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FIG. 8. Estimation of the time of the earthquake by plotting the moment rate versus a variety of possible times to the earthquake and seeing which time gave the most linear plot.

creeping section at 2.5 months before the mainshock. Whether this is a detectable rate for a 1-km square patch on the fault with a sampling time of a few weeks depends on the sensitivity of the seismic system. It might be detectable by using the down-hole seismic array around Middle Mountain at Parkfield. By a day before the earthquake, the moment rate on the hypocentral cell increases by a factor of 60 over the rate corresponding to 35 mm/year, but the available sampling time to detect this is much smaller. If this increase in moment rate occurs only via a few discrete earthquakes, then the increasing moment rate may not be clearly seen as part of a gradually accelerating signal. These earthquakes would be foreshocks, but the pattern might not be clear enough for them to be recognized as such.

Thus the problems of predicting the model earthquake seem similar to the problems of predicting real earthquakes, even if preceded by foreshocks. Namely, how does one discriminate a pattern of increasing moment rate preceding the eventual mainshock when that increasing moment rate is strongly discretized. Some kind of temporaral averaging of the moment rate may be a solution, but the accelerating pattern could be lost in the averaging.

Conclusions. The behavior of the model Parkfield earthquakes discussed here is based on laboratory determinations of rock friction constitutive laws. The model earthquakes show premonitory slip prior to the eventual mainshock, but the spatial and temporal extent of it is relatively small. Like prediction of real earthquakes, the prediction of these model earthquakes is not an easy task. It is encouraging for the usefulness of the models that they are similar in many ways to the behavior of real faults. However, even if in principle one could predict the model earthquakes, this may be impossible in a realistic field setting. This is due to one’s inability to place instruments close enough to the accelerating part of the fault to detect the motions and to recognize an accelerating slip pattern when it occurs via discrete events.

The mainshock grows out of accelerating local creep and failure as the stress reaches sufficiently high levels, just as in the laboratory experiments. The modeling suggests that monitoring microseismicity may be the most sensitive way to detect the growing failure.

Much of the modeling on which this work is based was done in collaboration with William Stuart and I am grateful for his generosity in sharing his computer programs and his insight. My work was supported by U.S. Geological Survey Grants 1434–93-G-2278 and 1434–94-G-2422 and by National Science Foundation Grants EAR-88–16791, 9206649, 9220005, and 9317038.

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