Results

Equation 8 was applied to the 3-D marine dataset. Figure  shows the same five CMP gathers as Figure . The CMP gathers were created by AMO stacking to zero hy,

$$\bf m(\rm hy=0,ihx) = \sum_{\rm hy} \bf T_{(\rm hx,\rm hy+ iy {\rm dhy} ) \Rightarrow (\rm hx,0)} \bf m(ihy,ihx) .$$ (10)

The resulting CMP gathers show a reduction in the dimming and brightening as function of offset but also show notable reduction in frequency content.

 

approx0.cmp
Figure 2 The same five CMP gathers from Figure  estimated by applying equation (8). Note the reduced frequency content in the image.

The approximation is more economical in forming a full 5-D space then the adjoint formulation and produces a greater continuity in the offset plane. On the other hand, noticeable brightening and dimming can still be seen. In addition transfer times, due to the transposes, dominate the processing time.