  Atmospheric neutrinos offer the possibility of exploring the internal
structure of Earth. This information is complementary to the traditional probes
of seismic and gravitational studies. While propagating through Earth, the
multi-GeV neutrinos encounter the Earth's matter effects due to the coherent
forward scattering with the ambient electrons, which alters the neutrino
oscillation probabilities. We present how well an atmospheric neutrino
oscillation experiment like the 50 kt Iron Calorimeter (ICAL) detector at
India-based Neutrino Observatory would validate the presence of Earth's core,
measure the location of the core-mantle boundary (CMB), and probe the dark
matter (DM) inside the Earth in a unique way through Earth matter effects in
neutrino oscillations. Owing to good angular resolution, ICAL can observe the
core-passing neutrinos efficiently. Due to its magnetized setup, it would be
able to observe neutrinos and antineutrinos separately. With 500 kt$\cdot$yr
exposure, the presence of Earth's core can be independently confirmed at ICAL
with a median $\Delta\chi^2$ of 7.45 (4.83) for normal (inverted) mass
ordering. With 1000 kt$\cdot$yr exposure, ICAL would be able to locate the CMB
with a precision of about $\pm$ 250 km at $1\sigma$. It would also be sensitive
to the possible presence of dark matter with 3.5% of the mass of Earth at
$1\sigma$. The charge identification capability of ICAL would play an important
role in achieving these precisions.
