  We find the static displacement, stress, strain and the modified Columb
failure stress produced in an elastic medium by a finite size rectangular fault
after its dislocation with uniform stress drop but a non uniform dislocation on
the source. The time-dependent rate of triggered earthquakes is estimated by a
rate-state model applied to a uniformly distributed population of faults whose
equilibrium is perturbated by a stress change caused only by the first
dislocation. The rate of triggered events in our simulations is exponentially
proportional to the stress change, but the time at which the maximum rate
begins to decrease is variable from fractions of hour for positive stress
changes of the order of some MPa, up to more than a year for smaller stress
changes. As a consequence, the final number of triggered events is proportional
to the stress change. The model predicts that the total number of events
triggered on a plane containing the fault is proportional to the 2/3 power of
the seismic moment. Indeed, the total number of aftershocks produced on the
fault plane scales in magnitude as 10^{M}. Including the negative contribution
of the stress drop inside the source, we observe that the number of events
inhibited on the fault is, at long term, nearly identical to the number of
those induced outside, representing a sort of conservative natural rule.
Considering its behaviour in time, our model doesn't completely match the
popular Omori law; in fact it has been shown that the seismicity induced
closely to the fault edges is intense but of short duration, while that
expected at large distances (up to some tens times the fault dimensions)
exhibits a much slower decay.
