SPECIAL SECTION: S e i s m i c a c q u i s i t i o n
`
`Changing the mindset in seismic data acquisition
`
`A.J. "GUUS" BERKHOUT, Delft University of Technology, the Netherlands
`
`Seismic acquisition surveys are designed such that the time
`
`intervals between shots are suffi ciently large to avoid the
`tail of the previous source response interfering with the next
`one (zero overlap in time). To economize on survey time
`and processing eff ort, the current compromise is to keep
`the number of shots to some acceptable minimum. Th e
`result is that in current practice the source domain is poorly
`sampled.
`It is proposed to abandon the condition of nonoverlap-
`ping shot records. Instead, a plea is made to move to densely
`sampled and wide-azimuth source distributions with relative-
`ly small time intervals between consecutive shots (“blended
`acquisition”). Th e underlying rationale is that interpolating
`missing shot records, meaning generating data that have not
`been recorded, is much harder than separating the data of
`overlapping shot records. In other words, removing interfer-
`ence is preferred to removing aliasing.
`A theoretical framework is presented that enables the de-
`sign of blended 3D seismic surveys. Th is framework also pro-
`vides directions about how to process blended data. Th e con-
`cept of blending has signifi cant implications for both quality
`and economics.
`
`Background
`In land seismics, the concept of interfering shot records is
`known from vibroseis acquisition. Th e duration of a vibro-
`seis survey is largely determined by the long signal sweeps of
`the vibroseis source (typically 10–20 s). Th ese long sweeps
`are required to obtain the necessary signal-to-noise ratio. It
`makes vibroseis surveys time-consuming. To reduce survey
`time, methods have been developed to deploy various vi-
`broseis groups simultaneously. Th ese methods are based on
`transmitting specially encoded source sweeps. Codes have
`been designed such that the interfering source responses
`can be separated in a preprocessing step. Th e simultaneous
`vibroseis recording methods are known as slip-sweep, fl ip-
`fl op, orthogonal sweeps, phase rotation, cascading, upsweep-
`downsweep, etc. Many oil companies and seismic contrac-
`tors have their own patented methods. An overview of the
`various simultaneous vibroseis sweep methods is given by
`Bagaini (2006).
`Beasley et al. (1998) propose to fi re impulsive seismic
`sources at diff erent locations at the same time (“simultaneous
`source fi ring”). Th ey illustrate this concept with two sources
`off the ends of a marine cable and show with a 2D fi eld ex-
`ample that CMP processing already provides a good separa-
`tion between the overlapping source responses. Stefani et al.
`(2007) elaborate on this concept and introduce small random
`time delays as well (“near simultaneous source fi ring”). Th ey
`demonstrate on 3D fi eld data that the interference between
`the overlapping shot records of two spatially well-separated
`sources can be eff ectively suppressed by PSTM. Ikelle (2007)
`
`924 The Leading Edge July 2008
`
`Figure 1. Up- and downgoing waves at and near the surface. Detector
`matrix D (zd,z0) contains both the properties of the detector arrays at zd
`and the infl uence of the stress-free surface at z0. Wavefi eld operators W
`represent propagation between zd and z0; wavefi eld operator R∩ rep-
`resents refl ection at the lower side of z0. For a fl at and stress-free surface
`R∩ = -I , where I equals the unity matrix.
`
`discusses the coding and decoding of seismic data using si-
`multaneous sources on land or at sea. He shows that the
`response of four simultaneous shots, being fi red four times
`with diff erent amplitudes, defi nes a fully determined system
`that can be decomposed into the responses of the individual
`shots. To overcome being underdetermined, Ikelle suggests
`the use of higher-order statistics, sparseness constraints and
`prior knowledge.
`In this paper, the method of (near) simultaneous shoot-
`ing is extended to the system concept of blended acquisition,
`where blended acquisition stands for continuous recording
`
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`

`
`S e i s m i c a c q u i s i t i o n
`
`of multisource responses that overlap
`in time. Th e multisource properties
`are characterized by the combination
`of off sets, azimuths, and delay times.
`Encoded source signatures are not re-
`quired and delay times may be large
`(up to seconds). Th e use of relatively
`large delay times makes blended ac-
`quisition diff erent from (near) simul-
`taneous shooting. It brings interfer-
`ence under user control. Note that for
`very large delay times, say larger than
`20 s, blended acquisition equals tradi-
`tional acquisition (no interference). A
`theoretical framework is proposed that
`enables the design of blended seismic
`acquisition with a focus on quality and
`economics. In addition, the proposed
`framework allows the formulation of a
`forward model for blended 3D seismic
`data. Th is model is used to propose dif-
`ferent options for preprocessing blend-
`ed data sets.
`
`Figure 2. (a) Vector-matrix equation for synthesizing an areal source. From the physics point
`of view, this equation quantifi es a weighted addition of the single sources as used in the fi eld.
`(b) Vector matrix equation for synthesizing an areal source response. From the physics point of
`view, this equation quantifi es a weighted addition of the shot records as measured in the fi eld.
`
`Operator presentation of seismic
`data
`Th e large amount of discrete measure-
`ments of a seismic survey can be con-
`veniently arranged with the aid of the
`so-called data matrix, P, each column
`representing a shot record and each
`row representing a receiver gather.
`Hence, matrix element Pij represents
`a single trace that is related to source
`position j and detector position i. In the temporal frequency
`domain Pij is a complex-valued scalar, representing one fre-
`quency component of a seismic trace. Data matrix P can be
`directly used for the formulation of wave-theory-based nu-
`merical algorithms in seismic processing such as multiple
`removal and prestack migration. After removal of the waves
`that have travelled along the surface, the data matrix can be
`expressed in terms of propagation and refl ection operators
`(feedback model).
`If matrix X0 (z0, z0)represents the multidimensional trans-
`fer function of the subsurface (z>z0), then each element of
`X0 (z0, z0) contains the impulse response that was generated
`by a unit dipole source at z0 and that was detected by a unit
`sensor at z0. Th e subscript “0” in X0 indicates that the surface
`is a refl ection-free boundary, meaning that the seismic signal
`has made only one round-trip through the subsurface (from
`z0 to z0). Using X0(z0, z0) as a multidimensional wavefi eld op-
`erator, the measurements at refl ection-free acquisition surface
`z0, P0 (z0, z0), can be written as (Figure 1a:)
`
`(1a)
`
`where P-0 (z0, z0) is the upward travelling wavefi eld at z0. In
`Equation 1a, each column of source matrix S+ represents one
`source array as used in the fi eld and, similarly, each row of
`detector matrix D represents one detector array that trans-
`forms the upgoing wavefi eld (P-0) into one measurement (one
`element of matrix P0). For a stress-free surface, both up- and
`downgoing wavefi elds exist (Figure 1b), and Equation 1a
`need be extended to:
`
`(1b)
`
`where detector level zd is generally closely situated at the sur-
`face (z0) and transfer function X (z0, z0) includes the sur-
`face multiples. Unlike X0, quantifying one seismic round-
`trip, X quantifi es many round-trips. In Equation 1b, matrix
`D (zd,z0) includes generation of the near-fi eld surface ghost
`(Figure 1c). Note that Equations 1a and 1b represent the
`refl ection data without and with surface multiples, respec-
`tively. Hence, by transforming the stress-free surface into a
`refl ection-free surface, both the surface ghost and the sur-
`face multiples are removed from the data: from P (zd ,z0) to
`P0(z0,z0).
`
`July 2008 The Leading Edge 925
`
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`
`S e i s m i c a c q u i s i t i o n
`
`Figure 3. (a) Synthesis of a plane source wavefi eld according to Equation 2a, showing a number of snapshots. Synthesis yields a coherent source
`wavefi eld. (b) Simulation of a blended source wave fi eld, according to Equation 3a, showing one snapshot. Blending yields an incoherent source
`wavefi eld.
`
`Synthesis of areal shot records
`Berkhout (1992) introduced the concept of areal shot re-
`cords. Unlike a conventional shot record, being basically a
`point source response, an areal shot record is the response of
`a source with signifi cant areal extension. Th is areal source
`may generate a downgoing source wavefi eld with any desired
`spatial shape. In the same publication, the synthesis operator
`Γ was introduced and examples were given for plane-wave
`sources, not only at the surface (z0) but also at the target
`level (zm), and focal sources with their focal points anywhere
`in the subsurface. Focal wavefi elds became the fundamental
`basis of the Common Focus Point (CFP) method.
`If we defi ne the synthesis operator by the column vector
` syn ,then any areal source can be
`written as a linear combination of point sources (Figure 2a):
`
`
`
`
`
`
`
`
`
`
`
`
` (2a)
`
`
`
`, determine
`where the synthesis coeffi cients,
`the shape of the areal source wavefi eld. Using Equation 1b,
`the response of this areal source is given by the data vector
`(Figure 2b):
`
`(2b)
`
`926 The Leading Edge July 2008
`
`Equation 2b shows that the response of any areal source can
`be constructed by a weighted addition of the shot records as
`measured in the fi eld.
`Note that in the simple situation of synthesizing a plane
`wave source at the surface the elements of Γ →
`syn (z0) are given by
` p being the ray parameter of the plane wave. Fig-
`ure 3a illustrates this for a horizontal plane wave. As early as
`the mid-1970s, Taner (1976) reported interesting results on
`plane wave synthesis at the surface. And in the mid-1980s,
`Rietveld (1985) showed how to generate plane waves at the
`reservoir level. Practical application, however, was (and still
`is) seriously hampered by the coarse sampling of the source
`space. In the following, the concept of wavefi eld synthesis is
`used to introduce the concept of “blended acquisition.”
`
`Principle of blended seismic acquisition
`Let us introduce the concept of blending in the source do-
`main:
`→
`where column
`vector Γ
`
`bl (z0) is the blending operator:
`
`(3a)
`
` T
`
`(3b)
`
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`S e i s m i c a c q u i s i t i o n
`
`Figure 4. (a) Subsurface model that is used to simulate unblended and blended seismic data. (b) Simulation of one blended shot record according
`to Equation 4. In this illustration, the blended source confi guration consists of fi ve individual shots.
`
` .
`with
`By comparing Equations 2a and 3a, we see that synthe-
`sis and blending both involve a linear combination of single
`sources. However, the fundamental diff erence between blend-
`ing and synthesis is that in the synthesis process, the com-
`bined sources generate a continuous wavefront (plane, con-
`verging, diverging, etc.), while in blending a confi guration
`of single sources generates separate wave fronts. Of course,
`these wavefronts interfere with each other (Figure 3b), but
`they do not merge into one wavefront (compare Figure 3b
`with Figure 3a). Blending is a process that creates incoherent
`
`928 The Leading Edge July 2008
`
`wavefi elds.
`After combining Equations 1b and 3a, the blended seis-
`mic data are given by the data vector
`
`(4)
`
`Equation 4 shows that blended seismic data can be simulated
`from densely sampled, unblended fi eld records by weighted
`addition.
`Figure 4 shows the principle. For the subsurface model in
`Figure 4a, unblended fi eld records were simulated with source
`
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`
`S e i s m i c a c q u i s i t i o n
`
`Figure 5. Feedback model, showing the generation of primary refl ections (one round-trip) and surface-related multiple scattering (many round-
`trips). Each wavefi eld operator is presented by a matrix
`
`Figure 6. Migration scheme for a blended shot record (no pre-deblending). Note that all involved sources of the blended shot record are individually
`extrapolated, but the blended shot record is extrapolated only once. Th is means that one blended shot record yields SDR-migrated shot records.
`
`spacing δxs = 60 m, and a blending process was carried out ac-
`cording to Equation 4. For this illustration, fi ve fi eld records
`were blended with source emission times (in seconds): T1 =
`0.0, T2= 0.7, T3 = 0.3, T4 = 1.3, T5 = 1.8. Th is is visualized in
`Figure 4b. In practice, one blended shot record may involve
`many more sources. Th is choice is part of acquisition design.
`Note that, unlike the multiple problem, interference due to
`blending is fully under user control (choice of Tn).
`
`A key performance indicator in the design of blended
`seismic surveys is the source density ratio:
`SDR = number of sources in the blended survey
` number of sources in the unblended survey
`
`In the 2D example of Figure 4, the SDR=5, but in 3D it
`could be (and should be) signifi cantly higher.
`July 2008 The Leading Edge 929
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`
`S e i s m i c a c q u i s i t i o n
`
`Figure 7. (a) Migration of unblended shot records (∆xs = 300 m). (b) Migration of blended shot records (SDR = 5) according to the scheme in
`Figure 6. (c) Migration of blended shot records (SDR = 5) according to the scheme in Figure 6, using median stacking when adding the migrated
`shot records. (d) Migration of unblended shot records after perfect deblending (δXS = 60 m).
`
`Forward model of unblended seismic data
`Figure 5 shows schematically the up- and downgoing wave-
`fi elds as they occur at the stress-free surface (z0). Using the
`operator presentation in Figure 5, leaving (z0, z0) out of the
`notation, it can be easily verifi ed that these wavefi elds can be
`written as
`
` (5a)
`
`where the up- and downgoing waves, P- and P+, are interre-
`lated by the surface refl ection coeffi cient:
`
` (5b)
`superscript “∩” indicating that refl ection occurs at the lower
`side of the surface. In Equation 5a, the primaries have trav-
`eled one round-trip and the multiples have traveled many
`round-trips. Note that primaries are used here in a wider
`sense, including internal multiples as well.
`
`930 The Leading Edge July 2008
`
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`
`S e i s m i c a c q u i s i t i o n
`
`Figure 8. Spatial and temporal source properties of conventional acquisition as well as blended acquisition. Note that blending allows for a large
`increase of the source density as well as an improved azimuth distribution.
`
`Figure 9. (left) Conventional seismic acquisition without blending. (center) Blending with focus on quality: by reducing the source interval times
`while keeping the survey time unchanged, the number of shots can be signifi cantly increased. (right) Blending with focus on survey time: by decreas-
`ing the source interval times while keeping the number of shots unchanged, the survey time can be signifi cantly reduced. Of course, any mixture
`may be chosen.
`Forward model of blended seismic data
`Using Equation 5a, simulation of the blending process can
`be formulated as:
`
`
`where the blended up- and downgoing waves,
`interrelated by the surface refl ection coeffi cient:
`
`(6)
`
`(7a)
`
` and
`
`, are
`
`in the
`if we carry out blended acquisition
`Hence,
`fi eld, then the model of a physically recorded blend-
`ed shot record can be presented by the data vector:
`
`(7b)
`In Equation 7a, the blended primaries have traveled one
`round-trip and the blended multiples have traveled many
`round-trips.
`
`932 The Leading Edge July 2008
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`S e i s m i c a c q u i s i t i o n
`
`Figure 10. Th e concept of crossblended seismic acquisition. In this
`example, crossblending is shown, leading to a decrease of the total
`survey time by a factor of three (STR = 3). Using fi ve shots in one
`blended source, an increase of information is achieved by a factor of 45
`(SDR = 45). Together, it results in a blending factor of 135. Note that
`each acquisition system may use its own blending operator.
`
`If Equation 7b is substituted into Equation 7a, then the
`blended version of the well-known multiple scattering equa-
`tion is obtained:
`
`(8)
`
`We will use Equation 8 later in this paper to show that sur-
`face multiples can be directly removed from blended data.
`
`Exploring the impact of interference
`To get a feeling for the eff ect of interference, an example of
`migrating blended data is given. Th e blended shot records
`used have been simulated via the blending process shown in
`Figure 4. Shot record migration was carried out by forward
`extrapolating the wavefi eld of each individual source, tak-
`ing into account the source delay in the extrapolation pro-
`cess, followed by backward extrapolating the blended shot
`record. Figure 6 shows the migration scheme. Note that for
`this example one blended shot array consists of fi ve sources
`and, therefore, the scheme yields fi ve times as many migrated
`output records as blended input records (SDR = 5). Figure
`7 compares the diff erent migration results: unblended input
`versus blended input. Looking at the large interference ef-
`fects in the blended shot records, we may conclude that the
`migration process suppresses these eff ects very well, particu-
`larly if the migrated shot records are added by median stack-
`ing. As expected, the image of the blended data has better
`resolution properties than the image of the conventional data
`(SDR = 5).
`
`Intelligent blending, strategic considerations
`Th e concept of blended acquisition creates extra degrees of
`freedom in the acquisition design: where do we position the
`
`934 The Leading Edge July 2008
`
`Figure 11. (a) One column of a blended source matrix represents a
`blended source array, and each element of a blended source array
`represents a single "point"source with a space-dependent time delay.
`(b) One column of a blended data matrix represents one blended shot
`record, and each element of a blended shot record represents a
`superposition of time-delayed traces.
`
`Figure 12. How well blended data can be deblended is controlled by the
`acquisition design: fully determined (left), underdetermined (middle),
`fully undetermined (right).
`
`extra shots and how do we choose the delay times between
`those shots? More specifi c, in the blending concept, each co-
`herent source (pattern) in the traditional survey is replaced
`by an incoherent source array in the blended survey (Fig-
`ure 8). Th e blended source arrays can be characterized by
`three attributes: the number of sources (size of the array); the
`distribution of off sets and azimuths (spatial confi guration
`of the array); and the distribution of delay times (temporal
`confi guration of the array). Th is diff ers from the 1D concept
`of encoding the source signature. Actually, if one still would
`like to think in terms of source encoding, the proposal here
`is a 3D encoding, where the required change on the source
`signature is minimal, (i.e., just a time delay). Th is means
`that increased complexity on the seismic source is avoided,
`
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`
`S e i s m i c a c q u i s i t i o n
`
`or could be even decreased. Th e option to decrease source
`complexity in blended acquisition will be clarifi ed later in
`this paper.
`On the one hand, the focus of blended acquisition can be
`on image quality, with the benefi t of a denser spatial sampling
`and a wider range of azimuths. For this reason we have already
`proposed the key performance indicator SDR. On the other
`hand, the focus can also be put on survey time (i.e., blended
`acquisition is carried out with the same number of shots), but
`with reduced survey time. Figures 9a and 9b illustrate that a
`higher source density leads to a reduced spatial source interval
`for the same survey time. In Figure 9b the focus is on quality:
`a denser spatial source sampling means better illumination
`of the subsurface. Figures 9a and 9c illustrate that the survey
`time can be decreased while the number of shots stays the
`same. Th is option may be particularly valuable in the situ-
`ation of multioff set/multiazimuth VSP acquisition, saving
`very costly borehole time. To emphasize this economic aspect
`of blended acquisition, a second key performance indicator is
`proposed that quantifi es the gain in acquisition time (survey
`time ratio):
`STR = number of acquisition days in the unblended survey
` number of acquisition days in the blended survey
`In many practical situations, it is essential that seismic
`surveys are carried out in a small time window (“acquisi-
`tion slot”). Th ink at the limited accessibility of permafrost
`areas, bad weather regions, biologically protected environ-
`ments, borehole availability in VSP, high repetition rates in
`seismic production monitoring, etc. Blended acquisition with
`an STR >1 will create a new opportunity in these cases. For
`instance, instead of working with one traditional marine ac-
`quisition system—the combination of source boat with cable
`vessel—one could use several blended acquisition systems at
`the same time (concept of crossblending). Figure 10 shows
`the parallel utilization of three blended systems. Th is smart
`design does not only lead to a decrease of survey time by a
`factor of three (STR = 3), when using fi ve sources for one
`blended shot record, it also increases the source density by
`a factor of 45 (SDR = 32 x 5). Th e result is an increase of
`information by 45 in 1/3 of the time! To characterize the ac-
`quisition performance of blended surveys by one number, the
`blending factor is proposed: blending factor = source density
`ratio × survey time ratio
`For the above example, the blending factor equals 135.
`Note that if the tow speed of the recording vessel could be
`increased by a factor of two, then STR = 6. Note also that if
`the number of cables would be decreased by a factor of three,
`then the total amount of information is still increased by a
`factor of 15. It illustrates that many variations are possible to
`optimize both quality and economics.
`
`Acquisition design
`In multishot blended acquisition surveys, the source vector
`matrix is replaced by:
`
`(9)
`
`936 The Leading Edge July 2008
`
`each column of Γ
`bl representing one blended source array
`and each column of matrix Γ
`bl defi ning the 3D confi gura-
`tion (off sets, azimuths, delay times) of a blended source array
`(Figure 11a). Hence, a column of Γ
`bl determines the illumina-
`tion capabilities of a blended source array and, therefore, the
`information content of the related blended shot record.
`It is proposed to design a blended acquisition survey
`such that, for a prespecifi ed number of source boats/vibrator
`units,
`
`or
`
`(10a)
`
`(10b)
`
`I being the unity matrix. In Equation 10b, Λ = (ΓH Γ)−1
`in case an L2-norm is used, superscript H meaning that the
`transpose should be taken.
`Design conditions 10a and 10b aim at
`
`or
`
`(11a)
`
`(11b)
`
`In physical terms, Equations 11a and 11b show that in the
`computer a blended source can be approximately decom-
`posed into its unblended components: deblending. Th e bet-
`ter the design, the better the decomposition. In practice the
`number of blended records will be smaller than the number
`of unblended records. Th is means that the system is under-
`determined. In Figure 12, Γ is shown for three cases of fi ve
`blended sources: from fully determined (left) to underdeter-
`mined (middle) to fully undetermined (right). In the fully
`undetermined case, the deblending procedure relies on prop-
`erties like causality and source sparseness, and data-driven
`considerations. Th erefore, inversion of blending operator Γ
`should be done in combination with processing algorithms.
`For nearby sources, the diff erence in arrival times between
`overlapping shot records is largely given by the superposition
`of diff erential moveout and source delay time. Hence, the
`deeper the refl ections, the more the diff erences in arrival time
`will approach the delay times that are given to the sources
`of the blended shot records. It is therefore advised to assign
`to nearby sources relatively large delay diff erences to avoid
`high correlation between unblended signal and interference
`noise: constrained minimization of Equations 11a and 11b.
`Th e correlation issue is very well known from the subtraction
`problem in multiple removal.
`
`Deblending as a preprocessing step
`In blended acquisition, the data matrix is given by
`
`each column of
` representing a blended shot record (Fig-
`ure 11b). From Equation 12 it follows that the deblending
`
`(12)
`
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`
`S e i s m i c a c q u i s i t i o n
`
`process in the forward data space can be formulated as
`
`or
`
`or
`
`or
`
`(13a)
`
`(13b)
`
`with
`
`(17b)
`
`(17c)
`
`(17d)
`
`Λ being determined by Equation 11b.
`Equations 13a and 13b mean that all the interference ef-
`fects in the measured blended shot records are approximately
`removed. Th e better the acquisition design, the better the ap-
`proximation. Note that in the migration example (Figure 7),
`we actually approximated Γ-1 by ΓH (“pseudo deblending”).
`Th is means that there is a lot of room for improvement!
`Using Equation 12, it can be easily verifi ed that blended
`data in the inverse data space can be formulated
`
`or
`
`(14a)
`
`(14b)
`Th is is an interesting result, as Equation 14b tells us that
`the unblended data in the inverse data space are obtained by
`a double forward blending process, once during acquisition
`and once during preprocessing.
`Note that in the inverse data space all surface-related mul-
`tiples map onto the origin (Berkhout, 2006):
`
`with
`
`(15a)
`
`(15b)
`Th is means that, similar to deblending, multiple removal is
`simple in the inverse data space.
`
`An outlook of processing blended data
`It is self-evident that blended data are deblended fi rst in a pre-
`processing step, followed by conventional processing such as
`multiple removal and migration. However, in the following
`we will outline that processing can also be directly applied
`to the blended measurements. Th is option has the signifi cant
`advantage that model information can be included in the
`implicit deblending process, allowing data-driven optimiza-
`tion.
`Combining deblending and multiple removal. Using the
`feedback model (Figure 5) and Equations 5a, and 5b, the
`measured data with surface-related multiples can be written
`as
`
`Equation 17c has exactly the same structure as Equation 16b
`and, therefore, surface multiples can be directly removed
`from the blended data with the iterative scheme for unblend-
`ed data (see e.g., Verschuur and Berkhout, 1997). Following
`this iterative scheme, the fi rst iteration starts with the initial
`. Th e fi nal output consists
`
`
`estimates P0bl = P0⌫bl and ⌫bl = ⌫
`of blended data without surface multiples:
`
`
`(18a)
`
`
`It is interesting to realize that in the iterative scheme (cid:75)
`is optimized by implicitly using information in the surface
`multiples (data-driven optimization of the deblending pro-
`cess). Th is opens the opportunity to combine multiple re-
`moval with deblending:
`
`(18b)
`
`Removal of blended multiples is currently under investiga-
`tion.
`Combining deblending with migration. In Figure 6, a mi-
`gration scheme has been proposed for blended shot records
`(no deblending):
`
`minimum for each depth level (19a)
`
`where R represents the desired, deblended, angle-dependent
`refl ectivity at a given depth level, W equals the forward ex-
`trapolation operator, and F equals the backward extrapo-
`lation operator to that depth level. Similarly, each column
` represents the blended CFP-gather (without surface
`of
`multiples) and each column of WS+ represents the unblended
`incident source wavefi eld for that depth level. Equation 19a
`can be extended to properly handle all blended wavefi elds,
`refl ected and incident, in the migration process:
`
` minimum for each depth level (19b)
`
`or, including detector matrix D,
`
`(16a)
`
`(16b)
`In Equation 16b, P0, P and A are given by Equations 1a, 1b,
`and 15b, respectively.
`Th e blended version of Equation 16b equals
`
`(17a)
`
` represents the blended CFP-gathers (with sur-
`where
` equals the blended incident source
`face multiples),
` equals the blended incident multiple
`wavefi elds and
`wavefi elds. Note that estimation of R occurs by making use
`of both the blended source wavefi eld and the blended sur-
`face multiples (double illumination). Th e author believes that
`Equation 19b describes the seismic imaging technology for
`the future.
`
`July 2008 The Leading Edge 937
`
`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 2019, WesternGeco v. PGS (IPR2015-00309, 310, 311)
`
`

`
`S e i s m i c a c q u i s i t i o n
`
`Conclusions
`It is proposed to replace current seismic acquisition meth-
`ods (discontinuous recording, zero overlap in time) by a
`blended alternative (continuous recording, signifi cant over-
`lap in time). It is believed that the interpolation of missing
`shot records in conventional acquisition is much harder to
`accomplish than the separation of overlapping shot records
`in blended acquisition. Th e key input parameter in blending
`is the source delay time (Tn) for each individual source. For a
`given source confi guration, Tn brings the interference in the
`blended recordings under user control.
`With the focus on quality, blended acquisition allows sig-
`nifi cantly denser spatial source sampling and a much wider
`range of source azimuths. Th ese properties may lead to the
`next principal step—improvement in seismic imaging qual-
`ity. For instance, blended acquisition may improve the qual-
`ity of seismic production monitoring signifi cantly.
`With the focus on economics, the blending concept al-
`lows signifi cantly shorter survey times. Th is property will
`be particularly valuable in critical situations where small ac-
`quisition time windows dominate due to severe safety, en-
`vironmental or economic restrictions. For instance, blended
`acquisition may improve the economics of VSP signifi cantly.
`In crossblended acquisition, several acquisition systems are
`shooting and recording blended data at the same time. Cross-
`blending allows better image quality as well as shorter survey
`times. For instance, in triple crossblending with fi ve sources
`per blended shot record the survey time decreases with a fac-
`tor of three (STR = 3) and the source density increases with
`a factor of 45 (SDR = 45). Th is leads to a blending factor of
`135. High blending factors open new opportunities in situa-
`tions where both image qua