Page 520 - Acquisition and Processing of Marine Seismic Data

11.3 FINITE-DIFFERENCE MIGRATION 511

FIG. 11.20 The effect of depth step size on the collapse of a theoretical diffraction hyperbola in a constant velocity medium
by finite-difference time migration. 1 ms is the sampling rate of the zero-offset section.

Higher depth step sizes also cause undermi- smaller depth steps. In practice, the value for
gration of steep dips, dispersions along the the depth step size is between T S and 0.5T S ,
reflections increase, and kinks arise at regular where T S is the dominant period of the input
time intervals corresponding to the depth step dataset.
size. Kinks become more and more evident as
the dip increases. Fig. 11.21 shows the effect of 11.3.2 Effect of Velocity on Finite-
depth step size on real marine seismic data. Difference Migration
For large step sizes, the diffractions cannot
be collapsed, and the dipping events cannot Finite-difference migration is also sensitive
be moved updip to their correct lateral posi- to the velocity errors. Similar to the Kirchhoff
tions. Although smaller depth steps produce migration, slower and faster velocities cause
better results, a step size typically as large as under- and overmigration, which results in
possible is preferred due to economical con- frowns and smiles in the output image, respec-
cerns. Steeply dipping events always require tively. In the case of overmigration, however,