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We perform a detailed study of the Earth matter effects on supernovaneutrinos with neutrino oscillation parameter LMA and small $\theta_{13}$. TheEarth effects show significant dependences on the neutrino path length insidethe Earth and the value of $\Delta m^{2}_{12}$. We investigate ratheroptimistically a possibility that we can probe the value of $\Delta m^{2}_{12}$by the Earth effects. We assume that $\theta_{12}$ and the direction of thesupernova are known with enough accuracy and that the resonance that occurs athigher density in supernova envelope is completely nonadiabatic. Further theneutrino spectra before neutrinos go through the Earth are assumed to be known.Then we show that making use of these dependences, we can obtain implicationfor the value of $\Delta m^{2}_{12}$ by comparing the observed energy spectrumto the predicted one. When SK detects neutrinos from supernova at 10kpc whichtraveled through the Earth (nadir angle $<$ 80 degree), $\Delta m^{2}_{12}$ canbe determined with an accuracy of $\sim 10%$. In much of theneutrino-detection-time-$\Delta m^{2}_{12}$ plane, $\Delta m^{2}_{12}$ might bedetermined with an accuracy equal to or better than $\pm 0.5 \times 10^{-5}{\rm eV}^{2}$.Comment: 20 pages, 14 figures, added some discussion

Earth effects on supernova neutrinos and their implications for neutrino parameters