What Can Strong-Motion Data Tell Us about Slip-Weakening Fault-Friction Laws?

We consider the resolution of parameters, such as strength excess, r y r o , and slip-weakening distance, dc, 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 dc. Specifically, we use a new inversion method to find two rupture models, model A having dc 0.3 m and high-strength excess, and model B having dc 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 dc 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 dc and large-strength excess might be to assume that dc is long where there are no aftershocks.