Neutrino radiography may provide an alternative tool to study the very deep structures of the Earth. Though these measurements are unable to resolve the fine density layer features, nevertheless the information which can be obtained are independent and complementary to the more conventional seismic studies. The aim of this paper is to assess how well the core and mantle averaged densities can be reconstructed through atmospheric neutrino radiography. We find that about a 2% sensitivity for the mantle and 5% for the core could be achieved for a ten year data taking at an underwater km^3 Neutrino Telescope. This result does not take into account systematics related to the details of the experimental apparatus.
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