Migration algorithms

The program that I used to migrate the data implements the common-azimuth downward continuation operator presented in previous reports by Biondi and Palacharla . The continuation operator is derived in the frequency-wavenumber domain, but, because it is applied to depth migration, it is implemented using a mixed space-wavenumber domain migration scheme. In particular, I implemented the method using a straightforward generalization of phase-shift plus interpolation (PSPI) Gazdag and Sguazzero (1984) to common-azimuth migration because of its simplicity and computational efficiency; other choices, such as split step Stoffa et al. (1990) would have probably been just as effective. The design a frequency-space (Fx) representation of the common-azimuth downward continuation operator would be a worthwhile effort, after common-azimuth migration has been proven effective and accurate to image a wide-class of 3-D data sets.

The results of multi-line 2-D migrations were computed by a simple modification of the common-azimuth migration program; the well known 2-D double square root operator Claerbout (1985) was substituted for the common-azimuth operator. The multi-line 2-D migration program is slightly faster than the full 3-D program. Because it propagates energy only along the in-line direction, it does not require repeated forward and inverse FFTs along the cross-line midpoint axis to take into account the velocity variations along the cross-line direction.