The modern state of the mantle and its evolution on geological timescales is 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 in the distribution of sediments. There now exists 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 roles 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 modelling choices on predicted instantaneous vertical surface deflections. We start by comparing results from numeric and analytic approaches to solving the equations of motion that are ostensibly parameterised to be as-similar-as-possible. Resultant deflections can vary by $\sim$10\%, increasing to $\sim25$\% when viscosity is temperature-dependent. Including self-gravitation and gravitational potential of the deflected surface are relatively small sources of discrepancy. However, spherical harmonic correlations between model predictions decrease dramatically with the excision of shallow structure to increasing depths, and when radial viscosity structure is modified. The results emphasise 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.

The modern state of the mantle and its evolution over geological timescales is 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, volcanism, and in the distribution of sediments. An obvious way to test theoretical understanding of mantle convection is to compare model predictions with independent observations. We take a step towards doing so by exploring sensitivities of theoretical surface deflections generated from a systematic exploration of global mantle convection simulations. Sources of uncertainty, model parameters that are crucial for predicting deflections, and those that are less so, are identified. We start by quantifying similarities and discrepancies between deflections generated using numerical and analytical methods that are ostensibly parameterised to be as-similar-as-possible. Numerical approaches have the advantage of high spatial resolution, and can capture effects of lateral viscosity variations. However, treatment of gravity is often simplified due to computational limitations. Analytic solutions, which leverage propagator matrices, are computationally cheap, easy to replicate, and can employ radial gravitation. However, spherical harmonic expansions used to generate solutions can result in coarser resolution, and the methodology cannot account for lateral viscosity variations. We quantify the impact of these factors for predicting surface deflections. We also examine contributions from radial gravity variations, perturbed gravitational potential, excised upper mantle, and temperature-dependent viscosity, to predicted surface deflections. Finally, we quantify effective contributions from the mantle to surface deflections. The results emphasise the sensitivity of surface deflections to the upper mantle.