Subsurface characterization with support vector machines

A typical subsurface environment is heterogeneous, consists of multiple materials (geologic facies), and is often insufficiently characterized by data. The ability to delineate geologic facies and to estimate their properties from sparse data is essential for modeling physical and biochemical processes occurring in the subsurface. We demonstrate that the support vector machine is a viable and efficient tool for lithofacies delineation, and we compare it with a geostatistical approach. To illustrate our approach, and to demonstrate its advantages, we construct a synthetic porous medium consisting of two heterogeneous materials and then estimate boundaries between these materials from a few selected data points. Our analysis shows that the error in facies delineation by means of support vector machines decreases logarithmically with increasing sampling density. We also introduce and analyze the use of regression support vector machines to estimate the parameter values between points where the parameter is sampled.