We evaluate the conversion probability for neutrinos by solving the evolution equations with a numerical method, taking into account a density distribution of the Earth, and calculate an upward-going neutrino flux ratio (νe +ν̄e)/(νμ +ν̄μ) by using the recent values of atmospheric neutrino fluxes, where the updated ratios νμ/ν̄μ and νe/ν̄e have been taken into account. It is found that the ratio, including the effect of neutrino-resonant oscillations, can well explain the Kamiokande data for ϕ = 0° and 30°, and the NUSEX and the Fréjus data (averaged over ϕ) at energies around 1 GeV, whilst the ratio with no neutrino oscillations or with the muon polarization cannot explain the measured data.