Earth medium effects in the three-neutrino oscillations of atmospheric
neutrinos are observable under appropriate conditions. This paper generalizes
the study of the medium effects and the possibility of their observation in the
atmospheric neutrino oscillations from the case of neutrinos traversing only
the Earth mantle, where the density is essentially constant, to the case of
atmospheric neutrinos crossing also the Earth core. In the latter case new
resonance-like effects become apparent. We calculate the CPT-odd asymmetry for
the survival probability of muon neutrinos and the observable muon-charge
asymmetry, taking into account the different atmospheric neutrino fluxes, and
show the dependence of these asymmetries on the sign of Δm312
and on the magnitude of the mixing angle θ13. A magnetized detector
with a sufficiently good neutrino momentum resolution is required for the
observation of the muon-charge asymmetry generated by the Earth mantle-core
effect.Comment: 14 pages, 5 figure