Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case

摘要

The area-characteristic, maximum possible earthquake magnitude $T_M$ isrequired by the earthquake engineering community, disaster management agenciesand the insurance industry. The Gutenberg-Richter law predicts that earthquakemagnitudes $M$ follow a truncated exponential distribution. In the geophysicalliterature several estimation procedures were proposed, see for instance Kijkoand Singh (Acta Geophys., 2011) and the references therein. Estimation of $T_M$is of course an extreme value problem to which the classical methods forendpoint estimation could be applied. We argue that recent methods on truncatedtails at high levels (Beirlant et al., Extremes, 2016; Electron. J. Stat.,2017) constitute a more appropriate setting for this estimation problem. Wepresent upper confidence bounds to quantify uncertainty of the point estimates.We also compare methods from the extreme value and geophysical literaturethrough simulations. Finally, the different methods are applied to themagnitude data for the earthquakes induced by gas extraction in the Groningenprovince of the Netherlands.