Revisiting Seismicity Criticality: A New Framework for Bias Correction of Statistical Seismology Model Calibrations

Abstract

The Epidemic-Type Aftershock Sequences (ETAS) model and its variants effectively capture the space-time clustering of seismicity, setting the standard for earthquake forecasting. Accurate unbiased ETAS calibration is thus crucial. But we identify three sources of bias, (a) boundary effects, (b) finite-size effects, and (c) censorship, which are often overlooked or misinterpreted, causing errors in seismic analysis and predictions. By employing an ETAS model variant with variable spatial background rates, we propose a method to correct for these biases, focusing on the branching ratio n, a key indicator of earthquake triggering potential. Our approach quantifies the variation in the apparent branching ratio (n_app) with increased cut-off magnitude (M_co) above the optimal cut-off ($M_{\text{co}}^{\text{best}}$), which is considered the best threshold for balancing catalog completeness and the amount of available data. The n_app(M_co) function yields insights superior to traditional point estimates. We validate our method using synthetic earthquake catalogs, accurately recovering the true branching ratio (n_true) after correcting biases with n_app(M_co). Additionally, our method introduces a refined estimation of the minimum triggering magnitude (m₀), a crucial parameter in the ETAS model. Applying our framework to the earthquake catalogs of California, New Zealand, the China Seismic Experimental Site in Sichuan and Yunnan provinces, and Noto Peninsula in Japan, we find that seismicity hovers away from the critical point, n_c = 1, remaining distinctly subcritical, however with values tending to be larger than recent reports that do not consider the above biases. Understanding seismicity's critical state significantly enhances our comprehension of seismic patterns, aftershock predictability, and informs earthquake risk mitigation and management strategies.