous in environmental sciences. In many applications, the parameters being estimated or mapped have physical constraints, such as nonnegativity (e.g. concentration, hydraulic conductivity), solubility limits, censored data (e.g. due to dry wells or detection limits), and other physical boundaries or missing data. Geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters, but these methods typically cannot enforce physical constraints. This paper describes a statistically rigorous and computationally efficient Gibbs sampler, a Markov chain Monte Carlo technique, based on an a priori truncated Gaussian distribution model, which allows for multiple and variable physical constraints to be enforced within a geostatistical framework. Sample interpolation and inverse modeling applications confirm that estimates, uncertainty bounds and conditional simulations reflect the specified constraints, leading to conclusions that are more consistent with the underlying conceptual model, and provide a more accurate measure of the posterior uncertainty of the parameters being estimated. In addition, especially in inverse modeling applications, a posteriori confidence bounds are narrower even in areas where constraints are not imposed. The method is applicable in multiple dimensions, for data with or without measurement error, and with any variogram model.

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“…All such studies have two components in common that determine the quality of the reconstructions-the spatial parameterization for the spatially variable soil-moisture field (also called the random field model (RFM), whose parameters are the target of inference from GPR first-arrival-travel time measurements) and the MCMC algorithm that estimates the RFM's parameters as a high-dimensional PDF. In Chen et al (2004), the authors used GPR measurements and a Gibbs sampler to infer iron concentration at the South Oyster site, where soil is a mixture of sand and mud. The field was modeled as a grid where an indicator denoted whether a grid-cell was sand or mud (the lithofacies).…”

Section: Introductionmentioning

confidence: 99%

Soil moisture estimation using tomographic ground penetrating radar in a MCMC–Bayesian framework

Bao

Hou

Ray

et al. 2018

Stoch Environ Res Risk Assess

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In this study, we focus on a hydrogeological inverse problem specifically targeting monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data. Technical challenges exist in the inversion of GPR tomographic data for handling non-uniqueness, nonlinearity and high-dimensionality of unknowns. We have developed a new method for estimating soil moisture fields from crosshole GPR data. It uses a pilot-point method to provide a lowdimensional representation of the relative dielectric permittivity field of the soil, which is the primary object of inference: the field can be converted to soil moisture using a petrophysical model. We integrate a multi-chain Markov chain Monte Carlo (MCMC)-Bayesian inversion framework with the pilot point concept, a curved-ray GPR travel time model, and a sequential Gaussian simulation algorithm, for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as the corresponding geostatistical parameters (i.e., spatial correlation range). We infer the dielectric permittivity as a probability density function, thus capturing the uncertainty in the inference. The multi-chain MCMC enables addressing high-dimensional inverse problems as required in the inversion setup. The method is scalable in terms of number of chains and processors, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. The proposed inversion approach can successfully approximate the posterior density distributions of the pilot points, and capture the true values. The computational efficiency, accuracy, and convergence behaviors of the inversion approach were also systematically evaluated, by comparing the inversion results obtained with different levels of noises in the observations, increased observational data, as well as increased number of pilot points.

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Geochemical characterization using geophysical data and Markov Chain Monte Carlo methods: A case study at the South Oyster bacterial transport site in Virginia

Cited by 41 publications

References 49 publications

A comparison between Gauss-Newton and Markov-chain Monte Carlo–based methods for inverting spectral induced-polarization data for Cole-Cole parameters

A comparison between Gauss-Newton and Markov-chain Monte Carlo–based methods for inverting spectral induced-polarization data for Cole-Cole parameters

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

Soil moisture estimation using tomographic ground penetrating radar in a MCMC–Bayesian framework

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