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Cambridge NERC Doctoral Training Partnerships

Graduate Research Opportunities

Lead Supervisor: John Rudge, Earth Sciences

Co-Supervisor: David Wallis, Earth Sciences

Brief summary: 
A project to develop novel mathematical models of rock rheology, to better understand the migration of melt through the Earth's mantle.
Importance of the area of research concerned: 
Rheology is the branch of physics which is concerned with the deformation and flow of materials. An understanding of rheology is crucial to understanding a wide variety of physical processes in the solid Earth. Such processes include, but are no means limited to: the propagation of seismic waves through the Earth; convection in the Earth's mantle; and the migration of magma to the Earth's surface. Partially-molten, polycrystalline rocks have a complex rheology with a wide range of different behaviour on different time-scales and under different conditions of temperature, stress, and chemistry. It remains challenging to perform suitable laboratory experiments on rocks for the parameter values appropriate for the Earth's deep interior. As a consequence, mathematical models of the underlying physical processes play a key role in allowing one to extrapolate from limited laboratory data to the Earth. An understanding of rheology allows one to connect the present-day view of the Earth from geophysics to longer-term dynamics e.g. variations in seismic wavespeed can be mapped to variations in temperature and porosity, which in turn control long-term mantle dynamics.
Project summary : 
The aim of the project is to develop novel mathematical models to provide new insights into the rheology and dynamics of the Earth's mantle. Such models will be grounded in observations, both from laboratory experiments and geophysics (particularly seismic and magnetotelluric imaging). A fruitful source of data comes from recent laboratory experiments on polycrystalline rock-analogues such as borneol, which undergoes the same kinds of diffusion and dislocation creep processes as rocks, but at much lower temperatures (around 40 degrees C). The supervisor has an ongoing collaboration with Yasuko Takei (Earthquake Research Institute, University of Tokyo) who performs such experiments, and who will provide laboratory data to assist the modelling effort.
What will the student do?: 
The student will produce novel partial differential equation (PDE) based models of physical processes acting at the scale of individual mineral grains, which can then be upscaled to produce a model of rheology appropriate at laboratory and planetary scales. The physical processes include diffusion of defects within the mineral lattice, and the key role of surface energy in determining the motion of interfaces between grains and between grains and melt. The development of such models pose a number of mathematical challenges due to nonlinear couplings between different processes, and the difficulty of solving PDEs with moving boundaries. Numerical methods will thus play an important role in the project.
References - references should provide further reading about the project: 
Rudge J.F. 2018. The viscosities of partially molten materials undergoing diffusion creep. J. Geophys. Res. Solid Earth vol. 123 doi:10.1029/2018JB016530
Sasaki Y., Takei Y., McCarthy C., Rudge J.F. 2019. Experimental study of dislocation damping using a rock analogue. J. Geophys. Res. Solid Earth 124, pp. 6523-6541, doi:10.1029/2018JB016906
Kohlstedt, D.L., Hansen L. N. 2015. Constitutive equations, rheological behaviour, and viscosity of rocks. in Treatise on Geophysics, 2nd edition, Chapter 2.18 pp. 441-472
You can find out about applying for this project on the Department of Earth Sciences page.
Dr David Wallis
Dr John Rudge
Department of Earth Sciences Graduate Administrator