Geodynamic models of lithospheric and mantle processes.

This thesis addresses outstanding scientific problems relating to the evolution of the Earth's interior and surface through the field of Geodynamics. Within this thesis fun-damentals of continuum mechanics was used to describe the long term Earth processes of mantle convection and lithospheric dynamics. These dynamic problems were consid¬ered from a fluid dynamic perspective with internal body forces (stresses) and density contrasts balancing to drive motion within the Earth. The solutions of these problems were obtained numerically using the software framework' Underworld'. The implementation of a viscoelastic rheology into the 'Underworld' software frame¬work is outlined with particular attention to the stress rate tensor and the quantification of the energy dissipation, stored energy rate and the orientation of the stress and strain rate tensor. This viscoelastic rheology was then used in models of free subduction. The variation in morphology and hinge energy rates from viscous to viscoelastic slab cores was highlighted with the stored energy rate found to be different for the viscoelastic case, releasing energy within the mantle at depth. The presence of a deep continental lithosphere attached to a plate moving at average Earth speeds was found to have a buffering effect on the down stream oceanic lithosphere, offshore of passive margins. Parameterising the upper mantle using a temperature and strain rate dependent man¬tle for this same deep continental lithosphere was shown to result in a varying surface topography including the formation of transient, in both space and time, continental basins near passive margins.