Investigating the initial condition of mantle models using data assimilation

Mantle convection models are computational models that utilise the equations defining the convective processes taking place in a terrestrial planet’s mantle. Mantle circulation models (MCMs) are a subclass of mantle convection models that constrain mantle flow by imposing a boundary condition that uses plate reconstructions. Time dependent assimilation of plate velocities generates structures within the mantle that have been shown to correspond with present day Earth observations. Inferences of past mantle structures in MCMs are however more difficult due to the lack of initial condition for models. Without access to an initial condition for MCMs, pseudo initial conditions are used in MCM studies. MCMs therefore contain some error due to this uncertainty in initial condition. This thesis addresses the uncertainties in MCMs caused by the lack of knowledge of the initial condition, and attempts to improve the initial condition for Earth models. Utilising perturbed twin experiments we show that assimilating plate reconstructions deters any chaotic growth over the assimilation period, minimising the influence of the initial condition at present day. We also investigate and utilise advanced assimilation techniques that constrain mantle flow back in time, using a method known as an adjoint. Running a series of synthetic test cases using the adjoint we determine its efficiencies and effectiveness at constraining initial condition estimates. We find the adjoint is an excellent method for reconstructing initial conditions. Using the adjoint, we conclude by running high resolution MCMs to construct initial conditions for differing viscosities, and compare these to the | iii standard method of obtaining an initial condition in MCM studies. We find that this yields mantle flow patterns markedly different from past studies, implying the adjoint can provide an alternate perspective for past mantle flow studies