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  A New Statistical Perspective on Båth’s Law

Grimm, C., Hainzl, S., Käser, M., Küchenhoff, H. (2024): A New Statistical Perspective on Båth’s Law. - Seismological Research Letters, 95, 1, 488-498.
https://doi.org/10.1785/0220230147

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Grimm, Christian1, Author
Hainzl, S.2, Author              
Käser, Martin1, Author
Küchenhoff, Helmut1, Author
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1External Organizations, ou_persistent22              
22.1 Physics of Earthquakes and Volcanoes, 2.0 Geophysics, Departments, GFZ Publication Database, Deutsches GeoForschungsZentrum, ou_146029              

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 Abstract: The empirical Båth’s law states that the average magnitude difference (⁠⁠) between a mainshock and its strongest aftershock is ∼1.2, independent of the size of the mainshock. Although this observation can generally be explained by a scaling of aftershock productivity with mainshock magnitude in combination with a Gutenberg–Richter frequency–magnitude distribution, estimates of may be preferable because they are directly related to the most interesting information, namely the magnitudes of the main events, without relying on assumptions. However, a major challenge in calculating this value is the bias introduced by missing data points when the strongest aftershock is below the observed cut‐off magnitude. Ignoring missing values leads to a systematic error because the data points removed are those with particularly large magnitude differences ⁠. The error can be minimized by restricting the statistics to mainshocks that are at least 2 magnitude units above the cutoff, but then the sample size is strongly reduced. This work provides an innovative approach for modeling by adapting methods for time‐to‐event data, which often suffer from incomplete observations (censoring). In doing so, we adequately account for unobserved values and estimate a fully parametric distribution of the magnitude differences for mainshocks in a global earthquake catalog. Our results suggest that magnitude differences are best modeled by the Gompertz distribution and that larger are expected at increasing depths and higher heat flows.

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 Dates: 2023-10-182024
 Publication Status: Finally published
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 Identifiers: DOI: 10.1785/0220230147
GFZPOF: p4 T3 Restless Earth
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Title: Seismological Research Letters
Source Genre: Journal, SCI, Scopus
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Pages: - Volume / Issue: 95 (1) Sequence Number: - Start / End Page: 488 - 498 Identifier: CoNE: https://gfzpublic.gfz-potsdam.de/cone/journals/resource/journals447
Publisher: Seismological Society of America (SSA)