Facies Classification with Copula Entropy

TL;DR

This work introduces Copula Entropy (CE) as a model-free, information-theoretic criterion for variable selection in facies classification. By computing CE between geological variables and facies labels, the method ranks variables by negative CE and selects a subset for training Random Forest classifiers, achieving comparable or improved accuracy with fewer inputs. CE’s non-parametric estimation via empirical copula density and kNN-based entropy provides robust, interpretable variable selections, demonstrated on a Council Grove dataset with 9 facies classes. The results show that important variables such as NM_M and Depth drive classification, while others like RELPOS and DeltaPHI can be dropped without performance loss, highlighting practical benefits for reservoir characterization tasks.

Abstract

In this paper we propose to apply copula entropy (CE) to facies classification. In our method, the correlations between geological variables and facies classes are measured with CE and then the variables associated with large negative CEs are selected for classification. We verified the proposed method on a typical facies dataset for facies classification and the experimental results show that the proposed method can select less geological variables for facies classification without sacrificing classification performance. The geological variables such selected are also interpretable to geologists with geological meanings due to the rigorous definition of CE.

Figures (5)

• Figure 1: The distribution of the classes of rock facies in the experimental data.
• Figure 2: The 5 variable of the well "SHRIMPLIN".
• Figure 3: Joint distributions between geological variables and facies classes in the experimental data.
• Figure 4: The estimated CEs between geological variables and facies classes.
• Figure 5: The performance of the RFs classifiers.

Theorems & Definitions (3)

• Definition 1: Copula Entropy
• Theorem 1
• Corollary 1