Figure 8.3-1 shows selected common-shot gathers associated with a land line recorded over a salt diapiric structure. Note the presence of coherent reflections on shot records to the left and to the right of the salt diapir, and poor reflection quality of the shot records above the salt diapir. Following the sorting to common-receiver gathers, we observe the missing shots along the line (Figure 8.3-2).
Figure 8.3-3a shows the CMP-stacked section with the salt diapir in the middle. The base-salt reflection with the velocity pull-up typical of salt diapirs is the most coherent event in this portion of the section. The poor imaging of the base-salt boundary by poststack depth migration is a direct consequence of the fact that the CMP-stacked section is only an approximation to a zero-offset section (Figure 8.3-3b). Compare with the image in depth derived from shot-geophone migration shown in Figure 8.3-3c. The geometry of the base-salt boundary indicates the presence of fault blocks. Also note some coherent events, albeit weak, in the subsalt region.
A bonus effect of prestack migration — be it time or depth, is its ability to attenuate multiples. Note, for instance, in Figure 8.3-3a the pegleg (m) on the left flank of the diapir. This multiple has been retained during CMP stacking and moved with the primary velocity during poststack migration (Figure 8.3-3b). However, it is not on the section derived from prestack depth migration. To explain this bonus effect of prestack migration, refer to the selected shot records after prestack depth migration (Figure 8.3-4). Since the migration velocity field is associated with the primary events, the primary energy has focused on the zero-offset traces, while the multiple energy has been dispersed to nonzero-offset traces. The focusing of the primary energy also is seen on the common-receiver gathers after migration (Figure 8.3-5). The image from prestack depth migration (Figure 8.3-3) is formed by compiling the zero-offset traces from the shot records after migration (Figure 8.3-4). All the remaining nonzero-offset traces in the shot records are simply abandoned.
The quality of focusing at zero offset by shot-geophone migration understandably depends on the accuracy of the velocity field used in migration. Erroneously too low or too high velocities would cause a partial collapse of the primary energy to zero offset. Note the curvature along some of the events in the vicinity of the zero-offset traces on the shot records (Figure 8.3-4) and receiver gathers (Figure 8.3-5). Some exhibit a curvature upward (erroneously low velocity above the event) and some exhibit a curvature downward (erroneously high velocity above the event). Theoretically, by measuring this curvature as if it is associated with residual moveout, velocities may be updated at each shot or receiver location. Such residual moveout analysis has been developed for shot-profile migration  and is discussed later in this section.
We shall extend the discussion on shot-geophone migration by comparing prestack depth migration with prestack time migration results. Shown in Figure 8.3-6 are the images obtained from post- and prestack time migration. First, note that both yield an incorrect image of the base-salt boundary. Since the problem of imaging the base-salt boundary is associated with a complex overburden structure, it only can be handled by depth migration. Strictly speaking, it should be handled by prestack depth migration (Figure 8.3-3).
Second, prestack time migration actually can produce, as in this example, a poorer image of the base-salt boundary compared to poststack time migration (Figure 8.3-6). Doing the migration before stack does not necessarily solve the problem of imaging beneath the salt diapir; doing it as depth migration is the key to solving this problem. The poor performance of prestack time migration can be verified by examining the focusing of energy at zero offset on common-shot (Figure 8.3-7) and common-receiver gathers (Figure 8.3-8). Specifically, note that the focusing of energy to zero offset by prestack time migration is not as good as it is by prestack depth migration (Figures 8.3-4 and 8.3-5).
Figure 8.3-3 (a) The CMP stack associated with the data shown in Figure 8.3-1; (b) poststack depth migration; (c) prestack depth migration. Trace spacing of the prestack depth-migrated section (the same as the shot or receiver group interval) is twice that of the poststack depth-migrated section (the same as the CMP interval). Event labeled as m is peg-leg multiple.
Figure 8.3-4 Selected common-shot gathers after shot-geophone depth migration from a land line over a salt diapiric structure. Note that primary energy has focused onto and at the vicinity of the zero-offset traces.
Figure 8.3-5 Selected common-receiver gathers after shot-geophone depth migration from a land line over a salt diapiric structure. Selected common-shot gathers are shown in Figure 8.3-4.
Figure 8.3-6 (a) The CMP stack associated with the data shown in Figure 8.3-1; (b) poststack time migration; (c) shot-geophone prestack time migration. Compare with the results from depth migration shown in Figure 8.3-3. Trace spacing of the prestack time-migrated section (the same as the shot or receiver group interval) is twice that of the poststack time-migrated section (the same as the CMP interval).
Figure 8.3-7 Selected common-shot gathers after shot-geophone time migration from a land line over a salt diapiric structure. Note that primary energy has collapsed onto and at the vicinity of the zero-offset traces.
Figure 8.3-8 Selected common-receiver gathers after shot-geophone time migration from a land line over a salt diapiric structure. Selected common-shot gathers are shown in Figure 8.3-7.
Figure 8.3-10 (Top) Selected synthetic shot records associated with the velocity-depth model in Figure 8.3-10; (bottom) same records after prestack depth migration.
Figure 8.3-11 (Top) Selected synthetic shot records as in Figure 8.3-10 with missing receivers; (bottom) same records after prestack depth migration.
We now complete our discussion on shot-geophone migration by examining the effect of missing data on imaging quality. Figure 8.3-9 shows a model of a salt diapir. A total of 193 shot records was created by using a nonzero-offset ray-theoretical modeling procedure. The receiver cable is split-spread with an offset range of 501200 m, and 48 receivers at 50-m interval. Putting aside the inadequacies of ray theory for modeling traveltimes, we should be able to make use of the modeled shot records for investigating the missing-data problem.
Selected shot records before and after shot-geophone migration using the true velocity-depth model (Figure 8.3-9a) are shown in Figure 8.3-10. Note that the events have focused onto and at the vicinity of the zero-offset traces. By extracting the zero-offset traces and placing them side by side, we obtain the depth image in Figure 8.3-9b. (The amplitude weakening along the top-salt event is caused by the limitations in the ray-theoretical modeling.)
A total of 15% of the traces from the modeled shot records was discarded arbitrarily and replaced with zero traces. As a result, some shot records contained few zero traces while some contained all zero traces. Shown in Figure 8.3-11 are the same shot records as in Figure 8.3-10 with missing traces. Note that, after prestack depth migration, focusing of the energy to zero-offset and its vicinity (Figure 8.3-11) has been achieved in a manner comparable to the case of the complete data set (Figure 8.3-10). Likewise, the prestack depth-migrated section derived from the missing data (Figure 8.3-9c) is very similar to the section derived from the complete data set (Figure 8.3-9b). We may conclude that shot-geophone depth migration can accommodate missing data resulting from recording geometry irregularities.
- 2-D prestack depth migration
- Shot-profile migration
- Sensitivity of image accuracy to velocity errors
- Field data examples