Feeding of a magma chamber by an ascending magma bubble

There is evidence that magma chambers are not fed by a continuous flow, but in the form of discrete magma batches. The possibility is considered that the chamber is fed by a magma bubble ascending through the region underneath, driven by buoyancy force. Due to the high ambient temperatures, it is assumed that the bubble moves through a viscoelastic medium with temperature-dependent viscosity. The motion of a spherical magma bubble and its inflow into the chamber are studied. The bubble volume is assumed to be at least equal to magma volumes in typical effusive eruptions on Mount Etna, corresponding to bubble radii of a few hundred metres. Under some simplifying assumptions, the problem is solved analytically. The bubble velocity is directly proportional to the square of its radius and inversely to the viscosity of surrounding rocks, but it is independent of magma viscosity. Velocity can reach values of the order of tens of metres per year in the proximity of the chamber. Since the characteristic time for heat diffusion is several hundred years, the bubble can cover several kilometres with only moderate cooling. During ascent, forced convection takes place in the bubble. Equations for convection streamlines are obtained and traveltimes of magma are calculated, giving a mixing time of the order of hundred years below the chamber. Inflow of the bubble in the magma chamber produces a pulse in flow rate. Under reasonable assumptions, pulse shape and duration are calculated analytically. Pulse duration can be several tens of years and can give rise to a sequence of eruptions, depending on the size of the bubble and the critical overpressure for eruption.