  We consider non-standard matter effect in flavor conversion of neutrinos
crossing the core of the Earth. We show that oscillation of core crossing
neutrinos with $E \gsim 0.5$ GeV can be well described by a first order
perturbation theory. We show that due to non-standard matter effect varying
chemical composition in the Earth can modify the neutrino flavor conversion by
100%. Effects of CP violating phases in non-standard Neutral Current
interactions are emphasized in particular.
