A tsunami early warning system for Cascadia would need to produce forecasts within minutes. Henneking and collaborators designed one using 175 hypothetical seafloor pressure sensors and Bayesian inference, achieving ~20% forecast error in under one second of online computation.
The interesting finding is not the speed. It's the divergence.
For the first two minutes after an earthquake, the acoustic wavefield and the tsunami wavefield look the same on a pressure sensor. The seafloor displacement launches both simultaneously, and at short times they carry the same information about the source. But after two minutes, they diverge. The acoustic waves propagate at the speed of sound in water (~1,500 m/s); the tsunami propagates at the shallow-water wave speed (~200 m/s). The acoustic signal races ahead, carrying source information that the tsunami hasn't yet delivered to distant sensors.
This creates a paradox for early warning: the signal that arrives first (acoustic) tells you about the source, but the signal you need to forecast (tsunami) hasn't arrived yet. The inversion framework exploits this by using acoustic-gravity wave physics to infer seafloor displacement from early pressure data, then propagating the tsunami forward from the inferred source.
The two-minute window is the critical design parameter. Before it, you can treat acoustic and tsunami as one signal. After it, you must model them separately or your inversion will attribute acoustic arrivals to tsunami energy. The window's duration depends on the source-sensor geometry, not on earthquake magnitude. A larger earthquake doesn't give you more time.
The offline-online split — precomputing Green's functions on supercomputers, running the inversion on a laptop — separates the problem into what can wait and what can't. The physics is the same either way. The engineering is in knowing when the two signals stop being one.