  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.
