Results

In Figure 2.4 we show the slip model. This model has a rise time of 0.008 seconds, and a rupture velocity of 1.8 km/s (78% of the local shear wave velocity), the median from models within 2% of the peak fit. The allowable range in the kinematic parameters given this level of fit is 1.2-2.3 km/s (52-100% of the shear wave velocity) in rupture velocity, and 0.004 to 0.012 seconds for rise time. Within this population of solutions there is a tradeoff in the rise time and rupture velocity where long rise times are associated with fast rupture velocities (or short rupture times), and vice versa. It is notable that the obtained rise time is more consistent with a slip pulse rather than crack-like rupture, and the slip velocity inferred from the ratio of slip to rise time is 167 cm/s, consistent with values obtained for larger events. There is a dominant asperity in which the slip is found to be extremely concentrated, roughly circular with a diameter of about 40 m with a peak (8.6 cm) at the center, which is similar to the 6.6 cm inferred by Nadeau and Johnson (1998).

Because the slip distribution is non-uniform, we use the method of Ripperger and Mai (2004), shown to be consistent with static or dynamic elastic dislocation models, to determine the coseismic stress change (stress drop). This method maps the spatially variable slip on the fault to the spatially variable stress change, or stress drop. Results applied to the SAFOD target event are shown in Figure 2.4B. In regions of high slip, the stress change is positive indicating a stress drop during rupture. The method also determines the degree of stress increase (negative stress change) on the region surrounding the rupture. The model has a peak stress drop of 80 MPa, and averages ranging from 3.7-19.7MPa depending on how the average is calculated.

The very high stress drop we obtain for much of the rupture area of the SAFOD repeaters (Figure 2.4B) is at odds with more traditional spectrally-based estimates (e.g. Imanishi et al., 2004). However, the stress drop averaged from Figure 2.4B over areas with positive stress drop is only 11.6 MPa, which is close to the Imanishi et al. (2004) result. On the other hand, the spatially variable high stress drop we obtain is required to fit the shape of the moment rate functions, and the peak is closer to the estimate obtained using the method of Nadeau and Johnson (1998). Thus, the finite-source results reconcile these disparate estimates of stress drop, illustrating that the two methods are apparently sensitive to different aspects of the rupture.

Assuming an average density of 2000 kg/$m^3$, hydrostatic pore pressure and a coefficient of friction of 0.4 gives a maximum frictional strength of only 7.8MPa at the depth of the events. On the other hand, it has been proposed that small dimension asperities with strength approaching that of intact rock can concentrate substantial stress levels (Nadeau and Johnson, 1998). High stress drop repeating earthquakes may represent those relatively isolated, small-scale, contact points where large stress concentrations can develop and be released on a fairly regular basis. The much larger fault areas of bigger earthquakes may be frictionally weak, but studded with sparsely distributed high strength asperities producing relatively low average stress-drops during large earthquake rupture.