3-D spherical high-resolution modelling of South Atlantic rifting-related mantle flow

The treatment of far-field boundary conditions (BCs) is one of the most poorly resolved issues for regional modelling of geodynamic processes. The mantle velocity field, along the side-walls and base of a modelling region, is typically much more poorly known than the geometry of past global motions of the surface plates, as constrained by global plate motion reconstructions. In this thesis, I have developed numerical tools that allow the study of 3-D spherical regional models with no fictitious internal boundaries using an embedded high resolution region within a global spherical coarse mesh.

A key piece in any numerical simulation using the Finite Element Method (FEM) is the mesh. I have developed an algorithm to generate high-quality unstructured meshes with embedded high resolution regions within 2-D and 3-D Cartesian, 2-D cylindrical and 3-D spherical shell domains. The mesh nodes are treated as if they were linked by virtual springs and the FEM is used to solve iteratively for the optimal nodal positions for the static equilibrium of this spring system. A 'guide-mesh' is incorporated to easily define preferred element sizes throughout the mesh.

A new technique, the 'Double Jacobian', is presented for more accurate solution in cylindrical or spherical geometries. This approach combines the advantages of working simultaneously in both Cartesian and polar or spherical coordinates. On the one hand, the governing matrix equations are kept in Cartesian coordinates, preserving their symmetry. On the other hand, the element geometry is described in 'straight-sided' polar or spherical coordinates, preserving the appropriate curved boundary surfaces and interfaces. These 'straight-sided' polar or spherical elements allow search routines to rapidly find arbitrary points in polar or spherical coordinates.

The tools described above have been applied to study the influence of the Tristan da Cunha plume during the early rifting and break-up of the South Atlantic. Global plate motion BCs are applied through time using GPlates. Models show a migration of hotter and weaker plume material towards the rifting region before the break-up, influenced by the lateral thickness variations in the initial structure of the lithosphere. Once the plume material reaches the rifting region, it is found to preferentially migrate southwards. This migration appears to be due to the presence of thicker S\~ao Francisco and conjugate Congo cratonic roots in the North combined with a ridge 'suction' force due to stretching of non-cratonic lithosphere in the South. This mechanism could explain the observed preferential southward formation of early-rifting-related Seaward Dipping Reflectors (SDRs) along South Atlantic margins with respect to their Tristan Plume progenitor.