Image copyright NOAA Image caption The map is about 1,750km across. Ocean Shield's detections have been made at about 20 degrees South

The search for MH370 has illustrated once again just how poor are our maps of the ocean floor.

Scientists aren't joking when they say we know better the shape of Mars than we know the hard surface of the Earth.

The oceans are vast and only a small fraction of the seafloor has so far been described in detail.

Look at the map at the top of this page. It shows the topography of the Indian Ocean bottom, west of Australia.

The star marks the rough location where the search vessel ADV Ocean Shield has been working this week, making encouraging pinger detections that could be the black boxes of MH370.

It's on the northern edge of a small oceanic plateau, sometimes called Wallaby Plateau or Zenith Plateau.

The geological interpretation of this region is that it incorporates scraps of continental crust that got stranded when India broke off from Australia about 120 million years ago. As a result, the topography is unusually rugged. Some of the shallows can be less than 200m below the surface, but the deep troughs on this map can exceed 7,600m.

If MH370's last resting place really is to be found here somewhere, the recovery of the wreckage could be a very extreme endeavour, indeed.

But look again at the map, at the black lines that criss-cross back and forth.

The thick bands indicate tracks surveyed by modern acoustic echosounders, which map a swath of area along the path of the ship, and these are very accurate (to about 2%).

The thin tracks indicate older, low-tech echosoundings, which are not as reliable. They are, though, "direct" measurements.

That cannot be said for everything else you see. This is mapping conducted by satellites that infer the shape of the ocean bottom from the shape of the water surface above.

Image copyright AFP/AUSTRALIAN DEFENCE Image caption ADV Ocean Shield is moving over ocean floor about which we know very little

Water follows the gravity, and it's pulled into highs above the mass of tall underwater mountains, or seamounts, and slumps into depressions over deep troughs.

This kind of fuzzy mapping is pursued by satellites fitted with radar altimeters. Most of our maps of the gross outlines of mountains on the seafloor were produced this way - thanks to a 1985-86 US Navy satellite campaign and a 1994-95 European Space Agency effort.

Fuzzy mapping is a good phrase. The best resolution is about 20km. It's thought there are somewhere between 50,000 and 100,000 seamounts that rise a kilometre or more above the seafloor, but which are invisible in these kinds of maps.

One estimate suggested it would take a ship, fitted with a modern swath-mapping echosounder system, about 200 years to map the entire ocean floor in high resolution.

Put that another way: it would take 20 dedicated ships 10 years to do the same task. This could be achieved for about $3bn. It sounds a lot of money, but it's the kind of investment we make when we go to Saturn or Jupiter with a big orbiting spacecraft to map those planets and their moons.

Ocean-floor mapping from space Image copyright ESA Most ocean maps are derived from satellite altimeter measurements

Satellites infer ocean-floor features from the shape of the sea surface

They detect surface height anomalies driven by variations in local gravity

The gravity from the extra mass of mountains makes the water pile up

In lower-mass regions, such as over troughs, the sea-surface will dip

Limited high-resolution ship data has calibrated the satellites' maps

And here are some good reasons to do a better job back on Earth.

Not knowing the locations of all the seamounts is a hazard, as the nuclear submarine USS San Francisco found out when it crashed into one in 2005.

But good maps are also important for fisheries management and conservation, because it's around the underwater mountains that wildlife tends to congregate. Each seamount is a biodiversity hotspot.

Furthermore, the rugged seafloor influences the behaviour of ocean currents and the vertical mixing of water. This is just the kind of information you need to improve the models that forecast future climate change. Remember: the oceans play an absolutely critical role in the climate system.

Governments, however, do not look like they'll commit the necessary $3bn anytime soon - which leaves us with the satellites.

And the latest space technologies could be making a four or five times' improvement on the fuzzy maps.

The problem is you really need not only the right kind of instrument on a satellite, but for that spacecraft to fly in the right kind of orbit around the Earth. And such missions are few and far between, and they often have other priorities.

Consider the European Union's exciting new constellation of Sentinels, the first of which was launched last week. The Sentinel-3 mission will go up next year with an altimeter that is certainly fit for the task, but it'll be flying repeat, overlapping paths around the globe. Not ideal.

One of the best bets at the moment is Europe's Cryosat-2 spacecraft. Again, the right kind of altimeter, and it's even in the right kind of orbit to sweep the ocean floor in a methodical way. But its primary mission is to measure the thickness of sea ice over the Arctic Ocean and the shape of the ice sheets over Greenland and Antarctica.

Nonetheless, the European Space Agency is now switching on Cryosat's instrument over the oceans to seek improvements in ocean-floor maps in selected places.

The best solution would be to fly a dedicated mission. Estimates say this could be done for as little as about $100m - to get substantially better maps than the ones now being used in the MH370 search, and across the rest of the world.