The maximum earthquake in future T years: Checking by a real catalog

The studies of disaster statistics are being largely carried out in recent decades. Some recent achievements in the field can be found in Pisarenko and Rodkin (2010). An important aspect in the seismic risk assessment is the using historical earthquake catalogs and the combining historical data with instrumental ones since historical catalogs cover very long time periods and can improve seismic statistics in the higher magnitude domain considerably. We suggest the new statistical technique for this purpose and apply it to two historical Japan catalogs and the instrumental JMA catalog. The main focus of these approaches is on the occurrence of disasters of extreme sizes as the most important ones from practical point of view. Our method of statistical analysis of the size distribution in the uppermost range of extremely rare events was suggested, based on maximum size M_max(τ) (e.g. earthquake energy, ground acceleration caused by earthquake, victims and economic losses from natural catastrophes, etc.) that will occur in a prescribed time interval τ. A new approach to the problem discrete data that we called “the magnitude spreading” is suggested. This method reduces discrete random value to continuous ones by addition a small uniformly distributed random components. We analyze this method in details and apply it to verification of parameters derived from two historical catalogs: the Usami earthquake catalog (599–1884) and the Utsu catalog (1885–1925). We compare their parameters with ones derived from the instrumental JMA catalog (1926–2014). The results of this verification are following: The Usami catalog is incompatible with the instrumental one, whereas parameters estimated from the Utsu catalog are statistically compatible in the higher magnitude domain with sample of M_max(τ) derived from the JMA catalog.