Gulf of Mexico data example

To test the accuracy of the RMO functions derived in this paper, I migrated a 2-D line extracted from a 3-D data set that was kindly provided to SEP by ExxonMobil. To minimize 3-D effects, the location of the 2-D line was chosen 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.

 

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Figure 9 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.

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.

 

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Figure 10 Images obtained by anisotropic prestack migration (panel a) and isotropic prestack migration (panel b). The two vertical lines superimposed onto the image identify the surface location of the ADCIGs displayed in Figure .

Figure  compares the result of anisotropic prestack depth migration (panel a) with the results of isotropic depth migration obtained using as migration velocity the vertical velocity function (panel b). The anisotropic-migration image is clearly superior to the isotropic-migration image that shows clear sign of undermigration of the salt-flanks reflections as well of the sediments terminating against the salt body. All the reflectors are nicely imaged by the anisotropic migration, except for the shallow tract of the salt flank on the left-hand side of the body because it has large cross-line dip components.

 

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Figure 11 ADCIGs computed by anisotropic migration (panels a) and c)) and isotropic migration (panels b) and d)). The ADCIG shown in panels a) and b) are taken at the surface location of 3,725 meters. The ADCIG shown in panel c) and d) are taken at the surface location of 11,625 meters.

Figure  shows two examples of ADCIGs computed from both the anisotropic and the isotropic migration results. The CIGs shown in panel a) and b) are taken at surface location of 3,725 meters (left vertical black line in Figure ) and the CIGs shown in panel c) and d) are taken at surface location of 11,625 meters (right vertical black line in Figure ). The ADCIGs obtained by anisotropic migration (panels a and c) are uniformly flatter than the ADCIGs obtained by isotropic migration (panels b and d). The ADCIGs obtained by isotropic migration display the typical hockey-stick behavior commonly seen in CIGs computed by isotropic Kirchoff migration in anisotropic media. Although the isotropic migration image is evidently not well focused, this result does not preclude the possibility that an isotropic migration velocity could be defined to focus the data satisfactorily. However, an isotropic migration with a different velocity model would also position the reflectors at substantially different locations. These location would not equally match the depth measured from the wells Bear et al. (2003).

The RMO function derived in this paper assumes a homogeneous layer above the reflector to be analyzed. To test the accuracy of the expressions for the RMO function I therefore estimated the average anisotropic parameters between the sea floor and two reflectors, one shallow and the other deep, easily identifiable in the ADCIG located at 3,725 meters (Figure a). Figures  and  show the result of my analysis.

Figure c shows the ADCIG obtained after anisotropic migration using the following average parameters below the sea floor: $V_V=1,750\;{\rm m/s},\;\epsilon=0.11,\;\delta=0.04,\;{\rm and}\; \eta=.065$.Figure d shows the ADCIG obtained after isotropic migration using $V_V=1,750\;{\rm m/s}$.The shallow reflection of interest is flat in Figure c, whereas it is smiling upward in Figure d. For comparison, Figures a and b show a zoom of Figures a and b into the same window of the ADCIGs as the one displayed in Figures c and d. The curve superimposed onto both Figures b and d was computed using the generalized RMO functions expressed in equations 24-26. The computed RMO function perfectly overlaps the event in the ADCIG in Figure d. In contrast, the computed RMO function overestimates the moveout in the ADCIG obtained by migrating the data using the original isotropic model (Figure b). The cause of this discrepancy is the ray bending induced by the vertical gradient in the original heterogeneous model. Because of ray bending the events propagate more vertically, and thus more slowly, in the heterogeneous medium than in the homogeneous one. In cases when explicit raytracing though the background velocity is necessary to compute the RMO function, equation 27 provides the necessary link between the traveltime perturbations accumulated along the rays and the depth perturbations measured in the ADCIGs.

The ADCIGs shown in Figure  display a behavior similar to the ones shown in Figure . Since the reflection of interest is now deep, the half-space below the sea floor is characterized by higher average parameters than for the shallow reflection; that is: $V_V=2,000\;{\rm m/s},\;\epsilon=0.143,\;\delta=0.045,\;{\rm and}\; \eta=.09$.As before, the reflection of interest in ADCIG migrated using these parameters (Figure c) is flat, whereas the same reflection in the ADCIG migrated with isotropic migration with the same vertical velocity ($V_V=2,000\;{\rm m/s}$)is smiling upward (Figure d). As before, the RMO curve computed using equations 24-26 perfectly overlaps the event in the ADCIG shown in Figure d, whereas it overestimates the moveout in the ADCIG obtained by migrating the data using the original isotropic model (Figure b).

 

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Figure 12 ADCIGs taken at the surface location of 3,725 meters and with the layer below the sea floor being: a) anisotropic and heterogeneous, b) isotropic and heterogeneous, c) anisotropic and homogeneous ($V_V=1,750\;{\rm m/s},\;\epsilon=0.11,\;\delta=0.04,\;{\rm and}\; \eta=.065$), d) isotropic and homogeneous ($V_V=1,750\;{\rm m/s}$). The RMO curve that is superimposed onto panels b) and d) is computed using equations 24-26.

 

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Figure 13 ADCIGs taken at the surface location of 3,725 meters and with the layer below the sea floor being: a) anisotropic and heterogeneous, b) isotropic and heterogeneous, c) anisotropic and homogeneous ($V_V=2,000\;{\rm m/s},\;\epsilon=0.143,\;\delta=0.045,\;{\rm and}\; \eta=.09$), d) isotropic and homogeneous ($V_V=2,000\;{\rm m/s}$). The RMO curve that is superimposed onto panels b) and d) is computed using equations 24-26.