Next: MIGRATION IN THE (omega,x)DOMAIN
Up: WAVEMOVIE PROGRAM
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Theory predicts that in two dimensions,
waves going through a focus
suffer a 90 phase shift.
You should be able to notice that a symmetrical waveform
is incident on the focus, but an antisymmetrical waveform emerges.
This is easily seen in Figure 10.
trick
Figure 10
The accuracy of the xderivative may be improved by
a technique that is analyzed later in chapter .
Briefly, instead of
representing by the tridiagonal
matrix with (1,2,1) on the main diagonal,
you use . Modify the extrapolation analysis by multiplying through
by the denominator.
Make the necessary changes to the 45 collapsing wave program.
Left without 1/6 trick; right, with 1/6 trick.
In migrations, waves go just to a focus, not through it.
So the migration impulse response in two dimensions
carries a 45 phase shift.
Even though real life is three dimensional,
the twodimensional response is appropriate
for migrating seismic lines where focusing
is presumed to arise from cylindrical, not spherical, reflectors.
Mabsorbside
Figure 11
Chapter explains how to absorb energy
at the side boundaries.
Make the necessary changes to the program
to absorb waves incident on the leftside boundary.

 
Next: MIGRATION IN THE (omega,x)DOMAIN
Up: WAVEMOVIE PROGRAM
Previous: Including lateral velocity variation
Stanford Exploration Project
10/31/1997