The Impact of Frictional Healing on Stick-Slip Recurrence Interval and Stress Drop: Implications for Earthquake Scaling

Interseismic frictional healing is an essential process in the seismic cycle. Observations of both natural and laboratory earthquakes demonstrate that the magnitude of stress drop scales with the logarithm of recurrence time, which is a cornerstone of the rate and state friction (RSF) laws. However, the origin of this log linear behavior and short time cutoff for small recurrence intervals remains poorly understood. Here we use RSF laws to demonstrate that the back-projected time of null-healing intrinsically scales with the initial frictional state (i). We explore this behavior and its implications for (1) the short-term cutoff time of frictional healing and (2) the connection between healing rates derived from stick-slip sliding versus slide-hold-slide tests. We use a novel, continuous solution of RSF for a one-dimensional spring-slider system with inertia. The numerical solution continuously traces frictional state evolution (and healing) and shows that stick-slip cutoff time also scales with frictional state at the conclusion of the dynamic slip process (i) (=D-c/V-peak). This numerical investigation on the origins of stick-slip response is verified by comparing laboratory data for a range of peak slip velocities. Slower slip motions yield lesser magnitude of friction drop at a given time due to higher frictional state at the end of each slip event. Our results provide insight on the origin of log linear stick-slip evolution and suggest an approach to estimating the critical slip distance on faults that exhibit gradual accelerations, such as for slow earthquakes.