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As shown in Figure 5, this wavefield in the tx domain
can be expressed by
 
(5) 
oneplanewave
Figure 5 A synthetic wavefield composed of a single plane wave.

 
After Fourier transform along the time axis, we get the expression in the
fx domain:
 
(6) 
It is easy to show that one trace can be predicted from an adjacent trace:
 
(7) 
Or in another form,
 
(8) 
This means that, each trace can be predicted with the propagator
. Up to now, we have not mentioned FIG
and FDG. Therefore, all above conclusions are effective for both cases.
But when we introduce the details of the two schemes, we will reach different
conclusions:
 Frequencyindependent grids
is constant. The propagator P_{1} is the function
of frequency f. It will change from one frequency slice to
another.
 Frequencydependent grids
From (3), we can choose
 
(9) 
Therefore, the propagator P_{1} becomes
 
(10) 
So the propagator P_{1} is frequencyinvariant.
Next: Wavefield composed of two
Up: ESTIMATION OF SPATIAL PREDICTION
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Stanford Exploration Project
11/11/1997