Physics-based models indicate a combined geometrical and mechanical origin of the b-value of earthquake aftershocks

The spatiotemporal characteristics and magnitude distributions of earthquake aftershocks provide critical insights into the dynamical processes within the Earth’s crust, carrying significant implications for seismic hazard assessment and mitigation. For example, the well-known Gutenberg-Richter law has been applied to characterize the frequency-magnitude distribution of aftershocks, with the b-value that reflects the relative frequency of small versus large events giving valuable information about heterogeneous crustal structures and regional stress conditions. Although great efforts have been made to study the mechanisms behind the b-value, no consensus has been reached, especially regarding its geometrical versus mechanical origin. Here, we develop physics-based analytical and numerical models to uncover the b-value’s origin within a fault network undergoing a mainshock-aftershock sequence. The analytical model relates the b-value to the power law exponents of the fault frequency-length distribution and the length-displacement scaling relation. High-fidelity 3D direct numerical simulations are then employed to model intricate mainshock-aftershock sequences in fault networks. In the model, the mainshock rupture initiated by a small stress drop at the hypocenter propagates spontaneously along the mainshock fault, triggering extensive aftershocks on spatially distributed secondary faults that obey a power law size scaling. The rupture and slip dynamics within the fault network assume a slip-weakening law captured by a static/kinetic friction model. We study aftershock statistics across various scenarios with different critical distances, which all show a two-branch frequency-magnitude scaling pattern. Through the analytical and numerical solutions, we show that the first branch of small-magnitude earthquakes, characterized by a lower b-value, is related to the faults that are partially-ruptured, while the second branch of large-magnitude earthquakes, with a higher b-value, is associated with faults that are (nearly) fully-ruptured. This provides a new perspective to interpret the commonly observed break in Gutenberg-Richter law that is conventionally attributed to catalogue incompleteness. We further interpret the mechanisms driving the emergence of this two-branch scaling statistics based on considerations of the energy budget. For events in the first branch, a significant portion of the available energy is dissipated as fracture energy, reducing the portion that sustains rupture propagation and leading to rupture arrest within a small area; for events belong to the second branch, only a small portion of the available energy is dissipated as fracture energy, leaving sufficient energy to drive spontaneous rupture and enabling faults to be fully ruptured. These findings and insights have important implications for understanding the origin of the b-value of earthquake aftershocks in the Earth’s crust.