Mantle-circulation models with sequential data assimilation: inferring present-day mantle structure from plate-motion histories

Data assimilation is an approach to studying geodynarnic models consistent simultaneously with observables and the governing equations of mantle flow. Such an approach is essential in mantle circulation models, where we seek to constrain an unknown initial condition some time in the past, and thus cannot hope to use first principles convection calculations to infer the flow history of the mantle. One of the most important observables for mantle-flow history comes from models of Mesozoic and Cenozoic plate motion that provide constraints not only on the surface velocity of the mantle but also on the evolution of internal mantle-buoyancy forces due to subducted oceanic slabs. Here we present five mantle circulation models with an assimilated plate-motion history spanning the past 120 Myr, a time period for which reliable plate-motion reconstructions are available. All models agree well with upper- and mid-mantle heterogeneity imaged by seismic tomography. A simple standard model of whole-mantle convection, including a factor 40 viscosity increase from the upper to the lower mantle and predominantly internal beat generation, reveals downwellings related to Farallon and Tethys subduction. Adding 35% bottom heating from the core has the predictable effect of producing prominent high-temperature anomalies and a strong thermal boundary layer at the base of the mantle. Significantly delaying mantle flow through the transition zone either by modelling the dynamic effects of an endothermic phase reaction or by including a steep, factor 100, viscosity rise from the upper to the lower mantle results in substantial transition-zone heterogeneity, enhanced by the effects of trench migration implicit in the assimilated plate-motion history. An expected result is the failure to account for heterogeneity structure in the deepest mantle below 1500 km, which is influenced by Jurassic plate motions and thus cannot be modelled from sequential assimilation of plate motion histories limited in age to the Cretaceous. This result implies that sequential assimilation of past plate-motion models is ineffective in studying the temporal evolution of core-mantle-boundary heterogeneity, and that a method for extrapolating present day information backwards in time is required. For short time periods (of the order of perhaps a few tens of Myr) such a method exists in the form of crude 'backward' convection calculations. For longer time periods (of the order of a mantle overturn), a rigorous approach to extrapolating information back in time exists in the form of iterative nonlinear optimization methods that carry assimilated information into the past through the use of an adjoint mantle convection model.