Magma chambers: what we can, and cannot, learn from volcano geodesy.

Geodetic observations on volcanoes can reveal important aspects of crustal magma chambers. The rate of decay of deformation with distance reflects the centroid depth of the chamber. The amplitude of the deformation is proportional to the product of the pressure change and volume of the reservoir. The ratio of horizontal to vertical displacement is sensitive to chamber shape: sills are efficient at generating vertical displacement, while stocks produce more horizontal deformation. Geodesy alone cannot constrain important parameters such as chamber volume or pressure; furthermore, kinematic models have no predictive power. Elastic response combined with influx proportional to pressure gradient predicts an exponentially decaying flux, leading to saw-tooth inflation cycles observed at some volcanoes. Yet many magmatic systems exhibit more complex temporal behaviour. Wall rock adjacent to magma reservoirs cannot behave fully elastically. Modern conceptual models of magma chambers also include cumulate and/or mush zones, with potentially multi-level melt lenses. A viscoelastic shell surrounding a spherical magma chamber significantly modifies the predicted time-dependent response; post-eruptive inflation can occur without recharge if the magma is sufficiently incompressible relative to the surrounding crust (Segall P. 2016 J. Geophys. Res. Solid Earth, 121, 8501-8522). Numerical calculations confirm this behaviour for both oblate and prolate ellipsoidal chambers surrounded by viscoelastic aureoles. Interestingly, the response to a nearly instantaneous pressure drop during an explosive eruption can be non-monotonic as the rock around the chamber relaxes at different rates. Pressure-dependent recharge of a non-Newtonian magma in an elastic crust leads to an initially high rate of inflation which slows over time; behaviour that has been observed in some magmatic systems. I close by discussing future challenges in volcano geodesy. This article is part of the Theo Murphy meeting issue 'Magma reservoir architecture and dynamics'.