High energy neutrino signals of four neutrino mixing

We evaluate the upward shower and muon event rates for two characteristic four neutrino mixing models for extragalactic neutrinos, as well as for the atmospheric neutrinos, with energy thresholds of 1 TeV, 10 TeV and 100 TeV. We show that by comparing the shower to muon event rates, one can distinguish between oscillation and no-oscillation models. By measuring shower and muon event rates for energy thresholds of 10 TeV and 100 TeV and by considering their ratio, it is possible to use extragalactic neutrino sources to determine the type of four-flavor mixing pattern. We find that over several years of data taking, a kilometer-size detector has a very good chance of providing valuable information about the physics beyond the standard model.