House of Mirrors

[Note: A version of this blog entry will appear in World Oil (June, 2010)]

Let's take a ride on a seismic wave. The setting is offshore and a cylindrical steel airgun is just now charging up, the pressure building till a signal triggers the release of compressed air. The gas expands rapidly, generating a bubble and pressure wave in the water; a seismic wave is born. The wave takes off in every direction, but let's follow it straight down toward the seafloor.

This wave has a certain amplitude, the excess pressure above ambient conditions as it passes by, and a corresponding amount of energy. Striking the seafloor, it splits into two parts, an upgoing reflected wave and a downgoing transmitted wave. Whether the seafloor is hard or soft, not much of the wave passes through the water-sediment interface. This may seem surprising since we have all seen those beautiful 3D seismic offshore images, and that must come from waves that made it through the seafloor. But the fact is that much of the wave action does not get through.

Even in the case of a muddy, soft seafloor, something like 45% of the wave is reflected back up into the water. For a hard seafloor, we can expect 60% or more of the wave to reflect. Now remember, we are following a vertical wave so this reflection heads back toward the ocean surface. The trip upward is not very exciting till the wave hits the water/air interface (or 'free surface').

You might think that with air being so compressible and low density compared to water, that the sound wave would pass right on through. But, in fact, the opposite is true. Nothing gets through, and the wave reflects at full strength back to the seafloor, half of it bounces there, then all of it reflects again from the free surface, and so on. The multiples are periodic, each round trip taking the same amount of time. Have you ever been on an elevator with mirrors on two sides? Remember the infinite copies of yourself that that peer back? That is the situation a receiver in the water sees as these waves ping back and forth between seafloor and surface. These are called free-surface multiples since they are bouncing off the air/water interface. Another kind of multiple can occur deeper in the earth, where extra bounces are taken in one or more layers. These are termed internal multiples.

Multiples of any kind are big trouble to seismic imaging for a couple of reasons. First, it is not hard to imagine that our free-surface multiple will continue for a long as we record. That means eventually there will be a weak reflection we want from somewhere deep in the earth, and a multiple is likely to crash right into it. It is all too common around the world that our delicate, carefully nurtured reservoir reflection sits under a big, strong multiple. The second reason imaging suffers, is more subtle. For half a century researchers have been devising ever better ways to image (or migrate) seismic data. But almost all of them have one thing in common: Only primary (one bounce) reflections are used for imaging, not multiples. So our data is full of multiples, but we consider it noise not signal. That means multiples have to be removed before migration.

So how do we get rid of these multiples? The classic method is deconvolution, a word with a lot of meaning. It can be used for things like spectral whitening, source signature removal, wave-shaping, and many others. The application of decon to multiple removal goes back to the earliest days of digital seismic processing. The method also goes by the more descriptive name of prediction error filtering.

As an analogy, imagine that you are walking across a parking lot on a completely dark night. As you pace along, you suddenly bump your toe on a curb. Stepping over it, you continue and hit another curb farther on, and another. After a while, you start counting steps and find you can predict the next curb; not perfectly at first, but you get better and finally can avoid them perfectly. In effect, this is what the mathematical machinery of deconvolution does when processing a seismic trace. Based on earlier data values, decon predicts what will come a few time steps ahead, then goes there, checks the value, updates the prediction, and keeps trying. Since our multiple is periodic, decon will be able to predict it and thus remove it from the data. Reflections due to deeper geology, however, are by nature unpredictable and will not be removed. Decon has the remarkable ability to find the multiple pattern, or patterns, embedded in a random sequence of geological reflections. Very clever.

Going back to the dark parking lot, what if we change the situation so the repeating curbs are very far apart. So far, in fact, that as you walk across the lot you only hit one or two. In that case you would not be able to figure out the repeat pattern because you get too few looks at it. In the same way, decon is great for short-period multiples from shallow water, but fails for long-period multiples that occur in deep water. Over the last 20 years or so, a completely different multiple removal technique has been developed for exactly this situation. It has the cumbersome name of surface-related multiple elimination (SRME).

SRME is a vital tool in the modern exploration for deep water resources. It can handle much more complicated cases than the simple, vertical multiple we described above. SRME can handle situations where decon breaks down, like seafloor topography, non-vertical waves, and 3D scattering effects. The way SRME works is by considering the raypath for a particular free-surface multiple, and breaking it down to look like two primary reflections glued together. This insight allows a free-surface multiple that shows up only one time to be neatly and effectively removed. It has lead to a vast improvement in detailed image quality in the deep water Gulf of Mexico and elsewhere.