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 a
nd 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.
The energy--zenith angular event distribution in a neutrino telescope provides a unique tool to determine at the same time the neutrino-nucleon cross section at extreme kinematical regions, and the high energy neutrino flux. By using a simple paramet
rization for fluxes and cross sections, we present a sensitivity analysis for the case of a km^3 neutrino telescope. In particular, we consider the specific case of an under-water Mediterranean telescope placed at the NEMO site, although most of our results also apply to an under-ice detector such as IceCube. We determine the sensitivity to departures from standard values of the cross sections above 1 PeV which can be probed independently from an a-priori knowledge of the normalization and energy dependence of the flux. We also stress that the capability to tag downgoing neutrino showers in the PeV range against the cosmic ray induced background of penetrating muons appears to be a crucial requirement to derive meaningful constraints on the cross section.
