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Gutenberg–Richter b-value determination and large-magnitudes sampling

Author

Listed:
  • F. A. Nava

    (CICESE)

  • V. H. Márquez-Ramírez

    (UNAM)

  • F. R. Zúñiga

    (UNAM)

  • C. Lomnitz

    (Ciudad Universitaria)

Abstract

Aki’s maximum likelihood method of Gutenberg–Richter b-value estimation is based on the premise that magnitudes above a given threshold are distributed exponentially and presupposes that sampling is adequate for all these magnitudes; clearly, sampling will not be adequate for magnitudes having average recurrence times longer than the observation time. Thus, for any given sample, there is a higher-magnitude completeness threshold. The importance of considering this higher-magnitude threshold is discussed, the effect of incomplete large-magnitude sampling is evaluated, and a method is given for correcting the observations.

Suggested Citation

  • F. A. Nava & V. H. Márquez-Ramírez & F. R. Zúñiga & C. Lomnitz, 2017. "Gutenberg–Richter b-value determination and large-magnitudes sampling," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 87(1), pages 1-11, May.
    • Handle: RePEc:spr:nathaz:v:87:y:2017:i:1:d:10.1007_s11069-017-2750-5
    DOI: 10.1007/s11069-017-2750-5
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    References listed on IDEAS

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    1. D. Sornette, "undated". "Dragon-Kings, Black Swans and the Prediction of Crises," Working Papers CCSS-09-005, ETH Zurich, Chair of Systems Design.
    2. Didier SORNETTE, 2009. "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
    3. Danijel Schorlemmer & Stefan Wiemer & Max Wyss, 2005. "Variations in earthquake-size distribution across different stress regimes," Nature, Nature, vol. 437(7058), pages 539-542, September.
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