Postseismic relaxation driven by brittle creep: A possible mechanism to reconcile geodetic measurements and the decay rate of aftershocks, application to the Chi-Chi earthquake, Taiwan

We evaluate the effect of coseismic stress changes on the fault slip at midcrustal depth, assuming a velocity-strengthening brittle creep rheology. We show that this model can help reconcile the time evolution of afterslip, as measured from geodesy, with aftershocks decay. We propose an analytical expression for slip of the brittle creeping fault zone (BCFZ) that applies to any dynamic or static stress perturbation, including shear stress and normal stress changes. The model predicts an initial logarithmic increase of slip with time. Postseismic slip rate decays over a characteristic time t_r=^aσ/_τ that does not depend on the amplitude of the stress perturbation, and it asymptotically joins the longterm creep imposed by interseismic stress buildup τ. Given that the seismicity rate might be considered proportional to the sliding velocity of the BCFZ, the model predicts a decay rate of aftershocks that follows Omori's law, with a mathematical formalism identical to that of Dieterich [1994] although based on a different mechanical rationale. Our model also differs from Dieterich's model in that it requires that aftershock sequences and deep afterslip, as constrained from geodetic measurements, should follow the same temporal evolution. We test this for the 1999 Chi-Chi earthquake, M_w=7.6 and find that both sets of data are consistent with a model of afterslip due to the response of the BCFZ. The inferred relaxation time t_r= 8.5 years requires a value for a - πtμ/πtlog(V)(μ being the coefficient of friction) in the range between 1.3 10^-3 and 10^-2.