Among the several approaches to prestack imaging, common azimuth migration is one of the fastest. While it may suffer from off-azimuth response problems, it produces usable output at a speed that makes it a viable technique for velocity analysis and velocity model construction.
Figure 18 shows a common azimuth migration. A common azimuth migration parameterizes input data by CDP and offset. Since the data are assumed to have been recorded with one and only one azimuth, the source and receiver locations can be computed from the midpoint (or CDP) and offset. This means that the data are defined by only four parameters: midpoint (2), offset (1), and time, and, as a consequence, are four-dimensional. Normally, data sets with more than one azimuth are really five-dimensional: source(2), receiver(2) and time (1).
The nice thing about common azimuth data is that they can be continued downward in the same manner as poststack data. Even though the poststack data set has only three-dimensions, the methodology of the two approaches is so similar that we can certainly think of them as being the same.
The disadvantage of the common azimuth approach is that real world data is never acquired in common azimuth form. Moreover, the approximations used to produce the algorithm usually result in a methodology that cannot image steeply dipping events well.
Perhaps the saving grace of this algorithm lies in its speed. For full volume migrations, it has the potential to be the fastest algorithm ever invented for prestack imaging.
Again, as was the case for poststack data, common azimuth approaches image the data one depth slice at a time. Figure 19 is just an illustration to emphasize that almost all one-way methods image the data one depth or time slice at at time.
The nice thing about common azimuth migration is that it reduces the complexity of the input data set by one dimension. Normal 2D data is actually three-dimensional—it is indexed by one space variable for the shot location, one for the receiver, and one for time. In contrast, 3D data is characterized by being five dimensional, where each shot location has at least two surface coordinates, each receiver also has two surface coordinates, and, of course, there is one time dimension. Since shot, m + h= 2, and receiver locations, m