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

Abstract

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.

Bayesian Integration Using Resistivity and Lithology for Improving Estimation of Hydraulic Conductivity

“…Metropolis-within-Gibbs sampling (Bao et al, 2018) is used (see Section 2.3) to generate realizations of…”

“…Metropolis‐within‐Gibbs sampling (Bao et al., 2018) is used (see Section 2.3) to generate realizations of H 0 , denoted as , from the posterior distribution. Then, the posterior mean and posterior variance are respectively calculated using the equations where N z is the total number of realizations.…”

“…Metropolis‐within‐Gibbs sampling combines two Markov chain Monte Carlo methods, namely Metropolis‐Hastings (MH) sampling and Gibbs sampling (Bao et al., 2018). The idea of Gibbs sampling is to randomly generate realizations from the high‐dimensional target distribution, that is, in this study, by sequentially drawing each H i from its corresponding full conditional distribution .…”

“…Metropolis-within-Gibbs sampling combines two Markov chain Monte Carlo methods, namely Metropolis-Hastings (MH) sampling and Gibbs sampling (Bao et al, 2018). The idea of Gibbs sampling is to randomly generate realizations from the high-dimensional target distribution, that is,…”

2016 International Land Model Benchmarking (ILAMB) Workshop Report

“…The capability of SAChES to invoke a large number of chains simultaneously has its obvious attraction in high-dimensional inversions, i.e., when a gridded field, rather than a few model parameters, has to be estimated. Some studies have begun to explore whether SAChES could be used to estimate saturation fields using ground penetrating radar measurements, as well as to estimate saturation and porosity fields using seismic and electromagnetic response observations (Bao et al, 2016), with potential applications to highly spatially resolved models such as the coupling between CLM and the reactive transport code PFLOTRAN (Hammond et al, 2014).…”