  Cosmic-ray interactions with the nuclei of the Earth's atmosphere produce a
flux of neutrinos in all directions with energies extending above the TeV
scale. However, the Earth is not a fully transparent medium for neutrinos with
energies above a few TeV. At these energies, the charged-current
neutrino-nucleon cross section is large enough so that the neutrino mean-free
path in a medium with the Earth's density is comparable to the Earth's
diameter. Therefore, when neutrinos of these energies cross the Earth, there is
a non-negligible probability for them to be absorbed. Since this effect depends
on the distance traveled by neutrinos and on their energy, studying the zenith
and energy distributions of TeV atmospheric neutrinos passing through the Earth
offers an opportunity to infer the Earth's density profile. Here we perform an
Earth tomography with neutrinos using actual data, the publicly available
one-year through-going muon sample of the atmospheric neutrino data of the
IceCube neutrino telescope. We are able to determine the mass of the Earth, its
moment of inertia, the mass of the Earth's core and to establish the core is
denser than the mantle, using weak interactions only, in a way completely
independent from gravitational measurements. Our results confirm that this can
be achieved with current neutrino detectors. This method to study the Earth's
internal structure, complementary to the traditional one from geophysics based
on seismological data, is starting to provide useful information and it could
become competitive as soon as more statistics is available thanks to the
current and larger future neutrino detectors.
