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Now that PeV neutrinos have been discovered by IceCube, we optimistically entertain the possibility that neutrinos with energy above 100 PeV exist. We evaluate the dependence of event rates of such neutrinos on the neutrino-nucleon cross section at observatories that detect particles, atmospheric fluorescence, or Cherenkov radiation, initiated by neutrino interactions. We consider how (i) a simple scaling of the total standard model neutrino-nucleon cross section, (ii) a new elastic neutral current interaction, and (iii) a new completely inelastic interaction, individually impact event rates.