The first line

Figure 1 shows a zero-offset section from offshore Trinidad that contains reflections from a large number of dipping faults. Amoco Trinidad Exploration provided the seismic data and the stacking velocities. The section was processed using a conventional 2-D isotropic processing sequence that included a conventional NMO (using the stacking velocities that Amoco provided), followed by a log-stretch (Notfors and Godfrey, 1987) version of Hale's (1984) DMO. Anisotropy is expected to vary with depth due to the alternating sand-dominated and shale-dominated layers. Shales are believed to be the main source of anisotropy in sedimentary basins (Banik, 1984).

 

dmoisi
Figure 1 Stacked section from offshore Trinidad, after applying NMO and isotropic homogeneous DMO. The NMO correction is based on the velocities provided by Amoco.

 

etav1100
Figure 2 Estimated interval values $v_{{\rm nmo}}$ and $\eta$ as a function of vertical time.

Carrying out the inversion process described by Alkhalifah (1997a), using the measured values of stacking velocities and corresponding ray parameters, we obtain the functions $v_{{\rm nmo}}(\tau)$ and $\eta(\tau)$ shown in Figure 2. The inversion assumes no lateral velocity variation in the region of the picks; the lateral velocity variation in this region, especially in the first 2 s, is exceptionally small (see Figure 10). In the water layer, $v_{{\rm nmo}}$ is 1.5 km/s and $\eta$ is zero. The accuracy of these estimated curves of $v_{{\rm nmo}}$ and $\eta$ depends on the accuracy of the stacking-velocity estimates for both dipping and horizontal reflectors, as discussed by Alkhalifah and Tsvankin (1995).

 

dmotii
Figure 3 Stacked section after v(z) anisotropic DMO using the parameters in Figure 2. The NMO correction is based on the velocities obtained from the conventional velocity analysis using exceptionally short spreads.

The smoothed interval values of $\eta$ in Figure 2 show variations that might depend on the shale-sand long-wavelength alterations. Specifically, shales are expected to induce anisotropic behavior (Banik, 1984; Sayers, 1994) of waves, while sands are usually isotropic. This $\eta$ curve best fits the measured stacking velocities, and thus is expected to improve the image. The measurement that resulted in Figure 2 corresponds to the fault under CMP location 1100. Later we will examine results from other faults.

Next, we apply a DMO algorithm that uses the derived functions $v_{{\rm nmo}}(\tau)$ and $\eta(\tau)$ in Figure 2. Figure 3 shows the result of TI DMO applied to the data, based on the ray-tracing DMO algorithm described by Alkhalifah (1996). Compared with the results of the isotropic DMO given in Figure 1, this section should be improved. A closer look at Figures 1 and 3 (shown in Figures 4 and 5) shows such improvements. In Figure 4 note the vast improvement in focusing both the dipping fault and the sub-horizontal reflections in the anisotropic DMO result (Figure 4b), as opposed to the isotropic one (Figure 4a). Such improvements in focusing are also observed at later times (i.e., Figure 5).

 

Amococ1
Figure 4 (a) Detail of Figure 1, and (b) detail of Figure 3 in the same region.

 

Amococ2
Figure 5 (a) Detail of Figure 1, and (b) detail of Figure 3 in the same region.

Figure 6 shows CMP gathers from CMP location 936, which contains the imaged fault-plane reflection shown in Figure 4a after (a) homogeneous isotropic DMO, and (b) v(z) VTI DMO. The arrows point to the time of the fault reflection at this CMP location. Whereas the v(z) VTI DMO aligns the fault reflection well, the dipping event after isotropic DMO is misaligned. Improvements are also achieved for sub-horizontal events where DMO managed to correct for the non-hyperbolic moveout that is often largest for small dips.

 

cmpTOZ936
Figure 6 CMP gathers for CMP location 936 after (a) homogeneous isotropic DMO, and (b) v(z) anisotropic DMO using the parameters estimated in Figure 2. The NMO correction for the isotropic DMO result is based on velocities provided by Amoco, while the NMO correction for the anisotropic DMO is based on the velocities obtained from velocity analysis using short spreads. The arrow points to the time of the dipping fault reflection.

Although the reflections shown on the seismic line correspond to features within or near the vertical 2-D plane that contains the sources and receivers, some events may represent out-of-plane reflections that require 3-D processing. These out-of-plane reflections, as mentioned earlier, might be expected to stack better at a lower velocity (closer to the isotropic NMO velocity), and therefore focus better in the isotropic image. However, contamination due to out-of-plane events is not expected to be significant for these lines.

 

mig1
Figure 7 Time-migrated sections after (a) isotropic processing, and (b) VTI processing using the inverted parameters shown in Figure 2. A detailed picture is shown in Figure 8.

Figure 7 show time-migrated sections after (a) isotropic processing, and (b) VTI processing using the inverted parameters shown in Figure 2. Although some improvements in the VTI results can be detected from this figure, a closeup look given by Figure 8 clearly demonstrates the improved imaging achieved by considering anisotropy. Presence of fault plane reflections suggest that the fault is probably a potential reservoir seal. Faults that generate reflections will probably have experienced sufficient movement to cause juxtaposition of different lithologies across the fault plane. These reflections are typically attenuated and/or lost by isotropic processing, while anisotropic processing is successful at preserving these fault plane images.

 

migc1
Figure 8 A detailed picture of Figure 7 of time-migrated sections after (a) isotropic processing, and (b) VTI processing.

 

etacurvesmig
Figure 9 Three interval $\eta$ curves superimposed on the time-migrated section of Figure 7b. These values correspond to the region above each fault.

Three large faults can be picked from the section in Figure 3. Independent estimates for interval $\eta$ are made at each of these faults. Figure 9 shows the three interval $\eta$ curves super imposed on the migrated section from Figure 7a. Because the left most fault shows relatively little throw, the corresponding $\eta$ curve lacks the detail evident in the other two curves, especially at depth. Note, the correlation among the three interval $\eta$ curves agrees well with the continuity of seismic reflections across the section. The lateral correlation of interval $\eta$ increases confidence that a geologic parameter is represented by the inversion. Correlation of interval $\eta$ estimates across faults could help to remove ambiguity in determining correlation of seismic picks across a seismic section.

 

vall
Figure 10 Three interval velocity curves obtained from CMP locations 800 (black solid curve), CMP location 1100 (dashed curve), CMP location 1300 (gray curve).

To demonstrate the mild lateral velocity variation that exists in this region, Figure 10 shows interval velocities obtained from three separate CMP locations that are more than 2.5 km apart. Velocity changes are insignificant down to 2.0 seconds, and remain very small even at later times.