Mixture decompositions and lithofacies clustering from wireline logs

• We present multivariate analysis of wireline logs.
• Lithofacies are classified using wireline logs.
• Principal component analysis is used to synthesize multiple logs and characterize rock physics of the resource formation.
• Probabilistic method of histogram decomposition of rock properties is performed using principal component analysis.
• We demonstrate the lithofacies classification and mixture decomposition using wireline logs with a number of examples.

Finite mixture models provide useful methods for modeling a wide variety of natural phenomena. Decomposing a mixture of distributions, however, has many difficulties, including separability of the component distributions, determination of the number of components, predictability of the clusters with realistic spatial patterns, and linkages between the component density functions and underlying physical processes. In this article, we use principal component analysis (PCA) to synthesize multiple wireline logs and decompose mixture populations for lithofacies clustering. The principal components of these logs characterize the rock physics; some of them contain essential information of lithofacies while others represent less relevant information or noise. In many cases, clustering based on one component is effective for decomposing the mixture and classifying lithofacies, although rotating principal components is often necessary to improve the lithofacies discrimination. In more complicated cases, PCA and direct mixture decomposition using histogram can be cascaded to decompose finite mixture models of a rock property. The proposed methodology combines the delicacy of probability theory and simplicity of linear transforms to classify lithofacies.