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Båth's law Derived from the Gutenberg-Richter law and Aftershock Properties

Agnes Helmstetter, & Didier Sornette

Published October 2003, SCEC Contribution #739

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.

Helmstetter, A., & Sornette, D. (2003). Båth's law Derived from the Gutenberg-Richter law and Aftershock Properties. Geophysical Research Letters, 30(20), 2069. doi: 10.1029/2003GL018186.