Thermoelastic models of minerals and the composition of the Earth’s lower mantle

Abstract

A thermoelastic model for polycrystalline solids is presented extending our previous work. The model describes consistently thermoelastic properties such as the equations of state and the compressional and shear velocities v p and v s of MgSiO 3 and CaSiO 3 perovskites and (Mg, Fe)O magnesiowüstite under high pressure and/or high temperature. The values of the parameters in the model are determined from experimental data. A number of the model compositions of the (upper) mantle have been proposed by several researchers where the compositions are specified by the wt.% of five major oxides, SiO 2, MgO, FeO, Al 2O 3, and CaO. From these model compositions, we have derived the model aggregates for the lower mantle assuming that the lower mantle consists of a homogeneous three-component aggregate of (Mg 1− x− u , Fe x , Al u )(Si 1− u , Al u )O 3 perovskite, (Mg 1− y , Fe y )O magnesiowüstite, and CaSiO 3 perovskite. Using our model, we have calculated density, bulk and shear moduli, and v p and v s of these aggregates under lower mantle conditions as a function of depth z. The temperature T( z) is calculated assuming that the lower mantle is adiabatic and T(670 km)=1873 K and the nonadiabatic effect is incorporated perturbatically following the work of Shankland and Brown. We have found that the chondritic model and the lower mantle model both by Anderson and Bass are in excellent agreement with preliminary reference earth model (PREM). Our results show that the elastic relaxation effect due to long-time-scale mantle convection is relatively small in the lower mantle.