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AGU: Geophysical Research Letters

 

Index Terms

  • Seismology: Earthquake dynamics and mechanics
  • Seismology: Seismic hazard assessment and prediction
  • Seismology: Theory and modeling

Abstract

Båth's law derived from the Gutenberg-Richter law and from aftershock properties

Agnès Helmstetter

Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA

Didier Sornette

Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA

Department of Earth and Space Sciences, University of California, Los Angeles, California, USA

Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622 Université de Nice-Sophia Antipolis, Parc Valrose, Nice, France

The empirical Båth's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere-Jones' [1969] and Console et al. [2003] , we show that the origin of Båth's law is to be found in the selection procedure used to define mainshocks and aftershocks rather than in any difference in the mechanisms controlling the magnitude of the mainshock and of the aftershocks. We use the ETAS model of seismicity, which provides a more realistic model of aftershocks, based on (i) a universal Gutenberg-Richter (GR) law for all earthquakes, and on (ii) the increase of the number of aftershocks with the mainshock magnitude. Using numerical simulations of the ETAS model, we show that this model is in good agreement with Båth's law in a certain range of the model parameters.

Received 16 July 2003; accepted 19 September 2003; published 30 October 2003.

Citation: Helmstetter, A., and D. Sornette (2003), Båth's law derived from the Gutenberg-Richter law and from aftershock properties, Geophys. Res. Lett., 30(20), 2069, doi:10.1029/2003GL018186.

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