Scaling of stress drop with recurrence interval and loading velocity for laboratory-derived fault strength relations

[1] The dynamics of a spring-slider system with a single degree of freedom was investigated, focusing on two different rate-and state-dependent friction laws. While the inertia-controlled behavior and stick-slip cycles for a system that obeys the slip law have been extensively simulated, this study presents a comparative study of a system that obeys the slowness law. A key conclusion is that for both friction laws the overall stress drops are linearly related to the logarithm of the loading velocity ( and the recurrence time) through the velocity-weakening parameter b - a and normal stress. Relatively higher peak stresses, larger quasi-static stress drop, and larger effective fracture energy are associated with a system that obeys the slowness law. Consequently, the partitioning of stress drop between quasi-static and dynamic slips, as well as dynamic overshoot and strength recovery, varies according to whether the slowness or slip law has been adopted. Analytic approximations were derived that elucidate the interplay of dynamics, energetics, and frictional constitutive behavior in controlling the scaling of stress drops with loading velocity and recurrence time. Seismological implications of the scaling behavior are also discussed.