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

Abstract

We consider the resolution of parameters, such as strength excess, r y ‫מ‬ r 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 waveform 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 ‫ס‬ 0.3 m and high-strength excess, and model B having d c ‫ס‬ 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 inversion 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 constrain 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.

Dynamic modeling of the 1992 Landers earthquake

“…Dynamic source parameters are often difficult to estimate because of their strong nonlinearity [Guatteri and Spudich, 2000]. Our results suggest that ther variable initial stress or variable yield stress.…”

Constitutive parameters for earthquake rupture dynamics based on high-velocity friction tests with variable sliprate

“…1). Guatteri and Spudich (2000) demonstrated that for band-limited analyses of seismic waveforms, slip weakening distance may not be determined uniquely and high frequency waves are required, which are usually difficult to be extracted from observed seismograms because of the heterogeneity of the crust. Instead, it is pointed out that seismological fracture energy can be estimated stably (Ide 2002;Tinti et al 2005b) because the seismological fracture energy is an integration quantity.…”

The dependence of traction evolution on the earthquake source time function adopted in kinematic rupture models

“…The dynamic traction evolution is commonly inferred from kinematic rupture models with the ambition to constrain the fault constitutive behavior [Ide and Takeo, 1997;Guatteri and Spudich, 2000]. Ground motion time histories are inverted to image a kinematic rupture model.…”

“…In the present study we aim to understand if the source time functions adopted in kinematic models can bias the retrieved dynamic parameters and partially explain the variability of D c estimates. Guatteri and Spudich [2000] also emphasized the limitations in estimating the critical slip weakening distance by modeling ground motion waveforms. In particular, they concluded that both the adoption of spatial and temporal smoothing constraints in the formulation of the inverse problem and the modeling of low-frequency seismic waves can bias the inferred values of D c .…”