3-D stacking velocity inversion combined with 3-D image-ray depth conversion
We now consider a traditional approach for obtaining structure maps in depth — stacking velocity inversion to estimate layer velocities and image-ray depth conversion of time horizons interpreted from the time-migrated volume of data to delineate reflector geometries. Image-ray depth conversion is the usual implementation of map migration (model building).
Application of stacking velocity inversion to 3-D data involves the same steps as for 2-D stacking velocity inversion (model with low-relief structure) except for 3-D ray tracing. As a reminder, stacking velocity inversion can be considered accurate for velocity-depth models with smoothly varying reflector geometries and lateral velocity variations much greater than a cable length.
Figures 10.7-10 and 10.7-11 show the results of this alternative procedure. The input to stacking velocity inversion is the set of horizon-consistent stacking velocities (Figure 10.7-4). The input to image-ray depth conversion is the set of time horizons picked from the time-migrated volume of stacked data (Figure 10.7-3). As in coherency inversion combined with poststack depth migration, this procedure was conducted layer-by-layer starting from the surface. Actually, it is conducted twice — without (Figure 10.7-10) and with (Figure 10.7-11) vertical velocity gradients from well data included in the analysis. In the latter case, vertical gradients are accounted for in ray tracing to compute the CMP traveltimes for coherency inversion (models with horizontal layers).
Figure 10.7-3 Time horizons interpreted from the volumes of unmigrated DMO-stacked and 3-D poststack time-migrated data as in Figures 10.7-1 and 10.7-2, respectively. Horizon 1, which is not shown here, corresponds to the water-bottom reflection. Horizons 2-7, in the ascending order, correspond to base Upper and Lower Tertiary, base Cretaceous chalk, base Upper and Lower Triassic, and base Zechstein.
The depth structure map for the target horizon — base Zechstein, has the gross features (Figure 10.7-10) similar to those of the map obtained from coherency inversion combined with poststack depth migration (Figure 10.7-9). Nevertheless, it is the subtle differences that can influence the interpretation.
A way to judge whether imaging can be done by time migration or needs to be done by depth migration is by examining behavior of image rays. Specifically, lateral displacement between the point of departure of an image ray at the target horizon and the point of emergence of the image ray at the surface is an indication of the degree of lateral velocity variations (Figure 10.7-12a). In the case of 3-D image rays, aside from lateral displacement, the azimuthal direction of the displacement is an additional attribute that needs to be examined (Figure 10.7-12b). Note that the largest displacements occur along the major fault zone within the survey area.
We shall end the discussion on this case study by comparing the results of the three inversion procedures that we have applied to the data. Shown in Figure 10.7-13 are the depth structure map of the target horizon — base Zechstein derived from the following procedures:
- coherency inversion, in which vertical velocity gradients were accounted for, combined with poststack depth migration,
- stacking velocity inversion, in which vertical velocity gradients were accounted for, combined with image-ray depth conversion,
- stacking velocity inversion, in which vertical velocity gradients were ignored, combined with image-ray depth conversion.
Figure 10.7-10 Layer velocities and reflector geometries derived from a layer-by-layer application of 3-D stacking velocity inversion and 3-D image-ray depth conversion (map migration). Vertical velocity gradients were not accounted for in the analysis. Horizons 2-7, in the ascending order, correspond to base Upper and Lower Tertiary, base Cretaceous chalk, base Upper and Lower Triassic, and base Zechstein.
Figure 10.7-11 Layer velocities and reflector geometries derived from a layer-by-layer application of 3-D stacking velocity inversion and 3-D image-ray depth conversion (map migration). Vertical velocity gradients from well data were included in the analysis. Horizons 2-7, in the ascending order, correspond to base Upper and Lower Tertiary, base Cretaceous chalk, base Upper and Lower Triassic, and base Zechstein.
Figure 10.7-13 Depth structure map of the base-Zechstein target horizon using three different procedures: (a) coherency inversion with vertical velocity gradients accounted for, (b) stacking velocity inversion with vertical velocity gradients accounted for, and (c) stacking velocity inversion without vertical velocity gradients accounted for.
Shown in Figure 10.7-14 are the difference maps, where the map of Figure 10.7-13a was taken as the reference map, assuming that it is the most accurate between the three maps shown in Figure 10.7-13. These difference maps are based on the subtraction of the maps of Figures 10.7-13b and 10.7-13c from the reference map. Note that there are differences in the results obtained from the different procedures outlined above. While procedures (a) and (b) appear to produce results that are comparable, procedure (c) produces results with significant discrepancies along the major fault zone.
- 3-D structural inversion applied to seismic data from the Central North Sea
- 3-D coherency inversion combined with 3-D poststack depth migration