Tsunami events are strongly related to earthquake.
In order to define precise position to the origin region, I guess you must measure diffrent points, in order to determine source in a 2D map.
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There is no "tsunami detector" in existence. Tsunami is created under special conditions:
-the earthquake must occur in the sea floor or ocean floor, to move big water mass
- as the water mass moves across the sea, it can only become a tsunami if the shore is smooth under water, so the water mass is pushed high over the shore. If the underwater shore is abrupt like a cliff, no tsunami occurs, the water-mass wave is reflected away without rising high.
Recently, tsunami warnings are issued by a large organization of seismic observatories that can detect earthquakes strong enough to cause a tsunami. Also, satellites can monitor sea surface and detect waves caused by huge water movement. Territories with "suitable" shore profiles can be selected, and population warned as the water-mass wave propagates typically at ~160 km/hour.
At locations that are potentially prone to a tsunami, simple water gauges can detect a "fast" level decline as a precursor to a tsunami. Water level declines and sea water leaves the shore fast away from the land. Such observation may be automated by a video processing of a local scene, to detect water movement other than a typical tide. If well designed, such warning system can be low-cost and effective, with minutes given to the population for evacuation.