New evidence and perspective to the poisson process and earthquake temporal distribution from 55,000 events around Taiwan since 1900

Earthquake prediction is by all means controversial and challenging, given the fact that some recent catastrophic earthquakes went unpredicted. Not surprisingly, statistical approaches have been utilized to model earthquake randomness in time or space. One of the suggestions is that the earthquake's temporal probability distribution should follow the Poisson model, which is suitable for rare events by definition. As a result, the customarily used hypothesis should be largely associated with the prior judgment that earthquakes are rare, but not as a result of abundant quantitative evidence or theoretical derivation. Therefore, this study aims to offer new empirical evidence to the hypothesis based on 110-year-long earthquake data around Taiwan. From the series of statistical tests, the first statistical inference is indeed in line with the model's proposition: the level of fitting between observation and theory is better for earthquakes with a lower mean rate. To be more specific, it shows that the Poissonian hypothesis applied to local magnitude (ML)≥3.0 earthquakes around Taiwan with a mean annual rate as high as 1,600 is clearly rejected, but as far as ML≥7.0 earthquakes with a mean rate of 0.35 per year are concerned, the same hypothesis is statistically accepted for modeling their temporal randomness. Also, according to the tests on a variety of conditions, the annual rate of approximately 0.1 per year (or 10-year return period) was suggested as a reasonable empirical estimate for Poissonian rareness. Accordingly, from a practical point of view, it should be a robust analytical presumption to use the Poisson model in daily earthquake engineering analyses because the return period of design earthquakes is longer than 10 years, if not much longer.