Gravity waves don't "go through" the earth but rather the earth expands and contracts in space-time. This contracting and expanding of the earth itself, although minute, is the evidence and detection of gravity waves.
Can LIGO "see" only upwards or it can "see" downwards too? Neutrinos can pass though the Earth because they only interact with week force and gravity, and both have a very small coupling. Can "gravitons" pass though Earth?
As someone noticed in an comment a few months ago, there is no experimental evidence of the gravitons and no complete theory about them, but I think it's a good guess.
So, in other words, the minute contracting and expanding of space inside the Earth while the gravitational waves pass though it must interact with any particle with mass. The coupling is weak, but there are plenty of them. So some of the energy of the waves will be dissipated as heat inside the Earth. How much of the energy of the waves is lost while passing though the Earth?
Yes. And the fact that there is no complete theory of gravitons doesn't really matter. It is sufficient to know that scare-quoted "gravitons" (which may be real fundamental particles or may simply be mathematically convenient pseudo-particles corresponding to a classical gravitational wave) can pass through the Earth.
They must be able to do so, for essentially exactly the same reason that neutrinos can: they couple extremely weakly to matter. Which should not be a surprise, because gravity is such a relatively weak force- weaker even than the eponymous "weak force". The fact that neutrinos couple so weakly to other matter is also why they are so dang hard to detect. Meanwhile, gravitons / gravitational waves couple even more weakly to matter, and thus are correspondingly even harder to detect than neutrinos, and pass through solid matter even more easily.
Annoyingly, if it were easier to detect them, that would necessarily imply that the Earth is less transparent to them, and vice-versa: they harder they are to detect, the more transparent the Earth must be. Because, if the Earth were not transparent to them, then that entails that there are materials in the Earth that interact strongly with them, and we could use those materials to build a better detector!
Can LIGO "see" only upwards or it can "see" downwards too? Neutrinos can pass though the Earth because they only interact with week force and gravity, and both have a very small coupling. Can "gravitons" pass though Earth?
As someone noticed in an comment a few months ago, there is no experimental evidence of the gravitons and no complete theory about them, but I think it's a good guess.
So, in other words, the minute contracting and expanding of space inside the Earth while the gravitational waves pass though it must interact with any particle with mass. The coupling is weak, but there are plenty of them. So some of the energy of the waves will be dissipated as heat inside the Earth. How much of the energy of the waves is lost while passing though the Earth?