be larger than the prior event, which by definition makes the prior event a foreshock (37). The other proposed mechanism for foreshocks is that premonitory processes, perhaps the fault creep related to mainshock nucleation, result in stress changes that drive the foreshock process in surrounding areas. Models based on state-dependent earthquake rates indicate that both mechanisms are in general agreement with time and distance statistics of foreshock-mainshock pairs (38).

Short-term clustering, as manifest in foreshock-mainshock pairs and aftershocks, attests to large but transient changes in the probabilities of additional earthquakes that occur whenever an earthquake takes place. The concepts of stress interaction and state-dependent seismicity permit physically based calculations of earthquake probability following large earthquakes (39). This approach has been used to evaluate the changes in earthquake probability that arose as a consequence of stress interactions along the Anatolian fault in Turkey (40) and following the M 6.9 earthquake that struck Kobe, Japan, in 1995 (41).

Accelerating Seismicity and Intermediate-Term Prediction A central issue for earthquake prediction is the degree to which the seismicity clustering can be used to monitor the stress changes leading to large earthquakes. Various studies have shown that large earthquakes tend to be preceded by clusters of intermediate-sized events (42). This increase in seismicity can be fit to a time-to-failure equation in the form of a power law, which is commonly used by engineers to describe progressive failures that result from the accumulation of structural damage (43). The power-law time-to-failure equation is also expected if large earthquakes represent critical points for regional seismicity (44).

As described in Section 5.1, regional seismicity has many of the characteristics of a self-organized critical system, including power-law (Gutenberg-Richter) frequency-size statistics and fractal spatial distributions of hypocenters. However, the near-critical behavior of fault systems is the subject of some debate. If the crust continuously maintains itself in a critical state, as originally proposed by Bak and Tang, then all small earthquakes will have the same probability of growing into a big event. This hypothesis has been used as the physical basis for assertions that earthquake prediction is inherently impossible (45). Alternatively, the crust could repeatedly approach and retreat from a critical state. The working hypotheses for this latter view are (1) large regional earthquakes become more probable when the stress field becomes correlated over increasingly larger distances, (2) this approach to a critical state is reflected in an acceleration of regional seismicity, and (3) a system-spanning event destroys criticality on its network, creating a period of relative quiescence after which the process repeats by rebuilding correlation

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