A Note on the Estimation of the Maximum Possible Earthquake Magnitude Based on Extreme Value Theory for the Groningen Gas Field

Abstract

ABSTRACT Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency–magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true Mmax is close to the maximum observed magnitude Mmax,observed restricts the class of the potential models a priori to those with Mmax=Mmax,observed+ΔM with an increment ΔM≈0.5…1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled “Mmax equals Mobs plus an increment.” The incomplete consideration of the entire model family for the frequency–magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.