PNNL

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, where challenges exist in the inversion of GPR tomographic data for handling non-uniqueness and nonlinearity and high-dimensionality of unknowns. We have developed a new method for estimating soil moisture fields from GPR data. It uses a pilot-point method to provide a low-dimensional 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 formulate a Bayesian inverse problem for the pilot-point parameters, predicted on a GPR travel time model. We integrate the multi-chain Markov chain Monte Carlo (MCMC) framework with the pilot point concept, a curved-ray GPR travel time model, and a sequential Gaussian simulation (SGSIM) algorithm for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as its spatial correlation range, which are used to construct the whole field of dielectric permittivity using SGSIM. We infer the permittivity field as a probability density function, thus capturing the uncertainty in the inference. The inverse problem is solved using a multi-chain MCMC method, which can address high-dimensional inverse problems when required (as we did in some of our performance tests). 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 distribution for 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 noise in the observation, increased observational data, as well as increased number of pilot points.