Geophysical searches for three-neutrino oscillations

The possibilities of using cosmic ray induced neutrinos to detect oscillations in deep underground experiments were considered. The matter effects are nonnegligible in the two neutrino case, they reduce a mixing angle of 45 deg to 7.5 deg for 1 GeV neutrinos of squared mass difference 10/4 eV59 going through the Earth making the oscillation totally unobservable. They produce a natural oscillation length of about 6000 km in the case of massless neutrinos. Adding a third neutrino flavor considerably modifies the oscillation pattern and suggests that scales down to 5 x 10/5 eV could be observed even when we take into account matter effects and the electron contribution to the incoming flux. The effect of matter on the probability curves for different cases are shown by varying the masses and the mixing matrix. The ratio upward upsilon + upsilon/downward upsilon + upsilon as a function of the zenith angle at Cleveland, neglecting angular smearing and energy threshold effects is predicted.