  We study the temporal and spatial correlations in a one-dimensional model of
a heterogeneous fault zone, in the presence of visco-elastic effects. As a
function of dynamical weakening and of dissipation, the system exhibits three
different "phases" : one in which there are no time correlations between the
events, a second, in which there are ``Omori's law'' type temporal
correlations, and a third, runaway phase with quasiperiodic system size events.
