Migration velocity analysis

As mentioned earlier, least-squares Kirchhoff migration involves using only a single slice out of a much larger transform domain cube. If the rest of the cube contained no interesting information, then the extra computations of the least-squares method would not be justified. However, the rest of the transform domain cube does serve a purpose. Figure  shows a single slice taken from two such cubes. This is for a non least-squares example. The x coordinate is fixed at the location of the single point scatterer; the axes are t and t₀. The cube has been shifted so that the single slice that corresponds to the migrated image lies along the top of the cube. On the left is the result of migrating with the correct constant velocity; we see energy focusing near the top of the plot. On the right is the result of migrating with too high a velocity (3.5 km/sec instead of 3 km/sec). The focusing of energy away from the t=t₀ plane tells us that an incorrect migration velocity was used. The cube contains important information, similar to a migration velocity analysis, away from the image plane. This gives us reason to think that the added cost of the least-squares method might be worthwhile.

 

focus
Figure 9 Left, migration with correct velocity. Slice for a single x coordinate, at the scatterer location. Focus is on the t=t₀ line, which has been shifted to lie along the top of the plot. Right, migration with incorrect velocity gives focus that is away from the t=t₀ line.