Suddenly they’re hitting gushers from the Gulf of Mexico to the South Atlantic off Brazil to the west coast of Africa off Ghana and Sierra Leone.

The oil from these finds will eventually become critical to global supply—once the global economic downturn is over. The downturn has brought us what the International Energy Agency projects will be a two year slump in demand. If the global economy recovers relatively quickly, the agency projects, we could be facing another supply squeeze by 2014.

But these finds themselves look like their end another oil industry slump well before that. Deep water exploration suddenly seems to be headed to a boom. And that means we’re likely to see rigs coming out of cold stacking and starting to earn day fees again well before 2011, the year that many analysts had picked for a turn in the drilling industry.

In other words, the way to play these big deep water discoveries now is by buying shares in the drilling companies most likely to profit from an earlier turn in the sector’s fortunes.

To see why take a look at the latest find, the one off the coast of West Africa. On September 16 a partnership that includes Anadarko Petroleum (APC), Repsol (REP), Tullow Oil (TUWLF), and Woodside Petroleum (WOPEF) reported that the Venus B-1 well, drilled to a depth of 18,500 feet, had struck significant oil in deep water off the coast of Sierra Leone.

What’s extraordinary about the find isn’t the amount of oil that the partners have discovered—it’s way too early to know exactly how many barrels might be trapped in the sediments there—but the geographic extent of this hydrocarbon system.

Add the evidence of this well to an earlier find by Tullow and Anadarko, the Jubilee field, off the coast of the Ivory Coast and Ghana and this is already a system that stretches almost 700 miles between those African countries.

And no one knows exactly how far out into the Atlantic this system of oil and natural gas deposits might stretch. Some geologists speculate that it could reach as far as Guyana on the northeast coast of South America. That’s a distance of roughly 5,000 miles of very deep water that could yield profitable amounts of oil.

Once up on a time the idea of exploring the deep ocean for oil would have been dismissed as ridiculous by oil company executives. But after the huge finds made by Brazil’s Petrobras in the deep water—and even deeper salt deposits—off that country’s coast, the idea of exploring that this kind of terrain and over that size of a region no longer seems especially outlandish.

In the last few months we’ve see announcements of huge finds in the South Atlantic off Brazil in the deep waters of the Gulf of Mexico, and now in deep waters off Africa.

The finds off Brazil set off something of a rush by Petrobras to lock up all the deep water drill rigs it thought it might need over the next few years. The world’s supply of rigs that can drill in deep, deep water is limited. (Jack-up rigs, for example, can’t work in much more than 500 feet of water and even with improvements in technology semi-submersible rigs can’t work in depths much greater than 5,000 feet. The Mahogany 1 well off Ghana is in 4,330 feet of water.) And it can take years to get a new deep water rig built.

That started to take some of the surplus out of the industry. Yes, companies were still putting rigs into storage but the pace seems to have slowed in the last quarter, especially for deep water rigs. That wouldn’t be such a big deal except that Wall Street has been shunning drilling stocks because it believed that revenues wouldn’t recover until 2011.

If the recovery is faster than that, these stocks, which have gone nowhere during the rally, will move up strongly. They are after all really cheap if you forecast any recovery in earnings at all.

If you want to give yourself the best chance to profit from that acceleration in the sector’s recovery, you should buy the stocks of the companies with the biggest exposure to exploration activity and to deep sea rigs in particular.

My top choice would be Transocean (RIG), which has, by my count of the data on rigzone.com, 16 drill ships or semi-submersible rigs in West Africa alone. (The company has biggest fleet of deep sea rigs in the world.)

But I already own the stock in Jubak’s Picks.

My next choices would be Schlumberger (SLB) and GulfMark Offshore (GLF). Schlumberger has the biggest exposure—about 30% of revenue—to the exploration market of any of the big drilling services companies. GulfMark operates oil service vehicles, the ships that bring supplies to drilling platforms and other offshore worksites. The company has traditionally specialized in the North Sea but with its July 2008 acquisition of Rigdon it added 33 ships (to the one it owned) in the Gulf of Mexico.

At the moment GulfMark is hugely cheaper with a trailing price to earnings ratio of just 4.7. So with this post I’m going to add GulfMark Offshore to Jubak’s Picks with a target price of $41 a share by September 2010. Schlumberger is a member of my long-term Jubak Picks 50 portfolio.

Full disclosure: I own shares of Schlumberger and Transocean in my personal account.