  We present a semi-analytic calculation of the tau-lepton flux emerging from
the Earth, induced by the incident high energy neutrinos interacting inside the
Earth for $10^{5} \leq E_{\nu}/{\rm GeV} \leq 10^{10}$. We obtain results for
the energy dependence of the tau-lepton flux coming from the Earth-skimming
neutrinos, because of the neutrino-nucleon charged-current scattering as well
as the resonant $\bar{\nu}_e e^-$ scattering. We illustrate our results for
several anticipated high energy astrophysical neutrino sources such as the
AGNs, the GRBs, and the GZK neutrino fluxes. The tau lepton fluxes resulting
from rock-skimming and ocean-skimming neutrinos are compared. Such comparisons
can render useful information for the spectral indices of incident neutrino
fluxes.
