The atmosphere directly above the tsunami will have a different TEC (total electron count) pattern due to the upward acoustic waves created by the tsunami waves. This patch of atmosphere may or may not be in the line of sight of your many GPS receivers, to some satellite. Those for which it is in the line of sight will show a disturbance. Others won't. You can now cross-compare to "triangulate" where the tsunami waves are.
You spoke correctly. But to further clarify, these are gravity waves, not gravitational waves.
Here's a previous thread on this topic[0].
For each (receiver, satellite) pair, you can calculate the TEC along the signal propagation path by comparing the time of flight of two carrier waves (e.g. L1 and L2)[1].
By fusing the data from each line of sight together you can get a rough, real time, 3D (4D) model of the ionosphere. Then, you have a separate problem of identifying ionospheric anomalies in the model and relating them to phenomena like earthquakes.
[0] https://news.ycombinator.com/item?id=42441772 [1] https://news.ycombinator.com/item?id=42471052
The fact that we are able to measure things globally indirectly and accurately based on our understanding of physics, hypotheses we make, and then apply those experiments is very cool.
Never mind the marvel of GPS that we've just taken for granted for decades...
That motion pushes air upwards, resulting in a wave reaching high up through the atmosphere, eventually hitting (!) the ionosphere. I didn't even know acoustic waves would propagate through ionised gas!
Finally, this ionosphere disturbance affects GPS signal reception, and can be measured via ground receiver stations.
The upside of this is that it measures, indirectly, motion of the sea, i.e. actual tsunami activity, rather than monitoring directly the potential causes thereof.
It is crazy to me that it works though!