2-D prestack depth migration
In this section, we shall review two methods of prestack depth migration applied to 2-D data. These methods both have historical and conceptual significance. An early method of prestack depth migration is based on downward continuation of sources and receivers (Section D.1). The method commonly is known as shot-geophone migration. A common-shot gather represents a wavefield and thus can be extrapolated in depth at discrete intervals. As a result, receivers are lowered from one depth level to the next. By invoking reciprocity, we may also consider a common-receiver gather representing a wavefield. Thus, by extrapolating a common-receiver gather, sources are lowered from one depth level to the next. By alternating between extrapolation of common-shot and common-receiver gathers at each depth level, all sources and receivers are lowered from the surface to each of the reflectors in the subsurface. While sources and receivers are lowered vertically downward from one depth level to the next, the recorded waves are back-propagated along the raypaths from source to a reflector back to receiver locations at the surface. When sources and receivers are lowered to the reflector, they coincide and the traveltime diminishes to naught. This satisfies the imaging condition.
When the maximum depth of extrapolation is reached, traces at zero-offset from each of the resulting common-shot gathers are extracted and placed side-by-side to produce the image from prestack depth migration. Nonzero-offset traces are abandoned since all primary energy has collapsed to zero-offset provided the velocity-depth model is correct.
Note that in practical implementation of shot-geophone migration, data need to be sorted from one gather type to another (common-shot and common-receiver) at each depth level. This sorting operation increases the cost of the method, formidably. Another practical aspect of this method is that missing near-offset traces in common-shot gathers are filled in with zero traces before downward continuation is started.
A more popular method of prestack depth migration is based on migration of shot records, individually. This is plausable since a shot record is a wavefield generated by a single source. The method commonly is known as shot-profile migration. The migrated shot records are then sorted into common-receiver gathers. Finally, traces in each receiver gather are summed to construct the image below the receiver location. By placing the traces that result from this summation side by side, we obtain the image from shot-profile migration.
A practical advantage of shot-profile migration is its ability to handle irregularities in recording geometry. Since each shot record is migrated independently, missing shots, duplicate shots or just irregularities in shot spacing are irrelevant.
- Shot-geophone migration
- Shot-profile migration
- Sensitivity of image accuracy to velocity errors
- Field data examples