The distribution of density as a function of position within the Earth is much less well constrained than the seismic velocities. The primary information comes from the mass and moment of inertia of the Earth and this information alone requires that there be a concentration of mass towards the centre of the globe. Additional information is to be found in the frequencies of the graver normal modes of the Earth which are sensitive to density through self-gravitation effects induced in deformation.
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Brian L. N. Kennett (1998) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: