Retrodiction Range of geodynamic earth models from twin experiments that account for model inconsistencies and limited resolution of present-day heterogeneity

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Retrodictions with the adjoint method are a powerful tool to reconstruct past mantle states. They open new avenues to test dynamic earth models against a range of geologic and geophysical observables. So far, at a theoretical level their convergence and uniqueness properties have been elucidated only with highly simplified twin experiments, where the most severe limitation stems from the (unrealistic) assumption of perfect knowledge of the mantle convection parameters and the present-day model state. Here we propose to improve our fundamental understanding of mantle flow retrodictions studying (1) how inconsistent model parameters, compositional variations, and the limited resolving power of seismic inferences of the mantle state enter the retrodiction problem, (2) how the inconsistencies map into retrodicted mantle flow trajectories, and (3) how the trajectories contribute to growth of spurious heterogeneity as one goes back in time, effectively limiting the temporal range for which viable retrodictions can be achieved. To address these fundamental questions, we propose a systematic study of specifically designed twin experiments, where admissible parameter variations and seismic filtering effects are introduced systematically into the inverse problem, to estimate the impact on geodynamic retrodictions of: 1) deviations in rheological parameters between the reference and inverse model, 2) absence of small-scale structures in the mantle heterogeneity field due to tomographic filtering, 3) inconsistent interpretations of mantle buoyancies as a result of wrongful assumptions for the bulk composition, 4) errors in past plate motion models in particular related to the choice of reference frame point 3 will involve the derivation of a new set of adjoint equations capable of representing thermo-chemical convection.