Unsupervised Likelihood Inference of the b ‐Value via Magnitude Differences

Estimating the Gutenberg–Richter b ‐value from seismic catalogs is critical for earthquake forecasting and hazard assessment. However, traditional approaches rely on predefined magnitude thresholds and are highly sensitive to catalog incompleteness, limiting their applicability in automated or real‐time settings. We propose a novel, unsupervised inference framework that estimates the b ‐value directly from the distribution of positive magnitude differences , without requiring manual threshold tuning. By introducing a two‐parameter probabilistic model, we account for deviations from the ideal exponential form due to spatial and temporal variations in detection capability. This formulation enables a robust and scalable likelihood‐based estimation of both the b ‐value and a correction factor , which quantifies incompleteness. We validate our algorithm using synthetic catalogs generated from the ETAS model under varying noise and detection conditions, and apply it to global instrumental data sets from five tectonically active regions: Italy, Japan, Southern California, Northern California, and New Zealand. The results demonstrate high accuracy, robustness to incomplete data, and strong potential for integration into machine learning pipelines for seismic monitoring and hazard modeling.