pure and applied geophysics

, Volume 160, Issue 12, pp 2343–2364

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


DOI: 10.1007/s00024-003-2397-x

Cite this article as:
Pisarenko, V. & Sornette, D. Pure appl. geophys. (2003) 160: 2343. doi:10.1007/s00024-003-2397-x


Recent results in extreme value theory suggest a new technique for statistical estimation of distribution tails (Embrechts et al., 1997), based on a limit theorem known as the Gnedenko-Pickands-Balkema-de Haan theorem. This theorem gives a natural limit law for peak-over-threshold values in the form of the Generalized Pareto Distribution (GPD), which is a family of distributions with two parameters. The GPD has been successfully applied in a number of statistical problems related to finance, insurance, hydrology, and other domains. Here, we apply the GPD approach to the well-known seismological problem of earthquake energy distribution described by the Gutenberg-Richter seismic moment-frequency law. We analyze shallow earthquakes (depth h<70 km) in the Harvard catalog over the period 1977–2000 in 12 seismic zones. The GPD is found to approximate the tails of the seismic moment distributions quite well over the lower threshold approximately M ≅ 1024 dyne-cm, or somewhat above (i.e., moment-magnitudes larger than mW=5.3). We confirm that the b-value is very different (b=2.06 ± 0.30) in mid-ocean ridges compared to other zones (b=1.00 ± 0.04) with a very high statistical confidence and propose a physical mechanism contrasting “crack-type” rupture with “dislocation-type” behavior. The GPD can as well be applied in many problems of seismic hazard assessment on a regional scale. However, in certain cases, deviations from the GPD at the very end of the tail may occur, in particular for large samples signaling a novel regime.


Extreme eventstail of distributionthe Generalized Pareto Distributionseismic energy distribution

Copyright information

© Birkhäuser Verlag, Basel, 2003

Authors and Affiliations

  1. 1.International Institute of Earthquake Prediction Theory and Mathematical GeophysicsRussian Ac. Sci. Warshavskoye sh.MoscowRussia Federation
  2. 2.Institute of Geophysics and Planetary Physics and Department of Earth and Space ScienceUniversity of CaliforniaLos AngelesUSA
  3. 3.Laboratoire de Physique de la Matière Condensée CNRS UMR6622Université des SciencesParc ValroseFrance