Earthquake Source Processes inferred from a 6-meter-long laboratory fault (1) Quantitative Evaluation of Critical Nucleation Length under Variable Stress Drops

The critical nucleation length (L_c) is a fundamental parameter that characterizes the earthquake nucleation process and is theoretically proportional to the fracture energy and the inverse square of shear stress drop (Andrews, 1976, JGR). However, quantitative verification of this relationship has been limited due to difficulties in controlling the nucleation location and in achieving spatially dense measurements capable of resolving the nucleation extent and associated stress drop on the fault.

In this study, we conducted large-scale rock-friction experiments using the biaxial friction apparatus to investigate the scaling characteristics of the critical nucleation length L_c. The experimental configuration consists of vertically stacked Indian metagabbro blocks, comprising an upper block (L6.0 m × W0.5 m × H0.75 m ) and a lower block (L7.5 m × W0.5 m × H0.75 m ), forming a simulated fault with a nominal contact area of 6.0 m × 0.5 m. Strain gauges were installed at a distance of 15 mm from the fault surface with a spacing of 130 mm, and continuous measurements were recorded at a sampling rate of 1 MHz. Normal loading was applied using six independently controlled jacks, enabling controlled rupture nucleation confined within the fault and high-resolution measurements of local shear-stress time history.

To establish a robust measurement criterion for L_c based on rupture velocity evolution, we performed 2D dynamic rupture simulations using spectral boundary integral equation software UGUCA (Kammer et al., 2021) with a linear slip-weakening law. We compared the theoretical L_c predicted from the frictional parameters and prescribed initial stress with L_c inferred from rupture-velocity-based criteria. By varying the critical slip distance D_c, we simulated nucleation processes with different L_c values. The results show that the preslip extent at which the rupture velocity reaches approximately 0.06V_s (where V_s is shear-wave velocity) is in good agreement with the theoretically predicted L_c, supporting the use of this criterion for quantifying and discussing the scaling of L_c.

Applying this criterion to the laboratory experiments, the estimated L_c values range from 0.4 m to 4.0 m, spanning nearly one order of magnitude. The average local shear stress drop within the estimated nucleation region was evaluated as the difference between the initial and residual shear stresses measured before and after the main shock. We observed that L_c clearly scales with the inverse of the shear stress drop, rather than the inverse square, which persists under different normal stress conditions. This scaling is consistent with the observation that the initial shear stress is close to the peak strength in the nucleation region, under the assumption that D_c remains nearly constant among events (approximately 1 μm in this study). These findings provide insight into the quantitative dependence of L_c on the shear stress drop and place important constraints on our understanding of earthquake nucleation processes.