Figure 7 Imaging of receiver-side diffracted water-bottom multiple from a diffractor sitting on top of a flat water-bottom. At the diffractor the reflection is non-specular. Notice that .
The coordinates of the image point, according to equations 2-4 are given by
Notice that the diffraction multiple does not migrate as a primary even if migrated with water velocity. In other words, even if , .The only exception is when Xdiff=mD+hD/2 since then the diffractor is in the right place to make a specular reflection and therefore is indistinguishable from a non-diffracted water-bottom multiple. In that case, (which in turn implies ) and from equations 5 and 6, and therefore equations 23-25 reduce to equations 14-16, respectively.
Figure shows two subsurface-offset sections of a migrated diffracted multiple from a diffractor sitting on top of a flat reflector as in the schematic of Figure . The diffractor position is Xdiff=2,500 m, the CMP range is from 2,000 m to 3,000 m, the offsets range from 0 to 2,000 m and the water depth is 500 m. The data were migrated with the same two-layer model described before. Panel (a) corresponds to zero subsurface offset () whereas panel (b) corresponds to subsurface offset of -400 m. Overlaid are the residual moveout curves computed with equations 24 and 25. Obviously, the zero subsurface offset section is not a good image of the water-bottom or the diffractor.
Figure shows three SODCIGs taken at locations 2,300 m, 2,500 m and 2,700 m. Unlike the non-diffracted multiple, this time energy maps to positive or negative subsurface offset depending on the relative position of the CMP with respect to the diffractor. In ADCIGs the aperture angle is given by equation 11 which, given the geometry of Figure , reduces to
Again, this equation shows that the diffracted multiple is not migrated as a primary even if (except in the trivial case Xdiff=mD+hD/2 discussed before for which, since , in agreement with equation 19 and so equation 30 reduces to equation 20).
Figure shows the angle gathers corresponding to the SODCIGs of Figure . Notice the shift in the apex of the moveout curves.