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The pattern of oscillation parameters emerging from current experimental datacan be further elucidated by the observation of matter effects. In contrast toplanned experiments with conventional neutrino beams, atmospheric neutrinosoffer the possibility to search for Earth-induced matter effects with very longbaselines. Resonant matter effects are asymmetric on neutrinos andanti-neutrinos, depending on the sign of $\Delta m^2$. In a three-generationoscillation scenario, this gives access to the mass hierarchy of neutrinos,while the size of the asymmetry would measure the admixture of electronneutrinos to muon/tau neutrino oscillations (the mixing angle $\Theta_{13}$).The sensitivity to these effects is discussed after the detailed simulation ofa realistic experiment based on a massive detector for atmospheric neutrinoswith charge identification. We show how a detector, which measure anddistinguish between $\nu_\mu$ and $\bar{\nu}_\mu$ charged current events, mightbe sensitive to matter effects using atmospheric neutrinos, provided the mixingangle $\Theta_{13}$ is large enough.Comment: (8 pages, 8 figures, submitted to Eur.Phys.J.C

Prospects of measuring $\sin^2 2\Theta_{13}$ and the sign of $\Delta m^2$ with a massive magnetized detector for atmospheric neutrinos