Delineation of geological facies from poorly differentiated 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. If such data are poorly differentiated, this challenging task is complicated further by the absence of a clear distinction between different hydrofacies at locations where data are   available. We consider three alternative approaches for analysis of poorly differentiated data: a k$k$-means clustering algorithm, an expectation–maximization algorithm, and a minimum-variance algorithm. Two distinct synthetically generated geological settings are used to analyze the ability of these algorithms to assign accurately the membership of such data in a given geologic facies. On average, the minimum-variance algorithm provides a more robust performance than its two counterparts, and when combined with a nearest neighbor algorithm, it also yields the most accurate reconstruction of the boundaries between the facies.