  We perform a detailed study of the Earth matter effects on supernova
neutrinos with neutrino oscillation parameter LMA and small $\theta_{13}$. The
Earth effects show significant dependences on the neutrino path length inside
the Earth and the value of $\Delta m^{2}_{12}$. We investigate rather
optimistically 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 the
supernova are known with enough accuracy and that the resonance that occurs at
higher density in supernova envelope is completely nonadiabatic. Further the
neutrino spectra before neutrinos go through the Earth are assumed to be known.
Then we show that making use of these dependences, we can obtain implication
for the value of $\Delta m^{2}_{12}$ by comparing the observed energy spectrum
to the predicted one. When SK detects neutrinos from supernova at 10kpc which
traveled through the Earth (nadir angle $<$ 80 degree), $\Delta m^{2}_{12}$ can
be determined with an accuracy of $\sim 10%$. In much of the
neutrino-detection-time-$\Delta m^{2}_{12}$ plane, $\Delta m^{2}_{12}$ might be
determined with an accuracy equal to or better than $\pm 0.5 \times 10^{-5}
{\rm eV}^{2}$.
