Gulf of Mexico data example

To illustrate the proposed methodology for computing ADCIGs from prestack images obtained by anisotropic migration, I migrated a 2-D line extracted from a 3-D data set that was kindly provided to SEP by ExxonMobil. I chose the location of the 2-D line in an area where the sediments are mostly flat in the cross-line direction and where the salt flanks are mostly perpendicular to the in-line direction.

The data set was acquired in the Gulf of Mexico over an existing reservoir. Therefore several borehole seismic data sets were available in addition to the surface data to constraint the estimation of the anisotropic parameters. ExxonMobil provided SEP with three anisotropic-parameter cubes resulting from a joint inversion of the surface data and the borehole data Krebs et al. (2003). Figure  shows the vertical slices cut through these cubes at the cross-line location corresponding to the 2-D line that I migrated. Panel a) displays the vertical velocity, panel b) displays the values of $\delta$,and panel c) displays the values of $\eta$.To avoid artifacts caused by sharp parameter contrasts, for migration I removed the salt body from the functions displayed in Figure . I ``infilled'' the salt body with sediment-like values by interpolating the functions inward starting from the sediment values at the salt-sediment interface.

 

Par-Sections-overn
Figure 7 Vertical slices cut through the anisotropic velocity parameters cubes. Panel a) shows the vertical velocity field, panel b) shows the $\delta$ field, and panel c) shows the $\eta$ field. I removed the salt body from the parameters functions used for migration, to avoid artifacts caused by sharp parameter discontinuities.

Figure  shows the result of anisotropic prestack depth migration. All the reflectors are nicely imaged, including the steep salt flank on the right-hand side of the salt body. The shallow tract of the salt flank on the left-hand side of the body is poorly imaged because it has large cross-line dip components. The two vertical lines superimposed onto the image identify the surface location of the ADCIGs displayed in Figure . The two black bars superimposed onto the image identify the reflections for which I analyzed the ADCIG in details.

 

Bar-Section-overn
Figure 8 Image obtained by anisotropic prestack migration. The two vertical lines superimposed onto the image identify the surface location of the ADCIGs displayed in Figure . The two black bars superimposed onto the image identify the reflections analyzed in Figure .

 

Duo-aniso-overn Figure 9 ADCIGs computed from the prestack image by slant stacking along the subsurface offset axis. The CIG shown in panel a) is taken at the surface location of 3,725 meters, and the CIG shown in panel b) is taken at the surface location of 11,625 meters.

Figure  shows two ADCIGs computed by slant stacking the prestack image along the subsurface axis. Both CIGs show fairly flat moveout, indicating that the anisotropic velocity model used for migration is accurate, though not perfect. The shallow reflections show the most noticeable departure from flatness (they frown downward) because these reflectors were not the focus of the velocity model-building efforts. The CIGs are taken at the location indicated by the vertical black lines in Figure ; the CIG shown in panel a) is taken at the surface location of 3,725 meters and the CIG shown in panel b) is taken at the surface location of 11,625 meters. Within these two CIGs, I selected for detailed analysis the reflections corresponding to the black bars superimposed onto the image because they represent two `typical' cases where the accuracy of the estimation of the reflection-aperture angle might be important. The shallow black bar on the left identifies a flat reflector illuminated with a wide range of aperture angles, up to 60 degrees. The wide angular range is potentially useful for constraining the value of the anisotropic parameters in the sediments. The deep black bar on the right identifies one of the potential reservoir sands, and thus it is a potential target for Amplitude Versus Angle (AVA) analysis using ADCIGs.

The plots in Figure  show the differences between the true phase aperture angle computed by iteratively solving the system of equations 16 and 17 and the aperture angle estimated by slant stacks (solid line) and the group aperture angle (dashed line). The group angles are computed by applying equation 2. The plot in panel a) corresponds to the shallow black bar on the left. The reflector is flat and the velocity parameters at the reflector are: $V_V=1,995\;{\rm m/s},\;\epsilon=0.058,\;\delta=0.0524,\;{\rm and}\; \eta=.0905$.As expected, the aperture angles estimated by slant stack are exactly the same as the true ones because the reflector is flat. The maximum difference between the group aperture angle and the phase aperture angle is at 60 degrees, where the group angle is smaller by about 9 degrees than the phase angle; that is, about an error of about 15%.

The plot in panel b) corresponds the reservoir reflector (the deep black bar on the right). The dip of the reflector is about 25 degrees and the velocity parameters at the reflector are: $V_V=3,060\;{\rm m/s},\;\epsilon=0.028,\;\delta=0.0133,\;{\rm and}\; \eta=.0144$.This area is weakly anisotropic (black in Figure b in Figure c) and thus the angular errors are small ($\leq$ 1 degree) even if the reflector is dipping. Finally, the plot in panel c) corresponds to the hypothetical situation in which the reservoir was located in a more strongly anisotropic area than it actually is. To test the accuracy limits of approximating the phase aperture angles with the subsurface-offset slopes in the prestack image, I set the anisotropic parameters to be the highest value in the section; that is: $;\epsilon=0.172,\;\delta=0.07,\;{\rm and}\; \eta=.09$,and kept the vertical velocity and reflector's dip the same as in the previous case. The reflector is dipping and consequently the aperture angle estimated by slant stacks is lower than the true aperture angle. However, the error is small ($\leq$ 2 degree) even at large aperture angle, and even smaller ($\leq$ 1 degree) within the angular range actually illuminated by the data ($0 \leq \widetilde{\gamma}\leq 30^{\circ}$). Even in this ``extreme'' case the angular error is unlikely to have any significant negative effect on the accuracy of the AVA analysis of the reservoir reflection.

 

Trio-Ang-overn
Figure 10 Differences between the true phase aperture angle and the aperture angle estimated by slant stacks (solid line) and the group aperture angle (dashed line). The plot in panel a) corresponds to the reflection identified with the shallow black bar on the left in Figure . The plot in panel b) corresponds the reservoir reflector (the deep black bar on the right). The plot in panel c) corresponds to the hypothetical situation in which the reservoir reflector was located in a more strongly anisotropic area than it actually is.