A Systematic Test of Time-to-Failure Analysis

Time-to-Failure analysis is a technique for predicting earthquakes in which a failure function is t to a time series of accumulated Benioo strain. Benioo strain is computed from regional seismicity in areas that may produce a large earthquake. We have tested the technique by tting two functions, a power-law proposed by Bufe & Varnes (1993) and a log-periodic function proposed by Sornette & Sammis (1995). We compared predictions from the two time-to-failure models to observed activity and to predicted levels of activity based upon the Poisson model. Likelihood ratios show that the most successful model is Poisson, with the simple Poisson model four times as likely to be correct as the best time-to-failure model. The best time-failure model is a blend of 90% Poisson and 10% log-periodic predictions. We tested the accuracy of the error estimates produced by the standard least-squares tter and found greater accuracy for ts of the simple power-law than for ts of the more complicated log-periodic function. The least-squares tter underestimates the true error in time-to-failure functions because the error estimates are based upon linearized versions of the functions being t.