On the coupled geometrical-mechanical origin of the earthquake b-value in fault networks

Abstract: The Gutenberg-Richter law is a fundamental empirical law in seismology describing earthquake frequency-magnitude distributions, with one of its key parameters, the so-called b-value, quantifying the relative frequency of small versus large events. While the b-value is commonly interpreted as reflecting crustal heterogeneity and regional stress conditions, its underlying physical origin remains poorly understood, particularly the relative roles of geometrical versus mechanical controls. Here, we develop analytical and numerical models to elucidate the origin of the b-value in three-dimensional fault networks subject to mainshock-aftershock sequences. We demonstrate that the b-value emerges from the power-law scaling of fault rupture area together with the scaling of slip magnitude. Our results reveal a two-branch frequency-magnitude distribution, with the regime transition governed by fault criticality and fracture energy dissipation, while the transition magnitude reflects the finite population of faults triggered during the sequence. Our findings provide a physically grounded interpretation of earthquake b-values, establishing a link between fault mechanics and earthquake statistics.