  Multi-megaton scale under ice and underwater detectors of atmospheric
neutrinos with few GeV's energy threshold (PINGU, ORCA) open up new
possibilities in the determination of neutrino properties, and in particular
the neutrino mass hierarchy. With a dense array of optical modules it will be
possible to determine the inelasticity, $y$, of the charged current $\nu_\mu$
events in addition to the neutrino energy $E_\nu$ and the muon zenith angle
$\theta_\mu$. The discovery potential of the detectors will substantially
increase with the measurement of $y$. It will enable (i) a partial separation
of the neutrino and antineutrino signals; (ii) a better reconstruction of the
neutrino direction; (iii) the reduction of the neutrino parameters degeneracy;
(iv) a better control of systematic uncertainties; (v) a better identification
of the $\nu_\mu$ events. It will improve the sensitivity to the CP-violation
phase. The three dimensional, $(E_\nu, \theta_\mu, y)$, $\nu_\mu-$oscillograms
with the kinematical as well as the experimental smearing are computed. We
present the asymmetry distributions in the $E_\nu - \theta_\mu$ plane for
different intervals of $y$ and study their properties. We show that the
inelasticity information reduces the effect of degeneracy of parameters by 30%.
With the inelasticity, the total significance of establishing mass hierarchy
may increase by 20% - 50%, thus effectively increasing the volume of the
detector by factor 1.5 - 2.
