The University of Oxford's Earth Sciences department is offering several PhDs. The projects are suitable for students with a first degree in applied mathematics, (geo, astro)physics, engineering, or theoretical mechanics. The projects and the attached full advertisements are listed below:
From dislocations to subduction: the microphysics of olivine deformation and its geodynamic implications
https://www.earth.ox.ac.uk/wp-content/uploads/2022/10/EARTH-23-RK1-advert.pdf
Granular dilatancy and the mechanics of faults
https://www.earth.ox.ac.uk/wp-content/uploads/2023/10/EARTH-24-RK4_advert.pdf
Tidal dissipation, magmatism and mantle convection on Io
https://www.earth.ox.ac.uk/wp-content/uploads/2022/11/EARTH-23-RK3_advert.pdf
For more information about how to apply, see here:
https://www.earth.ox.ac.uk/teaching/graduates/graduate-admissions/
https://www.earth.ox.ac.uk/teaching/graduates/dphil-projects/