Modeling with the proposed design

For the first step I used an analytic ray tracer to compute the surface emergence positions of rays originating at equally-spaced reflection points along the reflector. These reflection points were taken every 18 m, corresponding to the CMP interval in the traditional design. For the flat reflector the number of pairs of rays originating at each point was kept equal to the fold in the standard design. The rays correspond to a uniform increase in reflection aperture angle and therefore will not correspond to uniform offsets in a CMP gather. In the semicircle the number of rays was increased as a function of the reflector dip, so that where the dips are larger more rays were generated. The maximum offset was not constrained except for the obvious requirement that any reflection time were less than the chosen trace length.

The next step is to use non-linear inversion to find the optimum source and receiver positions from the different targets. In this case, since there is only one target, the inversion reduces to a simple binning to honor the constraint that the receivers should be at equal distance along the line profile. I chose for the receiver interval the same value obtained in the standard design so that the results can be easily compared. The shots were also binned at the same receiver interval to further regularize the design (and guarantee equal distance between CMPs and between the stacked traces). Only shots that contribute at least half the number of traces of the standard geometry shot (that is 36) were considered. A total of 402 shots met this criterion (which is rather arbitrary). The number of traces per shot, and hence the maximum offset, was allowed to change from shot to shot. In this example this is the only degree of freedom that I used to adapt the acquisition effort to variations in the subsurface dip. In a real case, where the reservoir location is known or suspected, we could locally vary the receiver group interval or more likely the shot interval. In 3-D there are extra degrees of freedom associated with the azimuth and the choice of geometry template.

The next step is to simulate the acquisition of the data using the computed shot and receiver positions. Again, this was done with an analytic ray tracer. Figure  shows some of the shots. Note that they have different number of traces. Also, they look irregular because the plotting program places the traces together at the same distance irrespective of their offset. Figure  shows some CMPs along the line profile. As with the shots, the number of traces changes from CMP to CMP. Also note that there are ``holes'' in the CMP's illustrating the difference between uniform offsets and uniform illumination. Figure  shows the fold diagram. In this case there are differences in the fold coverage from CMP to CMP. As long as the minimum CMP fold is maintained, this shouldn't be a problem. More importantly, note the large offsets at both sides of the semicircle and the smaller offsets above the semicircle (compare with Figure ). Figure  shows the stacked section. Comparison with Figure  does not reveal any striking difference because the stack smooths out the effect of the irregular offsets. The important difference between the two figures is the lateral extent of the semicircular reflection. Figure  shows the migrated section and Figure  shows a comparison with the migrated section obtained with the standard acquisition. Not surprisingly, the two images are almost the same, since they were computed with the same aperture. The proposed design, however, required about 80 fewer shots.

 

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Figure 7 Synthetic shot records modeled with the proposed acquisition design.

 

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Figure 8 Selected CMPs modeled with the proposed methodology.

 

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Figure 9 Fold diagram for the proposed methodology

 

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Figure 10 Stacked section of modeled data generated with the proposed design

 

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Figure 11 Post-stack migrated section of modeled data generated with the proposed design

 

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Figure 12 Close up comparison of post-stack migrated sections generated with the traditional (left) and proposed (right) design

This example is rather artificial in that the savings in the number of shots comes simply from a realization that not all shots contribute the same number of traces to the subsurface image. In the real case a more important consideration would be to what part of the image every shot contributes. Those shots that contribute to the reservoir location (or any other critical part of the image) will be kept even if they contribute only a small number of traces. This flexibility is important when faced with obstacles which force us to displace shots or receivers. The effort that we put into it may depend on the relative contribution of those shots and receivers to the critical parts of the image as opposed to the standard approach in which all shots and receivers are considered equally important.

In order to see the importance of the fewer shots in the quality of the image, I modeled the data again with the standard approach but using only 402 shots (the same that I used in the proposed approach). The first shot will now be at -5350 m which translates to a maximum dip angle of 69 degrees with one fold and 60 degrees with full fold. Figure  shows a comparison with the proposed approach. The difference in the high dips of the images on the left-hand-side of the semicircle is clearly visible.

 

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Figure 13 Close up comparison of post-stack migrated sections generated with the proposed design (left) and the standard design with the same number of shots.

An obvious improvement to the above methodology consists in acquiring, for every shot, not only those receiver positions obtained form the inversion, but also those in between. After all, if the intermediate receiver stations are available, why not use them? Figure  shows the fold diagram in this case. The number of shots is the same as in the previous case, and the increase in fold is due entirely to the intermediate receivers.

 

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Figure 14 Fold chart of modeled data generated with the proposed design using intermediate traces