where and are the components of the surface offset vector in the inline and crossline directions, and is the azimuth of the source-receiver line with respect to the inline direction.

3d-mul-sktch1
Raypath for a 3D Water-bottom multiple from a flat
water-bottom. The multiple propagation is entirely contained in a vertical plane.
Figure 1. | |
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The travelpath of the multiple itself is azimuthally invariant and so the depth of the image
point and its location are the same as in chapter 2 (equations
and ). The residual moveout equations of the multiple in the inline and crossline
directions are given by slightly modified versions of equation :

Notice that the azimuthal invariance of the depth and spatial location of the image means that, in terms of the subsurface offset magnitude and reflection azimuth (which for a flat reflector equals the surface azimuth), the residual moveout of the multiple in the SODCIG is exactly the same as in the 2D case of chapter 2. Figure 2 shows the inline SODCIG (panel (a)) taken at zero crossline offset and the crossline SODCIG (panel (b)) taken at zero inline offset. The data was modeled directly in CMP gathers and therefore is completely regular in inline and crossline surface offsets. I modeled both positive and negative crossline surface offset and hence the residual moveout of the multiple spans both positive and negative subsurface offsets.

sodcig
SODCIG for a water-bottom multiple from a
flat water-bottom. Panel (a) is the inline subsurface offset gather at zero crossline
subsurface offset and panel (b) is the crossline subsurface offset gather at zero
inline subsurface offset.
Figure 2. |
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2007-10-24