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Zero-offset prestack migration results

I first show in Figure [*] a comparison between the migration result of the Marmousi dataset (${\bf
 m_1}$) and the remodeled data (${\bf m_2}$). We notice that the migration of the remodeled data (Figure [*]b) lowers the amplitudes in the upper part of the model. Therefore, we expect the filters to correct for this difference. Figure [*] displays few estimated filters for the Marmousi result. The filters are ten by ten with 40 patches in depth and 80 along the midpoint axis. I shown only a fifth of these filters in both axes. It is interesting to notice that these filters have their highest value at zero-lag, meaning that we have a strong amplitude correction with few kinematic changes. The zero-lag values are also larger at the top of the model, as anticipated. Looking more closely at these filters, we see that the coefficients follow the structure of the Marmousi model (upper right corner).

Having estimated the filters ${\bf b}$ in equation (12), I apply them to ${\bf
 m_1}$ to obtain an improved image. To validate this approach I show in Figure [*]a the result of five conjugate gradient (CG) iterations with the Marmousi data. This results show higher amplitudes at the top but with inversion artifacts. This problem should be addressed with a proper regularization scheme Prucha et al. (1999). In Figure [*]b, I show the corrected image with the approximated Hessian ${\bf B}$. The amplitude behavior is very similar to Figure [*]a, without the inversion artifacts. Additionally, the cost is much lower.

I show in Figure [*] the ratio of the envelope of Figure [*]b and [*]a. This Figure illustrates that the effects of the non-stationary filters, i.e, the Hessian, are stronger on the top of the model.

 
m1.m2
m1.m2
Figure 1
(a) Migration result of the Marmousi dataset, i.e., ${\bf
 m_1}$ in equation (9). (b) Migration result of the remodeled data, i.e., ${\bf m_2}$ in equation (9).
[*] view burn build edit restore

 
filter-minv0
filter-minv0
Figure 2
Each cell represents a non-stationary filter with its zero-lag coefficient in the middle. A fifth of the filters are actually shown in both directions. Each filter position corresponds roughly to a similar area in the model space (Figure [*]a). After close inspection of the filter coefficients, these filters seem to follow the structure of the Marmousi model. They are also stronger at the top of the model, as expected.
view burn build edit restore

 
inv.ampcorr
inv.ampcorr
Figure 3
(a) Model estimated after five iterations of CG. The model is noisy because no regularization has been applied. (b) Model estimated after applying the adaptive filters to ${\bf
 m_1}$. The amplitude behavior is similar to (a) without the artifacts and with fewer iterations.
[*] view burn build edit restore

 
amplitude0
amplitude0
Figure 4
Ratio of the envelopes of Figures [*]a and [*]b. Brighter colors correspond to higher values. The main effect of the filters is clearly visible at the top.
view burn build edit restore


next up previous print clean
Next: Angle domain results Up: Migration results Previous: Migration results
Stanford Exploration Project
7/8/2003