Inversion for mantle viscosity profiles constrained by dynamic topography and the geoid, and their estimated errors

We perform a joint inversion of Earth's geoid and dynamic topography for radial mantle viscosity structure using a number of models of interior density heterogeneities, including an assessment of the error budget. We identify three classes of errors: those related to the density perturbations used as input, those due to insufficiently constrained observables, and those due to the limitations of our analytical model. We estimate the amplitudes of these errors in the spectral domain. Our minimization function weights the squared deviations of the compared quantities with the corresponding errors, so that the components with more reliability contribute to the solution more strongly than less certain ones. We develop a quasi-analytical solution for mantle flow in a compressible, spherical shell with Newtonian rheology, allowing for continuous radial variations of viscosity, together with a possible reduction of viscosity within the phase change regions due to the effects of transformational superplasticity. The inversion reveals three distinct families of viscosity profiles, all of which have an order of magnitude stiffening within the lower mantle, with a soft D layer below. The main distinction among the families is the location of the lowest-viscosity region-directly beneath the lithosphere, just above 400 km depth or just above 670 km depth. All profiles have a reduction of viscosity within one or more of the major phase transformations, leading to reduced dynamic topography, so that whole-mantle convection is consistent with small surface topography.