Journal of Seismology

, Volume 21, Issue 1, pp 127–135 | Cite as

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

  • F. A. Nava
  • V. H. Márquez-Ramírez
  • F. R. Zúñiga
  • L. Ávila-Barrientos
  • C. B. Quinteros


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.


Gutenberg-Richter b-value Maximum likelihood estimation Aki/Utsu method 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • F. A. Nava
    • 1
  • V. H. Márquez-Ramírez
    • 2
    • 3
  • F. R. Zúñiga
    • 2
  • L. Ávila-Barrientos
    • 1
  • C. B. Quinteros
    • 1
  1. 1.SismologíaCentro de investigación Cientifica y de Educación Superior de EnsenadaEnsenadaMexico
  2. 2.Centro de GeocienciasUniversidad Nacional Autónoma de MéxicoJuriquillaMexico
  3. 3.SisVoc, CUCUniversidad de GuadalajaraPuerto VallartaMexico

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