Inferring radial models of mantle viscosity from gravity (GRACE) data and an evolutionary algorithm

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