Sampling uncertainties and source <Emphasis Type="Italic">b</Emphasis> likelihood for the Gutenberg-Richter <Emphasis Type="Italic">b</Emphasis> value from the Aki-Utsu method |
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| Authors: | F A Nava L Ávila-Barrientos V H Márquez-Ramírez I Torres F R Zúñiga |
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| Institution: | 1.Sismología,Centro de Investigación Científica y de Educación Superior de Ensenada,Ensenada,Mexico;2.Centro de Geociencias,Universidad Nacional Autónoma de México,Juriquilla,Mexico;3.Fac. Ingeniería,Benemérita Universidad Autónoma de Puebla,Puebla,Mexico |
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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(b?b 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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