On the IceCube Result on $\bar{\nu}_{\mu} \to \bar{\nu}_{s}$ Oscillations

We elucidate the mechanism of enhancement of the $\bar{\nu}_{\mu} \to \bar{\nu}_{s}$ transitions at small mixing angles of Earth-core-crossing neutrinos, which is at the basis of the recent result of the IceCube experiment on atmospheric muon anti-neutrino oscillations into sterile anti-neutrino.