  High-energy muon- and electron-neutrinos yield a non-negligible flux of tau
neutrinos as they propagate through Earth. In this letter, we address the
impact of this additional component in the PeV and EeV energy regimes for the
first time. This contribution is predicted to be significantly larger than the
atmospheric background above 300 TeV, and alters current and future neutrino
telescopes' capabilities to discover a cosmic tau-neutrino flux. Further we
demonstrate that Earthskimming neutrino experiments, designed to observe tau
neutrinos, will be sensitive to cosmogenic neutrinos even in extreme scenarios
without a primary tau-neutrino component.
