WAZ Up?

[Note: A version of this blog entry appears in World Oil (October, 2010)]

Anyone keeping an eye on seismic advertisements in trade publications must have noticed the proliferation of azimuth (AZ). We are bombarded with WAZ (wide azimuth), NAZ (narrow azimuth), FAZ (full azimuth), RAZ (rich azimuth), etc. What is going on here? Why the blitz of promotion for AZ?

First, we need to understand that a prestack seismic trace is like a child, it has two parents: A source and a receiver. Each parent has a physical location and the trace is considered to live at exactly the half-way point between source and receiver. This location is called the midpoint, so each trace is said to have a midpoint coordinate. But like a child, the trace inherits other characteristics that are a blend of the parents. Looking around from the trace location, we see there is a certain distance between parents, a quantity termed the offset. Furthermore, there is an imaginary line from source to midpoint to receiver whose orientation we call azimuth. This is the bearing that you would read off a compass; 0 is North, 90 is East, and so on around to 360 which is, again, North.

We said earlier that a prestack seismic trace lives at the midpoint between source and receiver. This is true until we migrate the data. Migration is a process that maps observed seismic data into the earth. For example, imagine the source and receiver are very close together and we observe nothing on our trace except a reflection at 1 second.

How are we to make sense of this? Let's say the earth velocity is 2000 m/s, that means the wave went out, reflected, and came back; all in 1 second. Clearly the outward time is half of this, 1/2 second, traveling at 2000 m/s. So the reflecting object must be 1000 m away from the source/receiver/midpoint (S/R/M) location.

We know the object is 1000 m away, but in what direction? Ah, there is the rub. We do not, and cannot, know which way to look for the reflection point when we only have one prestack trace. But, strangely, that is no problem. Back in the 1940s some smart guys figured it out, and sone other smart guys coded it up in the 1970s. The trick is this: Since we don't know where the reflection comes from, we put it everywhere it could possibly have come from.

In our example, we know the reflector is 1000 m away from one point (where S/R/M all live). In other words, a bowl (or hemisphere) centered on that location. Let's be a little more specific. Underneath the data we have built an empty 3D grid that we call 'image space'. We grab the trace, note it's midpoint and reflection time, then take the observed reflection amplitude and spread it out evenly over the bowl. If we have only one trace with one event, that would be the migration result shipped to the client. A bowl-shaped feature embedded in a vast array of zeros. Good luck getting payment on that.

Those who know something about geology will immediately complain that the earth does not contain bowl-shaped objects. True. But remember, this is the result of migrating only one trace and we actually have many millions of traces in a modest 3D survey. All of these are migrated to generate a collection of closely spaced bowls in the subsurface and, when we add them up, something remarkable happens. The bowls tend to cancel in those places where nothing exists in the earth. But where the reflections actually originated the bowls constructively interfere to generate an image of the subsurface. Furthermore, this process can build all the interesting geology we want, including faults, channels, synclines, anticlines, and so on. Quite amazing actually.

Where does azimuth come in? So far we have considered the prestack seismic trace to have S/R/M all at the same location. In other words, there is no offset and no azimuth. When the source and receiver separate they do so along an azimuth, which the seismic trace inherits. Migration now involves the same kind of process described earlier, except the primitive migration shape is now a stretched bowl with the long axis along the S/R azimuth (technically, an ellipsoid).

Before all the excitement and activity about WAZ, marine surveys were shot with one, or a few, cables towed behind a ship steaming in, say, E-W lines. This is a narrow azimuth survey. Since all the traces have about the same azimuth and those millions of migration bowls are lined up E-W along the acquisition azimuth. Not surprisingly, when all the bowls are summed in the subsurface image, we get a good view of geology with an E-W dip direction. Geology oriented any other way is blurred, smeared, or just not visible.

Strange things can appear in such a data set, taxing the interpretation ability of even the most experienced geologist. Faults are a good case in point. Consider our narrow azimuth E-W survey shot in an area with faults oriented parallel (E-W) and perpendicular (N-S) to the shooting direction. The explanation is a bit technical, but the bottom line is that N-S faults will be beautifully imaged, while those running E-W will be poorly seen, if at all.

With this kind of narrow azimuth data, the industry spent decades using ever faster computers and better migration algorithms, only to see the data improvements get smaller and smaller. But then overnight, it seemed, the introduction of wide azimuth shooting brought a quantum leap in image quality. Of course, WAZ came along late and unleashed all that pent-up computing and algorithm power making the improvement seem all the more remarkable.

Almost from the first days of petroleum seismology, practitioners knew that to unravel 3D dip required shooting in different directions. This lesson was always heeded in the development of land 3D. But offshore operational difficulties, and related costs, pushed the full azimuth goal aside. Then subsalt prospecting introduced a new class of imaging problem and narrow azimuth data was just not good enough. WAZ is here to stay.