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

TL;DR

This paper applies advanced extreme value theory methods to estimate the maximum earthquake magnitude in Groningen, providing confidence bounds and comparing approaches through simulations and real data analysis.

Contribution

It introduces the use of recent truncated tail estimation methods for more accurate maximum earthquake magnitude estimation in geophysical data.

Findings

New upper confidence bounds for maximum magnitude estimates

Comparison showing improved accuracy of recent methods

Application to Groningen earthquake data demonstrates practical utility

Abstract

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