This is really interesting stuff, DethMarch. Its like our planet is breathing with tides. Did you perhaps mean millimeters per day instead of centimeters? I didn't realize the earth's surface fluctuated vertically so much.
Surveying for vertical control is based on leveling back to the previous benchmark, which is within eyesight, so both points move up or down about the same amount. So the fluctuations you're describing are not detectable between points close together using standard survey methods. GPS, based on satellite measurements with a global perspective can measure the up and down movement of both points, or any point for that matter.
GPS has allowed measurement of uplift of mountain ranges, fault slip, and tectonic drift. One way this is used is in predicting the probability of an earthquake on a particular fault. The chance of an earthquake occurring is based on an average annual "slip." The horizontal movement builds up stress over the years, and then lets go suddenly.
The most active reaches of the San Andreas fault move horizontally about an inch per year, and when it lets go, it can offset up to 30 feet near the epicenter.
Here's a paper describing how they measure the slip rate with GPS. Here's a paper comparing a leveling survey network with
GPS measurements in Poland.
Edited for more detail and to add another link.
