The influence of uncertain mantle density and viscosity structures on the calculations of deep mantle flow and lateral motion of plumes

Mantle plumes form from thermal boundary layers, such as Earth's core-mantle boundary. As plumes rise towards the surface, they are laterally deflected by the surrounding mantle flow that is governed by deep mantle density and viscosity structures. The lateral motions of mantle plumes carry information of deep mantle structure and dynamics and are used to setup reference frames by which absolute plate motions are reconstructed. In this study, we compare two methods to compute deep mantle flow and lateral motion of plumes. In mantle convection (MC) models, the mantle flow field and lateral motions of plumes are determined by solving conservation equations forward-in-time from given initial conditions. In plume advection (PA) models, approximate viscosity and present-day density structures are used to calculate present-day mantle flow which is then propagated backward-in-time assuming zero thermal diffusion, and plume conduits are represented by continuous lines and are passively advected within the background mantle flow. The question is how assumptions in PA models influence the predictions of deep mantle flow and plume lateral motions. Here, we perform purely thermal MC models and thermochemical MC models with intrinsically dense materials in the lowermost mantle. The deep mantle flow and plume lateral motions are determined accurately in each MC model. We also perform PA models using the approximated present-day viscosity and temperature structures in these MC models. We find that PA models without considering temperature-dependence of viscosity and/or only using long wavelength present-day temperature structure (up to degree 20) often lead to an average of ∼50-60 percent and ∼60-200 percent differences of present-day mantle flow velocities than purely thermal MC models and thermochemical MC models, respectively. By propagating inaccurate flow fields backward-in-time in PA models often cause even larger errors of mantle flow velocities in the past. Even using the same parameters and starting from the same present-day mantle flow fields as in MC models, the PA models still show an average of ∼10-30 percent misfit of mantle flow velocities after ∼40 Ma. In addition, we show that errors of mantle flow fields in PA models can cause ∼100-600 percent differences of plume lateral motions than that constrained in MC models in the past 60 Ma. Even we use the mantle flow in MC models to advected virtual plumes in PA models, the virtual plumes could still show ∼50-300 percent difference of lateral motions than dynamic plumes in MC models if the virtual plumes do not start with the same locations and/or shapes as plumes in MC models. We also find virtual plumes in PA models initiated at different locations and/or with different shapes can be later advected to similar locations, suggesting that the lateral motions of plumes in PA models can be non-unique. Therefore, it is important to consider the build-in assumptions of PA models when interpreting their predictions on deep mantle flow field and plume lateral motions. The accuracy of PA models would improve as we gain better understanding on Earth's deep mantle structure and dynamics.