Sensitivity of image accuracy to velocity errors

ADVERTISEMENT
From SEG Wiki
Jump to: navigation, search
Seismic Data Analysis
Seismic-data-analysis.jpg
Series Investigations in Geophysics
Author Öz Yilmaz
DOI http://dx.doi.org/10.1190/1.9781560801580
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store


Accuracy of the velocity-depth model used in prestack depth migration can be checked by examining event curvature on common-receiver gathers. Figure 8.3-14a shows three common-receiver gathers sorted from the shot records that were migrated using the constant overburden velocity above the salt diapir (Figure 8.3-14c). Note that the top-salt event exhibits flat character at all three receiver locations since the velocity used for migration is the same as the layer velocity above the top-salt boundary (3000 m/s). Whereas the base-salt event and the event corresponding to the flat reflector below do not exhibit flat character since the migration velocity, in this case, is erroneously lower than the true layer velocities.

Use three different trial constant velocities for the overburden assigned to all the layers in the subsurface and migrate the shot records. Consider a common-receiver gather at one specific location (179 in Figure 8.3-14b). The top-salt event exhibits a curvature upward with erroneously low velocity (2500 m/s), flat character with the correct velocity (3000 m/s), and downward curvature with erroneously high velocity (3500 m/s). Moreover, the event depth changes from one trial velocity to another — the low velocity causes the event to appear at shallow depth.

Event curvature on common-receiver gathers can be likened to residual moveout on moveout-corrected common-midpoint gathers caused by incorrect move-out velocities. By measuring the residual moveout, layer velocities can be updated at each receiver location. Residual moveout analysis can be formulated within the context of common-receiver gathers derived from shot-geophone migration [1], common-receiver gathers derived from shot-profile migration [2] [3], or common-depth-point gathers (image gathers) derived from common-offset migration [4] [5].

We shall examine the sensitivity of image accuracy to velocity errors based on event curvature on common-receiver gathers derived from the shot-profile migration of the salt diapir model data (Figure 8.3-12). This analysis also is a prelude to using the event curvature on image gathers as a criterion for layer-by-layer velocity determination (next chapter). Start with the velocity-depth model defined as a half space with three different trial constant velocities that may be considered appropriate for the overburden above the salt diapir (Figure 8.3-15). Perform shot-profile migration using each of the velocity-depth models and sort the output to common-receiver gathers. Then, stack the receiver gathers to obtain the images in depth.

Figure 8.3-16 shows the depth image and a receiver gather (location 249) from each of the three prestack depth migrations. Note that the top-salt event exhibits a strong curvature upward with the trial velocity 2500 m/s for the overburden layer under consideration (Figure 8.3-16a). We conclude that this velocity is too low for the overburden. The top-salt event exhibits a strong curvature downward with the trial velocity 3500 m/s for the overburden layer (Figure 8.3-16e). We conclude that this velocity is too high for the overburden. Finally, the top-salt event is flat with the trial velocity 3000 m/s for the overburden layer (Figure 8.3-16c). We conclude that this velocity is appropriate for the overburden.

Examine the stack power in Figure 8.3-16 for the top-salt event on the depth images and note that the highest stack power is attained with the trial velocity 3000 m/s for the overburden layer (Figure 8.3-16d). In contrast, the stack power with the too-low (2500 m/s) and too-high (3500 m/s) velocities (Figures 8.3-16b and f) is weaker because of the curvature of the top-salt event on common-receiver gathers.

Based on the results of prestack depth migration using the three trial velocities (Figure 8.3-16), we assign the optimum velocity 3000 m/s to the overburden. Next, we interpret the top-salt event on the corresponding depth image (Figure 8.3-16d). Then, we modify the velocity-depth model in Figure 8.3-15b as shown in Figure 8.3-17, accordingly. Here, we have specified a two-layer model — the overburden above the top-salt boundary interpreted from Figure 8.3-16d, and the new half-space below with three different trial velocities appropriate for the diapir layer.

Figure 8.3-18 shows the depth image and a receiver gather (location 249) from each of the three prestack depth migrations. Note that the top-salt event is flat in all three cases since the overburden layer is the same for all the three models. The base-salt event exhibits a moderate curvature upward with the trial velocity 4500 m/s for the diapir layer under consideration (Figure 8.3-18a). We conclude that this velocity is too low for the diapir layer. The base-salt event exhibits a moderate curvature downward with the trial velocity 5500 m/s for the diapir layer (Figure 8.3-18e). We conclude that this velocity is too high for the diapir layer. Finally, the base-salt event is flat with the trial velocity 5000 m/s for the diapir layer (Figure 8.3-18c). We conclude that this velocity is appropriate for the diapir layer.

Examine the stack power in Figure 8.3-18 for the top-salt event on the depth images and note that it is identical in all three cases since the overburden layer is the same for all the three models. The highest stack power for the base-salt event is attained with the trial velocity 5000 m/s for the diapir layer under consideration (Figure 8.3-18d). In contrast, the stack power with the too-low (4500 m/s) and too-high (5500 m/s) velocities (Figures 8.3-18b and f) is slightly weaker because of the curvature of the base-salt event on common-receiver gathers.

Based on the results of prestack depth migration using the three trial velocities (Figure 8.3-18), we assign the optimum velocity 5000 m/s to the diapir layer. Next, we interpret the base-salt event on the corresponding depth image (Figure 8.3-18d). Then, we modify the velocity-depth model in Figure 8.3-17b as shown in Figure 8.3-19, accordingly. Here, we have specified a three-layer model — the overburden above the top-salt boundary interpreted from Figure 8.3-16d, the diapir with the base-salt boundary interpreted from Figure 8.3-18d, and the new half-space below with three different trial velocities appropriate for the subsalt region.

Figure 8.3-20 shows the depth image and a receiver gather (location 249) from each of the three prestack depth migrations. Note that the top-salt and base-salt events are flat in all three cases since the overburden and the diapir layers are the same for all the three models. The deepest event associated with the flat reflector within the half-space exhibits a very mild curvature upward with the trial velocity 3500 m/s for the half-space (Figure 8.3-20a). We conclude that this velocity is low for the half-space. The same event exhibits a very mild curvature downward with the trial velocity 4500 m/s for the half-space (Figure 8.3-20e). We conclude that this velocity is high for the half-space. Finally, the same event is flat with the trial velocity 4000 m/s for the half-space (Figure 8.3-20c). We conclude that this velocity is appropriate for the half-space that represents the subsalt region with the flat reflector.

Examine the stack power in Figure 8.3-20 for the top-salt and base-salt events on the depth images, and note that they are identical in all three cases since the overburden and diapir layers are the same for all three models. It is difficult to distinguish the images of the deepest event associated with the flat reflector within the half-space based on stack power (Figures 8.3-20b, d, and f). Nevertheless, based on the subtle differences in stack power in favor of the trial velocity 4000 m/s and the implausable undulations in the geometry of the flat reflector that resulted from the trial velocities 3500 m/s and 4500 m/s, we may conclude that the optimum velocity for the subsalt region is 4000 m/s.

This concludes the estimation of the velocity-depth model using the event curvature on common-receiver gathers. The conceptual appeal of this analysis can be very attractive for construction of earth models in depth. In practice, however, the computational cost can be prohibitive. Instead, residual moveout analysis of image gathers derived from common-offset migration is used for updating layer velocities (earth modeling in depth).

Refer to the common-receiver gathers in Figures 8.3-16, 8.3-18, and 8.3-20 and note that the deeper the event, the higher the velocity and the shorter the cable length, the poorer the resolving power of curvature analysis for velocity determination. This observation is comparable to the case of conventional stacking velocity analysis, and it also applies to residual moveout analysis of image gathers derived from common-offset migration.

Compare the amplitudes on the images from depth migration of the zero-offset and prestack data (Figure 8.3-21). Note the differences in amplitude distribution along the flat reflector below the salt diapir. Imaging beneath complex structures has certain implications as to the acquisition geometry — specifically, on the choice of the cable length.

References

  1. Al-Yahya, 1989, Al-Yahya, K., 1989, Velocity analysis by iterative profile migration: Geophysics, 54, 718–729.
  2. Reshef and Kosloff, 1986, Reshef, M. and Kosloff, D., 1986, Migration of common-shot gathers: Geophysics, 51, 324–331.
  3. Lee and Zhang, 1992, Lee, W. B. and Zhang, L., 1992, Residual shot-profile migration: Geophysics, 57, 815–822.
  4. Deregowski, 1990, Deregowski, 1990, Common-offset migrations and velocity analysis: First Break, 8, 225–234.
  5. Cox and Wapenaar, 1992, Cox, H. L. H. and Wapenaar, C. P. A., 1992, Macromodel estimation by common-offset migration and by shot-record migration: J. Seis. Expl., 1, 29–37.

See also

External links

find literature about
Sensitivity of image accuracy to velocity errors
SEG button search.png Datapages button.png GeoScienceWorld button.png OnePetro button.png Schlumberger button.png Google button.png AGI button.png