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 ra dial mantle viscosity structure using a number of models of interior densit y heterogeneities, including an assessment of the error budget. We identify three classes of errors: those related to the density perturbations used a s 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 m ore 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 p ossible reduction of viscosity within the phase change regions due to the e ffects of transformational superplasticity. The inversion reveals three dis tinct families of viscosity profiles, all of which have an order of magnitu de stiffening within the lower mantle, with a soft D" layer below. The main distinction among the families is the location of the lowest-viscosity reg ion-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 mor e of the major phase transformations, leading to reduced dynamic topography , so that whole-mantle convection is consistent with small surface topograp hy.