The second line

Figure 11 shows a zero-offset section that contains a large number of faults. Because of the large offsets present in this data set, we will use the non-hyperbolic method to invert for $\eta$. VTI media induce non-hyperbolic moveout of reflections that depends on $V_{\rm nmo}$ and $\eta$ at large offsets. This non-hyperbolic moveout is used to invert for these two parameters, which provide important information about the subsurface. The direct output from such an inversion (or velocity analysis) is effective values of $V_{\rm nmo}$ and $\eta$, that include the combined (average) influence of the overburden. These effective values are converted to interval ones using layer-stripping equations given by Alkhalifah (1997b).

 

dmois
Figure 11 Stacked section of a second line from offshore Trinidad, after applying NMO and isotropic homogeneous DMO. The NMO correction is based on the velocities provided by Amoco.

Figure 12 shows a detail of CMP gather 3100 with a reflection from a horizontal event and the reflection are NMO corrected using different stacking velocities. The highest amplitude stack trace (stack power) is obtained using a velocity of 2100 m/s. Using this velocity, however, did not result in the best resolution of the stacked trace as indicated by the amplitude spectrum. Better resolution (higher-frequency content) is achieved at a lower velocity. However, the best solution is obtained through anisotropic processing as shown in Figure 13, where the non-hyperbolic moveout in the data is treated. A shift in the zero offset time of more than 10 ms from its true value (as given by the near-offset trace) occurs after stacking the 2100 m/s NMO-corrected data.

 

nmostackf
Figure 12 CMP gathers for CMP location 3100 after NMO correction with (a) $V_{\rm nmo}$=2060 m/s, (b) $V_{\rm nmo}$=2080 m/s, (c) $V_{\rm nmo}$=2100 m/s, and (d) $V_{\rm nmo}$=2120 m/s. The first column to the left is the CMP gather, the center column is the stack of the CMP gather, and right most column shows the amplitude spectrum of the stacked gather.

Clearly, a hyperbolic moveout approximation does not adequately approximate the non-hyperbolic moveout represented in the data. This non-hyperbolic moveout can not be explained solely by vertical velocity variations. Furthermore, the lateral inhomogeneity that is apparent in these data by observing velocities from various CMP locations is not sufficient to explain such a large non-hyperbolic moveout.

 

nmostackfti
Figure 13 The CMP gather of Figure 12 after non-hyperbolic correction. The first plot to the left is the CMP gather, the center plot is the stack of the CMP gather, and right most plot shows the amplitude spectrum of the stacked gather.

 

etav
Figure 14 Estimated interval values $v_{{\rm nmo}}$ and $\eta$ as a function of vertical time.

Figure 14 shows the interval velocity and $\eta$ values extracted from the non-hyperbolic moveout inversion for CMP location 3200. Considering that the lateral inhomogeneity is small, we will use these values to do VTI DMO and time migration on the whole section (time processing). The extremely high $\eta$ value at time 1.5 s is indicative of a highly anisotropic shale layer. Also, due to the integral relation between the interval values and the effective ones, the area under these $\eta$ curves, representing the cumulative anisotropy, tells a better story of the anisotropic impact on the seismic data than the values for the individual intervals. The presence of a thick, highly anisotropic shale at relatively shallow depths (i.e., above zones of interest) will have a serious impact on the effective anisotropy for all deeper layers. If this shallow anisotropy is not taken into account in this case, then degradation of the entire stacked section will result. Figure 15 shows the result of anisotropic DMO and when comparing it with Figure 11 the improvements in focusing the horizontal, as well as the dipping reflections, are obvious.

 

dmoti
Figure 15 Stacked section after v(z) anisotropic DMO using the parameters in Figure 14. The NMO correction is based on the velocities obtained from the conventional velocity analysis using exceptionally short spreads.

Figure 16a shows the result of isotropic migration on the isotropically DMO corrected data, while Figure 16b shows the results of a complete VTI processing, including migration. A closer look given by Figure 17 shows the improvement in fault imaging achieved with the VTI processing.

 

mig
Figure 16 Time-migrated sections after (a) isotropic processing, and (b) VTI processing using the inverted parameters shown in Figure 14. A detailed picture is shown in Figure 17.

 

migc
Figure 17 Detail of Figure 16 consisting of time-migrated sections after (a) isotropic processing, and (b) VTI processing.

 

etacurvesmig2
Figure 18 Three interval $\eta$ curves superimposed on the time-migrated section of Figure 16b. These $\eta$ values correspond to the region above each fault.

Figure 18 shows three $\eta$ curves superimposed on the migrated section from Figure 16b. These $\eta$ curves correspond to CMP locations 3000, 3200, and 3400, and as a result they are placed in their respective positions in the Figure 18. Recognizing that the $\eta$ highs and lows correspond to reflections from the bottom of the layer that caused these highs or lows, a crude blocky interpretation of the curves can be made and is given in Figure 19. The lateral correlation between these curves that are 2.5 km of lateral distance apart is remarkable. Especially remarkable is the correlation between the thickness of the shale layers and the size of $\eta$ (look at the first laterally continuous shale layer). The extremely high $\eta$ value at time 1.5 s is indicative of a highly anisotropic shale layer. While the actual value may appear unreasonable, CMPs 3200 and 3400 are over a gas field, while CMP 3000 is outside of the field (Figure 20). The high $\eta$ values over the field could suggest vertical migration of the gas into the unconsolidated shale (this shale is approximately 2000 feet thick at depths of 3000-5000 feet, see Figure 15).

 

etadismig
Figure 19 The same three interval $\eta$ curves shown in Figure 18. The white curves correspond to a crude interpretation of the layering in the subsurface that correspond to the $\eta$ curves.

Figure 20 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 $\eta$. Figure 14 shows the correlation between the estimate for $\eta$ at CMP 3200 and a blocky interpretation of shale volume from the gamma-ray log at a nearby well. Correlation is remarkably good down to 2.0 seconds, demonstrating the value of using the inversion for $\eta$ as a lithology estimator. Correlation is not as good below 2.0 seconds, though the $v_{{\rm nmo}}$ value shown in Figure 21 shows a large decrease in velocity below 2.0 seconds indicative of entering the overpressure zone (which could also impact anisotropy).

 

etalayermig2
Figure 20 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.

 

comparsh
Figure 21 Estimated interval values $\eta$ plotted next to an approximate long wavelength of shale content extracted from gamma-ray measurements. The gray dashed lines correspond to bottom of shale layer predicted by the $\eta$ curve and agrees well with the gamma-ray information.