Persistent Local Topological Indicators of Feature Relevance in Subsampled Reservoir Logs

Abstract

This study evaluates the local stability of topological complexity as a model-agnostic proxy for feature importance in subsurface machine learning. Building on our previous work linking Betti-0 persistence metrics to predictive utility, we apply the framework to eight distinct well configurations ranging from full-reservoir integration to single wells to assess whether topological simplicity reliably indicates predictive relevance at localized scales. For each configuration, Betti-0 lifetimes were computed across all valid log subsets derived from seven geophysical features. Through additive marginalization, log-specific complexity scores were generated and compared with feature importance rankings from Random Forest models. A consistent inverse relationship emerged: logs with lower topological complexity (low ) tended to rank higher in predictive relevance. In all cases, Spearman correlations exceeded ) and were statistically significant, confirming the strength of this alignment. Notably, well (15/9-F-1 A) recorded the lowest correlation ( ) among individual wells due to the vertical imbalance in landmark coverage. However, its alignment improved to a perfect inverse ( ) when paired with a geologically stable neighbor, highlighting the method’s robustness to local heterogeneity. These findings confirm that persistent homology captures meaningful geometric structure in well log data and provides a scalable, interpretable, and architecture-independent approach to feature selection. The proposed framework remains effective under data constraints and geological variability, supporting its integration into real-time log prioritization and geoscientific modeling workflows.