  The detection of ultra-high energy neutrinos, with energies in the PeV range
or above, is a topic of great interest in modern astroparticle physics. The
importance comes from the fact that these neutrinos point back to the most
energetic particle accelerators in the Universe, and provide information about
their underlying acceleration mechanisms. Atmospheric neutrinos are a
background for these challenging measurements, but their rate is expected to be
negligible above $\approx$ 1 PeV. In this work we describe the feasibility to
study ultra-high energy neutrinos based on the Earth-skimming technique, by
detecting the charged leptons produced in neutrino-nucleon interactions in a
high mass target. We propose to detect the charged leptons, or their decay
products, with the High Altitude Water Cherenkov (HAWC) observatory, and use as
a large mass target for the neutrino interactions the Pico de Orizaba volcano,
the highest mountain in Mexico. In this work we develop an estimate of the
detection rate using a geometrical model to calculate the effective area of the
observatory. Our results show that it may be feasible to perform measurements
of the ultra-high energy neutrino flux from cosmic origin during the expected
lifetime of the HAWC observatory.
