Simultaneous Sources Separation via Multi-Directional Vector-Median Filter
`Shoudong Huo, Yi Luo* & Panos Kelamis, Dhahran, Saudi Aramco
`
`
`
`Summary
`
`to as
`referred
`technology,
`The seismic acquisition
`“simultaneous sources”, records two or more shots (ignited
`with random delay time) in a single shot gather. Despite the
`fact that the recorded data is blended among different shot
`gathers, conventional processing procedures could still
`produce acceptable images for interpretation. However,
`separating the blended data into single shot gathers is still
`desirable for further improving the seismic image quality.
`This paper introduces a new Multi-Directional Vector-
`Median Filter (MD-VMF) to separate the blended seismic
`shot gathers. The vector median filter extends
`the
`conventional one from scalars to vectors. Moreover, it is
`applied in multiple directions centered at any sample point
`in a seismic (e.g., common receiver or CMP) gather and the
`filtered result in the most coherent direction is selected as
`the output. Tests on both synthetic and real marine seismic
`data
`simulating blended
`acquisition
`confirm
`the
`effectiveness of our proposed MD-VMF approach.
`
`Introduction
`
`The concept of simultaneous sources acquisition can
`significantly enhance field acquisition efficiency and
`improve the quality of seismic data. It is not new for
`vibroseis acquisition. The study on simultaneous shooting
`using vibratory sources has lasted for around two decades
`and various methods are proposed. For a complete review
`see Bagaini (2006). The methods commonly employ
`specially encoded source sweeps, which make it possible to
`separate the interfering source responses.
`
`In marine seismic, Lynn et al. (1987) described occasional
`interference from a second source, also called crosstalk,
`which was treated as noise and suppressed by stacking.
`Beasley et al. (1998) proposed to adopt simultaneous
`sources in marine acquisition to improve the efficiency.
`They suggested placing the air guns symmetrically off the
`ends of a 2D marine cable and firing the sources
`simultaneously, and used only a geometry filter in CMP
`domain to separate the overlapping source responses.
`Inspired by the encoded vibroseis acquisition, Ikelle (2007)
`introduced coding and decoding into marine cases.
`
`Stefani et al. (2007) and Hampson et al. (2008) applied a
`small random delay time onto the second source. As a
`consequence, the response of one source appears random in
`some special geometries such as the common-receiver,
`common-offset and CMP domain. Stacking the blended
`seismic data without any further processing produces
`acceptable results as stacking can effectively suppress
`random energy. However additional efforts towards source
`separation have been proposed. Moore et al. (2008)
`
`technique based on conventional Radon
`adopted a
`transforms while Akerberg et al. (2008) used sparse Radon
`transforms for the source separation. Spitz et al. (2008)
`proposed a prediction-subtraction approach which first
`estimates the primary wavefield of the second source and
`then subtracts it from the total wavefield via a PEF-based
`adaptive subtraction.
`
`Berkhout et al. (2008) extended the simultaneous shooting
`method to the concept of blended acquisition, which adopts
`continuous recording and requires neither randomized
`delay times nor encoded source signatures. In their
`approach, two processing routes are suggested: (1) process
`the blended records, and (2) separate the sources and apply
`conventional processing.
`
`In this paper, we capitalize on the randomness in the
`acquisition and propose a new approach for the separation.
`First, we apply a multi-directional vector-median filter
`(MD-VMF) in the CMP domain to separate the randomly
`located energy of the second source from the coherent one.
`Optionally, we may then employ a multi-channel Wiener
`filter to match the filtering results with the original input.
`The strategy has been tested by simulation with both
`synthetic and real marine data and proved to be effective.
`
`Multi-Directional Vector Median Filter
`
`Median filter is simple and effective in suppressing spike
`noises, especially in non-stationary signal processing.
`Bednar (1983) discussed some possible applications of
`median
`filtering
`in
`seismic prospecting,
`such as
`deconvolution, pulse estimation and statistical editing.
`Duncan and Beresford (1995) introduced a 2D median f-k
`filter which uses the coefficients of a truncated impulse
`response of an f-k filter as the weight coefficients for the
`weighted median process. Wang (2000) separated signal
`from noise by using median correlative filtering. Zhang and
`Ulrych (2003) used a hyperbolic median filter to suppress
`multiples, while Liu et al. (2006) adopted the 2D
`multistage median filter to suppress the random noise in
`land seismic.
`
`Astola et al. (1990) expanded the median filter for the
`application of vector-valued signals, such as color images,
`and introduced vector-median filtering. Liu et al. (2009)
`proposed to apply vector-median filter in Geophysics
`where vector-valued functions are often used. Among them,
`the seismic traces have its special characteristics, which
`behave more like vector elements rather than pixels, e.g.
`the neighboring traces are similar in a CMP gather.
`Therefore, the vector-median filter seems more suitable
`than conventional median filter in seismic data processing.
`
`
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`

`
`
`Simultaneous Sources Separation via Multi-Directional Vector-Median Filter
`
`
`In our approach, the vector is defined as a sliding window
`in the time direction. In each vector, the objective sample is
`located at the center of the window. The vector-median
`filter is then applied on a group of neighboring vectors with
`the same time window, and the objective vector is located
`at the center of the group.
`
`Both median and vector-median filters are designed to be
`applied along a straight line. In seismic data, they are
`normally applied along time slices. This requires all the
`events to be flat. However, even with a proper NMO, we
`cannot obtain perfectly flattened events in the CMP domain.
`Therefore, we propose an approach which deploys a vector-
`median filter along lines with different dips to relax the
`flattening requirement. Following Liu et al. (2009), we
`formulate MD-VMF using the L1 norm:
`
`
`r
`X
`vm
`:j∀
`
`=
`
`,1
`
`r
` ( |) ipX
`
`
`i
`r
`
`pX )(
`i
`
`p
`(
`{)
`∈
`N
`r
`∑
`X
`
`i
`
`1
`=
`
`vm
`
`
`
`p)(
`
`−
`
`,
`
`}, N
`
`L
`N
`r
`∑
`
`pX )(
`≤
`j
`
`1
`
`i
`
`1
`=
`
`−
`
`r
`
`pX )(
`i
`
`1
`
` (1)
`
`
`.
`
`where
`
`j
`
`,
`,1 L=
`
`N
`
`; p is the dip and
`
`p
`
`=
`
`p
`
`,
`
`,
`L
`
`p
`
`max
`
`min
`
` A
`
`where, yk stands for the value of the k-th sample along a
`trajectory through the t-x gather, and W is a spatial window
`containing a certain number of samples along the trajectory.
`
`From equation (2), we can see that semblance function
`yields a value (between 0 and 1) for each sample. The
`semblance amplitude for the sample inside a coherent
`window is high and vice versa. The semblance function can
`therefore be adopted as a weighting function for the MD-
`VMF. The slope with the biggest semblance is selected as
`the final output after MD-VMF. In this way, amplitudes of
`more coherent trajectories can be better preserved while
`aliasing caused by non-coherent events is suppressed.
`
`To prove the advantage of the vector median filter, we
`conduct an experiment to compare it with conventional
`median filtering on simulated blended marine gathers.
`Figure 1 shows the comparison between the conventional
`median filter and MD-VMF. Figure 1a depicts a CMP
`gather sorted from blended raw shot gathers. All the events
`from the first source are coherent and the energy from the
`second source appears random. Figure 1b shows the ideal
`non-blended gather. Figure 1c is the gather after the
`application of conventional median filter while Figure 1d
`after MD-VMF. We zoom in the area defined by the white
`frame to provide a clear demonstration. By comparing
`Figures 1b, 1c and 1d, we can see that conventional median
`filter can eliminate random energy but severely smears
`signal information by smoothing certain discontinuous
`events. It also damages some data characteristics contained
`in the gathers, e.g. the amplitude and phase. The MD-VMF
`approach appears to better preserve the signal and the data
`characteristics.
`
`
`
` series of filtering results are obtained as MD-VMF
`produces one filtering result for each single dip. A proper
`result is identified by adopting semblance as the criteria for
`selection. The semblance function has been widely applied
`in detecting coherent events across an array (Taner and
`Koehler, 1969), and it is defined as
`N
`∑ ∑
`
` (2)
`
`2
`
`⎟⎠⎞
`
`k
`
`y
`
`k
`
`=
`
`⎜⎝⎛
`
`1
`N
`
`∑ ∑
`
`W
`
`k
`
`=
`
`1
`
`y
`
`2
`k
`
`S
`
`=
`
`W
`N
`
`
` (a) (b) (c) (d) (e)
`Figure 1. Comparison between conventional median filter, MD-VMF and Wiener filter on a sample CMP gather. (a) Input blended CMP gather,
`(b) Ideal non-blended data, (c) After median filter, (d) After MD-VMF, and (e) After MD-VMF and Wiener filter. The randomly located
`crosstalk from the second source has been removed by all three approaches. Median filtering damages the signal by smearing the data, MD-VMF
`better preserves signal and avoids smearing. Subsequent Wiener filtering offers additional improvements by adaptively matching the input data.
`
`
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`

`
`
`Simultaneous Sources Separation via Multi-Directional Vector-Median Filter
`
`
`Figure 2 depicts the comparison in the amplitude spectrum
`domain. It is clear that the spectrum of MD-VMF result
`(Figure 2c) appears more similar to the ideal output (Figure
`2a) and has less high-frequency aliases comparing to the
`result of conventional median filter (Figure 2b).
`
`
`aliasing appearing in Figure 2c is successfully suppressed
`and the spectrum looks quite similar to the ideal output.
`
`Examples
`
`Our approach is first tested using the synthetic Pluto model
`dataset. We simulate simultaneous acquisition by blending
`two adjacent shot gathers with a random time-delay into
`one new input gather.
`
`Figure 3 demonstrates the comparison between MD-VMF
`and the sparse Radon transform approaches. Figures 3d and
`3a show the data before and after blending. We can see that
`stacking does well in suppressing the crosstalk, yet some
`energy still exists and contaminates the key reflections.
`Figure 3b exhibits the result of MD-VMF. Figure 3c shows
`the difference between the blended input and the MD-VMF
`filtering result. Note that our method eliminates most of the
`crosstalk while minimizing signal leakage. For comparison,
`the Sparse Radon Transform approach is applied on the
`same dataset. Figure 3e shows the separation result while
`the difference can be seen in Figure 3f. These results
`clearly confirm that the sparse Radon approach can
`suppress the crosstalk but cannot avoid the signal leakage.
`
`tested by
`is also
`The MD-VMF source separation
`simulation on a 2D dataset from the Red Sea. Figure 4a
`shows the stack profile of the data after blending. The
`second source crosstalk can be seen as strong dipping
`events. Figure 4b exhibits the stack after application of
`MD-VMF followed by Wiener filtering. Note that the
`crosstalk is now well eliminated while the coherent signal
`(reflection events) is well preserved. The difference section,
`shown in Figure 4c, also demonstrates the performance of
`our proposed de-blending methodology.
`
`Conclusions
`
`In this paper we demonstrate how the MD-VMF approach
`can successfully eliminate crosstalk inherent in data
`acquired by simultaneous sources. It employs seismic
`traces as vectors and thus improves on conventional median
`filtering. Moreover, it searches multiple directions for the
`optimum output. We further improve the result by applying
`an adaptive Wiener filter to suppress aliased frequencies.
`The results are considered satisfactory when seismic
`images are retained without introducing aliasing while
`honoring input signal levels. Promising results have been
`achieved using synthetic and simulated field data. We are
`thus encouraged to begin field experiments in both land and
`marine environments utilizing
`simultaneous
`sources
`acquisition.
`
`Acknowledgements
`
`The authors thank Saudi Aramco for permission to publish
`this work. We would also like to thank our colleagues, R.
`Burnstad, M. Broadhead and T. Keho for their enlightening
`discussions and suggestions.
`
` (a) (b)
`
`
`
`
`
`
`
` (c) (d)
`Figure 2. Amplitude spectrum comparison on a sample CMP
`gather. (a) Ideal output CMP gather, (b) After median filter, (c)
`After MD-VMF, and (d) After MD-VMF and Wiener filter.
`Aliasing is pointed out by the arrows. MD-VMF better matches the
`ideal output than median filtering, while Wiener filtering improves
`on MD-VMF by suppressing frequency aliasing.
`
`Wiener filter
`
`As a non-linear filter, the MD-VMF cannot completely
`avoid aliasing, as can be observed
`in Figure 2c.
`Furthermore, the waveform may sometimes be blurred
`during the filtering. As an option, we employ a Wiener
`filter to tackle both issues after MD-VMF. In our strategy,
`the MD-VMF result is treated as a model which is adapted
`to match the input data. The matching result is then used as
`the final output.
`
`The Wiener filter is a shaping filter which uses the least-
`squares criterion to design operators so as to minimize the
`power in a selected window for the desired output. The
`design error of the shaping filter, which shapes a single or
`group of model traces into the original data trace, is
`considered to have minimum energy. Once the model
`traces are obtained by using MD-VMF on input blended
`traces, the matching between the model traces and the
`original traces is carried out by a single or multi-channel
`Wiener filter within a sliding window.
`
`Figure 1e depicts the effects of Wiener filter on the sample
`CMP gather after MD-VMF. The Wiener filter helps to
`recover some coherent energy and preserves the waveform.
`Therefore, the result looks more similar to the ideal one
`(compare Figure 1b with 1e). The effects of Wiener filter
`can also be seen in the amplitude spectrum domain. The
`
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`

`
`
`
`
`Simultaneous Sources Separation via Multi-Directional Vector-Median Filter
`
`
`
` (a) (b) (c)
`
`
`
`
` (d) (e) (f)
`Figure 3. Comparison between MD-VMF and the sparse Radon transform approaches. (a) Stack of input blended sources data, (b) Stack of MD-
`VMF filtering result, (c) Differences between (a) and (b), (d) Stack of ideal output, (e) Stack of the sparse Radon transform result, (f) Difference
`between (a) and (e). Both approaches succeed in eliminating crosstalk of the second source. Note the leakage of signal energy after separation via
`sparse Radon (f), while (c) clearly indicates that the application of MD-VMF better preserves signal and minimizes leakage.
`
`
`
`
` (a) (b) (c)
`Figure 4. Application of MD-VMF and Wiener filtering on a simulated simultaneous sources dataset from Red Sea. (a) Stack of input blended
`sources, (b) Stack after MD-VMF, and (c) Difference between (a) and (b). Note the crosstalk suppression and the significant reduction of signal
`leakage.
`
`
`
`
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`
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`each paper will achieve a high degree of linking to cited sources that appear on the Web.
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`
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`
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