  Earth absorbs $\nue$ and $\numu$ of energies above about 100 TeV. As is
well-known, although $\nutau$ will also disappear through charged-current
interactions, the $\nutau$ flux will be regenerated by prompt tau decays. We
show that this process also produces relatively large fluxes of secondary
$\nube$ and $\nubmu$, greatly enhancing the detectability of the initial
$\nutau$. This is particularly important because at these energies $\nutau$ is
a significant fraction of the expected astrophysical neutrino flux, and only a
tiny portion of the atmospheric neutrino flux.
