If the wavefields are sampled with spacing , then equation () will image with half-offset spacing , as shown in Figure . Sampling in offset can be refined further by considering Figure ; however, to do so requires imaging onto midpoints which do not lie on the propagation grid.
Figure 2 Imaging offsets with based on equation () alone.
Figure 3 Imaging offsets with . The midpoint lies between propagation grid nodes.
This problem is experienced whenever data are transformed from shot-geophone to midpoint-offset space, and no perfect solution exists. A typical workaround is to refine the midpoint grid, and fill empty bins with zeros; however, this doubles the data-volume and hence also doubles the cost of migration. Another alternative is to process even and odd offset separately; the disadvantage of this approach is that each half of the dataset may be undersampled.
Since shot-profile migration works in the shot-geophone domain, these problems may be avoided until after the migration is complete. Migration decreases the data-volume, increases the signal-to-noise ratio, and resolves locally conflicting dips. Therefore, it is easier to resample the data on whatever grid suits the interpreter after migration.