We estimate the critical slip-weakening distance on earthquake faults by using a new approach, which is independent of the estimate of fracture energy or radiated seismic energy. The approach is to find a physically based relation between the breakdown time of shear stress Tb, the time of peak slip-velocity Tpv, and the slip-weakening distance Dc, from the time histories of shear stress, slip, and slip velocity at each point on the fault, which can be obtained from dynamic rupture calculations using a simple slip-weakening friction law. Numerical calculations are carried out for a dynamic shear crack propagating either spontaneously or at a fixed rupture velocity on a vertical fault located in a 3D half-space and a more realistic horizontally layered structure, with finite-difference schemes. The results show that Tpv is well correlated with Tb for faults even with a heterogeneous stress-drop distribution, except at locations near strong barriers and the fault edges. We also investigate this relation for different types of slip-weakening behavior.
We have applied the method to two recent, strike-slip earthquakes in western Japan, the 2000 Tottori and the 1995 Kobe events. We integrated the slip-velocity functions on the vertical fault obtained from kinematic waveform inversion of strong-motion and teleseismic records from the arrival time of rupture Tr to the time of the peak-slip velocity Tpv, and we then corrected the slip obtained at Tpv for the errors expected from the dynamic calculations. It was found that the slip-weakening distance Dc estimated in the frequency window between 0.05 and 0.5 Hz ranges between 40 and 90 cm on the two earthquake faults. However, if we consider the limited frequency resolution of the observed waveforms, probable time errors in the slip-velocity functions obtained from kinematic inversion, and the uncertainty of the slip-weakening behavior, the above estimates may be those located between the minimum resolvable limit and the upper bound of their real values. The estimated Dc values do not necessarily seem to indicate larger values in the shallower part and smaller values in the deeper part of the fault, but rather a spatially heterogeneous distribution that appears to be dependent on the local maximum slip. This possible dependence might be interpreted by the frictional properties of the fault such as the degree of roughness or the thickness of gouge layers, in addition to stress heterogeneities.