  Very often damage and fracture in heterogeneous materials exhibit bursty
dynamics made of successive impulse-like events which form characteristic
aftershock sequences obeying specific scaling laws initially derived in
seismology: Gutenberg-Richter law, productivity law, B\r{a}th's law and
Omori-Utsu law. We show here how these laws naturally arise in the model of the
long-range elastic depinning interface used as a paradigm to model crack
propagation in heterogeneous media. We unravel the specific conditions required
to observe this seismic-like organization in the crack propagation problem.
Beyond failure problems, the results extend to a variety of situations
described by models of the same universality class: contact line motion in the
wetting problem or domain wall motion in dirty ferromagnet, to name a few.
