Multiscale Fractal Feature Extraction and Identification of Fracture Images Using Complexity-Adaptive Box-Height Differential Box-Counting and SOM

Fractures exhibit complex spatial structures and multiscale geometric characteristics, and their accurate characterization is fundamental to reservoir evaluation, fluid migration analysis, and rock mechanics. To address the limitations of single-scale local fractal methods in simultaneously capturing fracture details and global structures, as well as the dependence of supervised learning on labeled data, this study proposes an unsupervised fracture identification method integrating Complexity-Adaptive Box-Height Differential Box-Counting (CABH-DBC) with a self-organizing map (SOM). Local fractal features are extracted using fixed multiscale windows, while the box height along the gray-level dimension is adaptively refined according to the local grayscale standard deviation. The multiscale features are then fed into the SOM for clustering, with grayscale information assisting in fracture-cluster determination. Experiments on borehole image logs from ten depth intervals of the CCSD main borehole yield mean F1 and IoU values of 0.659 and 0.493, respectively. Compared with DBC-Kmeans, the proposed method improves F1 and IoU by 39.0% and 58.0%, respectively; compared with DBC-SOM, the strongest baseline in this study, the improvements are 16.6% and 24.8%. Ablation experiments further demonstrate the complementary contributions of complexity-adaptive box-height refinement, fixed multiscale fractal features, and SOM clustering.