  We study the possibility to perform neutrino oscillation tomography and to
determine the neutrino mass hierarchy in kilometer-scale ice Cerenkov detectors
by means of the theta13-driven matter effects which occur during the
propagation of atmospheric neutrinos deep through the Earth. We consider the
ongoing IceCube/DeepCore neutrino observatory and future planned extensions,
such as the PINGU detector, which has a lower energy threshold. Our simulations
include the impact of marginalization over the neutrino oscillation parameters
and a fully correlated systematic uncertainty on the total number of events.
For the current best-fit value of the mixing angle theta13, the DeepCore
detector, due to its relatively high-energy threshold, could only be sensitive
to fluctuations on the normalization of the Earth's density of \Delta\rho
\simeq \pm 10% at ~ 1.6 sigma CL after 10 years in the case of a true normal
hierarchy. For the two PINGU configurations we consider, overall density
fluctuations of \Delta\rho \simeq \pm 3% (\pm 2%) could be measured at the 2
sigma CL after 10 years, also in the case of a normal mass hierarchy. We also
compare the prospects to determine the neutrino mass hierarchy in these three
configurations and find that this could be achieved at the 5 sigma CL, for both
hierarchies, after 5 years in DeepCore and about 1 year in PINGU. This clearly
shows the importance of lowering the energy threshold below 10 GeV so that
detectors are fully sensitive to the resonant matter effects.
