Unsteady slip pulses under spatially-varying prestress

Abstract

It has been recently established that self-healing slip pulses under uniform background/ambient stress (prestress) ${\tau }_b$ are intrinsically unstable frictional rupture modes, i.e., they either slowly expand or decay with time t. Furthermore, their spatiotemporal dynamics have been shown to follow a reduced-dimensionality description corresponding to a special one-dimensional curve $L\left(c\right)$, parameterized by ${\tau }_b$, in a plane defined by the pulse propagation velocity $c\left(t\right)$ and size $L\left(t\right)$. Yet, uniform prestress is rather the exception than the rule in natural faults. Here, we study the effects of a spatially-varying prestress ${\tau }_b\left(x\right)$ (in the fault direction x) on 2D slip pulses, initially generated under a uniform ${\tau }_b$ along a rate-and-state friction fault. We consider both periodic and constant-gradient prestress distributions ${\tau }_b\left(x\right)$ around the reference uniform ${\tau }_b$. For a periodic ${\tau }_b\left(x\right)$, pulses either sustain and form quasi-limit cycles in the $L-c$ plane or decay predominantly monotonically along the $L\left(c\right)$ curve depending on the instability index of the initial pulse and the properties of the periodic ${\tau }_b\left(x\right)$. For a constant-gradient ${\tau }_b\left(x\right)$, expanding and decaying pulses closely follow the $L\left(c\right)$ curve, with small systematic shifts determined by the sign and magnitude of the gradient. We also find that a spatially-varying ${\tau }_b\left(x\right)$ can revert the expanding/decaying nature of the initial reference pulse. Finally, we show that a constant-gradient ${\tau }_b\left(x\right)$, of sufficient magnitude and specific sign, can lead to the nucleation of a back-propagating rupture at the healing tail of the initial pulse, generating a bilateral crack-like rupture. This pulse-to-crack transition, along with the above-described effects, demonstrates that rather rich rupture dynamics can emerge from a simple, spatially-varying prestress. Furthermore, our results show that as long as pulses exist, their spatiotemporal dynamics are related to the special $L\left(c\right)$ curve, providing an effective, reduced-dimensionality description of unsteady slip pulses under spatially-varying prestress.