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 | Random noise attenuation using - regularized nonstationary autoregression |  |
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Random noise attenuation in seismic data can be implemented in the
frequency-space (
-
) and time-space (
-
) domain using prediction filters (Abma and Claerbout, 1995).
Linear prediction filtering assumes that the
signal can be described by an autoregressive (AR) model. When the data are
contaminated by random noise, the signal is considered to be predicted by
the AR filter and the noise is the residual (Bekara and van der Baan, 2009).
A number of approaches in
-
domain have been proposed and been used for
attenuating random noise. The
-
prediction technique was introduced by
Canales (1984) and further developed by Gulunay (1986). The
-
domain
prediction technique is also referred as
-
deconvolution by Gulunay (1986).
Sacchi and Kuehl (2001) utilized the autoregressive-moving average (ARMA)
structure of the signal to estimate a prediction error filter (PEF) and
the noise sequence is estimated by self-deconvolving the PEF from the
filtered data. Hodgson et al. (2002) presented a novel method of noise
attenuation for 3D seismic data, which applies a smoothing filter
(e.g. 2D median filter) to each targeted frequency slice and allows
targeted filtering of selected parts of the frequency spectrum. The
conventional
-
domain prediction uses windowing strategies to avoid
that the seismic events are not linear. The data are assumed to be
piecewise linear and stationary in an analysis temporal and spatial
window. To overcome the potentially low performance of
-
deconvolution
that arises with processing structural complex data, Bekara and van der Baan (2009)
proposed a new filtering technique for random and
coherent noise attenuation in seismic data by applying empirical
mode decomposition (EMD) (Huang et al., 1998) on constant-frequency
slices in the
-
domain and removing the first intrinsic mode
function. In addition, in the research field of seismic data
interpolation, Naghizadeh and Sacchi (2009) proposed an adaptive
-
prediction filter, which was used to interpolate waveforms
that have spatially variant dips. The
-
domain prediction
technique can be implemented in the frequency slice and also
in pyramid domain (Sun and Ronen, 1996). The implemented in
pyramid domain makes the operators more efficient because one
only needs to estimate one prediction filter from many different
frequencies (Sun and Ronen, 1996; Guitton and Claerbout, 2010; Hung et al., 2004).
The prediction process can be also achieved in
-
domain
(Claerbout, 1992). Abma and Claerbout (1995) discussed
-
and
-
approaches to predict linear events and concluded
that
-
prediction is equivalent to
-
prediction with a
long time length. Crawley et al. (1999) proposed smooth
nonstationary PEFs with micropatches and radial smoothing
in the application of seismic interpolation, which
typically produces better results than the rectangular
patching approach. Izquierdo et al. (2006) proposed a
technique for structural noise reduction in ultrasonic
nondestructive examination using time-varying prediction
filter. Sacchi and Naghizadeh (2009) proposed an algorithm
to compute time and space variant prediction filters for
noise attenuation, which is implemented by a recursive
scheme where the filter is continuously adapted to
predict the signal.
Fomel (2009) developed a general method of nonstationary
regression with shaping regularization (Fomel, 2007).
Shaping regularization has an advantage of a fast
iterative convergence. Regularized nonstationary
regression (RNA) has been used in multiple subtraction
Fomel (2009), time-frequency analysis (Liu et al., 2011b),
and nonstationary polynomial fitting (Liu et al., 2011a).
Liu and Fomel (2010) introduced an adaptive PEFs using
RNA in
-
domain which has been used for trace interpolation.
In this paper, we investigate the
-
domain prediction
technique and propose
-
domain RNA to attenuate
random noise in seismic data. Firstly, we review
the theory of
-
stationary autoregression. Then,
we describe the
-
RNA and extend to complex number
domain. Next we provide the methodology of random
noise attenuation using
-
RNA. Finally, we use
synthetic and real data examples to evaluate and compare
the proposed method with other noise attenuation techniques,
such as
-
domain and
-
domain prediction techniques.
 |
 |
 |
 | Random noise attenuation using - regularized nonstationary autoregression |  |
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Next: Review of - domain
Up: Liu et al.: Noise
Previous: Liu et al.: Noise
2013-11-13