  We study properties of the oscillation effects in the matter of the Earth on
antineutrino fluxes from supernovae. We show that these effects can provide
explanation of the difference in the energy spectra of the events detected by
Kamiokande-2 and IMB detectors from SN1987A as well as the absence of
high-energy events with $E\gta 40$ MeV. This explanation requires the neutrino
oscillation parameters $\Delta m^2$ and $\sin^2 2\theta $ to be in the region
of the LMA solution of the solar neutrino problem and the normal mass hierarchy
if $|U_{e 3}|^2\gta 10^{-3}$. The hierarchy can be inverted if $|U_{e 3}|^2\ll
10^{-3}$. The solution of the solar neutrino problem based on
$\nu_e$-conversion to a pure sterile state is disfavoured by SN1987A data.
