Two-pass versus one-pass 3-D poststack depth migration
In 3-D poststack migration, we examined the characteristics of two-pass and one-pass 3-D poststack time migration. We concluded that given the choice between one-pass and two-pass schemes, 3-D poststack time migration may be done in two passes provided the vertical velocity gradient is not excessively large and dips are gentle. Is the two-pass strategy also applicable to 3-D poststack depth migration? We shall experiment with the salt-dome synthetic data set (Figure 8.4-2) and conclude that 3-D poststack depth migration has to be done in one pass.
First, we consider two-pass implicit finite-difference 3-D time migration of the salt-dome synthetic data set. Start with the 3-D zero-offset wavefield (Figure 8.4-2), and apply time migration in the inline direction and display four selected inline sections and four selected crossline sections (Figure 8.4-5). After this first-pass migration, the imaging of the center inline (I-241) is complete, since there is no sideswipe energy that needs to be moved out of the plane of this inline. On the other hand, the center crossline (X-241) has not been imaged at all, because no movement of energy took place in this line as yet after the first-pass migration. On other lines, there is still some more imaging to be done — note, for instance, the sideswipe energy on inline I-151.
Now sort the data into crosslines, perform the second-pass migration on the already migrated data, and display the same inline and crossline sections (Figure 8.4-6). These are now the inlines and crosslines after the two-pass 3-D time migration. Since the overburden velocity above the salt layer is constant, the two-pass 3-D time migration correctly images the top-salt boundary. Since we have done time migration, whether it is two-pass or one-pass, we have not imaged the base-salt boundary correctly.
Figure 8.4-7 gives a summary of the results of one-pass (as in Figure 8.4-3) and two-pass (as in Figure 8.4-6) implicit 3-D time migration of the salt-dome model data (Figure 8.4-2). Although not evident from the inline sections in Figure 8.4-7, the top-salt boundary actually has been imaged more accurately by the two-pass migration as compared with the one-pass migration. The constant-velocity of the layer above the salt enables the two-pass scheme to produce an accurate result (Section G.1). On the other hand, even though the overburden velocity above the salt layer is constant, the approximation made in the splitting has caused the one-pass scheme to produce an incorrect image of the top-salt boundary, especially along the directions diagonal to inline and crossline directions (3-D poststack migration). Again, the base-salt boundary has not been imaged correctly by either one-pass or two-pass migrations, since we have done time migration rather than depth migration.
Figure 8.4-7 One-pass versus two-pass 3-D time migration of the salt-dome model data shown in Figure 8.4-2. The one-pass result is the same as in Figure 8.4-3 and the two-pass result is the same as in Figure 8.4-6.
We now examine the plausability of a hybrid two-pass 3-D migration of the salt-dome synthetic data set, wherein the first-pass migration is in time and the second-pass migration is in depth. In areas with a complex overburden structure, such as the overthrust belts, usually velocity varies laterally more in the dip direction perpendicular to the thrust fronts than the strike direction. When that is the case, it might be plausable to do time migration in the strike direction with mild lateral velocity variations, followed by depth migrations of selected lines in the dip direction with strong lateral velocity variations. Such two-step hybrid strategy may be useful in building the 3-D velocity-depth model for a subsequent, proper 3-D depth migration of the 3-D data.
For the synthetic data set in Figure 8.4-2, start with the results of time migration in the inline direction (Figure 8.4-5) and perform depth migration in the crossline direction. Then, display the same inlines and crosslines as in Figure 8.4-6. After time migration as the first-pass and depth migration as the second-pass (Figure 8.4-8), note that we certainly have restored the true geometry of the top-salt boundary correctly. This is because the overburden is constant velocity; therefore, it did not matter whether we did time or depth migration. However, we have not been able to restore the geometry of the base-salt boundary, except for the center crossline (X-241), because this salt structure is truly 3-D in character with no dominant strike or dip direction.
Figure 8.4-9 gives a summary of the results of one-pass (as in Figure 8.4-4) and two-pass (as in Figure 8.4-8) 3-D depth migration of the salt-dome model data (Figure 8.4-2). Again, note that the top-salt boundary actually has been imaged more accurately by the two-pass migration as compared with the one-pass migration. The constant-velocity of the layer above the salt enables the two-pass scheme to produce an accurate result. On the other hand, even though the overburden velocity above the salt layer is constant, the approximation made in the splitting has caused the one-pass scheme to produce an incorrect image of the top-salt boundary. The base-salt boundary, however, has not been imaged correctly by the two-pass scheme, while it has been imaged correctly by the one-pass scheme.
- If the velocity field is judged to be suitable for time migration, the two-pass strategy for 3-D time migration may be acceptable provided the vertical velocity gradient is not excessively large and dips are not very steep.
- If the velocity field requires depth migration, the one-pass strategy for 3-D depth migration is imperative.
Figures 8.4-10 and 8.4-11 show a field data example of 3-D depth migration using the one-pass scheme. The inline (top left) and crossline (top right) stacked sections in both figures show a structural high, which is associated with culminations in an overthrust belt. Figure 8.4-12a is an inline cross-section of the 3-D velocity-depth model. The deepest horizon on the velocity model (horizon 8) corresponds to the event below 2 s on the inline stacked section in Figure 8.4-10. The true geometry of this horizon has been distorted by the structure above acting as a complex overburden. Although in two dimensions, the image-ray plot (Figure 8.4-12b) through the velocity-depth model (Figure 8.4-12a) verifies the presence of a complex overburden above horizon 8. See 2-D poststack depth migration for a discussion on image rays.
Figure 8.4-9 One-pass versus two-pass 3-D depth migration of the salt-dome model data shown in Figure 8.4-2. The one-pass result is the same as in Figure 8.4-4 and the two-pass result (first-pass in time followed by second-pass in depth) is the same as in Figure 8.4-8.
Figure 8.4-10 An inline (top left) and a crossline stacked section (top right) from a land 3-D survey and the corresponding 2-D (center) and 3-D (bottom) depth migration results. A cross-section of the velocity-depth model is shown in Figure 8.4-12. (Data courtesy Chevron USA, Inc.)
Figure 8.4-11 Another inline (top left) and crossline stacked section (top right) from the same land 3-D survey as in Figure 8.4-10 with their 2-D (center) and 3-D (bottom) depth migrations. A cross-section of the velocity-depth model is shown in Figure 8.4-12. (Data courtesy Chevron USA, Inc.)
Figure 8.4-12 (a) An inline cross-section of a 3-D velocity-depth model that was used in 3-D depth migration of the data shown in Figures 8.4-10 and 8.4-11. (b) Image rays through this velocity-depth model.
Note the similarity between the inline velocity-depth model (Figure 8.4-12a) and line B after 3-D depth migration (bottom left, Figure 8.4-10). Despite this similarity, there are parts of the survey in which the data are overmigrated (on line A, bottom left, Figure 8.4-11) and parts in which the data are undermigrated (not shown). Differences between the output from depth migration and the velocity-depth model used requires an iterative modification of the velocity-depth model where it departs from the output of depth migration (2-D poststack depth migration). For comparison, Figures 8.4-10 and 8.4-11 show 2-D depth migrations of the selected lines. Note the obvious difference between 2-D and 3-D depth migrations of line D (Figure 8.4-11). Although the 2-D depth-migrated section contains an abundance of reflections as compared to the 3-D depth migrated section, that reflection energy does not belong on line D. From line A or B, note that energy should be migrated in the updip direction from line D to C. Hence, after 3-D migration, line D is depleted of reflection energy (Figure 8.4-11), while line C is enriched (Figure 8.4-10).
- 3-D poststack depth migration
- 3-D poststack time versus depth migration
- Implicit versus explicit 3-D poststack depth migration
- 3-D poststack datuming