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Knowledge of the composition of the Earth's interior is highly relevant tomany geophysical and geochemical problems. Neutrino oscillations are modifiedin a non-trivial way by the matter effects and can provide valuable and uniqueinformation not only on the density but also on the chemical and isotopiccomposition of the deep regions of the planet. In this paper, we re-examine thepossibility of performing an oscillation tomography of the Earth withatmospheric neutrinos and antineutrinos to obtain information on thecomposition and density of the outer core and the mantle, complementary to thatobtained by geophysical methods. Particular attention is paid to the D$^{\prime\prime}$ layer just above the core-mantle boundary and to the water (hydrogen)content in the mantle transition zone. Our analysis is based on a Monte-Carlosimulation of the energy and azimuthal angle distribution of $\mu$-like eventsgenerated by neutrinos. Taking as reference a model of the Earth consisting of55 concentric layers with constant densities determined from the PREM, weevaluate the effect on the number of events due to changes in the compositionand density of the outer core and the mantle. To examine the capacity of adetector like ORCA to resolve such variations, we construct regions in planesof two of these quantities where the statistical significance of thediscrepancies between the reference and the modified Earth are less than$1\sigma$. The variations are implemented in such a way that the constraintimposed by both the total mass of the Earth and its moment of inertia areverified.

Oscillation tomografy study of Earth's composition and density with atmospheric neutrinos