Geoid constraints on mantle viscosity from mantle convection models with plate motion history

The Earth's long-wavelength geoid anomalies are surface expression of mantle convection and are controlled by mantle viscosity. While previous studies of the geoid provide important constraints on the mantle radial viscosity variations, the mantle buoyancy used in these studies is derived from either slab density models or seismic tomography models, both of which suffer significant uncertainties and may not be dynamically consistent with the inverted viscosity. In this study, we formulate 3-D spherical mantle convection models with plate motion history of the last 130 Myr to generate dynamically self-consistent mantle buoyancy that is used together with the observed geoid to constrain the mantle viscosity. Our convection models reproduce both slab structures as observed in seismic models and the observed intermediate-wavelengths (l=4-12) geoid. We found that weak plate margins and strong plates are critical in reproducing the observed geoid and surface plate motion simultaneously. Models with a weak asthenosphere yield better-fit geoid than those with a weak mantle transition zone. In the best-fit model, which leads to 56% correlation between the modelled and observed geoid at degrees 4-12, the lower mantle viscosity is ~30 and ~600-1000 times higher than that in the transition zone and asthenosphere, respectively. Slab structures and geoid are also strongly affected by slab strength, and a moderately strong slab that is ~10-100 times stronger than the ambient mantle is preferred. Our models also place constraints on absolute viscosity and the preferred reference viscosity of the lower mantle is ~2.5×10²² Pa⋅s. While the geoid at degrees 4-12 is mainly controlled by subducted slab structures that are developed since the Cretaceous, the degrees 2-3 geoid anomalies that are strongly related to lower mantle structures are influenced by mantle convection further back in time.