The main issue is not simply one of detecting earthquakes - there have for example been hundreds of earthquakes in the Indian Ocean in the past few decades but the last great Tsunami was associated with the cataclysmic eruption of krakatoa in 1883. [explosions are far more effective at generating tsunami waves (50% of the energy can end up in a water wave) than are most earthquakes (few% or sub-% level). This is why ocean impacts carry such a tsunami risk] What is important is to identify the few special tsunamigenic earthquakes in time to give useful warning.

To some extent, a warning system based on sheer magnitude of the quake is of value - this recent one is the largest for 40 years and whatever it did, it was bound to do bigger than others.

It is vaguely possible to work out the characteristics of an earthquake from its seismic signal, but it's slow and innacurate - more post-facto modelling than real-time prediction. What one has to do is model the broadcast body wave radiation pattern (of both P and S waves) to generate a source signature. In practice, one also needs to add details of slower surface waves (e.g. Love waves, which are still seismic waves rather than water waves).

The crucial step in real-time prediction is to have a network of ocean bouys that continuously monitor sea level and can discriminate the <0.5 m long-period swell of a deep-ocean tsunami from the similar-scaled or larger wind waves of shorter period.

It isn't easy, and it's a bit expensive, but so are disasters.

The Pacific has an established tsunami warning system. Proposals are now being mooted for one in the Indian ocean. There is less* need for one in the Atlantic because it is subduction earthquakes that have the most likelihood of causing the widespread uplift of the seabed that is most tsunamigenic. Mid-ocean ridges are far less efficient.

*But not *no* need - recall the great Lisbon earthquake and tsunami of 1705.

Useful reading:

"Dr george"
CBS overview

Also try a Google search on +Tsunami +Prediction for a LOT of hits.

Oh, and one major, major feature is social.

High density populations lead inevitably to crowded littoral zones, which are the most at risk in the case of tsunami. In rich countries, these sought-after areas are built-up, but more sparesly than in poor countries where subsistence living is often practiced literally on the beach.

The one recurring feature of the descriptions of this tsunami is that people felt the earthquake, noticed the sea was doing something odd, and then WENT TO HAVE A CLOSER LOOK.

In many cases, the sea withdrew spectacularly minutes before the first onrushing wave, literally leaving fish flopping on the seabed. Poor families rushed out to scoop-up this bounty from the oceans, only to be scooped up themselves by the onrushing wave.

This is also recorded from the 1705 Lisbon quake and Tsunami.

It's partly a matter of education - if you're at the beach and the sea does something odd, then step back, not forwards. If the ocean drops 5 m, leaving fish exposed and out of their element, simple physics says that the next thing that will happen is that it will rise 5m, leaving land dwellers exposed and out of their element.

So if you want a better look at odd seas - do it from a high vantage point. And if you're not starving, let someone else scoop up the stranded fish.

Of course, curiosity might still get the better of rationality, but hundreds or even thousands of lives were lost in this way.