Imaging with an approximate velocity model

All of the previous results were obtained using the exact Marmousi velocity model, but in a real exploration scenario the determined velocity model would generally be less detailed and less accurate.

Figure  is an approximate model obtained by defining the gross features of the true model and smoothing the slowness within each of the defining regions. This is the same model used by Nichols and it is intended to to be a realistic representation of what an explorationist might reasonably attain using geological information, velocity estimation, and well information.

Figure  is the result of standard Kirchhoff migration with first-arrival traveltimes calculated from the surface using the approximate velocity model. There is not too much difference between this and the same migration using the actual velocity model (Figure ). The result of layer-stripping Kirchhoff migration is presented in Figure . The anticline and target structure is imaged, but not as well as with the actual velocity model (Figure ).

Figure  is a comparison of the target zone images generated with the approximate velocity and the actual velocity. Although the image obtained with the exact velocity is superior, the one obtained with the approximate velocity is surprisingly good. All the relevant features of the target are imaged, even though the lateral coherency and structural definition are not as good as when the actual velocity is used. This shows that although the method is sensitive to velocity, it still produces a good image which could be improved by a refinement of the velocity model.

 

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Figure 19 An approximate Marmousi velocity model.

 

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Figure 20 Standard Kirchhoff migration using the approximate velocity model. Standard Kirchhoff migration with first-arrival traveltimes calculated from the surface using the approximate velocity model of Figure . Compare to Figure . Movie.

 

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Figure 21 Layer-stripping Kirchhoff migration using traveltimes calculated from the surface and traveltimes calculated from a depth of 1500 m using the approximate velocity model of Figure . The lower part of the image was obtained by migrating data which was redatumed to a depth of 1500 m in three steps of 500 m each. Compare to Figure . Movie.

 

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Figure 22 Comparison of reflectivity and images generated by migration with the approximate velocity and the actual velocity. Closeup comparison at the target zone of (a) the ideal reflectivity, (b) the image after downward continuation to 1500 m in three steps of 500 m each using the approximate velocity of Figure , (c) the image after downward continuation to 1500 m in one step with the true velocity of Figure , and (d) the image after downward continuation to 1500 m in three steps of 500 m each with the true velocity of Figure . Movie.