Nonlinear Iteration Test  

In this section I test the nonlinear iteration outlined in section on the Mississippi Canyon data. I ran only one nonlinear iteration. Since the velocity model is already quite nicely determined, I did not do residual velocity analysis after the first run of LSJIMP. However, I did recompute the crosstalk weights and the reflection coefficients for each of the four multiple generators.

The updated crosstalk weights are shown in Figure , at CMP 55 of 750. The most notable difference after the nonlinear update is the infill of the near offsets. Although invisible in this case, the nonlinear update also allows us to model crosstalk energy below twice the onset of the first seabed multiple, which would be 7.5 seconds. This ability is very important for data recorded in shallower water.

 

crosstalk.gulf.iter
Figure 29 Crosstalk weights at CMP 55 of 750, before and after one nonlinear update. Left: Crosstalk weights before update. Right: Crosstalk weights after update.

Figure compares the weighted data residual at CMP 55 of 750 before and after the nonlinear update. The Figure is split in half along the time axis as explained earlier in section . The most striking differences are highlighted with ovals. As mentioned earlier, the R1 pure multiple and R2 seabed pegleg overlap over most of the 2-D line, which inhibits estimation of R1's reflection coefficient. Although I do not show the updated R1 reflection coefficient, Figure implicitly illustrates the beneficial change. The event highlighted in ovals on the residual panels, which has three visible peaks, does not have that wavelet shape in the raw data. Crosstalk between the overlapping events and an improperly high R1 reflection coefficient cause the event to be ``manufactured'' in the LSJIMP result. By better estimating the R1 reflection coefficient, the event is not present in the residual, and thus, not manufactured by LSJIMP. Other that this event, however, the differences between the two panels are minimal.

 

resd-iter1.gulf
Figure 30 LSJIMP data residual before and after nonlinear update of crosstalk weights and reflection coefficients. Left: residual before updating. Right: residual after updating. Panels split in half along time axis for display purposes and clipped as labeled.

Figure compares the LSJIMP estimated primaries at CMP 55 of 750 before and after the nonlinear update. The Figure is split in half along the time axis as explained earlier in section . Ovals highlight the same regions as were highlighted in Figure . The differences between the two estimated primary panels are quite subtle; the difference panel on the right is more englightening. Notice how the manufactured event discussed earlier is better suppressed after the nonlinear update.

 

model-iter1.gulf
Figure 31 LSJIMP estimated primaries before and after nonlinear update of crosstalk weights and reflection coefficients. Left: $\bold m_0$ before updating. Center: $\bold m_0$ after updating. Right: Difference. Panels split in half along time axis for display purposes and clipped as labeled.

Finally, Figure shows the stack of the LSJIMP estimated primaries after the nonlinear update. The Figure is directly comparable with Figure . Again, the differences are quite subtle. Notice an improvement in the removal of deep, salt-related multiple events, like BSPLTS.

 

stackcomp-iter1.gulf
Figure 32 Top: raw data stack. Center: estimated LSJIMP primaries stack after nonlinear updating of crosstalk weights and reflection coefficients. Bottom: difference panel (estimated multiples) stack. Figure annotated and displayed with same gain and clip as Figure .