Results

To demonstrate our 2-D Regularized Inversion with model Preconditioning (RIP), we choose to extract a 2-D line from a real 3-D Gulf of Mexico dataset provided to us by BP and ExxonMobil. A portion of the 3-D velocity model for this dataset can be seen in Figure 1. The velocity model is believed to be accurate, which is important given our choice of regularization operator Clapp (2003).

 

bpvel Figure 1 Subset of the BP Gulf of Mexico velocity model.

We first performed downward continuation migration on this 2-D line. The migration results can be seen in Figures 2 and 4. In these figures, the left part shows a common offset ray parameter section, taken from $p_{hx}\ =\ .153$and $p_{hx}\ =\ .317$ respectively. The right part shows a common image gather taken from $CRPX\ =\ 20.5$ and $CRPX\ =\ 22.225$respectively.

 

bpcube.mig2d
Figure 2 Result of downward continuation migration of 2-D line. Left part is a common offset ray parameter section, right part is a common image gather taken from $CRPX\ =\ 20.5$.

In Figure 2, note the clear shadow zones visible in the common offset ray parameter section. The poor illumination that causes these shadow zones is manifested in the common image gather as gaps in the events. These gaps are what we hope to fill with our regularization operator.

 

bpcube.1dprec.10it
Figure 3 Result of 10 iterations of RIP. Left part is a common offset ray parameter section, right part is a common image gather taken from $CRPX\ =\ 20.5$.

Figure 3 is the result of 10 iterations of RIP. The common p_hx section and common image gather correspond to those of the migration result in Figure 2. The inversion process has cleaned up many of the artifacts seen in the migration result. More importantly, the common image gathers show that we are filling the gaps in the events. Our regularization operator is successfully compensating for the illumination problems.

 

bpcubes.mig2d
Figure 4 Result of downward continuation migration of 2-D line. Left part is a common offset ray parameter section, right part is a common image gather taken from $CRPX\ =\ 22.225$.

The common p_hx section shown in the migration result in Figure 4 and the RIP result in Figure 5 is interesting. At the CRPX location from which we have extracted the common image gather ($CRPX\ =\ 22.225$), we note that the result after 10 iterations of RIP (Figure 5 is beginning to show real events beneath the salt that are not visible in the migration result (Figure 4. The common image gather shows that we have extended the events in p_hx, essentially allowing the inversion image to ``recapture'' energy that left the survey area. Additionally, as we saw in Figure 3, the inversion result is cleaner than the migration result.

 

bpcubes.1dprec.10it
Figure 5 Result of 10 iterations of RIP. Left part is a common offset ray parameter section, right part is a common image gather taken from $CRPX\ =\ 22.225$.

It is also interesting to stack the migration and RIP results for comparison. Figure 6 shows the stacked migration result and Figure 7 shows the stacked RIP result after 10 iterations. Each of these figures has been zoomed in to concentrate on the poorly illuminated areas under the salt. The RIP stack is slightly higher in frequency content, due to artifacts in the migration result that stack into lower frequencies. More importantly, the RIP stack has improved the imaging of events within the shadow zones. The events extend farther into the poorly illuminated areas, are more continuous, and have more consistent amplitudes.

 

bpzstacks.mig2d
Figure 6 Stack of the downward continuation migration result, zoomed in under the salt body.

 

bpzstacks.1dprec.10it
Figure 7 Stack of the RIP result after 10 iterations, zoomed in under the salt body.