Self-consistent Reconstructions of the Earth's Mantle in Space and Time using Nonlinear Rheologies

Reconstructing the spatial and temporal evolution of Earth’s mantle through the recent geological past stands as one of the grand challenges in Geodynamics. One method to invert for the mantle’s evolution is to reformulate mantle flow as an optimisation problem using the adjoint method, where uncertain properties, such as the mantle’s previous thermo-chemical states, are found by minimising a misfit functional that represents the difference between model predictions and geodynamic inferences from various disciplines, including seismology, geodesy, and geochemistry. While the rapid growth in high-performance computing capacities has underpinned an ever-growing number of such reconstruction models, they often make several simplifying physical assumptions, or are limited in the number of assimilated datasets, thus limiting their applicability.

Here we present our latest attempts at reconstructing the evolution of Earth’s mantle using complex non-linear rheologies. Our approach builds upon a novel algorithmic differentiation method as implemented in dolfin-adjoint, together with state-of-the-art optimisation methods, developed using the Rapid Optimisation Library. Using analytical and synthetic examples, we show that the self-consistent derivation of the adjoint equations in our approach provides a pathway for accurate inversions for past-mantle flow.