Elasticity, composition and temperature of the Earth’s lower mantle: a reappraisal

The interpretation of seismological models for the Earth’s lower mantle in terms of chemical composition and temperature is sensitive both to the details of the methodology employed and also to uncertainties in key thermoelastic parameters, especially for the dominant (Mg, Fe)SiO3 perovskite phase. Here the alternative approaches—adiabatic decompression of the lower mantle for comparison at zero pressure with laboratory data, and the projection of laboratory data to lower-mantle P–T conditions for direct comparison with seismological observations—are assessed, along with the equations of state on which they are based. It is argued that adiabatic decompression of the lower mantle is best effected by a strategy in which consistent third-order finite-strain expressions are required simultaneously to fit the strain dependence of both the seismic parameter and the density. This procedure accords due weight to the most robust seismological observations, namely the wave speeds, and reduces to an acceptable level the otherwise very strong covariance among the fitted coefficients. It is demonstrated that this approach can readily be adapted to include the effects of relaxation, from the Hill average to the Reuss lower bound, of the aggregate bulk modulus which governs the radial variation of density. For the projection of laboratory thermoelastic data to lower-mantle P–T conditions, the preferred equation of state is of the Mie–Gruneisen type, involving the addition at constant volume of the pressure along a finite-strain principal (300 K) isotherm and the thermal pressure calculated from the Debye approximation to the lattice vibrational energy. A high degree of consistency is demonstrated between these alternative equations of state. Possible departures of the lower mantle from conditions of adiabaticity and large-scale homogeneity are assessed; these are negligible for the PREM model (Bullen parameter ηB = 0.99 ± 0.01) but significant for ak135 (ηB ∼ 0.94 ± 0.02), reviving the possibility of a substantially superadiabatic temperature gradient. Experimentally determined thermoelastic properties of the major (Mg, Fe)SiO3 perovskite and (Mg, Fe)O magnesiowustite phases are used to constrain the equation-of-state parameters employed in the analysis of seismological information, although the scarcity of information concerning the pressure and temperature dependence of the elastic moduli for the perovskite phase remains a serious impediment. Nevertheless, it is demonstrated that the combination of a pyrolite composition simplified to the three-component system (SiO2–MgO–FeO) with molar XPv = 0.67 and XMg = 0.89, and a lower-mantle adiabat with a potential temperature of 1600 K—consistent with the preferred geotherm for the upper mantle and transition zone—is compatible with the PREM seismological model, within the residual uncertainties of the thermoelastic parameters for the perovskite phase. In particular, such consistency requires values for the perovskite phase of KS′ = (∂KS /∂P)T and q = (∂ ln γ/∂ ln V )T of approximately 3.8 and 2, and ∂G/∂T near −0.022 GPa K−1 for the lower-mantle assemblage. More silicic models, which have sometimes been advocated, can also be reconciled with the seismological data, but require lower-mantle temperatures which are much higher—by about 700 K for pyroxene stoichiometry. However, the absence of seismological and rheological evidence for the pair of thermal boundary layers separating convection above and below, which is implied by such models, remains a formidable difficulty. Under these circumstances, the simplest possible model, that of grossly uniform chemical composition throughout the mantle, is preferred.