Real data example

This test uses a portion of the 2-D real data set from the Mahogany field, located in the Gulf of Mexico. The 2-D data set is an Ocean Bottom Seismic (OBS) multicomponent line. The data has been already preprocessed. The hydrophone and the vertical components of the geophone has been combined to form the PZ section. Also, the data has also been separated into the PS section. We concentrate on the PZ section and the PS section.

Figure  presents a typical shot gather for this OBS data set. On the left we have the PZ common-shot gather, and on the right we have the PS common-shot gather. The PZ shot gather has fewer time samples than the PS shot gather because of the longer time 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 set.

 

shots
Figure 5 Typical common-shot gathers for the OBS Mahogany data set from the Gulf of Mexico. Shot gather after PZ summation (a), PS shot gather (b).

In both data sets, the PZ and the PS components were migrated using wave-equation shot-profile migration. Both, the P and the S velocity models are unknown for this problem; for simplicity, migrate using a velocity model with a linear gradient, Figure  shows both velocity models, the P-velocity model on the left panel, and the S-velocity model in the right panel. Complementary, Figure  represents the local step-out field for this experiment.

 

vels Figure 6 Velocity models used for the shot-gather migration. P-velocity on the left panel, S-velocity on the right panel.

 

dips Figure 7 Local step-out of the image; this represents the field $\d$ on equation 4.

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 at CIG=14500 in the image. The PS image was taken at zero subsurface offset, this is not the ideal position to take the final image, since the polarity flip destroys the image at this location. The ideal case will be flip the polarities in the angle domain Rosales and Rickett (2001); unfortunately, we do not have the correct velocity model yet; therefore, we have only an approximate solution to the final PS image.

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 $\tan{\theta_0}$ 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. The transformation to the angle-domain was performed with the diagram flow on Figure .

The geology for this section of the Mahogany data set consists of very low geological dips, with a relatively layering; therefore, the angle gather on panel (b) has the polarity flip very close to zero angle. The true angle gather also preserves this characteristic. The residual curvature for the events, whether primaries or multiples, is much larger than the residual curvature of the same events in the true angle-domain common-image gather. This effect is due to the correction for both the step-out of the image and the P-to-S velocity ratio, as presented in the theory section of this paper.

 

psimg-adcig
Figure 8 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, as represented by the solid line at CIG=14500 in the image.

Figure  presents the PS and the PZ results of shot-profile migration with the velocity models on Figure . Panel (a) presents the PS image on the top and its corresponding angle-domain common-image gathers on the bottom. Panel (b) presents the PZ image on the top and its corresponding angle-domain common-image gathers on the bottom. In both representations of the angle gathers, it is possible to observe events at a very similar depth, these events probably represent the same geological feature. Also notice the many multiples, due to the shallow sea bottom (120 m). These multiples are more prominent in the PS section because the PZ summation already eliminates the source ghost. This is not the case for the PS section.

Figure  compiles all the different angle-domain common-image gathers for this data set, all of which are taken at the same position, CIG=14500. From left to right, the panels show PP-ADCIG, PS-ADCIG, P-ADCIG, and S-ADCIG. Notice that most of the primary events have a residual curvature. The residual moveout is more prominent for those events that we identify as multiples.

 

imag-cigs
Figure 9 Panel (a) presents the PS image with its respective angle-domain common-image gathers. Panel (b) presents the PZ image with its respective angle-domain common-image gathers.

 

cigs-all
Figure 10 Compilation of angle-domain common-image gather for the 2-D Mahogany data set, all the CIGs are taken at the same image location (CIG=14500). (a) PP-ADCIG, (b) PS-ADCIG, (c) P-ADCIG, (d) S-ADCIG.

The initial linear P-velocity model is a pretty good approximation, since most of the primary events in the PZ section are flat in the angle-domain. However, there is a prominent residual curvature in the angle-domain common-image gathers for the PS section. This indicates an erroneous velocity model, most likely a very high initial S-velocity model. Moreover, the S section contains a large number of multiples, which are not all present in the PZ section.

The individuals P-ADCIG and the S-ADCIG contain information that potentially can be used for independent velocity updates. Notice that the angle coverage for these gathers is smaller than for the PP- and-PS ADCIGs, since the coverage of an individual plane-wave is smaller than the combination of two plane-waves, as is the case for converted-mode data.

It is very interesting to notice that the individual P-ADCIG has very similar characteristics with the PP-ADCIG. Most of the residual moveout of the PS-ADCIG seems to be due to the S component of the velocity model, as suggested for the individual S-ADCIG.