  We study analytically and by numerical simulations the statistics of the
aftershocks generated after large avalanches in models of interface depinning
that include viscoelastic relaxation effects. We find in all the analyzed cases
that the decay law of aftershocks with time can be understood by considering
the typical roughness of the interface and its evolution due to relaxation. In
models where there is a single viscoelastic relaxation time there is an
exponential decay of the number of aftershocks with time. In models in which
viscoelastic relaxation is wave-vector dependent we typically find a power law
dependence of the decay rate, compatible with the Omori law. The factors that
determine the value of the decay exponent are analyzed.
