Earth density distribution from shooting neutrinos? 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?
 A: Neutrinos are produced in the atmosphere all the time as a consequence of cosmic ray interactions, and they mostly then fly right through the planet. So there is no problem with a source.
In fact the "flying right through" bit is one of the problems: even the full diameter of a planet simply doesn't intercept a large enough fraction of the beam to make tomography practical (the situation with atmospheric neutrinos is slightly better than that link suggests because the energies and cross-sections are higher, but it is still pretty atrocious).
But it gets worse, though neutrino detectors have some degree of directional sensitivity, they get it from detecting the directionality of the products of a neutrino reaction not by detecting the neutrinos momentum itself. That's why Super-K's famous image of the solar core in neutrinos is 10s of degrees wide. This means that even with enough rate sensitivity, you wouldn't get anything like useful results because you have only the roughest idea of what chord any given neutrino actually traversed.
As for the possibility of using beam neutrinos you have to deal with the way we generate neutrino beams: every chord you wanted to use would require and hundred-meter-plus-long, several-meter-diameter tunnel to use as the decay pipe. And they have to start underground, because you need to be able to direct the accelerator beam down to a beam dump at the "start" of the tunnel. These things are often treated as a minor part of accelerator neutrino projects, but each one actually represents a pretty substantial investment in civil engineering (and money) all by itself. And you need the detectors. And the accelerators. And those are bigger projects (though you can presumably use each one for a bunch of chords). Ouch.
