Effects of a revised rate- and state-dependent friction law on aftershock triggering model

Tectonophysics (2012), http://dx.doi.org/10.1016/j.tecto.2012.11.028

Nobuki Kame, Satoshi Fujita, Masao Nakatani, Tetsuya Kusakabe

Abstract

Seismicity may be considered as a sequence of earthquake nucleation events controlled by regional loading history. On the basis of this concept, Dieterich (1994) modeled aftershock seismicity following an imposed stress step, by using a laboratory-derived rate- and state-dependent friction law (RSF). Although this model predicts the canonical 1/t decay of aftershock rate, two huge gaps from observations are known; the model, with frictional parameters assumed to be laboratory-observed values, predicts too low aftershock productivity and also too long a delay before the decay onset. These gaps are by orders of magnitude. We suspected that the problem might be the incorrectness of traditional RSFs, none of which was free from contradictions with laboratory data. Hence we modeled aftershock triggering with a revised RSF ( Nagata et al., 2012 ), which seems to have resolved the previously known flaws in reproducing laboratory data. The original analytic approach of Dieterich (1994) was found invalid for the revised RSF, so we did an equivalent analysis by numerically tracking individual nucleation sources. The revised RSF produced generally similar aftershock seismicity, with the gaps mentioned above narrowed by a factor, though these are far too small improvements of the huge gaps, that is, the revised RSF did not fully resolve the problem. On the other hand, our simulations found a counterintuitive response of a fault obeying the revised RSF; if imposed during a certain stage in the seismic cycle, a positive stress step can cause oscillatory slow slip events before eventual seismic instability, instead of a usual response of further monotonic acceleration to seismic instability. This delays the timing of the next earthquake. Due to this behavior, the exponent of the aftershock decay can be greater than unity. Also, the decay can once overshoot below the background seismicity before eventually returning to the background level.