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\begin{document}

\title{An analytic expression for the volcanic seismic swarms occurrence rate}



\author[1]{Cataldo Godano}%
\author[2]{Anna Tramelli}%
\author[1]{Giuseppe Petrillo}%
\author[3]{Mauricio M. Mora}%
\author[4]{Taylor Waldo}%
\affil[1]{Università della Campania - Luigi Vanvitelli}%
\affil[2]{Istituto Nazionale di Geofisica e Vulcanologia}%
\affil[3]{Universidad de Costa Rica}%
\affil[4]{Instituto Costarricense de Electricidad}%


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  \date{June 13, 2024}


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\begin{abstract}
Seismic swarms are defined as a group of earthquakes occurring very
close in time and space but without any larger 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. Such an expression exhibits some
differences in respect of the usual 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, in respect to the occurrence of a large earthquake, with a
duration compatible with a \$c=0\$. The exponential decay following the
power law one could explained by a viscoelastic relaxation of the stress
induced by the injection and/or movements of fluids in the earth crust.%
\end{abstract}%



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