Initiation and arrest of earthquake ruptures due to elongated overstressed regions

The initiation of natural and induced earthquakes is promoted in fault areas where shear stress is close to fault strength. In many real-world situations, these overstressed fault areas (or 'asperities') are very elongated; for example, in the case of a fault intersecting a reservoir subject to fluid-injection, or the stress concentration along the bottom of a seismogenic zone induced by deep fault creep. Theoretical estimates of the minimum overstressed asperity size leading to runaway rupture and of the final size of self-arrested ruptures are only available for 2-D problems and for 3-D problems with an asperity aspect ratio close to one. In this study, we determine how the nucleation of ruptures on elongated asperities, and their ensuing arrest, depends on the size and aspect ratio of the asperity and on the background stress. Based on a systematic set of 3-D dynamic rupture simulations assuming linear slip-weakening friction, we find that if the shortest asperity side is smaller than the 2-D critical length, the problem effectively reduces to a 2-D problem in which rupture nucleation and arrest are controlled by the shortest length of the asperity. Otherwise, nucleation and rupture arrest are controlled by the asperity area, with a minor exception: for asperities with shortest side slightly larger than the 2-D critical length, arrested ruptures are smaller than predicted by the asperity area. The fact that rupture arrest is dominantly controlled by area, even for elongated asperities, corroborates the finding that observed maximum magnitudes of earthquakes induced by fluid injection are consistent with the theoretical relation between the magnitude of the largest self-arrested rupture and the injected volume. In the context of induced seismicity, our simulations provide plausible scenarios that could be either favourable or challenging for traffic light systems and provide mechanical insights into the conditions leading to these situations.