Investigating the impact of the modeling of Earth structure on the neutrino propagation at ultra-high-energies

The flux of atmospheric and astrophysical neutrinos measured in UHE neutrino detectors is strongly dependent on the description of the propagation and absorption of the neutrinos during the passage through Earth to the detector. In particular, the attenuation of the incident neutrino flux depends on the details of the matter structure between the source and the detector. In this paper, we will investigate the impact of different descriptions for the density profile of Earth on the transmission coefficient, defined as the ratio between the flux measured in the detector and the incoming neutrino flux. We will consider five different models for the Earth's density profile and estimate how these different models modify the target column density and transmission coefficients for different flavors. The results are derived by solving the cascade equations taking into account the NC interactions and tau regeneration. A comparison with approximated solutions is also presented. Our results indicated that the predictions are sensitive to the model considered for the density profile, with the simplified three layer model providing a satisfactory description when compared with the PREM results.