Theoretical lunar mantle seismic velocity and density profiles are calculated for a series of proposed bulk compositions, present-day selenotherms, and models for early differentiation and evolution. The seismic velocity profiles are compared to the most recent observational model derived from the complete Apollo data set to evaluate compositional implications. The mantle density profiles are compared to mean density, moment-of-inertia, and crustal density/thickness constraints to evaluate the need for a metallic core. The calculated seismic velocity profiles are in qualitative agreement with the observational model in two general respects: (1) a quasicontinuous velocity decrease occurs in the upper mantle due to the large thermal gradients that characterized all three of the considered thermal models: (2) a discontinuous velocity increase occurs at the spinel-to-garnet transition (approximately 500 km depth) due mainly to the higher garnet velocities as compared to olivine and orthopyroxene. In the upper mantle, all four of the considered bulk compositions (spanning a range of plausible FeO and Al2O3 contents) are allowed when uncertainties in the temperature profile and depth of differentiation are taken into account.

However, in the middle mantle (depths >500 km), the most aluminous models (those with larger garnet abundances) consistently produce larger velocity increases that are most nearly in accord with the observational model. In general, models that assume differentiation of the upper mantle only, that are more aluminous in bulk composition, and that have strong thermal gradients in the upper mantle but smaller gradients in the middle mantle results in calculated velocity profiles that most nearly agree with the observational velocity model.

An alternate differentiation model in which the middle mantle is dominated by MgO-rich mafic silicates is also in accord with the observational seismic velocity model but results in density decreases that appear to violate stability arguments. In every case, calculated mantle density increases are insufficient to match the one-standard-deviation upper limit on the moment-of-inertia even when the most favorable combinations of allowed crustal thickness and density are assumed. Agreement with the moment-of-inertia upper limit is obtained if metallic cores representing 1--4% of the lunar mass are added to the bulk composition. Such cores are larger than needed to explain the observed depletions of lunar siderophile elements if the moon formed entirely from terrestrial mantle material. ¿ American Geophysical Union 1987