Asperity Models for Earthquakes

A quasi-static numerical method was used to simulate the failure of a strong stuck asperity on an otherwise creeping fault plane. The numerical model produced the same slip distribution as analytical asperity models, which, for constant loading rate, produced repeating events having a period T that scales with moment M0 as T (alpha)M(1/6)(0) , the scaling relation observed by Nadeau and Johnson (1998) at Parkfield. When the asperity is a composite of smaller hard unit asperities, we still find T(alpha)M(1/6)(0) but the constant of proportionality depends on the density of unit asperities within the cluster. Since only clusters with a fixed asperity density follow the observed T(alpha)M(1/6)(0) scaling, this result rules out the fractal spatial distribution (Cantor dust) of unit asperities at Parkfield suggested by Sammis et al. (1999). For solid asperities, the average stress drop on the asperity is on the order of 100 MPa, but the average stress drop over the entire rupture area is significantly lower, equivalent to that estimated from spectral analysis. However, the stress drop for asperity models is not independent of seismic moment but decreases with earthquake size. The energy release rate for asperity events is estimated to be g(greater-than or equivalent)10^7 J/m^2, near the upper limit of estimates by Li (1987) using parameters from large events on the San Andreas Fault.