Lateral variations in mantle rheology: implications for convection related surface observables and inferred viscosity models

Over the past decade numerous analyses of convection-related observables, such as horizontal surface divergence, geoid or gravity anomalies and dynamic surface topography, have been carried out in the context of tomography-based mantle flow models. One of the major objectives of this modelling has been the inference of the rheological structure of the mantle. With few exceptions, these studies have been conducted in the framework of a viscous flow theory which assumes that the mantle rheology may be represented in terms of an effective viscosity which varies with depth only. Here, we present a detailed assessment of the impact of lateral variations in viscosity on global convection related observables using forward modelling of buoyancy induced flow in a 3-D spherical shell. We find that the resulting dynamic topography at the surface and the core-mantle boundary, as well as the gravitational response of the earth, are affected relatively little by the inclusion of lateral viscosity variations (LVV) when compared with results for a purely 1-D radial viscosity model. In particular, we found that the effect of LVV on the global observables is significantly smaller than the variability due to uncertainties in the current seismic tomography models. We also quantify the effect of LVV in the context of the viscosity inverse problem using two synthetic data sets generated with a 1-D viscosity profile and with a fully 3-D viscosity model in which the LVV span across three orders of magnitude. We compared the 1-D viscosity profiles recovered from the inversions and found that LVV have virtually no effect on our inversion results. The synthetic viscosity inversion further revealed that the effect of LVV is small in comparison to the uncertainties arising from the seismic tomography models. The inversions also suggest that the 1-D viscosity profiles derived from actual surface data represent the depth variation of the horizontally averaged logarithm of the 3-D viscosity distribution in the mantle.