Reconciling surface deflections from simulations of global mantle convection

Abstract. The modern state of the mantle and its evolution on geological timescales are of widespread importance for the Earth sciences. For instance, it is generally agreed that mantle flow is manifest in topographic and drainage network evolution, glacio-eustasy, and the distribution of sediments. There are now a variety of theoretical approaches to predict histories of mantle convection and its impact on surface deflections. A general goal is to make use of observed deflections to identify Earth-like simulations and constrain the history of mantle convection. Several important insights into the role of radial and non-radial viscosity variations, gravitation, and the importance of shallow structure already exist. Here we seek to bring those insights into a single framework to elucidate the relative importance of popular modeling choices for predicted instantaneous vertical surface deflections. We start by comparing results from numeric and analytic approaches to solving the equations of motion that are ostensibly parameterized to be as similar as possible. Deflections predicted by such numeric and analytic models can vary by ∼ 10 %, and the difference increases to ∼ 25 % when viscosity is temperature-dependent. Including self-gravitation and the gravitational potential of the deflected surface is a relatively small source of discrepancy. However, spherical harmonic correlations between model predictions decrease dramatically with the removal of shallow structure to increasing depths and when radial viscosity structure is modified. The results emphasize the sensitivity of instantaneous surface deflections to density and viscosity anomalies in the upper mantle. They reinforce the view that a detailed understanding of lithospheric structure is crucial for relating mantle convective history to observations of vertical motions at Earth's surface.