2017 年 70 巻 p. 195-213
Only a few large or medium-sized repeating earthquakes are known in many sequences due to long recurrence intervals in comparison with observation period. Recurrence intervals are used to estimate long-term earthquake probability; however, the effect of the number of recurrence intervals on prediction performance is unclear. We studied the predictability dependence on the number of recurrences using small interplate repeating earthquakes along the Japan Trench. These earthquakes were extracted from Tohoku University’s catalog, and this data was used in the probability forecast experiments from 2006 to 2010. The number of forecasts is 524. Two to five events just prior to the forecasts are picked from each sequence to calculate the probabilities. We calculated the probabilities using the Bayesian statistics log-normal distribution model (LN-Bayes), the log-normal distribution model based on the small sample theory (LN-SST), and the exponential distribution model (Exp-pin). We then evaluated the forecast results using mean log-likelihood and Brier score. The performance of the LN-SST and LN-Bayes models was better than that of the Exp-pin model for almost all cases. In addition, we conducted some statistical tests to measure the consistency of forecast with the observed catalog and confirmed the tendency of underestimation of probabilities and the accuracy dependence of probabilities on the number of recurrences for all models. The LN-Bayes and LN-SST models were examined by random number experiments using a large number of simulated sequences of earthquakes. In statistical tests, we changed the number of repetitions and the elapsed time from the most recent earthquake. As a result, performance improvement, along with the increase of repetition number, was evident when the repetition number was small for both models. The LN-Bayes model is generally better than the LN-SST model if the number of repetitions is very small. However, one of the features of the LN-Bayes model is that probability is saturated when the number of repetitive events is small and longer time has passed since the last event.