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Sampling uncertainties and source b likelihood for the Gutenberg-Richter b value from the Aki-Utsu method

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Abstract

The Aki-Utsu method of Gutenberg-Richter (G-R) b value estimation is often misapplied so that estimations not using the G-R histogram are often meaningless because they are not based on adequate samples. We propose a method to estimate the likelihood Pr(bǀb m , N, M 1, M 2) that an observed b m estimate, based on a sample of N magnitudes within an [M 1 −  ≤ ΔM/2, M 2 + ΔM/2) range, where ΔM = 0.1 is the usual rounding applied to magnitudes, is due to a “true” source b value, b, and use these likelihoods to estimate source b ranges corresponding to various confidence levels. As an example of application of the method, we estimate the b values before and after the occurrence of a 7.4-magnitude earthquake in the Mexican subduction zone, and find a difference of 0.82 between them with 100% confidence that the b values are different.

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Acknowledgements

Many thanks to José Mojarro and Humberto Benítez for technical support. Our thanks to SCEC and SSN for use of their data. Our sincere thanks to two anonymous reviewers and to editor T. Braun for helpful comments and criticism.

Funding

This research was funded by CONACyT project 222795 (F.N.) and by the CONACyt Cátedras program (L.A.). Partial support from UNAM-PAPIIT IN108115 project is also acknowledged (R.Z., V.H.M.).

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Authors and Affiliations

  1. Sismología, Centro de Investigación Científica y de Educación Superior de Ensenada, Ensenada, B.C., Mexico

    F. A. Nava & L. Ávila-Barrientos

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

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

  3. Fac. Ingeniería, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

    I. Torres

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  1. F. A. Nava
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  2. L. Ávila-Barrientos
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  3. V. H. Márquez-Ramírez
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  4. I. Torres
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  5. F. R. Zúñiga
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Correspondence to F. A. Nava.

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Nava, F.A., Ávila-Barrientos, L., Márquez-Ramírez, V.H. et al. Sampling uncertainties and source b likelihood for the Gutenberg-Richter b value from the Aki-Utsu method. J Seismol 22, 315–324 (2018). https://doi.org/10.1007/s10950-017-9707-8

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