Here's a surprising fact. If you allow after-the-fact reprocessing of the GPS and significantly increased modeling technology, you can get millimeter accuracy from civilian GPS.
For more on this global network of re-analyzed GPS, see:
These plots are lat/lon/height (in centimeter units) versus time. In the height plot, you can see a several-cm drift which has annual/seasonal features. This is due to subsidence due to pumping of ground water in the summer. You can also see some green lines which I believe are large earthquakes.
Besides airborne and (coming soon) satellite radar interferometry, reprocessed GPS is one of the main ways we have to observe seismic displacement fields.
My GIS certificate is ancient at this point and I have never managed to work in the field I trained for, but my recollection is that they are accurate to within only about 10 meters, whether personal or professional, unless you spend quite a lot of time gathering data from multiple satellites (on the order of several hours, depending upon the level of accuracy you are seeking). EDIT: In other words, "I just turned mine on" shouldn't get any reading on any system that is more accurate than about 10 meters. It takes time to get accurate readings with GPS.
Someone with a more recent credential/professional experience want to confirm or deny that recollection -- or even update it with more recent facts? (For reference to my question of "more recent", IIRC, I got my certificate in 2002.)
According to http://en.wikipedia.org/wiki/Wide_Area_Augmentation_System#C... normal GPS systems will be accurate to within 2.5 m 95% of the time. Better accuracy can be achieved using differential GPS systems and things like WAAS, but they rely on ground-based systems and thus might not be a good way to measure how much the ground shifted.
That said Arch does have lots of documentation the answer is probably somewhere in the massive Arch docs.