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In chapter , we were introduced to the Kirchhoff
migration and modeling method by means of subroutines
kirchslow() and kirchfast() .
From chapter we know that these routines should be
supplemented by a filter such as subroutine halfdifa() .
Here, however,
we will compare results of the unadorned subroutine kirchfast()
with our new programs, phasemig() and phasemod() .
Figure 7 shows the result of modeling data and then migrating it.
Kirchhoff and phaseshift migration methods both work well.
As expected, the Kirchhoff method lacks some of the higher frequencies
that could be restored by .Another problem is the irregularity of the shallow bedding.
This is an operator aliasing problem
addressed in chapter .
comrecon
Figure 7
Reconstruction after modeling.
Left is by the nearestneighbor Kirchhoff method.
Right is by the phase shift method.
Figure 8 shows the temporal spectrum of the original sigmoid model,
along with the spectrum of the reconstruction via phaseshift methods.
We see the spectra are essentially identical
with little growth of high frequencies
as we noticed with the Kirchhoff method
in Figure .
phaspec
Figure 8
Top is the temporal spectrum of the model.
Bottom is the spectrum of the reconstructed model.

 
Figure 9 shows the effect of coarsening the space axis.
Synthetic data is generated from an increasingly subsampled model.
Again we notice that the phaseshift method of this chapter
produces more plausible results than
the simple Kirchhoff programs of chapter .
commod
Figure 9
Modeling with increasing amounts of lateral subsampling.
Left is the nearestneighbor Kirchhoff method.
Right is the phaseshift method.
Top has 200 channels,
middle has 100 channels,
and bottom has 50 channels.
Next: Damped square root
Up: PHASESHIFT MIGRATION
Previous: Pseudocode to working code
Stanford Exploration Project
12/26/2000