Neutrino detection in correlation with GRBs is problematic at best, because the events tend to be so far away and neutrino emissions are not expected to be focused into cones the same way EM and charged particles are, by virtue of not interacting with electromagnetic processes they'll be emitted in all directions. (There is some hypothetical neutrino/antineutrino emission within the GRB cone, but it's likely a weak signal and hasn't been measured in practice.)
We expect GRB neutrino flux to weaken far below the detection threshold by the time it gets here. Across these vast distances, neutrinos should also lag behind photons because they're not technically as fast as light.
The other question is what would we do with that advance warning if it existed? We can't do anything about the fact that our atmosphere is going to absorb these gamma rays, and chances are the event wouldn't be energetic enough to kill us directly as we're walking around so there is no point in taking cover either. The damage to our ecosystem is going to be what kills us, not radiation exposure.
How useful a barrier is the earth itself for the initial burst? Would there be any benefit in arranging to be on the opposite side of it for the duration?
now, nothing. In future, possibly raise some sort of (EM) shield? Of course nothing to for us/our kids, but I am sure within few millenia this would be perfectly feasible (at least my imagination wishing so :)
We already have one of those and it's pretty darn powerful :) of course, if we're talking millennia of technological development, all bets are off - but by then we and the planet will look very different.
However, I think this needs to be stretched once more: there will most likely be no advance detection through neutrinos.
We expect GRB neutrino flux to weaken far below the detection threshold by the time it gets here. Across these vast distances, neutrinos should also lag behind photons because they're not technically as fast as light.
The other question is what would we do with that advance warning if it existed? We can't do anything about the fact that our atmosphere is going to absorb these gamma rays, and chances are the event wouldn't be energetic enough to kill us directly as we're walking around so there is no point in taking cover either. The damage to our ecosystem is going to be what kills us, not radiation exposure.