  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.
