Actually, we have ample proof of the distortion of spacetime in a gravity well - gravitational lensing. It's an observed effect around very massive objects and we have been able to see it at work very well. Also, arguably, the fact that we're not falling towards the sky is itself evidence of a spacetime gradient near the Earth, but that was also explained by Newton's Law of Gravitation.
But back in 1916, Einstein also theorised, as part of his general theory of gravitation, that there would be such things as gravity waves, caused by very massive objects moving through spacetime making 4-dimensional ripples appear in spacetime. Until today, that was just an unproven theory, though everyone believed it was likely to be true. There is now solid evidence to back it.
Agree... my question, though poorly worded, is less about proof of spacetime gradients (they do in the ways you describe).
It's more about understanding what the measurable effects of a gravitational well on earth has on the LIGO experimental setup (or a similar one with infinite precision), in the absence of gravitational waves.
Well, something like LIGO can only measure gravitational waves, because it looks for changes in the geometry of spacetime. If you were to move the LIGO in and out of Earth's gravitational well, I guess then it would record a shift.
But back in 1916, Einstein also theorised, as part of his general theory of gravitation, that there would be such things as gravity waves, caused by very massive objects moving through spacetime making 4-dimensional ripples appear in spacetime. Until today, that was just an unproven theory, though everyone believed it was likely to be true. There is now solid evidence to back it.