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

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• 作者：F. A. Nava ; V. H. Márquez-Ramírez ; F. R. Zúñiga…
• 关键词：Gutenberg ; Richter b ; value ; Maximum likelihood estimation ; Aki/Utsu method
• 刊名：Journal of Seismology
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：21
• 期：1
• 页码：127-135
• 全文大小：
• 刊物类别：Earth and Environmental Science
• 刊物主题：Geophysics/Geodesy; Structural Geology; Hydrogeology; Geotechnical Engineering & Applied Earth Sciences;
• 出版者：Springer Netherlands
• ISSN：1573-157X
• 卷排序：21

文摘

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.