  We describe a method of observation for PeV--EeV tau neutrinos using
Cherenkov light from the air showers of decayed taus produced by tau neutrino
interactions in the Earth. Aiming for the realization of neutrino astronomy
utilizing the Earth-skimming tau neutrino detection technique, highly precise
determination of arrival direction is key due to the following issues: (1)
Clear identification of neutrinos by identifying those vertices originating
within the Earth's surface; (2) Identification of very high energy neutrino
sources. The Ashra detector uses newly developed light collectors which realize
both a 42 degree-diameter field-of-view and arcminute resolution. Therefore, it
has superior angular resolution for imaging Cherenkov air showers. In this
paper, we estimate the sensitivity of and cosmic-ray background resulting from
application of the Ashra-1 Cherenkov tau shower observation method. Both data
from a commissioning run and a long-term observation (with fully equipped
trigger system and one light collector) are presented. Our estimates are based
on a detailed Monte Carlo simulation which describes all relevant shower
processes from neutrino interaction to Cherenkov photon detection produced by
tau air showers. In addition, the potential to determine the arrival direction
of Cherenkov showers is evaluated by using the maximum likelihood method. We
conclude that the Ashra-1 detector is a unique probe into detection of very
high energy neutrinos and their accelerators.
