Bruce E. Shaw | Searcharxiv

arXiv2007

Afterslip and aftershocks in the rate-and-state friction law

We study how a stress perturbation generated by a mainshock affects a population of faults obeying a rate-state friction law. Depending on the model parameters and on the initial state, the fault exhibits aftershocks, slow earthquakes, or decaying afterslip. We found several regimes with slip rate decaying as a power-law of time, with different characteristic times and exponents. The complexity of the model makes it unrealistic to invert for the friction law parameters from afterslip data. We modeled afterslip measurements for the Southern California Superstition Hills earthquake using the complete rate-and-state law, and found a huge variety of model parameters that can fit the observed data. In particular, it is impossible to distinguish the stable velocity strengthening regime (A>B) from the (potentially) unstable velocity weakening regime (B>A and stiffness k<kc). Therefore, it is not necessary to involve small scale spatial or temporal fluctuations of friction parameters A or B in order to explain the transition between stable sliding and seismic slip. In addition to B/A and stiffness k/kc, the fault behavior is strongly controlled by stress levels following an event. Stress heterogeneity can thus explain most of the variety of postseismic behavior observed in nature. Afterslip will induce a progressive reloading of faults that are not slipping, which can trigger aftershocks. Using the relation between stress and seismicity derived from the rate-and-state friction law, we estimate the aftershock rate triggered by afterslip. Aftershock rate does not simply scale with stress rate, but exhibits a different characteristic time and power-law exponent.

physics.geo-ph↗

arXiv2006

Relation between stress heterogeneity and aftershock rate in the rate-and-state model

We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994].We show that an exponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay of aftershocks with time ~1/t^p, with an exponent p=1-A sigma_n/tau_0, where A is a parameter of the rate-and-state friction law, and σ_n the normal stress. Omori exponent p thus decreases if the stress "heterogeneity" tau_0 decreases. We also invert the stress distribution P(tau) from the seismicity rate R(t), assuming that the stress does not change with time. We apply this method to a synthetic stress map, using the (modified) scale invariant "k^2" slip model [Herrero and Bernard, 1994]. We generate synthetic aftershock catalogs from this stress change.The seismicity rate on the rupture area shows a huge increase at short times, even if the stress decreases on average. Aftershocks are clustered in the regions of low slip, but the spatial distribution is more diffuse than for a simple slip dislocation. Because the stress field is very heterogeneous, there are many patches of positive stress changes everywhere on the fault.This stochastic slip model gives a Gaussian stress distribution, but nevertheless produces an aftershock rate which is very close to Omori's law, with an effective p<=1, which increases slowly with time. We obtain a good estimation of the stress distribution for realistic catalogs, when we constrain the shape of the distribution. However, there are probably other factors which also affect the temporal decay of aftershocks with time. In particular, heterogeneity of Aσ_n can also modify the parameters p and c of Omori's law. Finally, we show that stress shadows are very difficult to observe in a heterogeneous stress context.

physics.geo-ph↗