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Keywords:

  • aftershocks;
  • earthquake triggering;
  • Lévy laws;
  • static stress

SUMMARY

Small-magnitude earthquakes have been shown to be negligible when estimating regional seismic moment release or seismic slip along major faults. However, they have a strong control on the redistribution of elastic stresses, and, according to statistical models of earthquake occurrences, on the triggering of subsequent earthquakes. This point is generally overlooked in stress-triggering model that only consider a limited set of earthquakes as stress sources. Elaborating on previous analyses, we here develop a probabilistic approach for estimating, at the hypocentre of an earthquake, the total stress caused by a large set of previous earthquakes, as a function of the magnitude range covered by these stress-generating earthquakes. A generic model that mimics the main features of earthquakes populations (most particularly: the Gutenberg–Richter relation and a fractal distribution of hypocentres with fractal dimension D) is constructed. The cumulative stresses generated in this model by sets of earthquakes are shown to follow a Lévy-stable law with stability index D/3. Similar conclusions are obtained when analysing the M3+ seismicity that occurred in southern California between 1981 and 2000. We show that the contribution to the cumulative static stress, caused by the occurrence of small earthquakes, at the site of pending earthquakes is at least as important as the contribution from the largest earthquakes. This is a direct consequence of the fractal clustering properties of earthquake hypocentre distributions. Including the stress redistribution due to small-scale seismicity should, therefore, significantly improve mechanical models of earthquake triggering.