Abstract
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.