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Arab J Geosci (2017) 10: 440
DOI 10.1007/s12517-017-3224-5
ORIGINAL PAPER
Denoising and improving the quality of seismic data using
combination of DBM filter and FX deconvolution
Majid Bagheri 1 & Mohammad Ali Riahi 1 & Hosein Hashemi 1
Received: 21 August 2016 / Accepted: 26 September 2017 / Published online: 11 October 2017
# Saudi Society for Geosciences 2017
Abstract Seismic data denoising, random noise attenuation
(RNA) and spike-like noise suppression, is a main consideration for improving the quality of records. RNA could increase
signal to noise ratio (S/N) to avoid misinterpretation of seismic
data. In this research, a novel method is created by using the
combination of frequency-offset deconvolution (FXD) and
decision-based median (DBM) filter for RNA from seismic
data. The method is applied in two main phases; FXD is focused to remove the Gaussian noise and DBM filter is focused
to attenuate the impulsive noise and spikes. To implement and
verify the method, three types of data are used: two synthetic
models (a model with linear events and a model with hyperbolic events) and an observed seismic section. The ability of
the proposed method (FXD-DBM) in comparison of applying
each in seismic RNA application is proven. The noise level is
reduced obviously, and hence, the S/N of all examined seismic
records is increased considerably after denoising by the combination of FX deconvolution and DBM filter. About the real
seismic section, suppressing random noise and spikes show up
improving the seismic reflector continuity and hence enhancing the interpretability of data. Moreover, some masked events
by random noise are clarified in different parts of data after
denoising using the planned method.
Keywords FX deconvolution . DBM filter . Random noise
attenuation . Seismic data . Signal to noise ratio
* Majid Bagheri
majidbagheri@ut.ac.ir
1
Institute of Geophysics, University of Tehran, PO Box 14115-6466,
Tehran, Iran
Introduction
Impulsive and seismic random noise elimination is always an
important and a challenging field in seismic processing to
enhance the interpretability of data. Random and impulse
noise could be generated by unspecific sources and could be
recorded during data acquisition, so it is hard to predict and
reduce the noise from seismic data. To achieve the goal, till
now, many strategies have been introduced by different researchers (Spitz 1991; Abma and Claerbout 1995; Liu and
Liu 2006; Cai et al. 2008; Bekara and Baan 2007, 2009;
Sacchi and Naghizadeh 2009). The main common consideration of all is to eliminate random and spike noise while preserving the signal.
Some other well-known examples of enormous researches
for RNA consist of conventional median filter which is a simple and strong filter (Bednar 1983) that is broadly used as an
effective filter. Deconvolution as an old technique is introduced by different researchers (i.e., Dimri 1992) and is improved for inverting and denoising data; for instance, a new
filter is recently developed for inverting geophysical models
(Ganguli et al. 2016). Curvelet transform appertains to a family of multiscale and also multidirectional data extensions that
capable to attenuate incoherent noise from seismic records
with low level of S/N (Starck et al. 2002). The curvelet domain is strongly appropriate for denoising since the incoherent
energy is spreading almost equally between all curvelet coefficients whereas the coherent seismic energy maps to a relatively small number of significant curvelet coefficients.
F-X prediction is well known and is the most common
techniques in seismic processing to suppress noise (Spitz
and Deschizeaux 1994; Abma and Claerbout 1995). In this
method, the prediction filter is applied in a window and predicts a dip for an example, and tries to attenuate all other dips
in that window. For impulsive seismic noise attenuation, a
440 Page 2 of 8
Arab J Geosci (2017) 10: 440
time-varying median filter is proposed by Liu et al. (2009). To
enhance removing spikes, a decision method (DM) is planned
which is capable to identify noise preceding to use of the
median filter (Arastehfar et al. 2013). DM is simple and effective to reduce the impulsive noise level while preserving the
signal samples.
Application mainly consists of two stages, a synthetic study
containing two models, and a real data seismic section.
Synthetic data helps to evaluate the noise suppression using
frequency-offset deconvolution (FXD) and decision-based
median (DBM) filter and indicate the advantages of the
planned method. Incoherent noise in the real seismic section
that degrades the quality of the data is attenuated considerably
using the proposed method.
not. Hence, from Eq. 2, random noised can be estimated. A
simple way to estimate white noise is possible using Eq. 3 by
estimation error filter. However, for a problem if Eq. 3 is not
satisfied, for instance when the signal not predicted well, Eq.2
will not be able to estimate random noise.
On the other words, using the Fourier transform, a prediction filter is calculated for the spatial series created at each
frequency. In general, the calculated filter can be applied in
two stages in order to separate predictable signal from unpredictable noise in each frequency slice: first, finding the filter h
by solving Eq. (1), and second, applying the filter to each
frequency slice. Each filter is applied forward and then reversed in space, and the results are averaged to maintain a
symmetrical application similar to the T-X prediction case
(Abma and Claerbout 1995).
The method
DBM filter
FX deconvolution
The conventional median filter is based on a smoothing process. After positioning traces with their true dip, median filter
replaces the sample in the center of the search window by the
median value of all samples within this window (Tukey 1977).
Having its drawback, median filter reduces the random noise
and spikes significantly. In general, the filter works in offset
(X) direction, and the running window slides down in the time
axis.
For data with high level of noise, conventional median
filter will be smearing the details and edges and random noise
could not be removed simply. To solve the problem, this strategy should be used that noisy samples initially be recognized
and then median filtering be performed, whereas other samples reserved unaffected (Arastehfar et al. 2013). In other
words, this strategy which called DBM method is planning a
median operator where it will be applied just on noisy samples
and the identity filter will be performed on the noise-free
samples.
In this method, the seismic record is considered as an image
(S) which is supposed to be a vector (R) made by the rows of
the image. In this way, the column vector R is constructed with
the rows of matrix S. It should be remembered that the first
and the last row along with the first and the last column must
be ignored in this method. So, an image Sa × b of size a × b
becomes a vector RN × 1 of size N × 1 in the vector outline,
where N = (a − 2) × (b − 2). Wx(y) is defined as a processing
window of size x × x, where x is an odd integer and y is the
central pixel within the window (Kulkarni and Bhaskar 2013).
In DM technique, one can detect a noisy pixels by comparing each pixel in the image with its neighboring pixels. Two
successive pixels in R are compared to see whether the difference if greater than the threshold d which is a factor related to
the noise level of data and the ‘Step’ parameter. The parameter
‘Step’ is also a pre-defined value, added to d depending on the
The method was introduced by Canales (1984) firstly and is
developed later by Gulunay (1986). The FX deconvolution
prediction process depends on the form of linear events in
frequency versus space direction. Linear events in the t–x
domain apparent is a superposition of periodic events in the
f–x domain where they could be predicted simply by an autoregression filter in this domain.
The F-X prediction filter for 2D data, A(t,n), can be
expressed as follows:
m
Að f ; nÞ ¼ ∑ hk Að f ; n−k Þ
;
n ¼ 1; 2; …; N
ð1Þ
k¼1
if each data point can be expressed as a linear combination
of previous ones. Here, A is a frequency slice with spatial
sequential index n and h is a filter operator with the length m.
The strategy of FX focuses to predict noise, and the
denoised data is the result of subtracting the noise from the
input noisy data (Sacchi and Kuehl 2001). To formulate the
method, this assumption should be considered that A = S + W,
where S is the clean signal and W is the added white noise to
signal, hence:
m
m
k¼0
k¼0
∑ pk An−k ¼ ∑ pk W n−k
ð2Þ
Here, p is the filter estimation error with p(0) = 1 and p(1:m) = − h(1:m). The Eq. 2 needs the:
m
∑ hk S ð f ; n−k Þ ¼ 0
ð3Þ
k¼1
The prediction error of the pure signal is white because it is
predictable, but about random noise as unpredictable event is
Arab J Geosci (2017) 10: 440
condition |ri – 1 − ri| > d, where |·| indicates the absolute
operator and ri denotes the ith component of R.
The chance to identify a sample as noisy is approximately
impossible when the level of noise is low. By rising d, it will
be getting harder to consider a sample as noisy when the
previous one is detected as noisy sample. Otherwise, the parameter d is changed to the pre-defined value of threshold. It
should be noted that the ‘Step’ is a main factor in exact detection of noisy samples and in protecting edges.
So, this filter is an adaptive median filter which determines
the affected noisy pixels of an image. Based on this procedure,
when the difference between two successive pixels is greater
than the threshold d, the pixel is considered as a noisy pixel
which makes it necessary to apply the median operation. It
incomes that the noisy sample will be replaced by the median
value of the samples in its surrounding while all the other
samples leave unaffected. The sample is not noisy and the
identity filter will be applied when the condition |ri – 1 − ri| > d
is not satisfied.
The proposed method is planned using combination of FX
deconvolution and DBM filter. In other words, the method is
applied into two main phases. FXD is focused to remove the
white noise using prediction strategy, and DBM filter is focused to attenuate the impulsive (spike-like) noise and spikes
using decision-based strategy.
Application
Page 3 of 8 440
Fig. 2. The close-up confirms the ability of combination of
FXD and DBM filter for random noise elimination, and the
noise level is reduced more using this trick.
Synthetic model 2
The second synthetic model consisting of four hyperbola
events is created to check the ability of the proposed method
face to hyperbola events (Fig. 3a) with random noise. For this
model, a high level of random noise is added to noise-free data
to create the noisy data, as shown in Fig. 3b. Figure 3c indicates the result of RNA from the second synthetic model. It is
clear that S/N ratio is increased after FX deconvolution but
again, some random noise is kept. If the DBM filter implemented as the second step of the presented method is applied,
the result of Fig. 3d is obtained. To implement the method, the
window size is fixed on 5 × 5, the threshold d is set to 90, and
the parameter ‘Step’ is set to 5. Comparing Figs. 3c and 3d
clarifies the power of the planned method for RNA by improving the S/N ratio of the second synthetic model.
For investigating the result for this model better, again, a
zoom of a part of this model is selected and is shown in Fig. 4.
The close-up could confirm the positive effect of the presented
method for RNA from this model too. Comparing Figs. 4b
and 4c shows that using the combination of FXD and DBM,
random noise is removed significantly and S/N ratio is
increased.
Synthetic model 1
Field data example
The first synthetic data consists of four linear events with
different dips to evaluate the proposed method to linear events
containing random noise. As shown in Fig. 1a, a Ricker wavelet is used to generate this model of 100 traces. Noisy synthetic
data (Fig. 1b) is created by adding random noise to noise-free
data. The random noise is white Gaussian noise type with
SNR value of 4, which the scalar SNR specifies the signal to
noise ratio per sample. Figure 1b displays where linear events
are covered by adding random noise and thereafter, the signal
to noise ratio is decreased. In Fig. 1c, the result of RNA using
FX deconvolution is shown; FXD succeeded to decrease the
noise level of data, but there is some remained noise. To diminish the remained random noise, the DBM filter is applied
with the window size of 5 × 5, the threshold d of 80, and the
parameter ‘Step’ of 6. After applying DBM filter in the second
step of noise attenuation, the noise level is reduced again and
the S/N ratio is improved greatly (Fig. 1d). Comparing
Figs. 1c and 1d indicates that the combination of FXD and
DBM filter is more successful for RNA compare to each one
of the methods.
To validate the outcomes better, a close-up of a part of
synthetic model 1 before and after denoising is shown in
A real seismic section is selected to further study the performance of the suggested method. The real data is related to
Marun oil field, located in the Khuzestan Province of Iran,
and is the second-largest oil field in Iran. It consists of two
oil reservoirs and one gas reservoir named Asmari, Bangestan,
and Khami, respectively. The Bangestan oil reservoir is located deeper than the Asmari oil reservoir and has been producing sour oil. This field is an anticline with NW-SE trend. The
dimensions of Marun oil field at the Asmari oil reservoir horizon are 67 and 7 km in length and width, respectively. The
seismic section with 4-ms time sampling interval, and trace
spacing of 50 m is selected from this oil field (see Fig. 5a).
From Fig. 5a, random noise is evident in most parts of the
section and all events are masked with random noise. The
denoised seismic section using FX deconvolution is shown
in Fig. 5b, where high level of noise is eliminated. Using
DBM filter in the second step of the proposed method, some
remained impulse noise is attenuated (see Fig. 5c). Calculating
the difference between Figs. 5a and 5c results the eliminated
noise (Fig. 5d). The difference confirms the suppression of
high level of noise from data and the performance of presented
method for RNA.
440 Page 4 of 8
Arab J Geosci (2017) 10: 440
Fig. 1 a Noise-free synthetic data consist of four linear events with
deferent dips. b Noisy synthetic data and linear events are covered after
adding noise. c Synthetic data after denoising using FXD. d Denoised
synthetic data using combination of FXD and DBM. Comparing c and d
indicates that the combination of FXD and DBM filter is more successful
in RNA
To investigate the results better, a zoom of the section
before and after denoising using FXD and the combination
of FXD and DBM filter is shown in Fig. 6. Comparing
Figs. 6a and 6c clarifies the power of the proposed method
Fig. 2 A close-up of a part of synthetic model 1 from Fig. 1. a Noisy data. b Denoised data using FXD. c Denoised data using FXD + DBM filter.
Comparing b and c shows the power of planned method for RNA from data
Arab J Geosci (2017) 10: 440
Page 5 of 8 440
Fig. 3 a Noise-free synthetic data consists of four hyperbola events. b
Noisy synthetic and hyperbola events are masked by adding random
noise. c Synthetic data after denoising using FXD. d Denoised synthetic
data by combination of FXD and DBM. Comparing c and d clarifies the
power of the planned method for RNA and improving S/N ratio
in removing random noise and an obvious increase in signal to noise ratio. The final result gives a much clearer
lateral continuity than original data and hence improving
the interpretability of data.
consider a sample as noisy when the previous one is detected as noisy sample. Otherwise, the parameter d is
changed to the pre-defined value of threshold. Also, it
should be noted that the ‘Step’ is a main factor in exact
detection of noisy samples and in protecting edges. DBM
filtering can lead to a well removal of spike-like noise by
increasing the window size (Arce 2005). However, this
may affect the signal and distort it during filtering.
DBM filtering is an attractive method because its application is much simpler and it needs less computational time
in comparison to FX deconvolution. However, it is not able
to handle complicated seismic events such as conflicting
dips versus FX deconvolution can deal with conflicting
dips and discontinuous seismic events (Sacchi 1999).
Clearly, the combination of FX deconvolution and DBM
filtering creates more powerful method to suppress white
and impulsive noise better. Combination strategy may
causes too smoothed seismic images; however, covered
seismic will be largely preserved.
Discussion
The FX deconvolution with this assumption that seismic
events are linearly continuous and noise is random can be
applied. Therefore, the F-X prediction should be performed
to small windows to guarantee that seismic events are almost linear, and thereafter, the Fourier transform will be
operated within each window. This process proved effective in reducing much of the white noise; however, some
leftover noise may be still not fully attenuated.
For DBM implementation, the chance to identify a sample as noisy is approximately impossible when the level of
noise is low. By rising d, it will be getting harder to
440 Page 6 of 8
Arab J Geosci (2017) 10: 440
Fig. 4 A zoom of a part of second synthetic model from Fig. 3. a Noisy data. b Denoised data using FXD. c Denoised data using FXD + DBM filter.
Comparing b and c shows that using the combination of FXD and DBM, random noise is removed significantly and S/N ratio is increased
Fig. 5 a A real seismic section. Random noise is observable in most parts
of the data and events are masked with them. b The section after
denoising using FXD. c The section after denoising using FXD +
DBM, random noise is suppressed significantly. d With the difference
between a and c, result shows that proposed method is powerful for RNA
Arab J Geosci (2017) 10: 440
Page 7 of 8 440
Fig. 6 a A close-up of a part of the section. b Denoised data using FXD.
c Denoised data using FXD + DBM filter. Comparing b and c clarifies
that random noise is attenuated and the S/N is improved considerably.
The lateral continuity of events is increased, and hence, the interpretability of data is enhanced significantly
Conclusion
presence of strongly curved events. The final result gives a
much clearer lateral continuity than original data and hence
enhancing the interpretability of data. Moreover, some
masked events by random noise were clarified in different
parts of the data after denoising with high signal-protection
ability.
Generally, the picked results showed that random and impulsive noise in seismic data can be effectively attenuated by
the combination of FXD and DBM filter. Results of both
synthetic and field seismic data have demonstrated reasonable
noise attenuation while the signal was preserved during
denoising.
The original seismic data must be denoised from random
noise in order to acquire high-quality seismic data to form a
reliable basis for subsequent geological interpretation. A new
approach was planned here by using the combination of FX
deconvolution and DBM filter to reduce the random noise and
spikes from seismic data. The proposed method is divided into
two main steps; the first step uses FX deconvolution to eliminate the Gaussian random noise. In the second step, other
noise type including impulsive noise will be removed using
DBM filter. FX deconvolution automatically calculates the
signal with spatial variations in dip or amplitude using f-x
regularized auto-regression. To overcome the supposition of
linearity of the signal in the f-x domain prediction technique,
the f-x domain prediction for non-linear events uses
windowing tricks. The DBM filter is an adaptive strategy that
just operates the median filter to noisy samples and not affects
healthy seismic samples. This makes the DBM filter an appropriate choice for detecting and suppressing impulsive noise.
To evaluate the method, two types of synthetic model were
created, and also, a real seismic section was used. The results
of the presented method on the different examined seismic
data (synthetic data include linear events, synthetic data include hyperbola events, a real seismic section) identified the
method as really powerful for RNA. About synthetic models,
the noise level was reduced obviously; also, the S/N of data
was improved considerably after denoising using the combination of FX deconvolution and DBM filter. About the real
seismic section, experiment showed that the proposed strategy
is really successful for random noise attenuation in the
Acknowledgments University of Tehran would be acknowledged for
financial support of this work under the research grant number of 28322/
1/01.
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