Evaluating the incompleteness magnitude using an unbiased estimate of the b value

Author:

Godano C12,Petrillo G3,Lippiello E1ORCID

Affiliation:

1. Department of Mathematics and Physics, Universitá della Campania “Luigi Vanvitelli” , Caserta 81100 , Italy

2. INGV-Osservatorio Vesuviano , via Diocleziano, 328 - 80124 Napoli , Italy

3. The Institute of Statistical Mathematics, Research Organization of Information and Systems , 10-3 Midori-cho, Tachikawa Tokyo 190-8562 , Japan

Abstract

SUMMARY The evaluation of the b value of the Gutenberg–Richter (GR) law, for a sample composed of n earthquakes, presents a systematic positive bias δb which is proportional to 1/n . In this study, we show how to incorporate in δb the bias introduced by deviations from the GR law. More precisely we show that δb is proportional to the square of the variability coefficient CV, defined as the ratio between the standard deviation of the magnitude distribution and its mean value. When the magnitude distribution follows the GR law CV = 1 and this allows us to introduce a new graphical procedure, based on the dependence of b on n, which allows us to identify the incompleteness magnitude mc as the threshold magnitude leading to CV = 1. The method is tested on synthetic catalogues and it is applied to estimate mc in Southern California, Japan and New Zealand.

Funder

Ministero dell'Istruzione e del Merito

Ministry of Education, Culture, Sports, Science and Technology

Publisher

Oxford University Press (OUP)

Subject

Geochemistry and Petrology,Geophysics

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