Deep Hierarchical Graph Correlation: A Two-Stage Approach to Well-Log Alignment Using CNNs and Dynamic Programming

Precise depth alignment of well logs is essential for reliable subsurface characterization, enabling accurate correlation of geological features across multiple wells. This study presents the Deep Hierarchical Graph Correlator (DHGC), a two-stage deep learning framework for scalable and automated well-log depth alignment. DHGC aligns a target log to a reference log by comparing fixed-size windows extracted from both signals. In the first stage, a one-dimensional convolutional neural network (1D CNN) trained on 177,026 triplets using triplet-margin loss learns discriminative embeddings of gamma-ray (GR) log windows from eight Norwegian North Sea wells. In the second stage, a feedforward scoring network evaluates embedded window pairs to estimate local similarity. Dynamic programming then computes the optimal nonlinear warping path from the resulting cost matrix. The feature extractor achieved 99.6% triplet accuracy, and the scoring network achieved 98.93% classification accuracy with an ROC-AUC of 0.9971. Evaluation on 89 unseen GR log pairs demonstrated that DHGC improves the mean Pearson correlation coefficient from 0.35 to 0.91, with successful alignment in 88 cases (98.9%). DHGC achieved an 8.2× speedup over DTW (3.16 s versus 25.83 s per log pair). While DTW achieves a higher mean correlation (0.96 versus 0.91), DHGC avoids singularity artifacts and exhibits lower variability in distance metrics than CC, suggesting improved robustness and scalability for well-log synchronization.