On the bulk composition of the lower mantle: Predictions and limitations from generalized inversion of radial seismic profiles

We examine the problem of obtaining the thermal structure and bulk chemical composition of the lower mantle from its seismologically determined velocity and density profiles, and the most recent results on the elastic properties of the relevant phases (including, of particular importance, shear moduli). A novel aspect of this paper is the application of an iterative technique solving generalized non-linear inverse problem, which allows us to simultaneously consider a complex chemical system (the MgO-FeO-SiO₂-Al₂O₃ -CaO system, which includes all major components in the lower mantle), and to rigorously evaluate the full covariance and resolution matrices. The effects of experimental uncertainties in the shear moduli are carefully accounted for. We show that although the a posteriori uncertainties in the results for lower-mantle compositions are relatively large, the averaged lower-mantle Mg/Si ratio should be lower than 1.3 in order to satisfactorily fit the 1-D seismic profiles. Two distinct families of best-fitting models are determined. The first is based upon a value for the pressure derivative of the perovskite shear modulus that is representative of various existing experimental measurements (μ′₀ = 1.8). Under this assumption, it is not possible to match the lower mantle seismic properties with an adiabatic geotherm and uniform chemical composition. Instead, this family of solutions is characterized by a geotherm with large temperature gradients (dT/dz increases from 0.5 to 0.9 K km^-1 between 800 and 2700 km and the temperature reaches 3400 K at the depth of 2700 km), and a depth dependent bulk composition with an Mg/Si ratio decreasing from 1.18 ± 0.14 to 1.03 ± 0.16 between 800 and 2700 km. The second family of solutions is obtained when we attempt to fit the lower mantle with a simpler compositional and thermal structure. This can only be done when the pressure derivative of the shear modulus for perovskite is close to the most recent values obtained by Brillouin spectroscopy, that is, with a μ′₀ close to 1.6 instead of 1.8. The resulting temperature gradient is 0.25 K km^-1 in the upper part of the lower mantle and 0.5 K km^-1 below 1700 km depth; the geotherm reaches 2800 K at a depth of 2700 km. Corresponding Mg/Si ratio remains rather constant and close to 1.16 throughout the lower mantle. We show that the temperature gradient is strongly correlated with the pressure derivative μ′₀ of the shear modulus of perovskite: lower values of μ′₀ imply lower thermal gradients. We also discuss the importance of the Bullen parameter as an additional constraint. In order to refine conclusions on the lower-mantle structure, additional independent observables, such as accurate observations on electrical conductivity and 1-D Q profiles, are necessary.