  The IceCube neutrino telescope at the South Pole has measured the atmospheric
muon neutrino spectrum as a function of zenith angle and energy in the
approximate 320 GeV to 20 TeV range, to search for the oscillation signatures
of light sterile neutrinos. No evidence for anomalous $\nu_\mu$ or
$\bar{\nu}_\mu$ disappearance is observed in either of two independently
developed analyses, each using one year of atmospheric neutrino data. New
exclusion limits are placed on the parameter space of the 3+1 model, in which
muon antineutrinos would experience a strong MSW-resonant oscillation. The
exclusion limits extend to $\mathrm{sin}^2 2\theta_{24} \leq$ 0.02 at $\Delta
m^2 \sim$ 0.3 $\mathrm{eV}^2$ at the 90\% confidence level. The allowed region
from global analysis of appearance experiments, including LSND and MiniBooNE,
is excluded at approximately the 99\% confidence level for the global best fit
value of $|$U$_{e4}|^2$.
