Physics-Informed Neural Networks for 3D Seismic Fault Segmentation with Topological and Geological Priors

Seismic fault interpretation is a critical task for subsurface modeling and resource exploration. Although data-driven deep learning methods have shown considerable potential in automating fault segmentation, they often suffer from poor generalizability, limited interpretability, and physical inconsistency. To address these challenges, we present the first adaptation of the Physics-Informed Neural Network (PINN) paradigm to the seismic fault detection domain, proposing a modular loss function framework that encodes domain-specific constraints into network training. Specifically, the framework includes: (i) a physics-informed loss that uses the steady-state Allen–Cahn residual as a curvature-regularization (surface-tension) prior to sharpen and smooth fault interfaces; (ii) a topology-informed loss that penalizes departures from target Betti numbers via persistent homology, promoting a single connected, hole-free surface; and (iii) a geology-informed loss combining total variation, dip-angle smoothness, local connectivity, and branch suppression to encourage structurally coherent, geologically plausible predictions.  This modular loss design is architecture-agnostic and can be seamlessly applied to any segmentation backbone. Experimental results on synthetic 3D seismic datasets demonstrate consistent improvements across four representative architectures (CNN, U-Net, ViT, and a Transformer-embedded U-Net), yielding higher accuracy, precision, recall, and F1-score. Qualitative analyses further confirm the generation of more continuous fault structures with reduced artifacts. Application to field seismic data validates the practical effectiveness of the proposed framework in enhancing geological interpretability. These findings underscore the value of embedding domain knowledge into loss functions as a principled and generalizable approach for improving the reliability of deep learning–based seismic fault interpretation.