We investigate the possibility to use the neutrinos coming from a future
galactic supernova explosion to perform neutrino oscillation tomography of the
Earth's core. We propose to use existing or planned detectors, resulting in an
additional payoff. Provided that all of the discussed uncertainties can be
reduced as expected, we find that the average matter densities of the Earth's
inner and outer cores could be measured with a precision competitive with
geophysics. However, since seismic waves are more sensitive to matter density
jumps than average matter densities, neutrino physics would give partly
complementary information.Comment: 17 pages, 6 figures, LaTeX. Final version to be published in
Astropart. Phy