I use a portion of the 2-D real dataset from the Mahogany field, located in the Gulf of Mexico. The 2-D dataset is an OBS multicomponent line. The data was already preprocessed by CGG. The hydrophone and the vertical components of the geophone have been combined to form the PZ section. The data have also been separated into the PS section. I focus on both the PZ section and the PS section.
Figure presents a typical shot gather. On the left is the PZ common-shot gather, and on the right the PS common-shot gather. The PZ shot gather has fewer time samples than the PS shot gather because a longer time is needed to observe the converted-wave events. Also, note the polarity flip in the PS common-shot gather, a typical characteristic of this type of data.
In both datasets, the PZ and the PS sections were migrated using wave-equation shot-profile migration. Both, the P and the S velocity models are unknown for this problem; therefore, I migrate the data using a simple velocity model with a vertical gradient. Figure shows both velocity models, the P-velocity model in the left panel, and the S-velocity model in the right panel.
Figure 11 Velocity models used for the shot-gather migration. (a) P-velocity, (b) S-velocity.
Figure presents a PS image on the left, and two angle-domain common-image gathers on the right. Both common-image gathers are taken at the same location, indicated by the solid line (CIG=14500) in the image. The PS image is taken at zero subsurface-offset. This is not the ideal position, since the polarity flip destroys the image at this location. The ideal case will be to flip the polarities in the angle domain, as it was discussed in the previous section; unfortunately, I do not have the correct velocity model; therefore, I have only an approximate solution to the final PS image. However, as we will see later, through an update on the velocity model I am able to obtain an image that is more accurate. Figure represents the image-dip field for this experiment, which was estimated along the zero subsurface-offset of the PS section.
Figure 13 Image dips, representing the field in equation .
The angle-domain common-image gather on panel (b) of Figure represents the angle-domain common-image gathers using the conventional methodology, which will be on the diagram flow on Figure . The angle-domain common-image gather on panel (c), represents the true converted-wave angle-domain common-image gather, that is obtained with the method described in this chapter.
The geology for this section consists of very gentle dips, representing a sedimentary depositional system with little structural deformation; therefore, the angle gather on panel (b) has the polarity flip very close to zero angle. The true PS-ADCIG, panel (c), also preserves this characteristic. The residual curvature for the events, whether primaries or multiples on panel (b), is larger than the residual curvature of the same events in the true PS angle-domain common-image gather.
Figure compiles the angle-domain common-image gathers for this dataset, all of which are taken at the same position, CIG=14500. From left to right, the PZ-ADCIG, the true PS-ADCIG, and both the P-and-S angle-gather representation, panels (c) and (d), for the true PS-ADCIG on panel (b). Notice that most of the primary events have a residual curvature. The residual moveout is more prominent for those events that I identify as multiples.
Notice that the angle coverage in both P-and-S ADCIGs representations is smaller than for the true PS-ADCIG, since the coverage of an individual plane-wave is smaller than the combination of two plane-waves, as it is the case in converted-mode data.
The difference in the residual moveout between the single-mode PZ-ADCIG and the PS-ADCIG suggests an erroneous S-velocity model. Therefore, I decided to run a second migration for the PS section alone with an slower S-velocity model; the ratio between the first and second S-velocity model is 2.
Figure presents the PZ and the updated PS results using shot-profile migration. The PZ migration was done with the P-velocity model in Figure . The PS migration was done with the updated S-velocity model. The left panel on Figure shows the PZ migration result, the top panel shows the image at zero subsurface-offset, and the center and bottom panels are four CIGs taken at locations indicated by the solid lines in the zero subsurface image. The center panel represents SODCIGs, and the bottom panel represents the angle-domain common-image gathers. Observe that most of the events in the ADCIGs are mainly flat, which suggests that the initial linear P-velocity model is a reasonable approximation.
The right panel on Figure shows the results of the PS migration. The top panel presents the stacking of the angle gathers after the polarity flip correction. Similar to the PZ results (left panels), the center panel represents four subsurface offset-domain common-image gathers. The bottom panel represents the true PS-ADCIGs that corresponds to the SODCIGs, at the locations indicated by the solid lines in the angle-stack image. Note that most of the events in the PS-ADCIGs are approximately flat. Although there is a resemblance between the PZ and the PS images with respect to the general geology, the events do not match. There is a strong presence of multiples, due to the shallow sea bottom (120 m). These multiples are more prominent in the PS section than in the PZ section, that is because the PZ summation already eliminates the source ghost.
Finally, Figure shows the same common-image gather as in Figure but after the second migration for the PS section. This gather is taken at a location of 14500 m from the images on Figure . Panel (a) presents the PZ-ADCIG, panel (b) presents the true PS-ADCIG, and panels (c) and (d) are the PS-ADCIG representation in both P-ADCIG and S-ADCIG, respectively. Note that the events in all the different angle gathers are nearly flat, and several events in both the PZ and PS angle-gathers correlate. This suggests that some of these reflections might come from the same geological feature. Also note that there is a residual moveout at high angles in the S-ADCIG, for the first 1000 m. This information might be useful for a residual moveout analysis to compute an S-velocity perturbation, which might produce a final PS image that matches the PZ image for the main events.