Shot to midpoint transformations

Implicit in the multi-offset imaging scheme outlined above is a transformation from shot-receiver to midpoint-offset space. Although this transformation is buried within the migration process, the subtleties associated with the conversion remain.

If the wavefields are sampled with spacing $\Delta x$, then equation () will image with half-offset spacing $\Delta h=\Delta x$, 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.

 

cmpeven Figure 2 Imaging offsets with $\Delta h=\Delta x$ based on equation () alone.

 

cmpodd Figure 3 Imaging offsets with $\Delta h=\Delta x/2$. 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.