Inferring radial models of mantle viscosity

8 Convective flow in the mantle can be thought of (and modeled) as exclusively driven 9 by density heterogeneities in the mantle itself, and the resulting lateral variations 10 in the Earth’s gravity field. With this assumption, and a model of mantle rhe11 ology, a theoretical relationship can be found between 3-D mantle structure and 12 flow-related quantities that can be measured on the Earth’s surface, like free-air 13 gravity anomalies. This relationship can be used to set up an inverse problem, 14 with 1-D mantle viscosity as a solution. In the assumption that seismic velocity 15 anomalies be of purely thermal origin, and related to density anomalies by a simple 16 scaling factor, we invert the large-scalelength component of the above-mentioned 17 measurements jointly with seismic observations (waveforms and/or travel times) to 18 derive an accurate 5-layer spherically symmetric model of upperand lower-mantle 19 viscosity. We attempt to account for non-uniqueness in the inverse problem by ex20 ploring the solution space, formed of all possible radial profiles of Earth viscosity, 21 by means of a non-deterministic global optimization method: the evolutionary algo22 rithm (EA). For each sampled point of the solution space, a forward calculation is 23 conducted to determine a map of gravity anomalies, whose similarity to GRACE is 24 then measured; the procedure is iterated to convergence, according to EA criteria. 25 The robustness of the inversion is tested by means of synthetic tests, indicating that 26 our gravity data set is able to constrain less than 6 radial layers, each with uniform 27 viscosity. Independently of the tomographic model or the scaling factor adopted to 28 convert seismic velocity into density structure, the EA optimization method finds 29 viscosity profiles characterized by low-viscosity in a depth range corresponding to 30 the transition zone, and relatively uniform elsewhere. 31