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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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NPG | Articles | Volume 25, issue 1
Nonlin. Processes Geophys., 25, 241–250, 2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Nonlin. Processes Geophys., 25, 241–250, 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

Abercrombie, R. and Leary, P.: Source parameters of small earthquakes recorded at 2.5 km depth, Cajon Pass, Southern California: Implications for earthquake scaling, Geophys. Res. Lett., 20, 1511–1514, 1993. 
Aki, K.: Maximum Likelihood Estimate of b in the Formula log N = a-bM and its Confidence Limits, B. Earthq. Res. I., 43, 237–239, 1965. 
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,, 2009. 
Deichmann, N.: Theoretical Basis for the Observed Break in MLMw Scaling between Small and Large Earthquakes, B. Seismol. Soc. Am., 107, 505–520,, 2017. 
Publications Copernicus
Short summary
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...