On Neutrino Absorption Tomography of the Earth

We study the passage of UHE neutrinos through the Earth in order to perform an absorption tomography of its inner structure. The aim of this work is to study the extraction methods of the Earth's density, in this conditions, we do not need to implement a realistic Monte Carlo simulation, as we are only interested in comparing the goodness of a standard method \cite{ralston} with the one we propose. The Earth's density is reconstructed using the 2-d Radon transform and we compare the density obtained considering neutral current regeneration through the complete transport equation, with the one obtained making use of the effective cross section approximation (standard method). We see that the effective cross section leads in general to inaccurate results, especially for flat initial neutrino fluxes, while the full transport equation method works regardless of the initial flux. Finally, an error propagation analysis made for different uncertainties in the surviving neutrino flux shows that the recovered density presents a percentage uncertainty less than two times the uncertainty in the flux.