An analytic expression for the volcanic seismic swarms occurrence rate. A case study of some volcanoes in the world

Seismic swarms are defined as a group of earthquakes occurring very close in time and space but without any distinctively large event triggering their occurrence. Up to now no simple law has been found to describe the swarm occurrence rate. Here we find an expression able to fit the average occurrence rate on some volcanic areas. This expression exhibits some differences in respect to the classical Omori law. Namely the c parameter of the Omori law is equal to zero and the power law decay of the average occurrence rate of the earthquakes is followed by an exponential decaying regime. Both the results can be interpreted in term of fluid injection and/or movements. Indeed this is a more impulsive phenomenon compared to the occurrence of a large earthquake, with a duration compatible with a c = 0. The exponential decay following the power law one could be explained by a viscoelastic relaxation of the stress induced by the injection and/or movements of fluids in the earth crust.