Distribution of maximum earthquake magnitudes in future time intervals: application to the seismicity of Japan (1923–2007)

Abstract

We have modified the new method for the statistical estimation of the tail distribution of earthquake seismic moments introduced by Pisarenko et al. (2009) and applied it to the earthquake catalog of Japan (1923–2007). The newly modified method is based on the two main limit theorems of the theory of extreme values and on the derived duality between the generalized Pareto distribution (GPD) and the generalized extreme value distribution (GEV). Using this method, we obtain the distribution of maximum earthquake magnitudes in future time intervals of arbitrary duration τ. This distribution can be characterized by its quantile Q_q (τ) at any desirable statistical level q. The quantile Q_q(τ) provides a much more stable and robust characteristic than the traditional absolute maximum magnitude Mmax (Mmax can be obtained as the limit of Q_q(τ) as q → 1, τ → ∞). The best estimates of the parameters governing the distribution of Q_q(τ) for Japan (1923–2007) are the following: ξ_GEV = −0.19 ± 0.07; μ_GEV(200) = 6.339 ± 0.038; σ_GEV (200) = 0.600 ± 0.022; Q_0.90,GEV(10) = 8.34 ± 0.32. We have also estimated Q_q(τ) for a set of q-values and future time periods in the range 1 ≤ τ ≤ 50 years from 2007 onwards. For comparison, the absolute maximum estimate M_max-GEV = 9.57 ± 0.86 has a scatter more than twice that of the 90% quantile Q_0.90,gev(10) of the maximum magnitude over the next 10 years beginning from 2007.