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## AMO in vertically inhomogeneous media

The v(z) modal used here is a linear one with velocity given by v(z)=1.5+0.6z km/s. This model is a good representation of many locations in the subsurface, including the Gulf of Mexico.

AMO2vzeta1
Figure 10
A side (left) and a top (right) view of the AMO operator for a VTI vertically inhomogeneous medium for an input and output offset of 2 km and correction to only the azimuth of 30 degrees. The medium has v=1.5+0.6z km/s and =0.1.

Figure 10 shows a side and a top view of the AMO operator that corrects for an azimuth of 30 degrees. The VTI medium has =0.1. The anisotropic AMO operator is clearly a stretched version of the isotropic one, shown in Figure 2. This operator is very similar to the homogeneous medium one (Figure 5), which clearly suggests that the impact of v(z) velocity variation on the operator is small. It also implies that the homogeneous VTI AMO operator can be used to successfully correct for data from v(z) VTI media.

AMO2vzeta3
Figure 11
A side (left) and a top (right) view of the AMO operator for a VTI vertically inhomogeneous medium for an input and output offset of 2 km and correction to only the azimuth of 30 degrees. The medium has v=1.5+0.6z km/s and =0.3.

The same observations hold for even stronger anisotropy given by . Figure 11 shows such an operator where clearly the shape of the operator is different from the isotropic one. Such strong anisotropy changes the shape of the AMO operator considerably. Also, the operator is very similar to the homogeneous medium one (Figure 9), again suggesting that the influence of such smooth vertical velocity variation is small on the AMO operator, even for such a strong anisotropy.

In summary, AMO operators in v(z) media are very similar to their homogeneous media counterparts, granted that the strength of anisotropy is the same. If the anisotropy strength changes between the models the AMO operator shape can change, as well. Anisotropy can cause triplications in the operator even at low angles.

Next: Residual AMO operators Up: AMO operators in VTI Previous: AMO in homogeneous media
Stanford Exploration Project
8/21/1998