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Gutenberg-Richter b-value maximum likelihood estimation and sample size

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Abstract

The Aki-Utsu maximum likelihood method is widely used for estimation of the Gutenberg-Richter b-value, but not all authors are conscious of the method’s limitations and implicit requirements. The Aki/Utsu method requires a representative estimate of the population mean magnitude; a requirement seldom satisfied in b-value studies, particularly in those that use data from small geographic and/or time windows, such as b-mapping and b-vs-time studies. Monte Carlo simulation methods are used to determine how large a sample is necessary to achieve representativity, particularly for rounded magnitudes. The size of a representative sample weakly depends on the actual b-value. It is shown that, for commonly used precisions, small samples give meaningless estimations of b. Our results give estimates on the probabilities of getting correct estimates of b for a given desired precision for samples of different sizes. We submit that all published studies reporting b-value estimations should include information about the size of the samples used.

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Acknowledgments

We sincerely thank two anonymouis reviewers for useful comments and suggestions. Thanks to Dr. J.L. Brioso for his guidance and patience. Many thanks to José Mojarro for technical support.

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Authors and Affiliations

  1. Sismología, Centro de investigación Cientifica y de Educación Superior de Ensenada, Ensenada, B.C., Mexico

    F. A. Nava, L. Ávila-Barrientos & C. B. Quinteros

  2. Centro de Geociencias, Universidad Nacional Autónoma de México, Juriquilla, Qro., Mexico

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

  3. SisVoc, CUC, Universidad de Guadalajara, Puerto Vallarta, Jal., Mexico

    V. H. Márquez-Ramírez

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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. L. Ávila-Barrientos
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  5. C. B. Quinteros
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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 maximum likelihood estimation and sample size. J Seismol 21, 127–135 (2017). https://doi.org/10.1007/s10950-016-9589-1

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