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![]() | Adaptive prediction filtering in ![]() ![]() ![]() | ![]() |
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Equation 5 shows that one sample in
-
domain can be
predicted by the samples in adjacent traces with weight coefficients
, which is time- and space-varying. The equation assumes
that the seismic data only consist of plane waves
and random noise
that corresponds to a least-squares error.
Figure 1a shows a 2D space-causal APF
structure, which is time-noncausal filter. White grids stand for
prediction samples and the dark-grey grid is the output (or target)
position, while light-grey grids are unused samples. The filter size
of the space-causal APF is
. Meanwhile, space-noncausal
APF (Figure 1b) has a symmetric structure
along time and space axes. The filter size of the space-noncausal APF
is
. The 3D
-
-
APF also has space-causal or
space-noncausal structure, Figure 2 shows the
noncausal one. In a 3D seismic datacube, the plane events can be
predicted along two different spatial directions. A 2D
-
APF
will have difficulty preserving accurate plane waves because it only
uses the information in
or
direction, however, a 3D
-
-
APF provides a more natural structure.
-
-
adaptive prediction filtering for random noise attenuation follows two
steps:
1. Estimating 3D space-noncausal APF coefficients
by solving the regularized least-squares
problem (equation 4 or 5 in 2D):
2pt
2. Calculating noise-free signal
according to
2pt
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causal2d,noncausal2d
Figure 1. Schematic illustration of a 2D ![]() ![]() |
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noncausal3d
Figure 2. Schematic illustration of a 3D ![]() ![]() ![]() |
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![]() | Adaptive prediction filtering in ![]() ![]() ![]() | ![]() |
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