How variable is the number of triggered aftershocks

Aftershock activity depends at first order on the mainshock magnitude, but also shows important fluctuations between shocks of equal magnitude. We here investigate these fluctuations, by quantifying them, and by relating them to the mainshock stress drop and other variables, for southern California earthquakes. A method is proposed in order to only count directly triggered aftershocks, rather than secondary aftershocks (i.e., triggered by previous aftershocks), and to only quantify fluctuations going beyond the natural Poisson variability. Testing of the method subjected to various model errors allows to quantify its robustness. It is found that these fluctuations follow a distribution that is well fitted by a log-normal distribution, with a coefficient of variation of about 1.0 to 1.1. A simple model is proposed to relate this observed dependence to mainshock stress drop variability.