Robust global mantle flow trajectories and their validation via dynamic topography histories

Abstract

SUMMARYThe ability to construct time-trajectories of mantle flow is crucial to move from studies of instantaneous to time-dependent earth models and to exploit geological constraints for mantle convection modelling. However mantle convection is chaotic and subject to the butterfly effect: the trajectories of two identical mantle convection models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated. Because one may use seismic inferences about the mantle state as a starting or terminal condition to project mantle flow forward or backward in time, and because the seismic inference is invariably subject to uncertainties, this seemingly would rule out any construction of robust mantle flow trajectories. Here we build upon earlier work which showed that assimilation of the horizontal component of the surface velocity field from a known reference model allows one to overcome the butterfly effect and to construct robust mantle flow trajectories, regardless of the choice of the initial state perturbation. To this end, we use high resolution 3-D spherical mantle convection models in four end-member configurations: an isoviscous purely internally heated model, an isoviscous purely bottom heated model, a model with a radial increase in viscosity along with pure internal heating as well as a model that combines the effects of radial viscosity increase, internal and bottom heating. In order to capture the impact of seismic filtering, we perturb the initial temperature fields of these end-member models through either radial or horizontal smoothing of the temperature field or the application of the tomographic filter of seismic model S20RTS. We assess the quality of the constructed model trajectories via a number of statistical measures as well as comparisons of their dynamic topography histories. The latter is an essential step since mantle flow cannot be directly observed but has to be inferred via its surface manifestations. Importantly, linking mantle flow to surface observations yields patterns representable on a latitude–longitude grid similar to meteorological observables such as precipitation. This invites the application of meteorological quality metrics, such as the power ratio and Taylor diagram, to assess the quality of mantle flow trajectories. We introduce these metrics for the first time in the context of mantle convection and demonstrate their viability based on the compact manner in which they summarize model performance.