Inversion of seismic and geodetic data for the major element chemistry and temperature of the Earth's mantle

We jointly invert global seismic traveltime data, mean mass, and mean moment of inertia for Earth's mantle composition and thermal state using a stochastic sampling algorithm. The chemical composition of the silicate Earth is modeled within the system CaO-FeO- MgO-Al₂O₃-SiO₂. Given these parameters we calculate the stable mineralogy and its elastic properties and density as a function of pressure and temperature using Gibbs free energy minimization. Bulk seismic P and S wave velocity profiles (V_P, V_S) are computed from Voigt-Reuss-Hill averaging, while anelastic contributions to V_P and V_S are calculated assuming shear attenuation to be linearly varying with depth. From these radial profiles, seismic traveltimes, mean mass, and mean moment of inertia are calculated, providing a range of compositions and temperatures that fit data within uncertainties. Specifically, we find an upper mantle composition that is depleted in CaO and Al₂O₃ relative to canonical values inferred for the upper mantle from analysis of mantle xenoliths. The lower mantle in contrast is found to be enriched in FeO and depleted in SiO₂, with a Mg/Si ratio of ∼1.2 and a Mg# of ∼0.83, resulting in a bulk silicate Earth composition that is unmatched by any of the common chondrites. The mantle geotherm is found to be superadiabatic for depths >1200 km, while lower mantle temperatures reach ∼2400°C at 2500 km depth. The presence of a chemical transition between upper and lower mantle is further suggested in the depth range 650-750 km.