Probabilistic Reconstruction of Hydrofacies With Support Vector Machines

Abstract

AbstractDelineation of geological features from limited hard and/or soft data is crucial to predicting subsurface phenomena. Ubiquitous sparsity of available data implies that the reliability of any delineation effort is inherently uncertain. We present probabilistic support vector machines (pSVM) as a viable method for both hydrofacies delineation from sparse data and quantification of the corresponding predictive uncertainty. Our numerical experiments with synthetic data demonstrate an agreement between the probability of a pixel classifier predicted with pSVM and indicator Kriging. While the latter requires manual inference of a variogram (two‐point correlation function) from spatial observations, pSVM are highly automated and less data intensive. We also investigate the robustness of pSVM with respect to its hyper‐parameters and the number of measurements. Having investigated these features of pSVM, we deploy them to delineate, from lithological data collected in a number of wells, the spatial extent of an aquitard separating two aquifers in Southern California.