Båth’s Law Derived from Gutenberg-Richter’s Law: a Simple Deduction with Implications for Earthquake Sequence Analysis

We provide the derivation of Båth’s law from Gutenberg-Richter’s law with a simple deduction through Zipf distribution for a set of data exhibiting power law scaling. It turns out that D , the difference between the magnitude of the mainshock and that of the largest aftershock (or the second largest...

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Bibliographic Details
Published inJournal of volcanology and seismology Vol. 18; no. 3; pp. 290 - 294
Main Authors Wu, Zhongliang, Liu, Yue
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.06.2024
Springer Nature B.V
Subjects
Earth and Environmental Science
Earth Sciences
Earthquakes
Geochemistry
Geology
Geophysics/Geodesy
Outliers (statistics)
Power law
Scaling
Seismic activity
Sequence analysis
Uncertainty
Gutenberg-Richter’s law
‘dragon king’ theory
Båth’s law
Zipf distribution
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Summary:We provide the derivation of Båth’s law from Gutenberg-Richter’s law with a simple deduction through Zipf distribution for a set of data exhibiting power law scaling. It turns out that D , the difference between the magnitude of the mainshock and that of the largest aftershock (or the second largest event in the mainshock-aftershock sequence) has positive correlation with the magnitude of the mainshock. The parameters of the aftershock sequence subject to analysis, including number of samples, cutoff magnitude, and b ‑value, also contribute to D and its uncertainty. The uncertainty of D is even larger associated with the ‘dragon king’ events which are the statistical outlier of the power law scaling.
Bibliography:ObjectType-Article-1
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ISSN:0742-0463
1819-7108
DOI:10.1134/S0742046324700544