We test the concept that seismicity prior to a large earthquake can be
understood in terms of the statistical physics of a critical phase tr
ansition. In this model, the cumulative seismic strain release increas
es as a power law time to failure before the final event. Furthermore,
the region of correlated seismicity predicted by this model is much g
reater than would be predicted from simple elastodynamic interactions.
We present a systematic procedure to test for the accelerating seismi
city predicted by the critical point model and to identify the region
approaching criticality, based on a comparison between the observed cu
mulative energy (Benioff strain) release and the power law behavior pr
edicted by theory. This method is used to find the critical region bef
ore all earthquakes along the San Andreas system since 1950 with M gre
ater than or equal to 6.5. The statistical significance of our results
is assessed by performing the same procedure on a large number of ran
domly generated synthetic catalogs. The null hypothesis, that the obse
rved acceleration in all these earthquakes could result from spurious
patterns generated by our procedure in purely random catalogs, is reje
cted with 99.5% confidence. An empirical relation between the logarith
m of the critical region radius (R) and the magnitude of the final eve
nt (M) is found, such that log R proportional to 0.5M, suggesting that
the largest probable event in a given region scales with the size of
the regional fault network.