The Scaling of the Slip Weakening Distance (Dc) With Final Slip During Dynamic Earthquake Rupture

Several numerical approaches have been recently proposed to retrieve the evolution of dynamic traction during the earthquake propagation on extended faults. Although many studies have shown that the shear traction evolution as a function of time and/or slip may be complex, they all reveal an evident dynamic weakening behavior during faulting. The main dynamic parameters describing traction evolution are: the yield stress, the residual kinetic stress level and the characteristic slip weakening distance Dc. Recent investigations on real data yield the estimate of large Dc values on the fault plane and a correlation between Dc and the final slip. In this study, we focus our attention on the characteristic slip weakening distance Dc and on its variability on the fault plane. Different physical mechanisms have been proposed to explain the origin of Dc, some of them consider this parameter as a scale dependent quantity. We have computed the rupture history from several spontaneous dynamic models imposing a slip weakening law with prescribed Dc distributions on the fault plane. These synthetic models provide the slip velocity evolution during the earthquake rupture. We have therefore generated a set of slip velocity models by fitting the "true" slip velocity time histories with an analytical source time function. To this goal we use the Yoffe function [Tinti et al. 2005], which is dynamically consistent and allows a flexible parameterization. We use these slip velocity histories as a boundary condition on the fault plane to compute the traction evolution. We estimate the Dc values from the traction versus slip curves. We therefore compare the inferred Dc values with those of the original dynamic models and we found that the Dc estimates are very sensitive to the adopted slip velocity function. Despite the problem of resolution that limits the estimate of Dc from kinematic earthquake models and the tradeoff that exists between Dc and strength excess, we show that to correctly retrieve the original Dc it is necessary to reproduce the details of the slip velocity function. In particular, the fast slip positive acceleration, the peak slip velocity and its duration.