Mariagiovanna Guatteri

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.

A Pseudo-Dynamic Approximation to Dynamic Rupture Models for Strong Ground Motion Prediction

Accurate prediction of the intensity and variability of strong ground motions from future large earthquakes depends on our ability to simulate realistic earthquake source models. We have developed a procedure to generate physically consistent earthquake-rupture models that should help make such simulations more accurate. We term these models “pseudo dynamic” because they are kinematic models that are designed to emulate important characteristics of dynamic rupture. We construct pseudo-dynamic models first by generating a slip distribution as a realization of a spatial random field that is consistent in its scaling and spatial variability with slip distributions observed in past earthquakes. We then compute the static stress drop associated with the slip distribution, which in turn is used to estimate the temporal evolution of slip through a set of empirical relationships derived from the analysis of spontaneous rupture models. Finally, a simple energy-budget calculation is used to eliminate models that are not likely to propagate spontaneously. The principal advantage of the pseudo-dynamic approach is that it avoids the computational demands of generating fully dynamic rupture models for multiple realizations of a scenario earthquake. While the relationships between source parameters described in this paper are simplifications of the true complexity of the physics of rupture, they help identify important interactions between source properties that are relevant for strong ground motion prediction, and should provide an improvement over purely kinematic models.

Inferring rate and state friction parameters from a rupture model of the 1995 Hyogo‐ken Nanbu (Kobe) Japan earthquake

We consider the applicability of laboratory-derived rate-and state-variable friction laws to the dynamic rupture of the 1995 Kobe earthquake. We analyze the shear stress and slip evolution of Ide and Takeos [1997] dislocation model, fitting the inferred stress change time histories by calculating the dynamic load and the instantaneous friction at a series of points within the rupture area. For points exhibiting a fast-weakening behavior, the Dieterich-Ruina friction law, with values of dc = 0.01–0.05 m for critical slip, fits the stress change time series well. This range of dc is 10–20 times smaller than the slip distance over which the stress is released, Dc, which previous studies have equated with the slip-weakening distance. The limited resolution and low-pass character of the strong motion inversion degrades the resolution of the frictional parameters and suggests that the actual dc is less than this value. Stress time series at points characterized by a slow-weakening behavior are well fitted by the Dieterich-Ruina friction law with values of dc≥0.01–0.05 m. The apparent fracture energy Gc can be estimated from waveform inversions more stably than the other friction parameters. We obtain a Gc ≈ 1.5×l06 J m−2 for the 1995 Kobe earthquake, in agreement with estimates for previous earthquakes. From this estimate and a plausible upper bound for the local rock strength we infer a lower bound for Dc of about 0.008 m.

Calculation of Broadband Time Histories of Ground Motion, Part II: Kinematic and Dynamic Modeling Using Theoretical Green's Functions and Comparison with the 1994 Northridge Earthquake

In the evolution of methods for calculating synthetic time histories of ground motion for postulated earthquakes, kinematic source models have dominated to date because of their ease of application. Dynamic models, however, which incorporate a physical relationship between important faulting parameters of stress drop, slip, rupture velocity, and rise time, are becoming more accessible. This article compares a class of kinematic models based on the summation of a fractal distribution of subevent sizes with a dynamic model based on the slip-weakening friction law. Kinematic modeling is done for the frequency band 0.2 to 10.0. Hz, dynamic models are calculated from 0.2 to 2.0. Hz. The strong motion data set for the 1994 Northridge earthquake is used to evaluate and compare the synthetic time histories. Source models are propagated to the far field by convolution with 1D and 3D theoretical Green’s functions. In addition, the kinematic model is used to evaluate the importance of propagation path effects: velocity structure, scattering, and nonlinearity. At present, the kinematic model gives a better broadband fit to the Northridge ground motion than the simple slip-weakening dynamic model. In general, the dynamic model overpredicts rise times and produces insufficient shorter-period energy. Within the context of the slip-weakening model, the Northridge ground motion requires a short slip-weakening distance, on the order of 0.15 m or less. A more complex dynamic model including rate weakening or one that allows shorter rise times near the hypocenter may fit the data better.

Stress drop for three M∼4.3-4.7 (1992-1994) Parkfield, CA, earthquakes

In a previous paper (Fletcher and Spudich, 1998) we determined the slip distribution for the three M∼4.3 to 4.7 Parkfield events that occurred between Oct. 20, 1992 and Dec. 20, 1994. The rupture characteristics of these events are of particular interest because they are the largest events to occur at Parkfield since the 1966 mainshock. To further investigate the rupture process of these events, we compute the static stress change or stress drop caused by the slip using a boundary integral method from Quin and Das (1989) adapted for the forward modeling case of computing stresses from a static slip distribution. We find that the initial phase at or very near the hypocenter has the largest stress change in all cases. This peak has a value of about 3.8 MPa for the Oct. 20, 1992 event (which also has the smallest magnitude of the three at 4.3) and about 45 MPa for the other Nov. 14, 1993 and 60 MPa for the Dec. 20, 1994 event. The rest of the stress release is comparatively small and smooth for the Nov. 14, 1993 event, which is the deepest event and the most impulsive. The pattern of stress release of the other two events (Oct. 20, 1992 and Dec. 20, 1994) is more complex with a greater spatial extent. The spatial distribution of stress is approximately similar to the spatial distribution of slip, but with the larger initial peak in stress drop at the hypocenter.