An Advanced Statistical Method to Unravel the Temporal Evolution of <i>b</i> -Value

Abstract The b-value (i.e., the slope of the Gutenberg–Richter magnitude–frequency distribution) has been reported as a potential seismic precursor, implying that its variation over time can provide diagnostic information about the imminent occurrence of large earthquakes. However, careful data analysis and rigorous statistical approaches are essential, as the estimation of the b-value—and, more importantly, the windowing process—is strongly affected by statistical noise and biases. This study proposes a methodology to optimize b-value time series to effectively unravel seismogenic changes from statistical fluctuations. We implement a time-based moving-window approach and assess the significance of b-value variations (through lag-one autocorrelation analysis) to initially capture a global view (i.e., large-scale view obtained with nonoverlapping windows) of the temporal evolution of the b-value. To reveal the small-scale variations, the time series is subsequently refined by applying window overlapping, which provides higher temporal resolution. The procedure yields a reference configuration (window size and overlapping percentage) for which the resulting b-value variations are statistically robust and physically interpretable, in agreement with empirical expectations.