A 3 dimensional example

The three dimensional model is built in a linearly varying velocity in all three coordinates: v(x,y,z)=v₀+ax+by+cz. The model is composed of three vertical letters, in a plane parallel with the front of the cube. The size of the grid (64x64x256) was imposed by the amount of memory available on the SEP Connection Machine. Figure 4 displays the 3-D cube of diffraction data while Figure 5 illustrates two dimensional sections through the center of the data set.

 

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Figure 4 The three dimensional diffraction cube (64x64x256). Each side of the cube displays a section through the middle of the data set.

 

model3Dcuts
Figure 5 Two cuts through the three dimensional diffraction cube.

The results of the 3-D PSPI migration program are displayed in Figure 6. I display the data cube such that on each side of the cube is revealed a section through the center of the data set. On the cube's front side the section shown is passing through the plane where the diffracting letters are positioned. In Figure 7 I show a section through the migrated data passing through the target plane of the letters.

 

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Figure 6 The three dimensional migration cube (64x64x64).

 

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Figure 7 3-D migration comparison: [LEFT] PSPI migrated data. [RIGHT] Split-step migrated data.