A generic recurrence interval distribution for earthquake forecasting

Abstract

Earthquake recurrence intervals for characteristic events from a number of plate boundaries are analyzed using a normalizing function, T/Tave , where Tave is the observed average recurrence interval for a specific fault segment, and T is an individual recurrence interval. The lognormal distribution is found to provide a better fit to the T/Tave data than the more commonly used Gaussian and Weibull distributions, and it has an appealing physical interpretation. The observation of a small and stable coefficient of variation (the ratio of the standard deviation to the mean) of normalized data covering a wide range of recurrence intervals, seismic moments, and tectonic environments indicates that the standard deviation of the recurrence intervals for each fault segment is a fixed fraction of the corresponding average recurrence interval. Given that the distribution of T/Tave data is approximately lognormal, the analysis is refined using the median recurrence interval, T, rather than Tave . An approximately optimal algorithm is derived for making stable estimates of T, its standard deviation , and the reliability of each T /T datum. By accounting for possible errors in the data, this algorithm treats both historical and geological data properly. All information is then combined to make an optimal estimate of the distribution of the T /T data. This refined distribution is finally used to estimate the probability of a recurrence in a future forecast time interval and the reliability of the forecast. It is found that the forecast interval must be short compared with T for the forecast to be statistically meaningful. In addition, the distribution of T /T data can be used to estimate an expected time and prediction time window for a future earthquake recurrence.