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The number of filter coefficients controls the computer time
required by both of these techniques. Since the applications being considered
here are post-stack and generally fast,
at least for 2-dimensional cases,
the computer time required is generally insignificant.
It is interesting to note that while the effective
t-x prediction time-domain filter has more
coefficients than the individual filters used in f-x prediction,
because f-x prediction
produces a different filter for each frequency,
the total number of filter coefficients is much larger
than the number for t-x prediction.
Nevertheless, the computer time needed to apply these two processes
in the 2-dimensional case
is comparable,
since each filter calculated by f-x prediction is smaller than the single
filter calculated by t-x prediction.
Since the time to calculate a filter is proportional to *n*^{3}
with the routine I used, where
*n* is the number of filter coefficients, the calculation times used
by the two approaches
become nearly equal.
For the 3-dimensional case, the application of t-x prediction tends to
be more costly than f-x prediction,
but not tremendously so,
since the filter sizes
used by t-x prediction can be smaller than those for
a comparable f-x prediction.
However, as the size of the t-x prediction filter increases,
the processing time increases rapidly.
On the other hand, should cost be an issue,
Claerbout 1992a pointed out that
the number of iterations in the conjugate-gradient routine
used by my t-x prediction can
be significantly reduced from its theoretical limit with good results.

** Next:** Three-dimensional lateral prediction
** Up:** Two-dimensional lateral prediction
** Previous:** The biasing of f-x
Stanford Exploration Project

2/9/2001