  We investigate the potential of a future kilometer-scale neutrino telescope
such as the proposed IceCube detector in the South Pole, to measure and
disentangle the yet unknown components of the cosmic neutrino flux, the prompt
atmospheric neutrinos coming from the decay of charmed particles and the
extra-galactic neutrinos, in the 10 TeV to 1 EeV energy range.
  Assuming a power law type spectra,
  $d\phi_\nu/dE_\nu \sim \alpha E_\nu^\beta$, we quantify the discriminating
power of the IceCube detector and discuss how well we can determine magnitude
($\alpha$) as well as slope ($\beta$) of these two components of the high
energy neutrino spectrum, taking into account the background coming from the
conventional atmospheric neutrinos.
