As predicted by our theory, in the presence of a wide range of reflector dips (e.g. flat sediments and salt edges), both the HOCIGS and the VOCIGs are affected by artifacts. Figure illustrates this problem. It displays orthogonal sections cut through the HOCIG cube (Figure a), and through the VOCIG cube (Figure b). The front faces show the images at zero offset and are the same in the two cubes. The side face of Figure a shows the HOCIGs taken at the horizontal location corresponding to the vertical salt edge. We immediately notice that, at the depth interval corresponding to the salt edge, the image is smeared along the offset axis, which is consistent with the horizontal-offset stretch described by equation (9). On the contrary, the image of the salt edge is well focused in the VOCIG displayed in the top face of Figure b, which is consistent with the vertical-offset stretch described by equation (10). However, the flattish reflectors are unfocused in the VOCIG cube, whereas they are well focused in the HOCIG cube. The stretching of the offset axes causes useful information to be lost when significant energy is pushed outside the range of offsets actually computed. In this example, the salt edge reflection is clearly truncated in the HOCIG cube displayed in Figure a, notwithstanding that the image was computed for a fairly wide offset-range (800 meters, starting at -375 meters and ending at 425 meters).
The ADCIGs computed from either the HOCIGs or the VOCIGS have similar problems with artifacts caused by the wide range of reflectors dips. Figure shows the ADCIG computed from the offset-domain CIGs shown in Figure . The salt edge is smeared in the ADCIG computed from HOCIG (side face of Figure a), whereas it is fairly well focused in the ADCIG computed from VOCIG (top face of Figure b). Conversely, the flattish reflectors are well focused in the ADCIG computed from HOCIG, whereas they are smeared in the ADCIG computed from VOCIG.
The artifacts mostly disappear when the ADCIG cubes shown in Figure are merged according to the simple scheme discussed above, which uses the weights defined in equations (20). Figure shows the ADCIG cube resulting from the merge. The moveouts for the salt edge and the sediment reflections are now clearly visible in the merged ADCIG cube and could be analyzed for extracting velocity information. To confirm these conclusions we migrated the same data after scaling the slowness function with a constant factor equal to 1.04. Figure shows the ADCIG cubes computed from the HOCIG cube (Figure a), and from the VOCIG cube (Figure b). When comparing Figure with Figure , we notice the 175-meter horizontal shift of the salt edge reflection toward the left, caused by the decrease in migration velocity. However, the artifacts related to the salt edge reflection are similar in the two figures, and they similarly obscure the moveout information. On the contrary, the moveout information is ready to be analyzed in the cube displayed in Figure , which shows the ADCIG cube resulting from the merge of the ADCIG cubes shown in Figure . In particular, both the flattish event above the salt edge (at about 1,000 meters depth) and the salt edge itself show a typical upward smile in the angle-domain gathers, indicating that the migration velocity was too slow.