  High-energy neutrinos are expected to be produced in a vareity of
astrophysical sources as well as in optically thick hidden sources. We explore
the matter-induced oscillation effects on emitted neutrino fluxes of three
different flavors from the latter class. We use the ratio of electron and tau
induced showers to muon tracks, in upcoming neutrino telescopes, as the
principal observable in our analysis. This ratio depends on the neutrino
energy, density profile of the sources and on the oscillation parameters. The
largely unknown flux normalization drops out of our calculation and only
affects the statistics. For the current knowledge of the oscillation parameters
we find that the matter-induced effects are non-negligible and the enhancement
of the ratio from its vacuum value takes place in an energy range where the
neutrino telescopes are the most sensitive. Quantifying the effect would be
useful to learn about the astrophysics of the sources as well as the
oscillation parameters. If the neutrino telescopes mostly detect diffuse
neutrinos without identifying their sources, then any deviation of the measured
flux ratios from the vacuum expectation values would be most naturally
explained by a large population of hidden sources for which matter-induced
neutrino oscillation effects are important.
