An equation of motion for unsteady frictional slip pulses

Frictional sliding, e.g., earthquakes along geological faults, are mediated either by frictional crack-like ruptures, where interfacial (fault) slip is accumulated during the entire sliding event, or by frictional pulse-like ruptures, featuring a finite length over which slip is accumulated. Our basic understanding of slip pulses, which are believed to dominate most crustal earthquakes, is still incomplete. Here, building on recent progress, we present an analytic equation of motion for rate-and-state frictional slip pulses, which are intrinsically unstable spatiotemporal objects, in terms of a single degree of freedom. The predictions of the equation are supported by large-scale simulations of growing pulses and reveal the origin of the slow development of their instability, which explains the dynamic relevance of pulses in a broad range of natural and manmade frictional systems.