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

V F Pisarenko,M V Rodkin,D Sornette

doi:10.5047/eps.2010.06.003

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 Qq (τ) at any desirable statistical level q. The quantile Qq(τ) provides a much more stable and robust characteristic than the traditional absolute maximum magnitude Mmax (Mmax can be obtained as the limit of Qq(τ) as q → 1, τ → ∞). The best estimates of the parameters governing the distribution of Qq(τ) for Japan (1923–2007) are the following: ξGEV = −0.19 ± 0.07; μGEV(200) = 6.339 ± 0.038; σGEV (200) = 0.600 ± 0.022; Q0.90,GEV(10) = 8.34 ± 0.32. We have also estimated Qq(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 Mmax-GEV = 9.57 ± 0.86 has a scatter more than twice that of the 90% quantile Q0.90,gev(10) of the maximum magnitude over the next 10 years beginning from 2007.

Highlights

To adapt the method suggested by Pisarenko et al (2009) for the statistical estimation of the tail of the distribution of earthquake magnitudes to catalogs in which earthquake magnitudes are reported in discrete values, and (2) to apply the newly developed method to the Japan Meteorological Agency (JMA) magnitude catalog of Japan (1923–2007) in order to estimate the maximum possible magnitude and other measures characterizing the tail of the distribution of magnitudes
We have adapted the new method of statistical estimation suggested by Pisarenko et al (2009) to earthquake catalogs with discrete magnitudes
One theorem leads to the generalized Pareto distribution (GPD), and the other theorem leads to the generalized extreme value distribution (GEV) (T -maximum method)

Summary

Introduction

The method of Pisarenko et al (2009) is a continuation and improvement of the technique suggested in Pisarenko et al (2008) Both rely on the assumption that the distribution of earthquake magnitudes is limited to some maximum value Mmax, which is itself probably significantly less than the absolute limit imposed by the finiteness of the Earth. This maximum value Mmax may reflect the largest possible set of seismo-tectonic structures in a given tectonic region that can support an earthquake, combined with an extremal. These modifications impose a finite-size constraint only on the statistical average of the energy released by

Objectives

Methods

Conclusion