What can strong-motion data tell us about slip-weakening fault-friction laws?

We consider the resolution of parameters, such as strength excess, sigma(y)-sigma(o), and slip-weakening distance, d(c), related to fault-constitutive properties, that may be obtained from the analysis of strong-ground motions. We show that wave;form inversion of a synthetic strong-motion-data set from a hypothetical M 6.5 event resembling the 1979 Imperial Valley earthquake cannot uniquely resolve both strength excess and d(c). Specifically, we use a new inversion method to find two rupture models, model A having d(c) = 0.3 m and high-strength excess, and model B having d(c) = 1 m and low-strength excess. Both models have uniform initial stress and the same moment-rate function and rupture time distribution, and they produce essentially indistinguishable ground-motion waveforms in the 0-1.6 Hz frequency band. These models are indistinguishable because there is a trade-off between strength excess and slip-weakening distance in controlling rupture velocity. However, fracture energy might be relatively stably estimated from waveform inversions. Our Models A and B had very similar fracture energies. If the stress drop is fixed by the slip distribution, the rupture velocity is controlled by fracture energy. We show that estimates of slip-weakening distance inferred from kinematic in version models of earthquakes are likely to be biased high due to the effects of spatial and temporal-smoothing constraints applied in such inverse-problem formulations. Regions of high-strength excess are often used to slow or stop rupture in models of observed earthquakes, but our results indicate that regions of long d(c) and lower strength excess might alternatively explain the slowing of rupture. One way to con strain d(c) would be to model ground-motion spectra at frequencies higher than those at which waveform modeling is possible. A second way to discriminate between regions of long d(c) and large-strength excess might be to assume that d(c) is long where there are no aftershocks.