Statistical forecasts and tests for small interplate repeating earthquakes along the Japan Trench

Earthquake predictability is a fundamental problem of seismology. Using a sophisticated model, a Bayesian approach with lognormal distribution on the renewal process, we theoretically formulated a method to calculate the conditional probability of a forthcoming recurrent event and forecast the probabilities of small interplate repeating earthquakes along the Japan Trench. The numbers of forecast sequences for 12 months were 93 for July 2006 to June 2007, 127 for 2008, 145 for 2009, and 163 for 2010. Forecasts except for 2006–07 were posted on a web site for impartial testing. Consistencies of the probabilities with catalog data of two early experiments were so good that they were statistically accepted. However, the 2009 forecasts were rejected by the statistical tests, mainly due to a large slow slip event on the plate boundary triggered by two events with M 7.0 and M 6.9. All 365 forecasts of the three experiments were statistically accepted by consistency tests. Comparison tests and the relative/receiver operating characteristic confirm that our model has significantly higher performance in probabilistic forecast than the exponential distribution model on the Poisson process. Therefore, we conclude that the occurrence of microrepeaters is statistically dependent on elapsed time since the last event and is not random in time.