A method to estimate the composition of the bulk silicate Earth in the presence of a hidden geochemical reservoir

The possibility of a hidden geochemical reservoir in the deep mantle has long been debated in geophysics and geochemistry, because of its bearings on the structure of the core-mantle boundary region, the origin of hotspots, the style of mantle convection, the history of the geomagnetic field, and the thermal evolution of Earth. The presence of such hidden reservoir, however, may invalidate existing models for the composition of the bulk silicate Earth because these models invariably assume that major chemical differentiation in the mantle follows the compositional trend exhibited by upper-mantle rocks. This article presents a new method to estimate the composition of the bulk silicate Earth by explicitly taking into account the possibility of a hidden reservoir. This geochemical inference is formulated as a nonlinear inverse problem, for which an efficient Markov chain Monte Carlo algorithm is developed. Inversion results indicate that the formation of a hidden reservoir, if any, took place at low pressures probably within the first 10 Myr of the history of the solar system and was subsequently lost from the Earth by impact erosion. The global mass balance of the bulk silicate Earth is revisited with the inversion results, and the depletion of highly incompatible elements in the present-day Earth is suggested to be moderate.