The isotropic migration

 

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Figure 8 Top: A prestack-migrated section of the anisotropic Marmousi data set, using an isotropic Kirchhoff migration with a smoothed version of the Marmousi velocity model. Bottom: A prestack-migrated section of the original Marmousi data set, using the same isotropic Kirchhoff migration as in top section with the same smoothed Marmousi velocity model.

To demonstrate the extent to which anisotropy influenced the new Marmousi data set, I isotropically prestack migrate the VTI Marmousi data set. I use the part of the data set with offsets equal or less than 2575 m, which is the limit on the original isotropic data set. This prestack migration, which is based on the Kirchhoff approach to imaging and raytracing for traveltime calculation, is applied using a smooth version on the original velocity model. Figure 8 (top) shows the stacked image after prestack migration on the new anisotropic Marmousi data set. Figure 8 (bottom), on the other hand, shows the result of using this same migration on the original Marmousi data set. I attribute the difference between the two migration results to anisotropy. Although the reservoir appears in both sections, its location is slightly shifted in Figure 8 (top). Also, many of the shallow faults are improperly imaged as a result of ignoring anisotropy. The degradation is far greater on the left side of the section, where the anisotropy is greater, than the right side.

To demonstrate why there are such large differences in imaging, Figure 9 shows common-midpoint gathers after prestack migration for the 4000 m location, which is highly anisotropic. The moveout is better aligned when we apply the isotropic migration to the original Marmousi data set (right) than when we apply the migration to anisotropic data. The difference in Figure 10, for CMP location 8000 m, is far less than what is apparent in Figure 9 which is a result of the reduced anisotropy at location 8000 m as compared to that at 4000 m.

 

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Figure 9 Common-midpoint gathers from the 4000 m location after isotropic prestack migration on the anisotropic Marmousi data set (left), and on the isotropic Marmousi data set (right).

 

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Figure 10 Common-midpoint gathers from the 8000 m location after isotropic prestack migration on the anisotropic Marmousi data set (left), and on the isotropic Marmousi data set (right).

An interesting application of the VTI Marmousi data set is to evaluate what isotropic velocity model would best image the data. This will give us some idea of how much velocity bias anisotropy introduces into the conventional isotropic processing scheme. The synthetic sections (Figure 5) clearly show that anisotropy results in faster traveltimes at the far offsets, and therefore, higher velocities in conventional velocity analysis. These higher velocities, if interpreted as vertical velocities, result in over-estimation of depth, even though $\delta$ (the anisotropy parameter responsible for depth mis-ties) is zero for the anisotropic model. Over-estimation of velocity is not the only problem with the isotropic assumption; both focusing and migration are negatively affected by ignoring anisotropy Alkhalifah and Tsvankin (1995).