  The rise with energy of the neutrino--nucleon cross section implies that at
energies above few TeV the Earth is becoming opaque to cosmic neutrinos. The
neutrinos interact with the nucleons through the weak charged current,
resulting into absorption, and the weak neutral current, which provides a
redistribution of the neutrino energy. We Mellin transform the neutrino
transport equation and find its exact solution in the moment space. A simple
analytical formula is provided, which describes accurately the neutrino
spectrum, after the neutrinos have traversed the Earth. The effect of the weak
neutral current is most prominent for an initial flat neutrino spectrum and we
find that at low energies (around 1 TeV) the neutrino intensity is even
enhanced.
