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

(Ultra-)High Energy Muon Neutrino Propagation through the Earth and Induced Muon Energy Distribution near the One Cubic Kilometer Detector