Figure illustrates the differences between HOCIGs and VOCIGs caused by the image-point shift, and it demonstrates that the image-point shift is corrected by the transformation to GOCIGs described in equations (9) and (10).

Figures a and b show orthogonal sections cut through the offset-domain image cubes in the case of the low velocity migration. Figure a displays the horizontal-offset image cube, while Figure b displays the vertical-offset image cube. Notice that the offset axis in Figure b has been reversed to facilitate its visual correlation with the image cube displayed in Figure a. The side faces of the cubes display the CIGs taken at the surface location corresponding to the apparent geological dip of 45 degrees. The events in the two types of CIGs have similar shapes, as expected from the geometric analysis presented in a previous section ( when = 45 degrees), but their extents are different. The differences between the two image cubes are more apparent when comparing the front faces, which show the image at a constant offset of 110 meters (-110 meters in Figure b). These differences are due to the differences in image-point shift for the two offset directions [equation (11) and equation (12)].

Figure c and d show the image cubes of Figures a and b after the application of the transformations to GOCIG, described in equations (9) and (10), respectively. The two transformed cubes are almost identical, because both the offset stretching and the image-point shift have been removed. The only significant differences are visible in the front face for the reflections corresponding to the top of the sphere. These reflections cannot be fully captured within the vertical-offset image cube because the expression in equation (10) diverges as goes to zero. Similarly, reflections from steeply dipping events are missing from the horizontal-offset image cube because the expression in equation (9) diverges as goes to 90 degrees.

7/8/2003