Frequency and magnitude of volcanic eruptions controlled by magma injection and buoyancy

Super-eruptions are extremely rare events. Indeed, the global frequency of explosive volcanic eruptions is inversely proportional to the volume of magma released in a single event(1,2). The rate of magma supply, mechanical properties of the crust and magma, and tectonic regime are known to play a role in controlling eruption frequency and magnitude(3-7), but their relative contributions have not been quantified. Here we use a thermomechanical numerical model of magma injection into Earth's crust and Monte Carlo simulations to explore the factors controlling the recurrence rates of eruptions of different magnitudes. We find that the rate of magma supply to the upper crust controls the volume of a single eruption. The time interval between magma injections into the subvolcanic reservoir, at a constant magma-supply rate, determines the duration of the magmatic activity that precedes eruptions. Our simulations reproduce the observed relationship between eruption volume and magma chamber residence times and replicate the observed correlation between erupted volumes and caldera dimensions(8,9). We also find that magma buoyancy is key to triggering super-eruptions, whereas pressurization associated with magma injection is responsible for relatively small and frequent eruptions. Our findings help improve our ability to decipher the long-term activity patterns of volcanic systems.