Graph-based probabilistic earthquake clustering and forecasting in Sumatra

Earthquake clustering is a fundamental feature of seismicity and underpins many short-term forecasting models. However, conventional clustering techniques based on fixed space-time windows often fail in tectonically complex regions such as the Sumatra subduction zone, where seismicity is heterogeneous, offshore station coverage is sparse, and location uncertainties are substantial. Here, we develop a region-specific, physics-informed framework for clustering and forecasting earthquakes in Sumatra, combining stochastic modelling with empirical spatial and temporal constraints. We apply GRETAS (GRaph-based approach to ETAS), a graph-theoretical method based on the Epidemic-Type Aftershock Sequence (ETAS) model, enhanced with physically motivated filtering. Compared to traditional window-based methods, GRETAS produces more compact and physically consistent clusters, with improved performance measured by the Silhouette coefficient and Davies-Bouldin index. We also evaluate the forecasting potential of the Gutenberg-Richter b-value using a probabilistic, weighted version of the b-more-positive estimator, which accounts for classification uncertainty and magnitude incompleteness. Our results show no statistically significant difference in b-values between background and triggered events, and no consistent precursory trend prior to large earthquakes. These findings underscore the importance of probabilistic, regionally tailored approaches for robust seismic analysis in complex tectonic settings.