  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.
