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![]() | Nonstationary pattern-based signal-noise separation using adaptive prediction-error filter | ![]() |
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To estimate the nonstationary pattern of a 2D seismic section
,
prediction coefficients An of the APEF can be obtained as:
To obtain the whitening output, one needs to design APEF
of data
with the causal filter structure. For example, a five-sample (time)
three-sample (space) template is shown as:
(i) Random noise: it supposes that the energy of random noise is spatially
uncorrelated, and its statistical property may slightly change with time.
To characterize the model of random noise, noise pattern N can be set as the
shape of a column. The following is an example of the noise pattern structure
with 4 (time)
1 (space) coefficients:
We can generate a noise model containing the characteristics of noise
,
and calculate APEF
from the noise model. Also, one can directly
estimate APEF
of random noise from dataset
, especially
when there exists strong random noise in the dataset.
with one-column
shape can only capture the temporal spectrum of random noise, but ignores the
signal predictability along the space direction in the dataset.
(ii) Ground-roll noise: due to the difference of the dominant frequency, ground-roll
noise and the effective signal can usually be separated in the frequency domain.
Using a low-pass filter to the data can produce a noise model. Similarly, according
to the difference of slowness, the primaries can be muted in the radon domain, and
a ground-roll noise model can be obtained through the inverse radon transform. Here,
we first use a reliable low-pass filter to generate the ground-roll noise model, then
APEF
of the ground-roll noise is calculated according to the structure
similar to that of data as equation 11. Due to the slower speed of
the ground-roll noise, it has steep events with larger local slope, and the filter
size needs to be adjusted to a larger length in the time direction.
Therefore, the proposed signal-noise separation method exploits a two-step strategy:
(i) estimating data pattern
and noise pattern
by using
the APEF, and (ii) separating signal and noise with the pattern-based method
(equation 7). The further examination of the proposed method will
be shown in the data examples section.
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![]() | Nonstationary pattern-based signal-noise separation using adaptive prediction-error filter | ![]() |
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