The Weibull - log Weibull transition of interoccurrence times for synthetic and natural earthquakes

We have studied interoccurrence time distributions by analyzing the synthetic and three natural catalogs of the Japan Meteorological Agency (JMA), the Southern California Earthquake Data Center (SCEDC), and Taiwan Central Weather Bureau (TCWB) and revealed the universal feature of the interoccurrence time statistics, Weibull - log Weibull transition. This transition reinforces the view that the interoccurrence time statistics possess Weibull statistics and log-Weibull statistics. Here in this paper, the crossover magnitude from the superposition regime to the Weibull regime $m_c^2$ is proportional to the plate velocity. In addition, we have found the region-independent relation, $m_c^2\mathrm{/}{m}_{max}=0.54\pm 0.004$.