Magma reservoir volume from ground deformation, eruption rate, and other observations

The volume of a volcano's magma reservoir places a fundamental limit on the maximum size of an eruption (neglecting significant co-eruptive recharge), and also controls the temporal evolution of eruptive activity. Geochemical residence times, the volumes of aseismic zones beneath volcanoes, and the volumes of past eruptive products may all be used to estimate reservoir volume, but most estimates are associated with a great deal of uncertainty and can vary by an order of magnitude or more for a single volcano.

Simple eruption models which assume that eruption rate is proportional to the pressure in a deflating elastic reservoir suggest that the reservoir volume should be directly proportional to the erupted volume, to the magnitude of ground deformation around the volcano, and to the rate of change of these observations during an eruption. However, these observations are inadequate for directly estimating reservoir volume; we must also place constraints on reservoir pressure or properties of the conduit linking the reservoir to the surface.

Using simple theoretical models and Monte Carlo simulations with more sophisticated models we evaluate our ability to place limits on reservoir volume using different combinations of information including ground deformation, eruption rate, the changing surface heights of active lava lakes, and the compressibility of the magma-reservoir system. Particularly useful in combination with geodetic data is constraint on co-eruptive pressure change, inferred from limitations on host rock strength or changing lava lake height; observations of the latter have allowed for a direct estimate of the shallow reservoir volume at Kīlauea Volcano (on the order of one cubic km). We also demonstrate that geodetic and eruption rate data can provide constraint on a magma’s volatile content; conversely, independent constraint on volatile content (such as from melt inclusion data) can place a lower bound, and sometimes an upper bound, on reservoir volume.