  We calculate high and (ultra-)high energy upward-going muon neutrino
propagation through the Earth and the induced muon energy distribution near the
one cubic kilometer detector using the Monte Carlo simulation, due to both
charged current interaction and neutral one. The initiated neutrino energies on
the surface of the Earth are 1PeV, 1EeV and 1ZeV. The mean free paths of
(ultra-)high energy neutrino events generated by the deep inelastic scattering
may be comparable with the diameter of the Earth or less than it. Therefore,
the induced muon production distribution is influenced by the change of the
densities interior to the Earth. Furthermore, in such situation, the
contribution from the neutral current neutrino interaction to the induced muon
production distribution cannot be neglected. We report several examples of the
deep inelastic scattered depth of muon neutrino in the Earth and the induced
muon energy distribution near the detector.
