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 motion s. We show that wave;form inversion of a synthetic strong-motion-data set f rom a hypothetical M 6.5 event resembling the 1979 Imperial Valley earthqua ke 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-str ength excess. Both models have uniform initial stress and the same moment-r ate function and rupture time distribution, and they produce essentially in distinguishable ground-motion waveforms in the 0-1.6 Hz frequency band. These models are indistinguishable because there is a trade-off between str ength excess and slip-weakening distance in controlling rupture velocity. H owever, fracture energy might be relatively stably estimated from waveform inversions. Our Models A and B had very similar fracture energies. If the s tress drop is fixed by the slip distribution, the rupture velocity is contr olled by fracture energy. We show that estimates of slip-weakening distance inferred from kinematic i n version models of earthquakes are likely to be biased high due to the eff ects 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 m odels of observed earthquakes, but our results indicate that regions of lon g 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 spectr a at frequencies higher than those at which waveform modeling is possible. A second way to discriminate between regions of long d(c) and large-strengt h excess might be to assume that d(c) is long where there are no aftershock s.