Episodic slow slip events and rate-and-state friction
There are several ways of generating episodic slow slip events in models of rate-and-state friction. Here I explore the possibility that they arise on velocity-weakening faults whose length is "tuned" in some sense. Unlike spring-block sliders, which have a unique critical stiffness for instability, elastically deformable faults have multiple length scales (stiffnesses) relevant to nucleation. Slow slip events occur when the fault is large enough to initiate an event but too small for that event to reach dynamic instability. The available window of lengths depends upon the effective fracture energy of the growing nucleation zone. For the "aging" evolution law this fracture energy increases rapidly with slip speed, and the range of permissible lengths increases nearly as b/(b - a), where a and b are the coefficients of the velocity and state dependence of the frictional strength. This range becomes very large for faults that are near velocity-neutral (a - b). However, existing lab data firmly favor the "slip" law as a predictor of nucleation style, and for this law the effective fracture energy increases much less rapidly with slip speed. The range of fault lengths capable of hosting slow slip events in this case seems too small to explain why they are common to so many subduction zones. Slow slip can be stabilized over an exceedingly large range of fault lengths if the fracture energy increases with slip speed much more rapidly than for the aging law. An appealing mechanism is inelastic dilation of the fault zone coupled with pore pressure reduction and diffusive recovery.