MZO and DMO in variable velocity media

I applied the MZO operator to a series of depth variable velocity models. Each model consists of four diffractors placed at equal time depths. In Figure 2, I show the zero-offset section and the maximum constant-offset section for a velocity model with a linear increase in velocity. In Figure 3, I show the zero-offset section and the maximum constant-offset section for a velocity model with a more general depth variable velocity. The two velocity models are shown in Figure 4. The maximum constant-offset is 3325 m. The normal moveout correction and the dip moveout correction are, in essence, an approximation to the migration to zero-offset in a variable velocity medium. Ideally, after each process the flattened hyperbola generated by a diffractor in a constant-offset section should be migrated to a zero-offset hyperbola. The alignment of the events in Figures 5 and 6 should be a measure of success in migrating the constant-offset sections to zero-offset. Kinematically, the MZO operator shows better alignment, but the amplitude of the events is attenuated, due to the unsophisticated amplitude scheme I used for the MZO operator.

 

allm1
Figure 5 NMO, DMO and MZO applied to four diffractors in a medium with linear velocity increase. Migration to Zero-Offset should align all the events. There are five groups of seven traces in each plot, each group representing the same event at increasing offsets. The MZO operator shows better alignment but inferior amplitude preservation.

 

allm4
Figure 6 NMO, DMO and MZO applied to four diffractors in a medium where velocity varies in depth v(z). Migration to Zero-Offset should align all the events. There are five groups of seven traces in each plot, each group representing the same event at increasing offsets. The MZO operator shows better alignment but inferior amplitude preservation.