A systematic test of time-to-failure analysis

Time-to-failure analysis is a technique for predicting earthquakes in which a failure function is fit to a time-series of accumulated Benioff strain. Benioff strain is computed from regional seismicity in areas that may produce a large earthquake. We have tested the technique by fitting 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 per cent Poisson and 10 per cent log-periodic predictions. We tested the accuracy of the error estimates produced by the standard least-squares fitter and found greater accuracy for fits of the simple power law than for fits of the more complicated log-periodic function. The least-squares fitter underestimates the true error in time-to-failure functions because the error estimates are based upon linearized versions of the functions being fitted.