Båth's law derived from the Gutenberg-Richter law and from aftershock properties
Article first published online: 30 OCT 2003
Copyright 2003 by the American Geophysical Union.
Geophysical Research Letters
Volume 30, Issue 20, October 2003
How to Cite
2003), Båth's law derived from the Gutenberg-Richter law and from aftershock properties, Geophys. Res. Lett., 30, 2069, doi:10.1029/2003GL018186, 20., and (
- Issue published online: 30 OCT 2003
- Article first published online: 30 OCT 2003
- Manuscript Accepted: 19 SEP 2003
- Manuscript Received: 16 JUL 2003
 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'  and Console et al. , 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.