Constraints on the Size of the Smallest Triggering Earthquake from the   ETAS Model, Baath's Law, and Observed Aftershock Sequences
  The physics of earthquake triggering together with simple assumptions of self-similarity impose the existence of a minimum magnitude m0 below which earthquakes do not trigger other earthquakes. Noting that the magnitude md of completeness of seismic catalogs has no reason to be the same as the magnitude m0 of the smallest triggering earthquake, we use quantitative fits and maximum likelihood inversions of observed aftershock sequences as well as Baath's law, compare with ETAS model predictions and thereby constrain the value of m0. We show that the branching ratio $n$ (average number of triggered earthquake per earthquake also equal to the fraction of aftershocks in seismic catalogs) is the key parameter controlling the minimum triggering magnitude m0. Conversely, physical upper bounds for m0 derived from state- and velocity-weakening friction indicate that at least 60 to 70 percent of all earthquakes are aftershocks. 
D. Sornette (UCLA and CNRS/Univ. Nice) and M.J. Werner (UCLA)