RESULTS

To test how much the migration could be sped up I chose a 2-D line from a 3-D land dataset provided by Ecopetrol. Figure 1 shows the result using the conventional approach. The left plot shows the zero offset image (the standard imaging condition), the right panel shows three selected angle CRP gathers Sava and Fomel (2000). Using five reference velocities and four processors it took 2034 seconds to run.

 

mig-slow
Figure 1 The left panel is the result of split-step migration. The right panel is three gathers from the same migration.

Figure 3 shows the same migrated image calculated with variable depth sampling, accounting for attenuation, and reducing the size of the offset domain as we go down in depth. The left panel of Figure 2 shows the sampling in depth for several frequencies. The right panel shows how the offsets downward continued decrease as the depth increased. The result was achieved in 1042 seconds (almost half of the time) and is nearly identical to the result in Figure 1.

 

fast-sample
Figure 2 The left panel shows every tenth depth for various frequencies for the migration show in Figure 3. The right panel shows the reduction in the migrated offset domain as a function of depth. Note how the sampling in depth sparser, the offset domain is decreased quicker, and the frequencies are assumed to be of inconsequential energy than in Figure 3.

 

mig-fast
Figure 3 The left panel is the result of split-step migration. The right panel are three gathers from the same migration. Note how the image is almost identical to Figure 1 but is calculated three times faster.

For velocity analysis the image quality requirements are reduced. By using the sampling in Figure 4 image gathers can be produced that give accurate moveout information (Figure 5) while further reducing the migration time to 758 seconds.

 

faster-sample
Figure 4 The left panel shows every tenth depth for various frequencies. The right panel shows the reduction in the migrated offset domain as a function of depth. Note how the sampling in depth sparser, the offset domain is decreased quicker, and the frequencies are assumed to be of inconsequential energy than in Figure 5.

 

mig-faster
Figure 5 The left panel is the result of split-step migration. The right panel is three gathers from the same migration. Note how the image is slightly different from Figures 1 and 5, but the moveout information is nearly identical.