Fault instability on a finite and planar fault related to early phase of nucleation

Abstract

We numerically investigate the early phase of nucleation on a planar fault with the rate- and state-dependent friction law, loaded externally by steady slip, to clarify its relation to fault instability. We define R[n] as the invasion distance of the inward creep to characterize that phase. For a circular fault, the dependence of R[n] on the dimensionless parameters l[b], l[b−a], and l[RA] (all of these are proportional to the rigidity and the characteristic distance of the state evolution L and inversely proportional to the normal stress and the fault radius) can be compiled. We found that Rn is proportional to l[b] (both aging law and slip law of the state evolution) and l[b−a] (aging law). In the case of the aging law only, there are two regimes (ordinary events and slow events) separated by the value of l[RA]. The regimes have different trend lines, although we could not measure Rn for the case of l[RA] < 0.35 because of breaking of the mirror symmetry of instability along the loading direction. R[n] in the slow event regime is smaller. Moreover, we investigated the effect of fault shape and found that a model with a long radius along the mode 2 direction has similar parameter dependence to circular faults, but a model with a long radius along the mode 3 direction has different ones. Our results imply that we can qualitatively estimate the fault instability parameters from the early phase of nucleation, although further research is necessary to enable application to actual faults.