Cross section dependence of event rates at neutrino telescopes

We examine the dependence of event rates at neutrino telescopes on the neutrino-nucleon cross section for neutrinos with energy above 1 PeV. Simple scaling of the Standard Model cross sections leaves the rates of upward events essentially unchanged. Details, such as detector depth and cross section inelasticity, can influence rates. Numerical estimates of upward shower, muon and tau event rates in the IceCube detector confirm these results