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

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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.

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Acknowledgements

This research was funded by CONACYT Grant 222795 and was partially carried out within Project CGL2011-29474-C01-01, and was partially funded by UNAM-DGAPA postdoctoral scholarship (V.H.M.). Many thanks to José Mojarro for technical advise. We thank the anonymous reviewers for constructive criticism.

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Authors and Affiliations

  1. Seismology Department, CICESE, Carretera Tijuana-Ensenada No. 3918, Zona Playitas, 22860, Ensenada, B. C., Mexico

    F. A. Nava

  2. Centro de Geociencias, UNAM, Campus Querétaro, Blvd. Juriquilla No. 3001, 76230, Querétaro, Qro., Mexico

    V. H. Márquez-Ramírez & F. R. Zúñiga

  3. Institute of Geophysics, UNAM, Ciudad Universitaria, 04150, Coyoacán, D. F., Mexico

    C. Lomnitz

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  1. F. A. Nava
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  2. V. H. Márquez-Ramírez
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  3. F. R. Zúñiga
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  4. C. Lomnitz
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Correspondence to F. A. Nava.

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Nava, F.A., Márquez-Ramírez, V.H., Zúñiga, F.R. et al. Gutenberg–Richter b-value determination and large-magnitudes sampling. Nat Hazards 87, 1–11 (2017). https://doi.org/10.1007/s11069-017-2750-5

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  • DOI: https://doi.org/10.1007/s11069-017-2750-5

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