Abstract
Using the epidemic-type aftershock sequence (ETAS) branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Båth’s law. Our theory shows that Båth’s law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars for Båth’s constant value around 1.2, our exact analytical treatment of Båth’s law provides new constraints on the productivity exponent and the branching ratio : and . We propose a method for measuring based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the “second Båth law for foreshocks:” the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude .
1 More- Received 20 January 2005
DOI:https://doi.org/10.1103/PhysRevE.71.056127
©2005 American Physical Society