NDLI: Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory

Content Provider	Springer Nature Link
Author	Pisarenko, V. F. Sornette, A. Sornette, D. Rodkin, M. V.
Copyright Year	2014
Abstract	The present work is a continuation and improvement of the method suggested in Pisarenko et al. (Pure Appl Geophys 165:1–42, 2008) for the statistical estimation of the tail of the distribution of earthquake sizes. The chief innovation is to combine the two main limit theorems of Extreme Value Theory (EVT) that allow us to derive the distribution of T-maxima (maximum magnitude occurring in sequential time intervals of duration T) for arbitrary T. This distribution enables one to derive any desired statistical characteristic of the future T-maximum. We propose a method for the estimation of the unknown parameters involved in the two limit theorems corresponding to the Generalized Extreme Value distribution (GEV) and to the Generalized Pareto Distribution (GPD). We establish the direct relations between the parameters of these distributions, which permit to evaluate the distribution of the T-maxima for arbitrary T. The duality between the GEV and GPD provides a new way to check the consistency of the estimation of the tail characteristics of the distribution of earthquake magnitudes for earthquake occurring over an arbitrary time interval. We develop several procedures and check points to decrease the scatter of the estimates and to verify their consistency. We test our full procedure on the global Harvard catalog (1977–2006) and on the Fennoscandia catalog (1900–2005). For the global catalog, we obtain the following estimates: $$ \hat{M}_{{\rm max} } $$ = 9.53 ± 0.52 and $$ \hat{Q}_{10} (0.97) $$ = 9.21 ± 0.20. For Fennoscandia, we obtain $$ \hat{M}_{{\rm max} } $$ = 5.76 ± 0.165 and $$ \hat{Q}_{10} (0.97) $$ = 5.44 ± 0.073. The estimates of all related parameters for the GEV and GPD, including the most important form parameter, are also provided. We demonstrate again the absence of robustness of the generally accepted parameter characterizing the tail of the magnitude-frequency law, the maximum possible magnitude M max, and study the more stable parameter Q T (q), defined as the q-quantile of the distribution of T-maxima on a future interval of duration T.
Starting Page	1599
Ending Page	1624
Page Count	26
File Format	PDF
ISSN	00334553
Journal	Pure and applied geophysics
Volume Number	171
Issue Number	8
e-ISSN	14209136
Language	English
Publisher	Springer Basel
Publisher Date	2014-09-10
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geophysics/Geodesy
Content Type	Text
Resource Type	Article
Subject	Geochemistry and Petrology Geophysics

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Comment on Pisarenko et al., “Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory”

Reply to: “Comment on Pisarenko et al., ‘Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory’” by Mathias Raschke in Pure Appl Geophys (2015)

Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory

Characterization of the tail of the distribution of earthquake magnitudes by combining the GEV and GPD descriptions of Extreme Value Theory

Comment on Pisarenko et al. "Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory"

New Approach to the Characterization of M max and of the Tail of the Distribution of Earthquake Magnitudes

Characterization of the Frequency of Extreme Earthquake Events by the Generalized Pareto Distribution

Uncertainties in the estimation of earthquake magnitudes in Greece

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Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory

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Comment on Pisarenko et al., “Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory”

Reply to: “Comment on Pisarenko et al., ‘Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory’” by Mathias Raschke in Pure Appl Geophys (2015)

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