Abstract
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.
Highlights
A better understanding of what controls nucleation and arrest of earthquake ruptures is naturally important
Our results extend and complement previous research on rupture nucleation and arrest based on fracture mechanics (e.g. Ampuero et al 2006; Ripperger et al 2007; Galis et al 2015) including those developed in the context of induced seismicity but limited to 2-D (Garagash & Germanovich 2012; Dempsey & Suckale 2016; Azad et al 2017) or to 3-D with asperity aspect ratio near 1 (Galis et al 2017)
The absence of ruptures arrested outside the asperity eliminates a potential precursor to runaway ruptures, which poses a particular challenge for traffic light systems (TLSs). (3) The sensitivity of the system to relatively mild changes of width b together with higher permeability along a fault imply that the transitions from asperity-confined ruptures to ruptures self-arrested outside the asperity and to runaway ruptures could occur faster in the second scenario than in the first one, posing another challenge for TLSs
Summary
A better understanding of what controls nucleation and arrest (and magnitude) of earthquake ruptures is naturally important. Galis et al (2017) applied a theoretical 3-D model of rupture arrest to induced seismicity They considered earthquakes initiated over a limited fault area (hereafter referred to as an asperity), weakened by an increased pore fluid pressure to investigate how large ruptures may grow. Ruptures that nucleated on deep stress concentrations may remain confined at depth without breaking the entire fault width like, for example, the 2015 M7.8 Gorkha, Nepal earthquake (Avouac et al 2015; Michel et al 2017) Such partial ruptures may be examples of self-arrested ruptures that precede a larger event (Galis et al 2017). The Appendices A and B present a derivation of critical lengths for runaway rupture in 2-D and their verification using numerical simulations and Appendix C presents a summary of equations for determining conditions for runaway ruptures and rupture arrest
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