We have determined by means of first principles quasiharmonic calculations the elastic constants and acoustic velocities of MgSiO3 perovskite, the most abundant mineral of the Earth's lower mantle (LM), at pertinent pressures and temperatures. Using these results, along with the effects of low concentration iron alloying and the thermoelasticity of the most important secondary LM phase, MgO, we predict the isotropic elastic moduli of likely LM aggregates. Comparison with seismic values extracted from the preliminary reference Earth model indicates that the top of the LM behaves as a typical aggregate of pyrolitic composition, likewise the upper mantle. But systematic deviations that cannot be accounted for by alterations in the geotherm alone develop toward the deep LM. This result could be viewed as evidence in support of radially inhomogeneous LM models.