A Model for the Effusion Rate Produced by a Magma Pulse

We assume that a magma pulse enters a magma chamber from the plumbing system, producing an overpressure triggering an effusive volcanic eruption. The chamber is modeled as a spherical cavity in an elastic half-space, connected to the Earth's surface by a vertical conduit, and the magma as an incompressible Newtonian liquid. Overpressure in the chamber is calculated as a function of time during the eruption and has different behaviors depending on the characteristics of the magma pulse and of the volcanic system. The time history of effusion rate is controlled by the pulse duration and the geometrical and rheological parameters of the model. The calculated effusion rates are compared with different classes of effusion rates extrapolated from historical data of Mount Etna, which are asymmetric functions of time. For appropriate values of the model parameters, the calculated time histories are found to fit well those derived from observation.