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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2017-38
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
18 Jul 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).
Utsu aftershock productivity law explained from geometric operations on the permanent static stress field of mainshocks
Arnaud Mignan ETHZ, Institute of Geophysics, NO H66, Sonneggstrasse 5, 8092 Zurich, Switzerland
Abstract. The aftershock productivity law is an exponential function of the form K ∝ exp (αM) with K the number of aftershocks, M the mainshock magnitude, and α ≈ ln(10) the productivity parameter. This law remains empirical in nature although it has also been retrieved in static stress simulations. Here, we explain this law based on Solid Seismicity, a geometrical theory of seismicity where seismicity patterns are described by mathematical expressions obtained from geometric operations on a permanent static stress field. We recover the exponential function with a break in scaling between small and large M, with α = 1.5 ln(10) and ln(10), respectively, in agreement with results from previous static stress simulations. Possible biases of aftershock selection, verified to exist in Epidemic-Type Aftershock Sequence (ETAS) simulations, may explain the lack of break in scaling observed in seismicity catalogues. The existence of the theoretical kink therefore remains to be proven.

Citation: Mignan, A.: Utsu aftershock productivity law explained from geometric operations on the permanent static stress field of mainshocks, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2017-38, in review, 2017.
Arnaud Mignan
Arnaud Mignan
Arnaud Mignan

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