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E342: Magma Rise Times from Finite Element Models of Crystal Growth and Diffusion (Lead Supervisor: John Maclennan, Earth Sciences)

Supervisors: John Maclennan (Earth Sciences) and John Rudge (Earth Sciences)

Importance of the area of research:

Compositional zonation within crystals found in volcanic rocks preserves a record of the timescales of magma storage and rise before eruption. Recent advances in microanalysis and chemical mapping have significantly improved our ability to image such zonation. Compositional profiles are now routinely modelled with 1D approximations in order to extract constraints on timescales and these timescales are often linked to other observations of pre-eruptive activity such as seismicity. It is now crucial that models can be developed to accurately recover timescales of magmatic processes whilst providing robust and realistic understanding of the uncertainties.

Project summary:

The observational record of pre-eruptive processes preserved in crystal chemical zonation has dramatically improved. However, modeling approaches have not yet been developed to optimise our ability to extract information about magmatic processes from the substantial quantities of new data. This data is starting to provide 2D and sometimes 3D images of crystal zonation in tens or hundreds of crystals from individual eruptions. There have been a few attempts to consider 2D and 3D effects when modelling the data, but there are several opportunities to significantly improve the modelling framework that allows us to link the observations to magmatic behaviour at depth.  This project benefits from the supervisors expertise in observational petrology (Maclennan), development of finite element modelling techniques (Richardson) and modelling of crystal-melt interaction (Rudge).

What the student will do:

The student will develop novel three-dimensional finite element models of the diffusion of chemical species within volcanic crystals using the software package FEniCS ( At first, idealised 3D geometries will be considered, but later the code will be adapted to model observed crystal shapes, and to include the interaction between crystals and melt during crystal growth. Innovative adjoint-based inversion techniques will be used extract robust estimates of the timescales of magmatic processes from new observations. The student will be expected to interact with researchers that are carrying out observations, in the field and in the laboratory, but their main focus will be on model development.

Please contact the lead supervisor directly for further information relating to what the successful applicant will be expected to do, training to be provided, and any specific educational background requirements.


Sides IR, Shea, T. et al., 2015, Cracking the olivine zoning code: Distinguishing

between crystal growth and diffusion, Geology, vol. 43, pp 935-938


Hartley, M.E. et al., 2016, Tracking timescales of short-term precursors

to large basaltic fissure eruptions through Fe-Mg diffusion in olivine,

Earth and Planetary Science Letters, vol 439, pp 58-70.


Farrell P.E., Ham D.A., Funke S.W. and Rognes M.E. (2013). Automated

derivation of the adjoint of high-level transient finite element programs, SIAM

J. Sci. Comp., vol. 35.4, pp. C369-C393. doi:10.1137/120873558


Follow this link to find out about applying for this project

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