Effusion Rate From a Volcanic Conduit Subject to Pressure Oscillations in a Viscoelastic Medium

Effusion rate in basaltic eruptions typically depends on time: there is an initial, relatively fast increase followed by a much slower decrease until the eruption vanishes; in addition, changes are observed in the effusion rate having durations much shorter than the total duration of the eruption. For an effusive eruption, we calculate the deformation of the volcanic conduit due to short-term pressure oscillations. The model considers an elliptical conduit embedded in a viscoelastic medium, described by a Maxwell body. As a consequence of pressure oscillations, the semi axes of the conduit are quasi periodic functions of time with the same period as pressure. For volcanic fissures the viscoelastic rheology entails a remarkable increase in oscillation amplitude of flow rate with respect to the elastic case and a time delay in flow rate oscillation with respect to overpressure oscillation. For a given value of overpressure amplitude, this effect is controlled by the conduit eccentricity and the ratio between overpressure period and Maxwell time; for larger values of this ratio and/or for eccentricity values closer to unity, flow rate oscillates around a value larger than its initial value and can vary from 5% to 30% with respect to it. The model can approximate the in-situ observations of short-time fluctuations of flow rate during the 2018 eruption of Kı̄lauea Volcano.