Data-Driven Site Characterization Based on a Markov Random Field Model

This study presents a method for data-driven site characterization (DDSC) based on a Markov random field (MRF) model called Potts model. A Potts model is a graphical model of interacting spins on a lattice and has been successfully applied in image processing such as image de-noising, restoration, and inpainting. Existing Potts model-based methods have been generally designed for image processing, and they do not fit the setting of subsurface modeling in which the available observation data is very limited. In the proposed method, an anisotropic Potts model under fixed external magnetic fields is used as an MRF model, and the hyperparameters are trained using leave-one borehole-out cross-validation. The proposed method is simple and requires only a few borehole data on soil types to train the Potts model. The proposed method was demonstrated through numerical tests, and the effects of the number of training set on estimations were investigated. The proposed method can quantify the uncertainty/accuracy of the estimation, and spatial distributions of estimation uncertainty are also shown in this paper.