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Synthetic data

We applied our methodology to a synthetic 2-D dataset. This dataset was provided to us by SMART JV and is designed to have serious illumination problems. A common angle section from the migration of this dataset can be seen in Figure 1. We are particularly interested in the area beneath the edge of the salt. As you can see inside the oval drawn on Figure 1, the amplitude of the reflectors decreases very sharply underneath the salt. Also, there is a lot of noise under the salt edge. This is not a surprise since this is a prestack section.

 
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Figure 1
Constant angle panel from migration.
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We first applied just an inversion to this data, with no type of regularization. Inversion is simply the first equation from the set shown in equation (1). Figure 2 shows a constant angle panel after 8 iterations. This result looks even worse than the migration result.

 
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Figure 2
Constant angle panel using inversion only.
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We then applied regularization only in the angle - depth direction. Figure 3 shows a constant angle section after 5 iterations of the method described above. Within the oval we can see that the amplitude along the reflectors is more constant. The reflectors can almost be traced all of the way to the salt. The noise under the salt is much weaker than is seen in the migrated result. The image of the salt flank is also sharper than in the migration result.

 
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Figure 3
Constant angle panel with preconditioning only along the angle axis.
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Finally, we applied regularization in both directions described in the theory section. To do so, we first picked reflectors from the stacked migration (Figure 4). As you can see, we extended our picked reflectors beyond what can be seen in the migration (Figure 1), in the way that seems most reasonable.

Figures 5 and Figure 6 show the constant angle panel after one and five iterations. The reflectors continue at almost a constant amplitude as far as they were picked in Figure 4, then even farther with decreasing amplitude. More iterations increase the amplitudes. Unfortunately, increasing the number of iterations also decreases the frequency of the data. Even the first iteration causes a slight decrease in frequency. Although these sections look artificial because of the smoothing, we have also cleaned up almost all of the noise. These results seem promising.

 
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Figure 4
Stacked migration with picked reflectors overlaid. The dip penalty filters smooth along these reflectors.
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Figure 5
Constant angle panel with one iteration of 2-D preconditioning.
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Figure 6
Constant angle panel with five iterations of 2-D preconditioning.
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We can also analyze the effects of inversion and regularization in Angle-Domain Common Image Gathers (ADCIG). Figure 7 shows an ADCIG from the migrated image. Figure 8 shows the same gather after inversion with no regularization. It is actually noisier than the migration result, although the real reflectors are also stronger. Figure 9 is the same ADCIG with regularization only along the angle axis. This gather is smoother and less noisy than the migrated angle gather and the inverted gather. The real reflectors are easier to see. For example, the reflection at depth of about 1.6 km can be followed all the way across the angle axis. In the ADCIG obtained by migration (Figure 7) the same reflection is visible only at small offset ray parameters.

Figure 10 shows the same angle gather after five iterations of 2-D preconditioning. This gather is much smoother, with more constant amplitudes, and almost all of the noise is gone. It is possible to see where the preconditioning tries to fill in for the reflectors that can't normally be imaged due to our limited survey geometry. It does seem that the preconditioning may be too strong, but the results are encouraging.

 
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Figure 7
Migrated angle gather from CMP location 9.9 km.
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Figure 8
Inverted angle gather from CMP location 9.9 km.
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Figure 9
Angle gather after 5 iterations of preconditioning only along the angle axis at CMP location 9.9 km.
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Figure 10
Angle gather after 5 iterations of 2-D preconditioning at CMP location 9.9 km.
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next up previous print clean
Next: Real data Up: Results Previous: Results
Stanford Exploration Project
4/29/2001