For appropriate uncertainty quantification in hydrogeological applications (e.g., contaminant plume forecasting), it is essential to infer subsurface models that feature geologically realistic geometries and property contrasts. Recently, an efficient multiple-point statistics probabilistic inversion approach, with model proposals based on graph cuts, has been shown to provide posterior model realizations that honor pre-defined geometrical shapes and property contrasts. It has been tested for both synthetic and field examples involving crosshole ground-penetrating radar. Here, we present the approach and proceed with initial findings on how to extend this method to 3D and hydraulic tomography data. Improvements and modifications in the Markov chain Monte Carlo algorithm are proposed that allow for appropriate acceptance and convergence rates. We also discuss possible ways to circumvent long computing times, for example, by including physical approximations and machine learning techniques, or to focus on global optimization rather than Bayesian posterior sampling.


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