Yes, LIGO's detectors include a slew of detectors attempting to detect just about every possible form of noise, including noises due to rumblings of the Earth. They also include elaborate suspension systems which attempt to damp out these effects. There is an easy way to explain how this works if you have a "slinky" toy: hold it from one edge and let it hang down, then vibrate its edge very rapidly: you will notice that the lowest end shakes but does not move up-down very dramatically. Now move its edge up and down very slowly: you will notice that the lowest end follows your hand's motion. Only when you shake it up and down near a very precise frequency, the resonance frequency of the system, do you get a dramatic result where the bottom goes up and down more independently of the top. This is called a "band pass filter", we can ensure that any waveforms outside of this particular band of frequencies are very strongly damped-out, and then measure the frequencies that are allowed to pass through the suspension very precisely. They do not use these "slinkies" precisely that way, but the cable systems which suspend the mirrors involved have essentially the same role in removing geological vibrations.
- Measure all sorts of other phenomena, and this effect was not attributable to any of those other phenomena;
- Measured the exact same effect in tandem with a small time delay on two different places on Earth separated by 3,000km: so this effect was not local to any single part of the Earth but seemed to "wash over it";
- Measured a signal which was exactly in line with what the radiation from a certain known astrophysics event predicts: slow oscillations ramping up in a certain precise way in frequency, leading to a sudden crescendo of vibration followed by an immediate cut-off -- so this is not a typical signal for any other typical terrestrial events;
- Measured a signal which visibly appears above the normal "noise floor" that you can observe in the detectors normally -- so this is not part of their typical noise that we can observe;
- Measured a signal very soon after they were turned on, so this is not a likely statistical anomaly visible in any large swath of data.
For these reasons, it seems to be a signal from space in the exact regime that the detectors were built for, not a terrestrial signal that somehow messed with everything in the right way.