Bayesian Inversion for Surface Magnetic Resonance Tomography Based on Geostatistics

Magnetic resonance tomography (MRT) has the advantages of direct, quantitative, and unique interpretation in the field of groundwater detection. Currently, the inversion of MRT data primarily uses the
$Q$
-time (QT) inversion method based on the Tikhonov regularization. However, when the heterogeneity of an aquifer is high and the water content distribution is markedly uneven, this method removes many details in the model and cannot perform uncertainty analysis on the results. To solve these problems, we propose a Bayesian inversion for MRT data based on geostatistics. The method uses previously known geological data, such as drilling, to determine prior information models containing variograms and mixture Gaussian probability distributions for generating many stochastic realizations. Under the Bayesian framework, a modified Markov chain Monte Carlo (MCMC) strategy is used to obtain the posterior probability distributions of subsurface aquifers and hydraulic conductivity, and the results of quantitative uncertainty analysis. By comparing the inversion performance for simulated models, the imaging result of the Bayesian method is found to be markedly more accurate than that of the QT method for subsurface 2-D aquifers, particularly in explaining the stochastic model (i.e., the water-bearing model with an uneven distribution of water content). This method can also intuitively quantify the uncertainty of the imaging results, which mitigates the shortcomings of existing inversion methods. This article also discusses the effects of prior information, number of chains, and noise levels on the results and also validates the effectiveness and practicability of the proposed method using field-measured data.