I am interested in possibility of inferring Earth interior structure from gravitational data. As classical calculus problem shows, it is impossible to understand non-uniform density distribution inside the Earth from gravitational measurement outside the surface alone. So various Earth models use seismic tomography to infer the density distribution.
My question is: would it be possible to build a more precise model by shooting neutrinos in various directions through the Earth, detect them at the other end and infer density information from variation in positions and travel times? Will these changes be within the tolerance of our current detection methods, and would it be mathematically feasible to extract meaningful information?
I found there is a geoneutrino approach, but it seems quite limited and I was wondering if we could be more proactive than waiting for neutrinos emitted from inside?