Attenuation of Diffracted and Specularly-reflected Multiples

With ideal data, attenuating both specularly-reflected and diffracted multiples could, in principle, be accomplished simply by zeroing out (with a suitable taper) all the q-planes except the one corresponding to q=0 in the model cube m(z',q,h) and taking the inverse apex-shifted Radon transform. In practice, however, the primaries may not be well-corrected and primary energy may map to a few other q-planes. Energy from the multiples may also map to those planes and so we have the usual trade-off of primary preservation versus multiple attenuation. The advantage now is that the diffracted multiples are well focused to their corresponding h-planes and can therefore be easily attenuated. Rather than suppressing the multiples in the model domain, we chose to suppress the primaries and inverse transform the multiples to the data space. The primaries were then recovered by subtracting the multiples from the data.

Figure 5 shows a close-up comparison of the primaries extracted with the standard 2D transform (Sava and Guitton, 2003) and with the apex-shifted Radon transform for the two ADCIGs at the top in Figure 2. The standard transform (Figures 5a and 5c) was effective in attenuating the specularly-reflected multiples, but failed at attenuating the diffracted multiples (below 4000 m), which are left as residual multiple energy in the primary data. Again, this is a consequence of the apex shift of these multiples. There appears not to be any subsalt primary in Figures 5a and 5b and only one clearly visible subsalt primary in Figures 5c and 5d (just above 4400 m). This primary was well preserved with both transformations.

Figure 6 shows a similar comparison for the extracted multiples. Notice how the diffracted multiples were correctly identified and extracted by the 3D Radon transform, in particular in Figure 6b. In contrast, the standard 2D transform misrepresent the diffracted multiples as though they are specularly-reflected multiples as seen in Figure 6a. We can take advantage of the 3D model representation to separate the diffracted multiples from the specularly-reflected ones. This is shown in Figure 7. The diffracted multiples are clearly seen in Figure 7c.

 

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Figure 5 Comparison of primaries extracted with the 2D Radon transform (a) and (c) and with the apex-shifted Radon transform (b) and (d). Notice that some of the diffracted multiples remain in the result with the 2D transform.

 

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Figure 6 Comparison of multiples extracted with the 2D Radon transform (a) and (c) and with the apex-shifted Radon transform (b) and (d).

 

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Figure 7 Comparison of (a) diffracted and (b) specularly-reflected multiples for the ADCIG in Figure 2a. Notice the lateral shifts in the apexes of the diffracted multiples.

In order to assess the effect of better attenuating the diffracted multiples on the angle stack of the ADCIGs we processed a total of 310 ADCIGs corresponding to horizontal positions 3000 m to 11000 m in Figure 1. Figure 8 shows a close-up view of the stack of the primaries extracted with the 2D Radon transform, the stack of the primaries extracted with the 3D Radon transform and their difference. Notice that the diffracted multiple energy below the edge of the salt (5000 m to 7000 m) that appears as highly dipping events with the 2D transform, has been attenuated with the 3D transform. This is shown in detail in Figure 8c. It is very difficult to identify any primary reflections below the edge of the salt, so it is hard to assess if the primaries have been equally preserved with both methods. It is known, however, that for this dataset, there are no multiples above a depth of about 3600 m, between CMP positions 3000 m to 5000 m. The fact that the difference panel appears nearly white in that zone shows that the attenuation of the diffracted multiples did not affect the primaries. Of course, this is only true for those primaries that were correctly imaged, so that their moveout in the ADCIGs was nearly flat. Weak subsalt primaries may not have been well-imaged due to inaccuracies in the migration velocity field and may therefore have been attenuated with both the 2D and the 3D Radon transform.

 

comp_prim1_stack
Figure 8 Comparison of angle stacks for primaries.

For the sake of completeness, Figure 9 shows the extracted multiples with the 2D and the 3D Radon transform and their difference. Again, the main difference is largely in the diffracted multiples.

 

comp_mult1_stack
Figure 9 Comparison of angle stacks for multiples.