Signal of New Physics and Chemical Composition of Matter in Core Crossing Neutrinos

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.