It has been recently claimed that there is a local enhancement of neutrino-antineutrino asymmetry in the Cosmic Neutrino Background (CNB) near the surface of the Earth of order $10^{-4}$ due to the in-matter potential experienced by relic neutrinos. This asymmetry is significantly larger than the expected $10^{-9}$ from the baryon asymmetry and is a promising step towards detecting the CNB. However, this claim makes many simplifying assumptions to reach this outcome, the most significant of which is the geometry used to model the Earth. Here, we approach the problem with a more realistic geometry for the Earth, and we find that the neutrino-antineutrino asymmetry near Earth is $10^{-8}$, which agrees with other recently reported results from other authors}.