Dip-moveout correction in practice
Figure 5.2-2 shows selected CMP gathers along a marine line over a salt structure. CMP gathers 1381 (at 1.5 s), 1461 (at 2.2 s), and 1701 (at 1.55 s) exhibit cases of conflicting dips associated with two events with significantly different moveouts.
The DMO processing sequence includes the following steps.
- Perform velocity analysis sparsely along the line at locations with prominently flat events and create an initial velocity field.
- Apply normal-moveout correction using flat-event velocities. Note the events associated with steep dips have been overcorrected as demonstrated in Figure 5.2-3, whereas reflections with no dip or negligibly small dip have been flattened.
- Apply partial stacking to CMP gathers to reduce the fold from 60 to 30. A partial stack up to a 4:1 reduction in fold usually is acceptable before DMO correction. While fold reduction provides significant computational savings, it must not be done excessively. Following the fold reduction, sort the moveout-corrected gathers (Figure 5.2-3) to common-offset sections and perform dip-moveout correction. Then, sort back to CMP gathers. Compare the selected gathers after DMO correction (Figure 5.2-4) with the same gathers without DMO correction (Figure 5.2-3), and note that the duality in event moveout on CMP gathers 1381 (at 1.5 s), 1461 (at 2.2 s), and 1701 (at 1.55 s) has been removed. This is a direct result of the partial migration effect of the DMO correction.
- Apply inverse moveout correction (Figure 5.2-5) with the same velocity field that was used for the NMO correction prior to DMO correction (Figure 5.2-3).
- Perform velocity analysis at frequent intervals along the line and pick velocity functions which now are supposed to have been corrected for the dip effect. Refer to the velocity analysis at midpoint 1381 shown in Figure 5.2-6. Note the improved velocity trend after DMO correction. Close-up displays of the semblance spectrum and the moveout-corrected gather before and after DMO correction are shown in Figure 5.2-7 and 5.2-8, respectively. Note the two semblance peaks at 1.5 s — one at 2050 m/s and the other at 2750 m/s. Because the gather was moveout corrected using the denoted velocity function that includes the 2050-m/s peak, the event associated with the 2750-m/s peak has been overcorrected (Figure 5.2-7). DMO correction has removed the duality in the velocity spectrum at about 1.5 s and yielded a more distinctive trend (Figure 5.2-8) compared to the spectrum derived from the gather with no DMO correction. The distinctive trend is a direct result of the fact that DMO correction removes reflection-point smearing by mapping reflection points on a dipping reflector associated with nonzero source-receiver separation onto normal-incidence reflection point. The partial migration effect of DMO correction has actually moved the dipping event with the 2750-m/s peak to a different midpoint location.
- Create a velocity field using the velocity functions picked from the velocity spectra computed from the DMO-corrected gathers (Figure 5.2-9b). This velocity field has more detail than the initial field (Figure 5.2-9a) used for NMO correction prior to DMO correction (step b). This initial velocity field also was used to apply the inverse NMO correction as in step (d).
- Apply moveout correction to the DMO-corrected gathers using the velocity field as in Figure 5.2-9b. Selected CMP gathers are shown in Figure 5.2-10, and the corresponding CMP stack is shown in Figure 5.2-11. As a result of DMO correction, the steeply dipping salt-flank reflections have been stacked with as much power as the flat events associated with the surrounding strata. Since a DMO stack is a closer approximation to a zero-offset section in comparison with a CMP stack, time migration of the DMO stack yields an image of the salt diapirs with their flanks clearly delineated, especially between 1-1.5 s (Figure 5.2-12). For comparison, conventional CMP stack and its migration are shown in Figures 5.2-13 and 5.2-14, respectively. Because the reflections off the flanks of the salt diapirs have not been preserved with adequate strength on the CMP stack (Figure 5.2-13), time migration yields a poor definition of the salt boundaries (Figure 5.2-14).
Figure 5.2-7 A close-up view of the velocity spectrum shown in Figure 5.2-6a and the associated CMP gather without DMO correction followed by moveout correction using the velocity function depicted in (a).
Figure 5.2-8 A close-up view of the velocity spectrum shown in Figure 5.2-6b and the associated CMP gather with DMO correction followed by moveout correction using the velocity function depicted in (a).
Figure 5.2-12 Migration of the DMO stack shown in Figure 5.2-11. Compare with Figure 5.2-14.
Figure 5.2-14 Migration of the CMP stack shown in Figure 5.2-13. Compare with Figure 5.2-12.
Prestack time migration
DMO correction maps moveout-corrected common-offset data to zero-offset. As a direct result of this aspect of DMO correction, the process decouples common-offset sections, thus enabling treatment of each of the common-offset sections, independently. A DMO-corrected common-offset section can be considered a replica of a zero-offset section, and therefore, can be migrated using a method applicable to zero-offset wave-field.
- Starting with input prestack data in midpoint, offset and two-way event time in the unmigrated position, apply NMO correction using flat-event velocities. These are picked from velocity spectra computed sparsely along the line. Figure 5.3-4 shows three common-offset sections associated with the data as in Figure 5.2-3 with offsets 78.5 m, 1078.5 m, and 2078.5 m, following NMO correction.
- Apply DMO correction to each common-offset section (Figure 5.3-5).
- Following DMO correction, each common-offset section is assumed to be a replica of zero-offset section, and thus, can be migrated using a zero-offset migration algorithm. How could these common-offset sections be migrated before we even know migration velocities? The conjecture is that a smoothed stacking velocity field (Figure 5.2-9a) can be used to perform the migrations of common-offset data. As a result, events will be moved spatially to locations that are between their unmigrated and correctly migrated positions, but fairly close to the latter. Figure 5.3-6 shows three selected common-offset sections as in Figure 5.3-5 after migration.
- Sort the migrated common-offset sections into CMP gathers (Figure 5.3-7). Events on these gathers are now assumingly close to correct subsurface positions after migration. Note the presence of residual moveout on some events, which suggest errors in the velocity field used for migration.
- Apply inverse NMO correction and perform velocity analysis. Although event positioning in the spatial sense will not be affected by this velocity analysis, use of updated velocities will improve the stacking of the CMP gathers after migration. Figure 5.3-8 shows selected CMP gathers as in Figure 5.3-7 after inverse moveout correction, and Figure 5.3-9b shows the migration velocity field derived from the analysis of such gathers. For comparison, the DMO velocity field using the DMO-corrected gathers as in Figure 5.2-5 is shown in Figure 5.3-9a.
- Apply NMO correction (Figure 5.3-10) using the migration velocity field (Figure 5.3-9b) and stack the migrated data (Figure 5.3-11). Keep in mind that migration actually has been done using an initial estimate for the velocity field (Figure 5.2-9a).
- To obtain the migrated section with the updated velocity field (Figure 5.3-9b), we can follow two alternative approaches. First, compute the residual velocity field (Section D.8) from the initial (Figure 5.2-9a) and updated (Figure 5.3-9b) velocity fields, and use it to perform residual migration (frequency-wavenumber migration in practice) for which the input is the stacked section from step (f). The residual migration is acceptable provided the initial velocity field varies vertically, only, and the vertical variation in velocity is expressed with moderate gradients. The second approach involves first simulation of an unmigrated stacked section by forward modeling (inverse migration) of the migrated section obtained in step (f) (Figure 5.3-11) using the initial velocity field (Figure 5.2-9a). The modeled section is shown in Figure 5.3-12 and may be treated as equivalent to the unmigrated stacked section. The next step involves migrating the modeled section using the updated velocity field (Figure 5.3-9b). The final result of prestack time migration sequence described above is shown in Figure 5.3-13.
Figure 5.3-6 Three common-offset sections as in Figure 5.3-5 with offsets (a) 78.5 m, (b) 1078.5 m, and (c) 2078.5 m, following common-offset time migration using the velocity field shown in Figure 5.2-9a.
Figure 5.3-7 Selected CMP gathers after prestack time migration (selected common-offset sections are shown in Figure 5.3-6).
Figure 5.3-9 (a) The velocity field, same as that shown in Figure 5.2-9b, used to stack the CMP gathers as in Figure 5.2-5 with DMO correction, and (b) the velocity field used to stack the gathers after prestack time migration as in Figure 5.3-8.
Figure 5.3-12 Inverse migration of the stack shown in Figure 5.3-11 using the velocity field shown in Figure 5.2-9b.
Figure 5.3-13 Migration of the stack shown in Figure 5.3-12 using the velocity field shown in Figure 5.3-9b.
- Fault planes
- DMO and multiples
- DMO and coherent linear noise
- Other considerations
- Aspects of DMO correction — a summary
- DMO correction and common-offset migration
- Fault planes
- Common-reflection-point versus common-reflection-surface stacking