Methods for tracking material properties within an unstructured, adaptive mesh computational modelling framework, with application to simulating the development of seismic anisotropy at spreading centres and transform faults

Abstract

The ability to accurately and efficiently track material properties in a Lagrangian sense during geodynamical flows, as well as evaluate how they evolve through both space and time, is of vital importance to our understanding of the structure, dynamics and evolution of Earth's mantle and lithosphere. An approach for achieving this, widely advocated by the geodynamics community, is the so-called particle-in cell technique. With this scheme, material properties are tracked by a large number of particles that are advected with the flow field. These properties can represent a wide range of parameters (e.g. material composition or strain) and the information they carry can be accessed during a simulation to feed back into the flow equations (e.g. composition controlling material density), as well as generate diagnostic fields for analysis (e.g. the generation of lattice-preferred orientation).

In Chapter 2, we develop a particle-in-cell scheme within an adaptive, unstructured, anisotropic mesh computational modelling framework called Fluidity. Regions of geodynamic interest often vary throughout a simulation, and the combination of the particle-in-cell scheme with a state of the art adaptive mesh algorithm enables both the mesh resolution and particle density to capture areas of interest with high resolution (or density), while reducing resolution (or density) in areas of little geodynamic interest. This ensures that a high level of accuracy is maintained throughout the computational domain, while also greatly improving numerical efficiency. The implementation of this scheme saw several inherent challenges which had to be overcome, including the treatment of particles during mesh adaptivity, the transfer of particle between processors, and the interpolation of values between particles and nodes of the mesh. In Chapter 3, validation of the implemented particle-in-cell scheme is undertaken for a series of well-known thermo-chemical convection benchmark tests. For each benchmark, particles track material composition as they are advected throughout the computational domain, with material composition feeding back onto the density field and influencing the buoyancy of materials. Results from the particle scheme are compared with results from a field-based control volume, flux-limited conservative difference scheme known as HyperC. Both schemes perform favourably across the series of benchmark tests, with HyperC displaying superior mass conservation and the particle scheme exhibiting superior shape preservation, resulting in a smoother material interface and the visualization of finer scale features. The particle-in-cell scheme is favoured, as it is more flexible in its application to tracking generalized material properties, enabling it to be applied to a wide range of geodynamical problems, such as the tracking of material texture. In Chapter 4, we develop the software package PyDRex, which is capable of converting tracked deformation parameters into predictions of material lattice-preferred orientation and seismic anisotropy. The generation of lattice-preferred orientation and subsequent observations of seismic anisotropy within Earth's mantle yields some of the most direct constrains available on both past and present-day deformation. By simulating these processes with geodynamics models, it is possible to generate synthetic seismic anisotropy predictions, which can be compared with observations in an attempt to constrain the prevalent flow regime in the upper mantle. In Chapter 5, we utilize the PyDRex software package with Fluidity and develop three sets of oceanic plate boundary models, being 2-D and 3-D mid-ocean ridge models, and 3-D mid-ocean ridge models with a transform fault offset. We compare anisotropy predictions from these models with seismic observations of anisotropy, allowing inferences to be made on the prevalent flow regime and distribution of material anisotropy surrounding oceanic plate boundaries. Show more