But strikes of this magnitude are comparatively rare. According to United States Geological Survey data, the earth, as it was before oil companies started drilling, held between five trillion and six trillion barrels of oil, most of which has been discovered or remains inaccessible. In 2000, the U.S.G.S. estimated that there were around 650 billion barrels on the planet yet to be found, and most analysts say that the estimate is a pretty good one. “We may still see some new basins on the scale of offshore Ghana,” Kepes, of PFC Energy, says. “But there aren’t going to be new Gulfs of Mexico or Nigerias that we haven’t yet discovered.”

These legendary basins have sustained careers for the life of the industry. The seduction of the Gulf of Mexico has always been its complexity — the physics of continental shift compressed into a small, enclosed basin. The gulf has been the laboratory in which explorers experimented with the deep — they call it the GOM, as if it were a discarded character from Tolkien. The first deepwater play came in minibasins on the slope that had caught young sands as they tumbled out of the ancient Mississippi; now there are the Perdido folds, in very deep water, that bunched up like a rug on a slick floor, trapping oil underneath. This play depends upon a compacted sheet of sandstone and shale deposited here approximately 50 million years ago by the uplift that produced the Rocky Mountains and, almost as an afterthought, sent an anaconda of sediment sliding down toward Texas and out into the sea. The depths here are so extreme that Shell, which operates the enormous Perdido field, has moved more equipment to the sea floor. The wells extend out — each one long and flexible, like the legs of a mantis — over an area as large as metro New Orleans.

“We’ve got four, five, six years left in the Gulf of Mexico,” James Painter, who leads Cobalt’s team there, told me. He could imagine a couple of possibilities beyond that, but neither was perfect — there were very likely to be gas fields deep underneath the continental shelf, where high pressures make drilling very complicated, and there might be a Cretaceous play left in the gulf, though that was iffy. “In my mind, we’ve got one more shot,” he said.

Last February, Richard Sears, a geophysicist who was vice president for exploration and deepwater technical evaluation at Shell and is now senior science adviser to the National Oil Spill Commission, appeared at the TED ideas conference in Long Beach, Calif., to give a talk about the future of energy. Sears says that there are between 30 and 50 years left before a broad gap opens between worldwide oil supply and demand. It is hard, he says, to describe a situation that is either a lot more optimistic or pessimistic than that. At TED, Sears held up a pincushion of the globe, with red thumbtacks stuck in. Each thumbtack represented an oil basin. “This is it,” he said. “This is the oil in the world. Geologists have a pretty good idea of where it is.”

These last 650 billion barrels are the hardest. “There are still some areas — Iran or Iraq or Russia — where you can literally fly over in a plane and see big structures lying right out there, and they are undrilled,” Farnsworth told me. But much of that territory has been reserved for national oil companies, and so in the last decade 43 percent of the industry’s new reserves have come from the deep water. “It’s gotten harder all along. And the structures, generally, have gotten smaller.”

But as the map has compressed, and the possibility of finding new basins has dwindled, explorers have returned their attention to the regions where vast deposits of oil have already been found, in the belief that new technologies might allow them to drill deeper. These aspirations drove new finds earlier this decade in offshore Brazil, and the continued work in the Gulf of Mexico. They also compelled the industry toward Angola, where Western oil companies have sustained production onshore and in shallow water for decades, even through a long civil war. There had been some deepwater exploration and production, but few had looked beneath the broad layers of salt.

Salt, in the deep water, is the hydrocarbons’ shroud, the mask that obscures the prize. Geologists use seismic instruments to map the earth’s layers — shooting pulses of compressed air down into the subsurface and measuring the time it takes for the sound to travel back to the surface. But salt — the evaporates of ancient oceans, trapped deep in the rock — scatters the signal. And so for years the zones that interested oil companies looked like blurred daubs underneath the thick aprons of salt — it was difficult to distinguish sedimentary layers or to scout for traps. Companies left those areas alone and explored where they could see. By the middle of the decade, though, seismic techniques were finally becoming refined enough to permit companies to make out the details of subsalt geology. “In the Gulf of Mexico, deepwater is more or less a subsalt business right now,” Keith Jantz, a geophysicist at Cobalt, says.