magnetic evolution of planetary bodies [@monteux_2011; @williams_2004], and the formation and evolution of primitives magma oceans [@sun_2018], with in particular the possibility of forming a basal magma ocean [@labrosse_2007]. The partitioning of chemical elements has also profound geodynamical implications. For example, the identity and abundance of light and radioactive elements in the core [@badro_2015; @corgne_2007], which are key parameters for the dynamics and evolution of the core, depend on ($P$,$T$,$fO_2$) conditions at which metal and silicate have equilibrated.

Geochemical data such as geochronometers, estimates of the mantle and core composition, meteorite geochemistry, and partition coefficients [@li_1996; @righter_2011; @siebert_2011] constitute an inverse problem for the timing of accretion, the ($P$,$T$,$fO_2$) segregation conditions and the degree of chemical equilibration of the impactors’ cores with the mantle of the Earth. This inverse problem is under-determined since there are more degree of freedom than constraints. The interpretation of core formation chronometers well illustrates this issue since there is a strong trade-off between the estimated accretion time and the equilibration efficiency: the Hf-W chronometer predicts an accretion time around 30 Myr if perfect equilibration is assumed [@kleine_2002], but that time is significantly increased in case of imperfect equilibration [@rudge_2010].

The interpretation of geochemical data crucially 