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NPG | Articles | Volume 25, issue 1
Nonlin. Processes Geophys., 25, 241-250, 2018
https://doi.org/10.5194/npg-25-241-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Nonlin. Processes Geophys., 25, 241-250, 2018
https://doi.org/10.5194/npg-25-241-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 29 Mar 2018

Research article | 29 Mar 2018

Utsu aftershock productivity law explained from geometric operations on the permanent static stress field of mainshocks

Arnaud Mignan
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Cited articles  
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Båth, M.: Lateral inhomogeneities of the upper mantle, Tectonophysics, 2, 483–514, 1965. 
Clauset, A., Shalizi, C. R., and Newman, M. E. J.: Power-Law Distributions in Empirical Data, SIAM Review, 51, 661–703, https://doi.org/10.1137/070710111, 2009. 
Deichmann, N.: Theoretical Basis for the Observed Break in MLMw Scaling between Small and Large Earthquakes, B. Seismol. Soc. Am., 107, 505–520, https://doi.org/10.1785/0120160318, 2017. 
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The Utsu productivity law, one of the main relationships in seismicity statistics, gives the average number of aftershocks produced by a mainshock of a given magnitude. I demonstrate that the law can be formulated in the solid seismicity theory, where it is parameterized in terms of aftershock density within a geometrical solid, constrained by the mainshock size. This suggests that aftershocks can be studied by applying simple rules of analytic geometry on a static stress field.
The Utsu productivity law, one of the main relationships in seismicity statistics, gives the...
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