Results

We began our experiments on the synthetic Elf North Sea dataset. Figure 1 shows the result of conjugate gradient inversion. The deepest reflector seems to disappear as it passes under the edge of the salt body. This behavior is known to be caused by poor illumination Prucha et al. (1998).

Figures 2 through 5 show the estimated resolution for the synthetic dataset, with increasing numbers of iteration. After only 5 iterations, there is high resolution along the major reflectors (black indicates high resolution, white indicates low resolution). Note that the area of poor illumination has low resolution. As the number of iterations increases, the areas between the reflectors become better resolved. This tells us that conjugate gradient algorithm is spending most of its effort at low iterations resolving model components around the reflector. It moves onto the area between reflectors only at large iterations. This is not surprising behavior, since most of the energy in the model space is found around the reflectors so that is what will be minimized first.

 

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Figure 1 Inversion result on synthetic.

 

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Figure 2 Resolution using conjugate gradient method after 5 iterations. Dark indicates higher resolution.

 

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Figure 3 Resolution using conjugate gradient method after 10 iterations. Dark indicates higher resolution.

 

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Figure 4 Resolution using conjugate gradient method after 15 iterations. Dark indicates higher resolution.

 

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Figure 5 Resolution using conjugate gradient method after 20 iterations. Dark indicates higher resolution.

After experimenting with the synthetic dataset, we conducted the same trials on the real Elf North Sea dataset (Figure 6). Note that the x-axis in the real dataset is reversed from that in the synthetic so that the salt structure tilts to the left rather than the right. Figures 8 through 11 show the results of increasing the iterations for estimating the resolution. Once again, there are Kirchhoff-type artifacts in all of the figures. Note that we again see resolution energy beginning around the reflectors, spreading to areas between reflectors at higher iterations. We can see corresponding changes in our image. After 5 iterations the image shows strong energy along the primaries reflectors, but is generally low frequency, Figure 6. After 20 iterations we have an image with more noise, but also a significantly higher frequency image. The later iterations resolved smaller eigenvalues of the model, which corresponded to higher frequency, lower amplitude portions of the model space.

 

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Figure 6 Inversion result on real data after 5 iterations.

 

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Figure 7 Inversion result on real data after 20 iterations.

 

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Figure 8 Resolution using conjugate gradient method after 5 iterations of the real data.

 

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Figure 9 Resolution using conjugate gradient method after 10 iterations of the real data.

 

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Figure 10 Resolution using conjugate gradient method after 15 iterations of the real data.

 

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Figure 11 Resolution using conjugate gradient method after 20 iterations of the real data.