Plates move a few centimeters a year, about as fast as fingernails grow. Magnetic stripes give average rates over millions of years. Today, GPS stations bolted to bedrock measure plate motion directly, to a fraction of a millimeter per year, every day.
Why it works
A GPS station's velocity is an arrow (a vector) with an east part and a north part, measured against a fixed global frame. That frame is a convenience; what matters at a plate boundary is how one side moves relative to the other. Relative velocity is a subtraction, done part by part: $\vec v_{B \text{ rel } A} = (v_{E,B} - v_{E,A},\; v_{N,B} - v_{N,A})$. Its size comes from the Pythagorean theorem, $\sqrt{v_E^2 + v_N^2}$. And whether the boundary opens or closes depends on whether the relative velocity points away from or toward the other station.
Key idea
A GPS velocity has east and north parts. Subtract one station's velocity from the other's to get relative motion; use Pythagoras for its speed, and its direction along the line between them to see whether the gap opens or closes.
Worked examples
Worked example: A station's speed
A station moves 21 mm/yr east and 20 mm/yr north. How fast is it moving?
- $\sqrt{21^2 + 20^2} = \sqrt{441 + 400} = \sqrt{841} = 29\,\text{mm/yr}$.
Answer: $29\,\text{mm/yr}$.
Worked example: Opening or closing?
Station B is 100 km east of station A. A moves 10 mm/yr east and 5 mm/yr north; B moves 30 mm/yr east and 20 mm/yr north. How does B move relative to A?
- East: $30 - 10 = 20\,\text{mm/yr}$. North: $20 - 5 = 15\,\text{mm/yr}$.
- Relative speed: $\sqrt{20^2 + 15^2} = 25\,\text{mm/yr}$.
- B lies east of A and moves 20 mm/yr farther east, so the gap opens by 20 mm/yr; the 15 mm/yr north part slides B sideways past A.
Answer: $25\,\text{mm/yr}$: opening and sliding.
Common mistake
It is natural to read each station's arrow as its motion relative to its neighbor. Two stations with big arrows pointing the same way might hardly be moving relative to each other at all. Check by subtracting: only the difference shows what the boundary between them is doing.