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`Simultaneous source separation
`
`Simultaneous source separation using dithered sources
`Ian Moore*, Bill Dragoset, Tor Ommundsen, David Wilson, Camille Ward and Daniel Eke, WesternGeco
`
`Summary
`
`We describe a new algorithm that uses known firing times
`to separate data from two or more impulsive, simultaneous
`seismic sources. Synthetic and field data tests show that the
`algorithm works well, especially when the data are not
`spatially aliased. Aliasing effects can be reduced if
`assumptions, such as that the data are in some sense sparse,
`are made.
`
`Introduction
`
`In conventional data acquisition, the delay time between
`the firing of one source and the next is such that the energy
`from the previous source has decayed to an acceptable level
`before data associated with the following source arrives.
`This minimum delay time imposes constraints on the data
`acquisition rate. For marine data, the minimum delay time
`also implies a minimum inline shot interval, because the
`vessel’s minimum speed is limited.
`
`compared to marine data, but also pose extra problems. For
`example, land data allow for more flexible geometries and
`better source signature control. However, they are generally
`noisier than marine data, and the effect of statics could be
`significant.
`
`Separation Method
`
`The separation method can be applied to any number of
`sources, but is described here for the case of two, denoted
`S1 and S2. In a domain in which each trace corresponds to a
`different pair of sources, define d1 and d2 to be the data
`associated with S1 and S2, respectively, such that we record
`d=d1+d2. The elements of the data vectors correspond to
`different traces, and we assume the traces are in “S1-time”,
`i.e., they are aligned such that time zero corresponds to the
`firing time for S1.
`
`Acquisition of simultaneous source data, such that signals
`from two or more sources interfere for at least part of each
`record, clearly has enormous potential benefits in terms of
`acquisition efficiency and inline source sampling. For such
`data to be useful, however, it is necessary to develop
`processing algorithms to handle the source interference.
`The simplest methodology is to separate the energy
`associated with each source as a preprocessing step, and
`then to proceed with conventional processing. Beasley et al.
`(1998) describe one method by which this separation may
`be achieved when the sources are spatially separated.
`
`Another method for enabling or enhancing separability is to
`make
`the delay
`times between
`interfering sources
`incoherent (Lynn, et al., 1987). When traces are then
`collected into a domain that includes many firings of each
`source, and are aligned such that time zero corresponds to
`the firing time for a specific source, then signal from that
`source appears coherent while signal from the other sources
`appears incoherent. This allows the signals to be separated
`based on coherency. Stefani et al. (2007) have used random
`noise attenuation to separate the coherent signal from the
`apparently incoherent signal with some success.
`
`The following section describes a better separation method.
`The improvements come from the observation that the
`apparently
`incoherent signal
`is not mathematically
`incoherent, because the time delays that make it appear
`incoherent are known.
`
`The separation method also has applications for ocean-
`bottom cable and land data, and for seismic interference
`noise removal. These applications have extra opportunities
`
`We further assume that the data from each source are
`linearly related to unknown models, m1 and m2, i.e., d1 =
`A1m1 and d2 = D2A2m2. The known operators, Ai, map the
`models to the data spaces in Si-time, and the operator, D2,
`shifts the traces from S2-time to S1-time.
`
`We then have
`
`
`
`which is a simple, linear system that can be solved for m
`using, for example, the LSQR algorithm. Once m is known,
`the separated data are readily constructed using forward
`modeling. The residual, d-Am, containing energy that has
`not been associated with either source, is typically added
`onto both sets of separated data.
`
`The operators must be capable of modeling the majority of
`the recorded data, but must also be as constrained as
`possible to reduce leakage between sources. Most of our
`work so far has used linear Radon operators applied in the
`frequency domain, i.e.,
`
`
`
`wherein xs, ps, and t are vectors of the trace locations,
`slownesses, and
`timing delays,
`respectively. These
`operators only require that the data from each source are
`coherent and fall within the slowness ranges defined by ps.
`There is no requirement that the sources be spatially
`separated, though this may improve the separation because
`p1 and p2 may then be made significantly different. The
`power of the separation process comes from the apparent
`incoherency of the delays, t, which prevents data from one
`source being modeled using the operator for the other
`source.
`
`SEG Las Vegas 2008 Annual Meeting
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`Downloaded 09/18/15 to 64.124.209.76. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
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`PGS Exhibit 2025
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`

`
`Simultaneous source separation
`
`Conclusions
`
` A
`
` new approach to the shooting and subsequent separation
`of simultaneous impulsive sources has been derived and
`successfully tested. In its simplest form, the method does
`not handle spatially aliased signals properly. However,
`constraining
`the model,
`for example by assuming
`sparseness in some domain, can improve the results
`significantly.
`
`Acknowledgments
`
`The authors thank Chevron for permission to use the
`Petronius dataset for algorithm testing, and WesternGeco
`for publication permission.
`
`
`The method works very well on synthetic data (Figure 1),
`provided certain assumptions are met. The main limitation
`in the testing so far has been aliasing, which creates
`leakage of high-frequency, high-dip events between the
`sources (Figure 2). The use of high-resolution (sparse)
`Radon transforms (Moore and Kostov, 2002) mitigates, but
`does not eliminate, this limitation (Figure 3).
`
` A
`
` real data example is shown in Figure 4. The process
`worked quite well, though some steep dips were lost in the
`S1 component, and there is some leakage of steep dips from
`S2 to S1. The high-resolution Radon transform was not used
`for this example, and its use would probably improve the
`results in this respect.
`
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`Main Menu
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`
`Figure 1: Simple synthetic example of the separation process. The input data (pcs1) are the sum of the data related to sources 1 and 2 (p1s1 and
`p2s1, respectively) with time zero corresponding to the firing time for source 1. If static shifts are applied such that time zero becomes the firing
`time for source 2, then the energy related to source 2 becomes coherent (pcs2). The outputs from the separation process are the estimated data for
`each source (p1s1e and p2s1e) and the residual (pcs1r), which represents energy that has not been modeled. A measure of the separation error is
`obtained by subtracting p1s1e from p1s1. In this example, this error (p1s1r) is essentially zero, indicating almost perfect separation. Note that the
`horizontal axis represents the offset for the most appropriate source for that panel.
`
`
`
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`
`Simultaneous source separation
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`Figure 2: Aliased example. See the caption for Figure 1 for a description of the panels. The residual (pcs1r) is low, indicating that almost all of
`the data have been modeled. However, it is clear from the separated panels (p1s1e and p2s1e) and the error (p1s1r) that a significant amount of
`high-frequency energy has leaked between the sources.
`
`
`
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`
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`Figure 3: Same panels as in the bottom row of Figure 2, except using a high-resolution Radon transform. Note the improvements in the separated
`data (p1s1e and p2s2e) and in the error (p1s1r), at the expense of a slight increase in the residual (pcs1r).
`
`
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`Downloaded 09/18/15 to 64.124.209.76. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
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`PGS Exhibit 2025
`WesternGeco v. PGS (IPR2015-00309, 310, 311)
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`

`
`Simultaneous source separation
`
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`
`Figure 4: Common (near) offset plane from a real dataset, with time zero corresponding to the firing time of the source on the recording boat, S1.
`The dithered source, S2, is offset crossline by 3200 m and astern by 900 m. The graph shows the timing dither. The horizontal scale covers 250
`shots at 50-m separation (12.5 km). Left: before separation; Right: the separated S1 component. There is some leakage of high-frequency, steeply
`dipping energy between the sources, though it should be noted that the high-resolution transform was not used for this example.
`
`
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`EDITED REFERENCES
`Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2008
`SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for
`each paper will achieve a high degree of linking to cited sources that appear on the Web.
`
`
`REFERENCES
`Beasley, C. J., R. E. Chambers, and Z. Jiang, 1998, A new look at simultaneous sources: 68th Annual International Meeting,
`SEG, Expanded Abstracts, 133–136.
`Lynn, W., M. Doyle, K. Larner, and R. Marschall, 1987, Experimental investigation of interference from other seismic crews:
`Geophysics, 52, 1501–1524.
`Moore, I., and C. Kostov, 2002, Stable, efficient: High-resolution radon transforms: 64th Annual International Conference and
`Exhibition, EAGE, Extended Abstracts, F034.
`Stefani, J., G. Hampson, and E. F. Herkenhoff, 2007, Acquisition using simultaneous sources: 69th Annual International
`Conference and Exhibition, EAGE, Extended Abstracts, B006.
`
`
`
`
`SEG Las Vegas 2008 Annual Meeting
`
`2810
`
`2810
`
`Downloaded 09/18/15 to 64.124.209.76. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
`
`PGS Exhibit 2025
`WesternGeco v. PGS (IPR2015-00309, 310, 311)