Th P03 14 Random Noise Attenuation by a Hybrid

Th P03 14
Random Noise Attenuation by a Hybrid Approach
Using f-x Empirical Mode Decomposition and
Multichannel Singular Spectrum
Y. Chen (The University of Texas at Austin), T. Liu* (China University of
Petroleum-Beijing) & Y. Zhang (The University of Edinburgh)
SUMMARY
Empirical mode decomposition (EMD) becomes popular recently for random noise attenuation because of
its convenient implementation and ability in dealing with non-stationary seismic data. In this paper, we
summarize the existing use of EMD in seismic data denoising and introduce a general hybrid scheme
which combine f-x EMD with one other existing denoising approach. The novel hybrid scheme can
achieve a better denoising performance compared with the conventional f-x EMD and the other selected
denoising approach. Instead of combining f-x EMD with f-x predictive filtering, wavelet thresholding and
curvelet thresholding, we propose to combine f-x EMD with f-x multichannel singular spectrum analysis
(MSSA), which can obtain cleaner denoised section compared with f-x MSSA and can preserve dipping
energy compared with f-x EMD.
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
Introduction
The rapid development of the exploration for unconventional resource raise a higher demand
for random noise attenuation of pre- and post-stack seismic profile. Recently a type of hybrid
denoising approach using EMD is becoming popular. Chen and Ma (2013) notice the problem
of f − x EMD in dealing with complex structure and solve it by introducing f − x empirical
mode decomposition predictive filtering, which combine the advantage of both f − x EMD and
f − x predictive filtering. Chen et al. (2012) propose to combine EEMD, an enhanced version
of EMD, with wavelet domain thresholding, to obtained a better denoised result. Similarly,
Dong et al. (2013) combine f − x EMD with curvelet domain thresholding, and also obtained
better results compared with individual denoising performance. A combination between f − x
EMD and some other random noise attenuation approach is becoming more and more popular
because of the especial property of f − x EMD in preserving horizontal events.
In this paper, we summarize a general denoising framework, using a combination between
f − x EMD and one other approach. The new framework not only contains all the previously
mentioned f − x EMD based denoising approach, but also can be extended to other novel
denoising approach. One new combination is between f − x EMD and f − x MSSA. A hybrid
f − x EMD & MSSA approach can both improve conventional f − x EMD by preserving the
dipping events, and improve f − x MSSA by obtaining cleaner denoised image. Both synthetic
and field data examples demonstrate the superior property of the proposed approach.
Review of f − x EMD and f − x MSSA
f − x EMD
f − x EMD was proposed by Bekara and van der Baan (2009) to attenuate random noise. They
apply EMD on each frequency slice in the f − x domain, and remove the first IMF, which
mainly represent the higher wavenumber components, e.g., random noise. The methodology
can be summarized as:
s(m,t)
ˆ
= F −1
N
!
∑ Cn(m, w)
,
n=2
F d(m,t) =
N
(1)
∑ Cn(m, w),
n=1
where s(m,t)
ˆ
and d(m,t) denote the estimated signal and acquired noisy signal, respectively.
−1
F and F denote the forward and inverse Fourier transform along the time axis, respectively.
Cn denotes the nth EMD decomposed component. However, a problem occurs when applying
f − x EMD, because the dipping events will also be removed. This problem occurs because, for
many data sets, the random noise and any steeply dipping coherent energy make a significantly
larger contribution to the high-wavenumber energy in the f − x domain than any desired signal
(Bekara and van der Baan, 2009).
f − x MSSA
Considering 2D seismic data acquired on a regular grid D(m, w), m = 1, · · · , M, where M denotes the number of traces in the spatial dimension. The a Hankel matrix for each frequency
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
slice D(m, w) is constructed as:

D(1, w)
D(2, w)
 D(2, w)
D(3,
w)

H=
..
..

.
.
D(L, w) D(L + 1, w)
···
D(K, w)
· · · D(K + 1, w)
..
...
.
···
D(M, w)



,

(2)
where L = b M2 c + 1 and K = M − L + 1, and b·c denotes the integer part of its argument. It can
be proved that if the processing window contains k plane waves of independent dips, then the
block Hankel matrix H is rank k. The added random noise will increase the rank of matrix H.
It’s natural that the random noise can be removed by rank reduction for H (Oropeza and Sacchi,
2011).
Formulation of the new approach
Provided that the noisy data d is composed of the clean data s and noise n, f − x EMD can get a
denoised section with all the horizontal events sˆh , while leaving the dipping events in the noise
section:
sˆh ≈ E[d],
sd + n ≈ d − E[d].
(3)
Here, E denotes the noise attenuation operator by f − x EMD, sd denotes the true dipping
events, and n denotes random noise in the original seismic section. We can retrieve the useful
dipping events by applying another denoising operator onto the noise section,
sˆd ≈ P[d − E[d]],
(4)
where P denotes a denoising operator which estimate the lost dipping events from the initial
noise section, and sˆd denotes the estimated dipping events. The final denoised section sˆ is given
by the summation of the horizontal and dipping signal section:
sˆ = sˆh + sˆd ≈ E[d] + P[d − E[d]].
(5)
Equation 5 is a general framework for all those f − x EMD based random noise attenuation
approaches.The denoising operator P can be chosen as f − x predictive filtering (Chen and Ma,
2013), wavelet transform (Chen et al., 2012), and curvelet transform (Dong et al., 2013). In
this paper, we propose to use f − x MSSA (Oropeza and Sacchi, 2011) as P.
Example
Synthetic example
The synthetic example is composed of three horizontal and one dipping events. 40 Hz ricker
wavelet is used. The sampling interval is 2 ms. The clean and noise sections are shown in
Figure 1. After using f − x EMD, f − x MSSA and the proposed hybrid approach, the denoised
results and their corresponding noise sections are shown in Figure 2.
Field example
The field data is a multi-component p-wave image, shown in Figure 1(c). The seismic section is
very noisy, especially in the shallow part, which makes random noise attenuation a requirement.
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
The denoising results using three mentioned approaches and their corresponding noise sections
are shown in Figure 3. To better compare the denoising performance, two pair of frame boxes
in Figure 3 are zoomed in Figure 4.
(a)
(b)
(c)
Figure 1 Synthetic and field data examples for testing. (a) Clean synthetic data. (b) Noisy
synthetic data. (c) Field data.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2 Comparison of denoising performance. (a) Denoised using f − x EMD. (b) Denoised
using f − x MSSA. (c) Denoised using the proposed hybrid approach. (d)-(f) Noise sections
corresponding to (a)-(c) respectively.
Conclusions
We have proposed a novel hybrid denoising framework, combining f − x EMD with one other
denoising approach. f − x MSSA is chosen to be combined with f − x EMD in this paper,
even though there are many other options. The proposed approach fully utilize the preservation
ability of f − x EMD for horizontal events, and use f − x MSSA to retrieve the dipping events,
which can be small part of the total events. From the synthetic and field data examples, it’s
obvious that, the proposed hybrid approach can obtain cleaner denoised image compared with
f − x MSSA and can preserve more dipping energy compared with f − x EMD.
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014
(a)
(b)
(c)
(d)
(e)
(f)
Figure 3 Comparison of denoising performance. (a) Denoised using f − x EMD. (b) Denoised
using f − x MSSA. (c) Denoised using the proposed hybrid approach. (d)-(f) Noise sections
corresponding to (a)-(c) respectively.
(a)
(b)
(c)
(d)
Figure 4 Comparison of zoomed sections. (a) & (b): comparison for frame box A. (c) & (d):
comparison for frame box B.
References
Bekara, M. and van der Baan, M. [2009] Random and coherent noise attenuation by empirical mode decomposition. Geophysics, 74(5), V89–V98.
Chen, W., Wang, S., Zhang, Z. and Chuai, X. [2012] Noise reduction based on wavelet threshold filtering and
ensemble empirical mode decomposition. 82nd Annual International Meeting, SEG, Expanded Abstracts, 1–6.
Chen, Y. and Ma, J. [2013] Random noise attenuation by f-x emprical mode decomposition predictive filtering.
83rd Annual International Meeting, SEG, Expanded Abstracts, 4340–4346.
Dong, L., Li, Z. and Wang, D. [2013] Curvelet threshold denoising joint with empirical mode decomposition. 83rd
Annual International Meeting, SEG, Expanded Abstracts, 4412–4416.
Oropeza, V. and Sacchi, M. [2011] Simultaneous seismic data denoising and reconstruction via multichannel
singular spectrum analysis. Geophysics, 76, V25–V32.
76th EAGE Conference & Exhibition 2014
Amsterdam RAI, The Netherlands, 16-19 June 2014

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