Real data

We applied our preconditioning method to a 2-D line from the 3-D Elf North Sea dataset. The results are encouraging. Figure 11 is the migrated stack of the 2-D line. Figure 13 is the result of 1 iteration of the preconditioned inversion. Note the the inversion result is lower frequency than the migration. Also, by comparing the inversion result with the picked reflectors (Figure 12) we can see that the smoothing is too strong and may smooth poorly where there are no reflectors picked. Overall, the result looks too artificial.

Performing more iterations helps to increase the frequency content of the inversion result. Figure 14 shows the result of five iterations. Although it is higher frequency than Figure 13, it still looks artificial.

 

mig.stack
Figure 11 Stacked migration

 

overlay
Figure 12 Stacked migration with picked reflectors. Dip penalty filters smooth along a dip field created from the picked reflectors.

 

prec.1iter
Figure 13 Zero angle panel after one iteration of preconditioned inversion. Note the helix wrap arround artifact at 0.8 km.

 

prec.5iter
Figure 14 Zero angle panel after five; iterations of preconditioned inversion.

We can also consider the results of the smoothing along the angle axis. Figure 15 shows the angle gather that results from migration. Figure 16 is the angle gather after 3 iterations of preconditioned inversion. The preconditioned result is lower frequency and smoothes energy all across the gather, but it is possible to see where the true events end on the preconditioned results. This shows where the linear operator ${\bf L}$ from equations (1) and (2) stops operating and where the preconditioner ${\bf A^{-1}}$ takes over. The events change in character as they are smoothed across angles where our survey geometry does not provide large angle information.

 

mig.ang Figure 15 Migrated angle gather

 

prec.ang Figure 16 Angle gather after 3 iterations of preconditioned inversion