Lay summary
Geophysical inversion is the primary source of information on the composition, temperature, and structure of the Earth's deep interior. Typically, geophysical inversion is used to infer secondary geophysical properties, such as seismic velocity or electrical conductivity, from direct geophysical observations. These secondary geophysical properties are then compared with those of various rocks to constrain the composition of planetary interiors. The disadvantage of this classical strategy is that it is generally not possible to simultaneously consider different types of geophysical data, i.e., seismic data is largely independent of conductivity data. This study employs a distinctly different strategy in that inversion is done directly for composition and temperature. The virtue of this approach is that it permits simultaneous inversion of different types of geophysical data, e.g., both electrical conductivity and seismic velocity are directly dependent on rock mineralogy and temperature. The complication in this strategy is that it requires a complete model for the geophysical properties of rocks as a function of composition and temperature. This difficulty is resolved by using thermodynamic models to predict the mineralogy of rocks at high temperature and pressure.