S U M M A R YA generalized inverse method is applied to infer the radial lower mantle composition and temperature profile from seismological models of density and bulk sound velocity. The computations are performed for a five-component system, MgO-FeO-CaO-Al 2 O 3 -SiO 2 and three phases: (Mg,Fe,Al)(Si,Al)O 3 perovskite, (Mg,Fe)O magnesiowustite, and CaSiO 3 perovskite. A detailed review of the elasticity data set used to compute the elastic properties of mineral assemblages is given. We consider three different a priori compositional models-pyrolite, chondritic and a model based on cosmic abundances of elements-as a priori knowledge for the inversions in order to investigate the sensitivity of any given best-fit solution to the assumed initial composition. Consistent features in all inversions, independent of the a priori model, are a total iron content of X Fe 0.10 ± 0.06 and a subadiabatic temperature gradient over most of the lower mantle depth range. A peculiar correlated behaviour of the two most sensitive parameters (iron content and temperature) is found below the 660 km discontinuity: over the depth range from 660 km down to 1300 km. Significantly, we find that the bulk composition inferred from any given inversion is strongly dependent on the choice of a priori model. Equally satisfactory fits to the lower mantle bulk sound velocity and density profiles can be obtained using any of the a priori models. However, the thermal structure associated with these compositional models differs significantly. Pyrolite yields a relatively cool geotherm (T 660 1800 K and X Pv 0.64), while perovskite-rich models such as chondritic or cosmic models yield hot geotherms (T 660 2500 K and X Pv 0.84 for the latter), but all of the geotherms are subadiabatic. The results of inversions are virtually unaffected by the partitioning of iron between perovskite and magnesiowustite. Out of the five oxide components considered in our models, the bulk Al 2 O 3 and CaO contents of the mineral assemblages are least well constrained from our inversions. Our results show that a major shortcoming of lower mantle compositional and thermal models based on inversions of bulk sound velocity and density is the strong dependence of the final solution on the a priori model. That is, a wide variety of best-fit compositional and thermal models can be obtained, all of which provide satisfactory fits to global average seismic models. It is, in fact, this non-uniqueness that dominates the resulting a posteriori uncertainties and prevents a clear discrimination between different compositional models. Independent constraints on the thermal structure or on the shear properties of lower mantle assemblages are needed to infer lower mantle composition with a higher degree of certainty.Key words: bulk modulus, density, inverse problem, mantle, mineralogy, seismic velocities. INTROD U C T I O NThe lower mantle accounts for nearly half of the mass of the Earth. It is generally accepted that its mineralogy mostly consists of magnesium silicate perovskite (Mg...

S U M M A R YWe 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-SiO 2 -Al 2 O 3 -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.

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