  Atmospheric neutrino experiments can show the "oscillation dip" feature in
data, due to their sensitivity over a large $L/E$ range. In experiments that
can distinguish between neutrinos and antineutrinos, like INO, oscillation dips
can be observed in both these channels separately. We present the
dip-identification algorithm employing a data-driven approach -- one that uses
the asymmetry in the upward-going and downward-going events, binned in the
reconstructed $L/E$ of muons -- to demonstrate the dip, which would confirm the
oscillation hypothesis. We further propose, for the first time, the
identification of an "oscillation valley" in the reconstructed
($E_\mu$,$\,\cos\theta_\mu$) plane, feasible for detectors like ICAL having
excellent muon energy and direction resolutions. We illustrate how this
two-dimensional valley would offer a clear visual representation and test of
the $L/E$ dependence, the alignment of the valley quantifying the atmospheric
mass-squared difference. Owing to the charge identification capability of the
ICAL detector at INO, we always present our results using $\mu^{-}$ and
$\mu^{+}$ events separately. Taking into account the statistical fluctuations
and systematic errors, and varying oscillation parameters over their currently
allowed ranges, we estimate the precision to which atmospheric neutrino
oscillation parameters would be determined with the 10-year simulated data at
ICAL using our procedure.
