How to Choose a Magnitude Interval to Evaluate the Slope of the Magnitude-frequency Graph

V. F. Pisarenko; Писаренко В. Ф.; A. A. Skorkina; Скоркина А. А.; T. A. Rukavishnikova; Рукавишникова Т. А.

doi:10.31857/S0203030623700128

How to Choose a Magnitude Interval to Evaluate the Slope of the Magnitude-frequency Graph

Authors: Pisarenko V.F.¹, Skorkina A.A.¹, Rukavishnikova T.A.¹
Affiliations:
1. The Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS
Issue: No 2 (2023)
Pages: 3-11
Section: Articles
URL: https://journals.rcsi.science/0203-0306/article/view/134625
DOI: https://doi.org/10.31857/S0203030623700128
EDN: https://elibrary.ru/MHWWRC
ID: 134625

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Abstract
About the authors
References
Supplementary files
Statistics

Abstract

In modern seismological practice, to describe the distribution of magnitudes, the Gutenberg-Richter law is widely used, one of the parameters of which is the b-value (the slope of the magnitude-frequency graph on a log scale). Authors propose new approaches to the problem of adequate and efficient statistical estimation of this parameter. The problem of the correct choice of the magnitude interval is discussed, on which the straightness of the Gutenberg-Richter law is observed with an acceptable degree of accuracy and which should be used to estimate the b-value. An efficient method of accounting for discreteness and aggregation of magnitudes in earthquake catalogs (the maximum likelihood method for discrete distributions) is proposed. The problem of changes in time of the lower limit of representative earthquakes registration is considered and a statistical approach is proposed for their description.

Keywords

b-value, interval of linearity of the Gutenberg-Richter law, discretization and aggregation of magnitudes, threshold of representative earthquake registration

References

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