Parameter estimation

We use the nonhyperbolic moveout inversion of Alkhalifah (1997) to estimate interval $\eta$ for the seismic line from Trinidad. The result of this inversion is an interval $\eta$curve as a function of time. This inversion, though based on a laterally homogeneous medium assumption, has some tolerance to lateral inhomogeneity, such as the lateral inhomogeneity associated with most faults.

 

dmois
Figure 1 A stacked section of the line from offshore Trinidad, after applying NMO and isotropic homogeneous DMO. The NMO correction is based on the velocities provided by Amoco.

Figure 1 shows a zero-offset section that contains a large number of faults. Note that the data beyond 2.5 s are of poor quality.

Figure 2 shows five $\eta$ curves superimposed on a migrated section from this region. Specifically, the zero $\eta$ value at the top of each curve is placed at the position of the measurement corresponding to that curve. The lateral correlation, especially up shallow, between these curves, which are nearly 1.25 km apart, is notable. The difference between the curves at depth is a result of the complexity of the medium at depth. We can attribute some of these differences to the limitations of this inversion at later times (Alkhalifah, 1997).

 

migcurv2900-3500f
Figure 2 Five interval $\eta$ curves superimposed on a time-migrated section. These $\eta$ values are placed in their accurate location on the migrated image. The plot range for each curve is between -0.01 and 0.24.

A more laterally continuous representation is given by the 2-D plot of interval $\eta$ in Figure 3 (at the bottom), where measurements were taken at practically every CMP location and subsequently used to estimate a more continuous interval $\eta$ distribution. Figure 3 (at the top) shows the interval velocity extracted through the same process. Most of the observations obtained from Figure 2 apply to Figure 3 as well. Moreover, the correlation between the layering and the $\eta$ distribution is even more apparent in Figure 3. Faults probably explain the sudden variations of $\eta$ at certain locations. Overall, however, $\eta$ has good lateral continuity. Some faulting has disrupted this continuity, and these faults are indicated in gray. The lack of information beyond 2.0 s is a result of the methods depth limitation and the poor data quality at depth.

 

fault2900-3500
Figure 3 Top: the interval NMO velocity corresponding to the data in Figure 1. Bottom: the interval $\eta$ values for the same data. The gray lines correspond to some interpreted faults in the area.

Also, data at CMP locations 3450-3600 are of low quality, because of the presence of shallow gas in the area. Some of the effect of the shallow gas can be seen on the stacked section in Figure 1. The estimates in Figure 3 are of low resolution both laterally and vertically, and as a result no abrupt fault affects are apparent. Nevertheless, there is some vertical shift in the $\eta$distribution between the sides of some of the large faults.

 

stack700-1400
Figure 4 Stacked section of another part of the line from offshore Trinidad, after applying NMO and isotropic homogeneous DMO. The NMO correction is based on the velocities provided by Amoco.

Figure 4 shows a zero-offset section that also contains a large number of faults. Wells are located at CMP 1100 and 1220; both above an anticline structure. Overall, this area has the same characteristics as the area depicted in Figure 1 despite the large distance between the two regions ($\approx 25$ km).

 

migcurvfff
Figure 5 Seven interval $\eta$ curves superimposed on the time-migrated section. These $\eta$ values are placed in their accurate location on the migrated image. The plot range for each curve is between -0.01 and 0.24.

Figure 5 shows seven $\eta$ curves superimposed on a migrated section from this region. These $\eta$ curves are placed in their respective positions in Figure 5. The lateral correlation between these curves, which are about 1.25 km apart, is also remarkable. Especially remarkable is the correlation between the thickness of the shale layers and the size of $\eta$ as we can see by comparing the measurements at CMP 750 with that at CMP 1050 for the top layer. These $\eta$ values are plausible, especially compared with the large $\eta$ values we obtained for our earlier paper. Part of the reason for this improvement is the improved stability measures applied to the new estimates.

A more continuous estimation of $\eta$ is given by the 2-D plot of $\eta$ in Figure 6 (at the bottom), which resembles Figure 3. Figure 6 (at the top) also shows the interval velocity extracted through the same process. Again, most of the observations regarding Figure 5 apply here as well. However, more detail is apparent in this continuous $\eta$ representation. The three major faults in the area are drawn to show their effect on the measurements. Again, the poor quality of data at later times is the reason behind the lack of estimates at depth. Figure 7 shows a sample CMP gather (CMP 1000) after NMO correction. Probably, the last laterally-continues reflection appears just above the 2-second mark.

 

fault700-1400
Figure 6 Top: the interval NMO velocity corresponding to the data in Figure 4. Bottom: interval $\eta$ values for the same data.

 

cmp1000 Figure 7 Common-midpoint gather (CMP) 1000 after NMO correction with the proper NMO velocity obtained from conventional velocity analysis.

Figure 8 shows a crude lithologic interpretation estimated solely from the anisotropic inversion. The interpretation is based on the fact that shales are anisotropic, and therefore exhibit large positive $\eta$ values, while sands are essentially isotropic with near-zero values of $\eta$. The second sand layer may also include a lot of shales because the drop in $\eta$ is not very definite. Also, at this depth the data quality is bad.

 

intersand
Figure 8 A lithological interpretation of the sand and shale content of the surface as estimated by the interval $\eta$ values obtained from the inversion. The white lateral lines follow seismic reflections. The second sand layer may include respectable amounts of shale.