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Using Bayes inversion approach and Markov chain Monte Carlo method (MCMC), we studied the effect of temperature distribution in the lunar mantle on the chemical composition (concentrations of main oxides Al 2 O 3 , FeO, MgO) and seismic velocities in the mantle. The temperature and concentrations of the main oxides were calculated with thermodynamic methods for phase relations and physical properties modeling in the system CaO-FeO-MgO-Al 2 O 3 -SiO 2  using the Gibbs free energy minimization method. A set of geophysical data was used for the inversion (slenodetic: mean radius (R), mass (M), normalized moment of inertia (Is / MR 2 ), Love number k2 and seismic data – seismic travel times (TT). The Moon is assumed to be viscoelastic, spherically symmetric, and consists of nine layers with constant physical properties in each layer: megaregolith, crust, four mantle layers, low viscosity zone (LVZ), liquid outer core and solid inner core. Physical properties in each zone are assumed to be constant. The division of the mantle into layers was performed in accordance with the seismic model. The concentrations of the main oxides were set equal in the three upper layers of the mantle; the magma ocean model was used to calculate oxide concentrations in the lower mantle. Two types of geochemical models of bulk composition of the Moon were considered: 1 -models with similar to silicate Earth Al 2 O 3  content, 2 - models enriched in Al 2 O 3  (&gt; 4.5 wt.%). Linear temperature profiles in the mantle were considered, the temperature was set in the middle of the mantle layers at depths of 150, 375, 625 and 1000 km. At a depth of 150 km, the temperature was set at 600 ° C; in the lower mantle, it varied from 1000 to 1400 ° C. For both types of models and wide temperature range in the lower mantle, it is possible to obtain distributions of the main oxides concentrations in the mantle which are consistent with a given Al 2 O 3  and FeO bulk composition. Calculated concentrations and velocities in the mantle are in good agreement with the results obtained by other authors.

journal of physics. conference series

The effect of temperature distribution in the lunar mantle on joint inversion of geochemical (bulk chemical composition), seismic and selenodetic (GRAIL and LLR) data