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Since f-x prediction has been shown to be equivalent to a t-x prediction
with a long time length,
it may not be surprising that
t-x prediction generally produces results similar to
those of f-x prediction.
Although both these techniques work equally well in low noise cases,
t-x prediction provides better random noise reduction than
the older f-x prediction technique in the presence of
moderate- to high-amplitude noise.
The t-x prediction also avoids the generation of false events
in the presence of parallel events when using f-x prediction,
at least for parallel events with spacings wider than the
filter length in time.
The advantages of t-x prediction
are the result of its ability to control the length of the prediction
filters in time.
Because t-x prediction has
a shorter effective filter length in time than f-x prediction,
t-x prediction passes significantly less random noise than f-x prediction.
While Gulunay's f-x prediction
biases the prediction toward the traces nearest to the output
point,
allowing more noise to be passed,
this bias appears unimportant when compared to the problem with the
length of the effective filter in time.
3-dimensional prediction allows improved noise attenuation because
more samples are used to make predictions.
3-dimensional prediction also relaxes the requirement that events
be linear.
Comparisons of one- and two-pass predictions on a land data set
show that the one-pass results retain significantly more detail
than the two-pass
results.
In both one- and two-pass predictions, the f-x prediction passes more
random noise than the t-x prediction.

In the next chapter, the generation of spurious events is examined
in more detail.
In chapter , I will examine two more shortcomings of
f-x and t-x prediction, that of the amplitude loss in the signal and
that of the filter response to the noise being left in the signal.
To avoid these difficulties, a method of extending t-x prediction
is presented in chapter .

** Next:** Spurious event generation with
** Up:** Noise removal by filtering
** Previous:** Examples of three-dimensional lateral
Stanford Exploration Project

2/9/2001