Constraining the composition and thermal state of the moon from an inversion of electromagnetic lunar day-side transfer functions

We present a general method to constrain planetary composition and thermal state from an inversion of long-period electromagnetic sounding data. As an example of our approach, we reexamine the problem of inverting lunar day-side transfer functions to constrain the internal structure of the Moon. We go beyond the conventional approach by inverting directly for chemical composition and thermal state, using the model system CaO–FeO–MgO–Al2O3–SiO2, rather than subsurface electrical conductivity structure, which is only an indirect means of estimating the former parameters. Using Gibbs free energy minimisation, we calculate the stable mineral phases, their modes and densities. The mineral modes are combined with laboratory electrical conductivity measurements to estimate the bulk lunar electrical conductivity structure from which transfer functions are calculated. To further constrain the radial density profile in the inversion we also consider lunar mass and moment of inertia. The joint inversion of electromagnetic sounding and gravity data for lunar composition and selenotherm as posited here is found to be feasible, although uncertainties in the forward modeling of bulk conductivity have the potential to significantly influence the inversion results. In order to improve future inferences about lunar composition and thermal state, more electrical conductivity measurements are needed especially for minerals appropriate to the Moon, such as pyrope and almandine.