Numerical Modelling of Three-phase Magma Chamber Dynamics

Crustal magma chambers are thought of as the locus of magmatic differentiation as well as the source of volcanic eruptions. Magma chamber dynamics conceptually comprise fractional crystallisation, wall rock assimilation, mafic recharge, and volatile degassing. The time evolution and eruptability of magma chambers has been studied using 0-D box models1; however, these do not resolve the spatial evolution and complex reaction-transport dynamics of silicate melt and crystals, and volatile fluid bubbles including magma convection and phase segregation. Few models2,3 have resolved the coupled fluid mechanics and thermo-chemistry of magma chamber dynamics, but their results have not been reproduced nor their methods further developed or applied in more than a decade.

Here, I introduce a new 2-D numerical model of the three-phase fluid mechanics of crystals and bubbles suspended in melt coupled to simplified chemical thermodynamics including silicates and volatiles based on an idealised phase diagram calibrated to petrological experiments and/or thermodynamic equilibrium models. The model tracks the geochemical evolution of idealised trace elements, stable isotope ratios, and radiogenic isotope decay systems. The mathematical model is based on a recent theory framework4 and is numerically implemented in Matlab using the finite-difference staggered-grid method5. The numerical model is benchmarked by the Method of Manufactured Solutions and by confirming conservation of total mass and energy in the domain. The simulation code will be made openly available to the community.

First results demonstrate the utility of the model for studying fractional crystallisation, wall rock assimilation, and mafic recharge in magma chambers. Various expressions of stratified convection are observed under a range of conditions, with the presence of an exsolved volatile phase having major implications on the dynamics. A key advance of the model is that it elucidates relationships between geochemical signatures and underlying magma dynamics, hence providing new avenues for the process-based interpretation of igneous rock chemistry.

Degruyter & Huber, Earth Planet Sc Lett, 2014.

Dufek & Bachmann, Geology, 2010.

Gutiérrez & Parada, J Petrol, 2010.

Keller & Suckale, Geophys J Int, 2019.

Gerya, Cambridge Univ Press, 2009.