An analytical model for gas overpressure in slug-driven explosions: Insights into Strombolian volcanic eruptions

Strombolian eruptions, common at basaltic volcanoes, are mildly explosive events that are driven by a large bubble of magmatic gas (a slug) rising up the conduit and bursting at the surface. Gas overpressure within the bursting slug governs explosion dynamics and vigor and is the main factor controlling associated acoustic and seismic signals. We present a theoretical investigation of slug overpressure based on magma-static and geometric considerations and develop a set of equations that can be used to calculate the overpressure in a slug when it bursts, slug length at burst, and the depth at which the burst process begins. We find that burst overpressure is controlled by two dimensionless parameters: V', which represents the amount of gas in the slug, and A', which represents the thickness of the film of magma that falls around the rising slug. Burst overpressure increases nonlinearly as V' and A' increase. We consider two eruptive scenarios: (1) the standard model, in which magma remains confined to the vent during slug expansion, and (2) the overflow model, in which slug expansion is associated with lava effusion, as occasionally observed in the field. We find that slug overpressure is higher for the overflow model by a factor of 1.2-2.4. Applying our model to typical Strombolian eruptions at Stromboli, we find that the transition from passive degassing to explosive bursting occurs for slugs with volume >24-230 m(3), depending on magma viscosity and conduit diameter, and that at burst, a typical Strombolian slug (with a volume of 100-1000 m(3)) has an internal gas pressure of 1-5 bars and a length of 13-120 m. We compare model predictions with field data from Stromboli for low-energy puffers, mildly explosive Strombolian eruptions, and the violently explosive 5 April 2003 paroxysm. We find that model predictions are consistent with field observations across this broad spectrum of eruptive styles, suggesting a common slug-driven mechanism; we propose that paroxysms are driven by unusually large slugs (large V').