  We show that a kilometer-scale neutrino observatory, though optimized for
detecting neutrinos of TeV to PeV energy, can reveal the science associated
with the enigmatic super-EeV radiation in the Universe. Speculations regarding
its origin include heavy relics from the early Universe, particle interactions
associated with the Greisen cutoff, and topological defects which are remnant
cosmic structures associated with phase transitions in grand unified gauge
theories. We show that it is a misconception that new instruments optimized to
EeV energy can exclusively do this important science. Because kilometer-scale
neutrino telescopes such as IceCube can reject the atmospheric neutrino
background by identifying the very high energy of the signal events, they have
sensitivity over the full solid angle, including the horizon where most of the
signal is concentrated. This is critical because upgoing neutrino-induced
muons, considered in previous calculations, are absorbed by the Earth. Previous
calculations have underestimated the event rates of IceCube for EeV signals by
over one order of magnitude.
