Image: 3DGeo Inc./REPSOL

BITS AND BARRELS: A 3-D image reveals a salt dome trapping a hydrocarbon reservoir whose core area is visible in the horizontal slice.

Oil exploration is a hit-or-miss business. Just drilling one well in the deep waters of the Gulf of Mexico to find out if it contains oil can cost $100 million. So oil companies do all they can to avoid hitting dry wells. That’s where seismic imaging comes in. Better images mean less risk. So Repsol is not alone in its quest to solve the two-way wave equation.

“Every major oil company and seismic contractor is going after this,” says William W. Symes, a computational seismology specialist at Rice University, in Houston, who is not involved with the Kaleidoscope Project. Access to MareNostrum may give the American-Spanish team “a bit of a leg up,” he says, adding, “The main thing they’ve got is some very smart people with a great deal of theoretical background—and they are crackerjack programmers.”

One of those hotshot ­coders is Dimitri Bevc (pronounced “BAY‑oats”), who is president and a cofounder of 3DGeo. From the picture windows of his fourth-floor office in Santa Clara, he can see the Diablo Range, and it’s a source of inspiration for Bevc, an experienced mountain climber.

But today he’s pondering deeper things. He taps his keyboard and opens two large images on the screen. Each shows a cross section of a cube of earth below the seafloor, 14 km on its sides, that contains a mushroom-shaped salt body. To the untrained eye, the two grayscale images are very similar. But there’s a key difference.

“Look at these vertical lines,” Bevc says, pointing to the stem of the salt mushroom, where its edges merge with the surrounding sediments. In one image, ­created using the one-way wave equation, the stem is blurry; in the other image, based on the two-way wave equation, it’s sharp. “This has huge implications in the drilling planning,” he says. “Here you can’t see very clearly where the target is. Here you can.”

Bevc explains that oil is less dense than the sediments, so it tends to flow up through the Earth’s layers. But it can’t flow through impermeable salt ­bodies. As a result, oil accumulates in pockets resting against the salt structures. When you drill, you want to reach the top of the reservoir so that the oil flows up into your pipe. And when planning where to make a $100 million hole, you don’t want a blurry image.

To appreciate how 3DGeo solves the two-way wave equation, it helps to understand how seismic imaging works. It begins with a marine seismic survey. A specially built ship cruises over an area of interest and fires an air gun that sends a powerful sound wave into the ocean. This wave propagates through the water and down through subseafloor layers of sandstone, shale, salt, and other materials, producing echoes that return to the surface. The ship tows a dozen or so cables, each up to 10 km long, carrying thousands of hydrophones that measure the minute pressure waves of the echoes. In a typical survey, the ship covers 3000 square kilometers, about three times the area of Hong Kong, and fires the air gun tens of thousands of times. Hard-disk drives on the ship record many terabytes of echo data.

Then comes the real challenge: transforming that data into images of the Earth’s interior. Today’s most advanced seismic-imaging codes rely on an ingenious technique devised by Stanford University geophysicist Jon Claerbout in the 1970s. Basically, Claerbout’s method takes the recorded echoes, runs them through the wave ­equation as a mathematical extrapolation tool, and tells you the depths at which the echoes originated. With enough echoes, you can get a detailed image of the subsurface realm.

The wave equation consists of a single expression—a ­second-order linear partial differential equation—that describes the propagation of a wave as a function of space and time. It is commonly used not only in geophysics but also in acoustics, fluid ­dynamics, and electromagnetism. It can describe the behavior of a vibrating string, sound in air, waves in water, and light waves. In geophysics, the equation gives you the pressure produced by a sound wave at a specific point and time.

To solve the wave equation in three dimensions for a large volume, you need a very powerful computer. You start by creating a large 3-D grid of numbers that represent the surveyed volume of ocean and subseafloor earth. Each point in the grid stores the pressure of one or more sound waves present at that spot. Seismic-­imaging codes use the wave equation to extrapolate, or “push,” the echoes from the top of the grid, where they were recorded, to intermediary positions, where they originated. To keep things simple, this extrapolation assumes that the echoes traveled in only one direction: from the intermediary positions within the Earth straight to the surface—hence the name one-way wave equation.

The method worked beautifully for years in such areas as shelf waters, but geophysicists recently discovered that it can’t accurately image sites with more complex geological structures, such as salt bodies buried deep below the seafloor. The reason is that the one-way wave equation doesn’t account for the specific echoes ricocheting in multiple directions around those structures.

Now solutions for the two-way wave equation, which emerged in the 1980s, promise to overcome those limitations. The two-way wave equation method is different from its one-way counterpart because it accounts for cases in which a wave bounces a few times under, say, a salt dome before emerging as an echo. The two-way wave equation can retrace that propagation and thus image the area under the salt body.

The idea is to get rid of the extrapolations and instead use the complete wave equation to simulate the actual path of the echoes through the subsurface sediments. But how do you retrace those paths when all you have is information about the echo as it entered the hydrophones on the ship? Such a simulation would require going backward in time! The good news is, you can—in a computer, at least.