Which GPS? The typical GPS receiver is not able to discern any sort of ground movement. High-end real-time or post-processed differential GPS with millimeter accuracies are being used to measure earth movement around earthquake faults.
They measure relative movement. Earth's crust moves just like the oceans, but only on a smaller scale - related to the density difference between water and rock. That's why it's important to use differential GPS when surveying. A base station is set up on a known point and the difference between what the point is known as and is being reported is subtracted from the roving unit's readings.
