GB2584285A - Method for seismic data acquisition and processing - Google Patents

Abstract

Methods are described for separating the unknown contributions of three or more seismic sources from a commonly acquired set of wavefield signals based on varying parameters at the firing time, location and/or depth of the individual sources in a lateral 2D plane. Estimates of at least two blends of contributions from at least two sources may be determined. These blends may be interpolated or reconstructed to a fine spatial sampling interval along the activation line, and contributions from the three or more sources then separated from the interpolated or reconstructed estimated blends. Signal apparition or random dithering may be used to encode the sources. The encoding may result in a number o diamond or lozenge shaped regions in the frequency wavenumber domain which is less than the number of sources.

Description

Method for seismic data acquisition and processing

Field of the invention

[0001] The present invention relates to methods for acquiring and separating contributions from three or more different simultaneously or near simultaneously emitting sources in a common set of measured signals representing a wavefield. The invention would apply equally to onshore and offshore seismic surveys, and for implosive, explosive or vibratory type sources.

Background

(3) [0002] Seismic data can be acquired in land, marine, seabed, transition zone and boreholes for instance. Depending on in (3) what environment the seismic survey is taking place the survey CD equipment and acquisition practices will vary.

CD [0003] In towed marine seismic data acquisition a vessel tows streamers that contain seismic sensors (hydrophones and sometimes particle motion sensors). A seismic source usually but not necessarily towed by the same vessel excites acoustic energy in the water that reflects from the sub-surface and is recorded by the sensors in the streamers. The seismic source is typically an array of airguns customarily deployed as a set of sub-arrays, each of which includes a set of individual airguns. These are normally programmed to fire at the same instant, providing a close to instantaneous peak of energy followed by a longer, lower energy output as a result of oscillating air bubbles. A marine source can also be a marine vibrator for instance, which may be a single unit or a set of individual units composing an array. In either case, the intent is to provide a seismic source output which contains as far as possible a broad range of frequencies within the usable seismic frequency ranges, typically from 1-2 Hz up to around 500Hz. In modern marine seismic operations many streamers are towed behind the vessel (3D seismic data acquisition). It is also common that several source and/or receiver vessels are involved in the same seismic survey in order to acquire data that is rich in offsets and azimuths between source and receiver locations.

[0004] In seabed seismic data acquisition, nodes or cables containing sensors (hydrophones and/or particle motion sensors) are deployed on the seafloor. These sensors can also record the waves on and below the seabottom and in particular shear waves which are not transmitted into the water. Similar sources are used as in towed marine seismic data acquisition. The sources are towed by one or several source vessels.

[0005] In land seismic data acquisition, the sensors on the ground are typically geophones and the sources are commonly vibroseis trucks. Vibroseis trucks are usually operated in arrays with two or more vibroseis trucks emitting energy close to each other roughly corresponding to the same shot location.

(,) In this invention we refer to such source configurations as CD groups of sources. C)J

CD [0006] Explosive sources may also be used onshore, which may be one large charge or a series of smaller ones.

[0007] Impulsive marine sources are traditionally formed from a combination of individual energy emitting source elements, typically being of the airgun type, by which a volume of compressed air is released into the water column to produce energy in the preferred frequency spectrum. Each airgun element is typically deployed a few metres below the surface, arranged into arrays of similar units.

[0008] There are various brand names and designs of such units, including but not limited to Sleeve Guns, GI Guns and Bolt Airguns and donut guns. All such units work in a similar way and will be referred to herein as "airgun" for the sake of convenience.

[0009] Each individual airgun unit has a specific volume of air, which can be configured by the user. As each unit is initiated, the air volume is ejected almost instantaneously into the water column, and the resulting bubble rises towards the surface, oscillating with a given periodicity with decaying amplitude. This continues for up to a second or two. The periodicity is a function of the volume and pressure of the air.

[0010] Individual airgun elements are combined into sub-arrays in various configurations, consisting of airguns with a range of volumes such that the bubble periodicity is different for each airgun element. Airgun units are commonly combined together in such sub-arrays such that the overall output consists of a short, aligned initial output (referred to as the "peak"), followed by a period in which the various bubble periodicity times result in largely destructive interference, in order to make the overall radiating pressure wave, referred to as the sub-array signature, as close as possible to the a) idealized spike. Such a process is referred to as sub-array CD tuning, and the techniques involved in this are well established practice and beyond the scope of this description.

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[0011] Following the firing of a shot, after a short period of time, since the source vessel is moving continuously, a subsequent shot is fired after a few seconds. This is generally between five and twenty seconds for mainstream seismic acquisition. The objective, quite apart from giving time for the source vessel to move, is also to allow the energy from each shot-point to decay before the next one is initiated. Some approaches use shorter shot intervals (two or more seconds), often but not universally combined with some element of timing change on sequential shots in order to limit the impact of the insufficient decay time on sequential shot records. These approaches are referred to as "simultaneous source" and are discussed below. These approaches enable more source points per unit area, albeit at some compromise in terms of interference or fold.

[0012] The present invention applies to sources towed by one single or several vessels.

[0013] Traditionally seismic data have been acquired sequentially: an impulsive source, typically formed of two or more airgun sub-arrays or vibroseis units is excited and data are recorded until the energy that comes back has diminished to an acceptable level and all reflections of interest have been captured after which a new shot at a different shot location is excited. Being able to acquire data from several sources at the same time is clearly highly desirable. Not only would it allow to cut expensive acquisition time drastically but it could also better sample the wavefield on the source side which typically is much sparser sampled than the distribution of receiver positions. It would also allow for better illumination of the target from a wide range of azimuths as well as to better sample the wavefield in areas with surface obstructions. In addition, for some applications such as 3D VSP acquisition, or marine seismic surveying in Oenvironmentally sensitive areas, reducing the duration of the CD survey is critical to save costs external to the seismic acquisition itself (e.g., down-time of a producing well) or minimize the impact on marine life (e.g., avoiding mating or spawning seasons of fish species).

[0014] Simultaneously emitting sources, such that their signals overlap in the (seismic) record, is also known in the industry as "blending". Conversely, separating signals from two or more simultaneously emitting sources is also known as "deblending" and the data from such acquisitions as "blended data".

[0015] Simultaneous source acquisition has a long history in land seismic acquisition dating back at least to the early 1980's. Commonly used seismic sources in land acquisition are vibroseis sources which offer the possibility to design source signal sweeps such that it is possible to illuminate the subsurface "sharing" the use of certain frequency bands to avoid simultaneous interference at a given time from different sources. By carefully choosing source sweep functions, activation times and locations of different vibroseis sources, it is to a large degree possible to mitigate interference between sources. Such approaches are often referred to as slip sweep acquisition techniques. In marine seismic data contexts the term overlapping shooting times is often used for related practices. Moreover, it is also possible to design sweeps that are mutually orthogonal to each other (in time) such that the response from different sources can be isolated after acquisition through simple cross-correlation procedures with sweep signals from individual sources. We refer to all of these methods and related methods to as "time encoded simultaneous source acquisition" methods and 'time encoded simultaneous source separation" methods.

[0016] The use of simultaneous source acquisition in marine seismic applications is more recent as marine seismic sources (i.e., airgun sources) do not appear to yield the same benefits of providing orthogonal properties as land seismic (,) vibroseis sources, at least not at a first glance. Western CD Geophysical was among the early proponents of simultaneous source marine seismic acquisition suggesting to carry out the separation as a pre-processing step by assuming that the reflections caused by the interfering sources have different characteristics. Beasley et al. (1998) exploited the fact that provided that the sub-surface structure is approximately layered, a simple simultaneous source separation scheme can be achieved for instance by having one source vessel behind the spread acquiring data simultaneously with the source towed by the streamer vessel in front of the spread. Simultaneous source data recorded in such a fashion is straightforward to separate after a frequency-wavenumber (wk) transform as the source in front of the spread generates data with positive wavenumbers only whereas the source behind the spread generates data with negative wavenumbers only.

[0017] Another method for enabling or enhancing separability is to make the delay times between interfering sources incoherent (Lynn et al., 1987). Since the shot time is known for each source, they can be lined up coherently for a specific source in for instance a common receiver gather or a common offset gather. In such a gather all arrivals from all other simultaneously firing sources will appear incoherent. To a first approximation it may be sufficient to just process the data for such a shot gather to final image relying on the processing chain to attenuate the random interference from the simultaneous sources (aka. passive separation). However, it is of course possible to achieve better results for instance through random noise attenuation or more sophisticated methods to separate the coherent signal from the apparently incoherent signal (Stefani et al., 2007; Ikelle 2010; Kumar et al. 2015). In recent years, with elaborate acquisition schemes to for instance acquire wide azimuth data with multiple source and receiver vessels (Moldoveanu et al., 2008), several methods for simultaneous source separation of such data have been described, for example methods that separate "random dithered sources" through inversion exploiting the sparse nature of seismic data in the time-domain (i.e., seismic traces can be Othought of as a subset of discrete reflections with "quiet CD periods" in between; e.g., Akerberg et al., 2008; Kumar et al. 2015). A recent state-of-the-art land example of simultaneous source separation applied to reservoir characterization is presented by Shipilova et al. (2016). Existing simultaneous source acquisition and separation methods based on similar principles include quasi random shooting times, and pseudo random shooting times. We refer to all of these methods and related methods to as "random dithered source acquisition" methods and "random dithered source separation" methods. "Random dithered source acquisition" methods and "random dithered source separation" methods are examples of "space encoded simultaneous source acquisition" methods and "space encoded simultaneous source separation" methods.

[0018] A different approach to simultaneous source separation has been to modify the source signature emitted by airgun sources. Airgun sources comprise multiple (typically three) sub-arrays each comprised of several individual airguns or clusters of smaller airguns. Whereas in contrast to land vibroseis sources, it is not possible to design arbitrary source signatures for marine airgun sources, one in principle has the ability to choose firing time (and amplitude i.e., volume) of individual airgun elements within the array. In such a fashion it is possible to choose source signatures that are dispersed as opposed to focused in a single peak. Such approaches have been proposed to reduce the environmental impact in the past (Ziolkowski, 1987) but also for simultaneous source shooting.

[0019] Abma et al. (2015) suggested to use a library of "popcorn" source sequences to encode multiple airgun sources such that the responses can be separated after simultaneous source acquisition by correlation with the corresponding source signatures following a practice that is similar to land simultaneous source acquisition. The principle is based on the fact that the cross-correlation between two (infinite) random sequences is zero whereas the autocorrelation is a spike. It is also possible to choose binary encoding Osequences with better or optimal orthogonality properties such CD as Kasami sequences to encode marine airgun arrays (Robertsson et al., 2012). Mueller et al. (2015) propose to use a combination of random dithers from shot to shot with deterministically encoded source sequences at each shot point. Similar to the methods described above for land seismic acquisition we refer to all of these methods and related methods to as "time encoded simultaneous source acquisition" methods and "time encoded simultaneous source separation" methods.

[0020] Yet another approach is to fire a sequence of source arrays, one or more of which has a random time dither applied relative to the adjacent source points, but at a shorter time interval, for example, five seconds rather than the conventional ten. This has the advantage of keeping the shallow part of each shot free from interference, whilst mitigating the drop in fold. For example, conventional exploration seismic involves two identical source arrays, offset laterally from each other by, for example, 50m (source centre to source centre). The firing cycle is Port -starboard -port -starboard, such that a source fires every ten seconds, into different sub-surface lines. This results in half-fold data relative to single source. Experiments with triple source using the same approach resulted in 1/3 fold data, considered insufficient. The partially overlapping approach in the above dual source example, would involve firing every 5 seconds, returning to full fold. Employing the same approach with three partially overlapping sources and a five second shot interval would result in limited fold drop and undisturbed shallow data. However, extrapolating this form three to four sources, for example (and temporarily ignoring the issues outlined above about overall sub-array capacity) would require, for example, a 2-3 second shot interval, resulting in limited undisturbed data lengths and loss of fold. Taking into consideration the practicalities, it has also been presented (for example, Hager, 2016), to arrange the firing sequence such that individual airgun sub-arrays may form part of more than one array, as noted above. However, the a) interference of adjacent shots (even mitigated by dither) and CD the loss of fold are unavoidable and their effects increase as attempts are made to increase the total number of arrays.

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[0021] Recently there has been an interest in industry to explore the feasibility of marine vibrator sources as they would, for instance, appear to provide more degrees of freedom to optimize mutually orthogonal source functions beyond just binary orthogonal sequences that would allow for a step change in simultaneous source separation of marine seismic data. Halliday et al. (2014) suggest to shift energy in wk-space using the well-known Fourier shift theorem in space to separate the response from multiple marine vibrator sources. Such an approach is not possible with most other seismic source technology (e.g., marine airgun sources) which lack the ability to carefully control the phase of the source signature (e.g., flip polarity).

[0022] The recent development of "signal apparition" suggests an alternative approach to deterministic simultaneous source acquisition that belongs in the family of "space encoded simultaneous source acquisition" methods and "space encoded simultaneous source separation" methods. Robertsson et al. (2016) show that by using modulation functions from shot to shot (e.g., a short time delay or an amplitude variation from shot to shot), the recorded data on a common receiver gather or a common offset gather will be deterministically mapped onto known parts of for instance the wk-space outside the conventional "signal cone" where conventional data is strictly located (Figure la). The signal cone contains all propagating seismic energy with apparent velocities between water velocity (straight lines with apparent slowness of +-1/1500 s/m in wk space) for the towed marine seismic case and infinite velocity (i.e., vertically arriving events plotting on a vertical line with wavenumber 0). The shot modulation generates multiple new signal cones that are offset along the wavenumber axis thereby populating the wk-space much better and enabling exact simultaneous source separation below a certain frequency (Figure lb). Robertsson et al. (2016) referred to the process (,) as "signal apparition" in the meaning of the act of becoming CD visible". In the spectral domain, the wavefield caused by the periodic source sequence is nearly "ghostly apparent" and isolated. A critical observation and insight in the "signal apparition" approach is that partially shifting energy along the wk-axis is sufficient as long as the source variations are known as the shifted energy fully predicts the energy that was left behind in the "conventional" signal cone. Following this methodology simultaneously emitting sources can be exactly separated using a modulation scheme where for instance amplitudes and or firing times are varied deterministically from shot to shot in a periodic pattern.

[0023] Consider a seismic experiment where a source is excited sequentially for multiple source locations along a line while recording the reflected wavefield on at least one receiver. The source may be characterized by its temporal signature. In the conventional way of acquiring signals representing a wavefield the source may be excited using the same signature from source location to source location, denoted by integer n.

Next, consider the alternative way of acquiring such a line of data using a periodic sequence of source signatures: every second source may have a constant signature and every other second source may have a signature which can for example be a scaled or filtered function of the first source signature. Let this scaling or convolution filter be denoted by a(t), with frequency-domain transform A(w). Analyzed in the frequency domain, using for example a receiver gather (one receiver station measuring the response from a sequence of sources) recorded in this way, can be constructed from the following modulating function m(n) applied to a conventionally sampled and recorded set of wavefield signals: m(n) = + (-1)1 -(-1)n] , which can also be written as 1-- (0.1) CY) m(n) = I + e urn] ± -1 A [1 -e tirn] . C:) 2 I- 2 ('Si C:) [0024] By applying the function m in Eq. 0.1 as a modulating function to data f(n) before taking a discrete Fourier transform in space (over n), F(k) ="f(n)), the following result can be obtained: 1+A - (0.2) (rt)m(n)) = -F (k) + 12A - -kN) which follows from a standard Fourier transform result (wavenumber shift) (Bracewell, 1999).

[0025] Eq. 0.2 shows that the recorded data f will be scaled and replicated into two places in the spectral domain as illustrated in Fig. 1(B) and as quantified in Tab. I for different choices of A(w).

A(w) Et= (1-A)/2 El, = (1+ A)/2 1 0 1 -1 1 0 0 1/2 1/2 1/4 3/4 euoT (1 _eiwT)/2 (1 ± el)/2 1+ e"T -' 2 1 + eud72 TAB. I. Mapping of signal to cone centered at k =0 (14) and cone centered at k = kN (H_) for different choices of A(w) for signal separation or signal apparition in Eq. (0.2).

[0026] Part of the data will remain at the signal cone 1-- centered around k = 0 (denoted by H+ in Fig. 1(b)) and part of (3) the data will be scaled and replicated to a signal cone O centered around kN (denoted by H_). It can be observed that by only knowing one of these parts of the data it is possible to O predict the other.

[0027] This process may be referred to as, "signal apparition" in the meaning of "the act of becoming visible". In the spectral domain, the wavefield caused by the periodic source sequence is nearly "ghostly apparent" and isolated.

[0028] In practice the length of the source sequences is finite. While it is true that the Fourier series transform of any finite sequence will be periodic with a periodicity related to the length of the sequence, this type of periodicity is not what we refer to when describing periodic constraints in the current invention. Instead, in this invention we use the term periodic to denote a sequence that repeats itself at least once within the length of the sequence (i.e., the periodicity is less than half the sequence length).

[0029] A particular application of interest that can be solved by using the result in Eq. (0.2) is that of simultaneous source separation. Assume that a first source with constant signature is moved along an essentially straight line with uniform sampling of the source locations where it generates the wavefield g. Along another essentially straight line a second source is also moved with uniform sampling. Its signature is varied for every second source location according to the deterministic modulating sequence 77-(n), generating the wavefield h. The summed, interfering data f =9 +h are recorded at a receiver location.

[0030] In the frequency-wavenumber domain, where the recorded data are denoted by F = G +H, the H-part is partitioned into two components H+ and H_with H = H+ +H_ where the H_-component is nearly "ghostly apparent" and isolated around the Nyquistwavenumber [Fig. 1(B)], whereas G and H+ are overlapping wavefields around k = O. Furthermore, H_ is a known, scaled function of H. The scaling depends on the chosen A(w) function (,) (Tab. I), and can be deterministically removed, thereby CD producing the full appearance of the transformed wavefield H. When H is found, then G =F-H yielding the separate wavefields g and h in the time-space domain.

[0031] Although the above description has focused on acquisition along essentially straight lines, the methodology applies equally well to curved trajectories such as coil-shaped trajectories, circles, or other smoothly varying trajectories or sequences of source activations.

[0032] The concept may be extended to the simultaneous acquisition of more than two source lines by choosing different modulation functions for each source.

[0033] Acquiring a source line where the first two source locations have the same signature, followed by two again with the same signature but modified from the previous two by the function A(w) and then repeating the pattern again until the full source line has been acquired, will generate additional signal cones centered around +kv/2.

[0034] Fig. 1(B) also illustrates a possible limitation of signal apparition. The 114 and H_ parts are separated within the respective lozenge-shaped (or diamond-shaped) regions in Fig. 1(B). In the triangle-shaped parts they interfere and may no longer be separately predicted without further assumptions. In the example shown in Fig. 1(B), it can therefore be noted that the maximum non-aliased frequency for a certain spatial sampling is reduced by a factor of two after applying signal apparition. Assuming that data are adequately sampled, the method nevertheless enables full separation of data recorded in wavefield experimentation where two source lines are acquired simultaneously.

[0035] For data acquired along a single line, the dimension of the lozenge-shaped regions is a function of the velocity of the recording medium c, the number of simultaneously emitting (,) sources it and the distance between source tiring locations CD along the direction of the source line Ax. The frequency at the top of the lozenge-shaped regions, ftop, is:

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ft.P = nar- ( 0. 3) . [0036] The frequency at the middle of the lozenge-shaped regions, fpia, below which the data are fully separated is: /Mid = (0.4). 2nAx

[0037] It can be proven that as opposed to the method of signal apparition, no other method can produce a larger region where it is possible to fully separate the sources, i.e., the lozenge-shaped or diamond-shaped region is optimally large for simultaneous source separation (Wittsten et al., 2019).

[0038] Outside the lozenge-shaped region the response from the sources is not separated and overlap. Different methods for separating the wavefield contributions from the different sources in this region have been proposed, many of which rely on the exact or nearly exact separation of the wavefields within the lozenge-shaped regions (e.g., Andersson et al., 2016). Therefore, the larger the lozenge-shaped region is the larger area can first of all be exactly or nearly exactly reconstructed. However, in addition a larger lozenge-shaped region will also enhance the quality of separating wavefields in the overlapping region.

[0039] Instead of using the method of signal apparition, other methods for simultaneous source separation such as random dithering encoding can also be used to exactly or nearly exactly separate the response from different sources (Andersson et al., 2017a). The region of exact or nearly exact separation will be smaller than the case of signal apparition. However, in a region in the frequency wavenumber space the number of unknowns is smaller than the number of equations under the assumption that the signal belongs in cones bounded by the velocity of the recording medium (,) resulting in the ability to exactly or nearly exactly separate CD source contributions in a simultaneous source experiment below a certain frequency also in the case of randomly dithered sources.

[0040] It is herein proposed to use acquisition patterns in a plane instead of just a line to reduce ambiguity in the overlapping region thereby causing the area of exact or nearly exact separation to be larger.

[0041] By a plane it is meant a portion of the (infinite) horizontal plane covering an area corresponding to the length of the shotlines and the length in the crossline direction occupied by adjacent shotlines. Note that the number of sampling locations in the inline and crossline directions will limit the resolution properties of the Fourier transform. In practice the number of points should be greater than or equal to 8 or more. Specifically, for a Bravais lattice (x1,x2)= (uLiki -Fu1,2k2,u2,1k1 +u2,2k2), thus including rectangular sampling, staggered grid and hexagonal sampling, Kinin < < Kr ax Kr in < k2 <K2nax, it should hold that Kinax _ Kimin > 8 and Krax /Tin > 8 [0042] Method for separating wavefields in the overlapping region includes utilizing the analytic part or the quaternion analytic part of the wavefields (Andersson et al., 2017b) . [0043] So far, we have limited the discussion to encoding along a horizontal line of shot locations. Andersson and Robertsson [2018] disclose a method for encoding and decoding sources in the horizontal plane, whereby the maximum frequency for fully recovering the contributions in recorded a wavefield from individual sources in a simultaneous source survey is increased. More precisely, this is achieved by considering sampling the same wavefield along a plurality of parallel sail-lines to unambiguously delineate regions of overlap in a Fourier-wavenumber plane of at least two spatial dimensions.

[0044] Let us begin by introducing notation and recapitulating Othe theory for regular seismic apparition. We will use the CD notation ('Si (:) 7(0 = (x)e-2rnxedx for the Fourier transform in one variable, and consequently I(w,)2) for the Fourier transform of two dimensional function f(t,xi,x2) with a time (t) and spatial (ci,x2) dependence. When referring to Fourier transforms with respect to only part of the variables we will use the " notation and use the variable names to implicitly specify with regards to which dimensions the transform is applied.

[0045] Suppose that f(t,x1,x2) is a function with frequency support in two cones of the form 0)2 (ti t2)' [0046] The constraint comes from assuming that the function f represent the recording of a wavefield at time t at a fixed receiver coordinate, source coordinates (x1,x2), and fixed depth, where the recorded wave field at this depth is a solution to the homogeneous wave equation with a velocity c. The wavefields are generated at discrete values of (CI,X2) which we assume to be equally spaced with sampling distances.6E,, and A,2 meters. For the sake of transparency we will assume the two

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spacing coordinates to be equal with a distance set to 1 in the presentation that follows, i.e. ti,=0x2= 1. The derived expressions hold in a more general setting, and it is fairly straightforward to incorporaty kind of Bravais sampling lattice (xi, x2) =(uijki-Put2k2,u2,1ki±u2,2k2), thus including rectangular sampling, staggered grid and hexagonal sampling.

[0047] We now consider the case where several sources are used simultaneously. In this presentation we assume that the M sources are aligned sequentially, although the theory can easily be adjusted to cover more general sampling formations. Moreover, in this presentation, we will assume that the different sources are fired with a small internal time delays, Othat vary with period M. This variation can be of more general CD form, for instance varying with a delay pattern that includes C\I a heteroscale variation (several superimposed or products of periodic or non-periodic functions), random or quasi-random time delay patterns or variations in source amplitude for instance. Let us denote the periodic delay pattern by Ami,m2. One formulation for the representation described above is d(t, M + mi, k2) = E;;12=1 f (t -Am,"""2, (M + mi) Aix, (Mk2 + M2) Ax) = (if (w, c2)e-2'nzi rn24°)(t, (M + m") Ax, (Mk2 M.2) Ax), [0048] The Poisson sum formula Ek f (k) = (k) can be modified (by using the Fourier modulation rule) as EZ),_on f (k)e-2'nek = (fe-27"*)(k) =D1.-.RC+k).

[0049] By the standard properties of the Fourier transform it is straightforward to show that Eicl_co f (k Ax + xo)e-27/(cAx+xo)e = k) 2Trixo-k non k=-en + e A x hold for the spatial sampling parameter Ax and some fixed spatial shift xo.

[0050] Let us now consider Fourier representation of the data.

We can assume that the sampling in time is fine enough to use the continuous Fourier transform for the temporal part. For the spatial parts, we will expand the data by means of Fourier series representation, thus obtained a representation that is (,) periodic with respect to the continuous frequency-wavenumber CD parameters el and c2. ('Si

CD [0051] The transform thus takes the shape D (co, G, = f Eki=_," Ek,=_an d (t,k1,k2)e-2in((k2. c k2e2m)+to dt =I Zm Zce _Go in1=1 L.k2 -co d (t, Mk, + m1, k)e-2Thi((ltilci-Fmr)C1 1, 2 ±frik22+ted) dt Vm Vcc yr.

=f "-i.L.,m2-1 z..k"--.0 L.,k2__00 f (t, Mk, + mi, M k2 + m2) xe-2Tri((mk1+m1g1+(mk2){2+tw+A.,,m2(0) dt [0052] By taking a one-dimensional Fourier transform with respect to the time variable it holds that D (a), 6_, = Zmiw 1-1Z,n412=1_ Ek"),=-co Ekcc2 =-oo (CO, Mkl Mkt + m2) xe-27-rd(Mici+Tni)ei-F(Mk2)e2+Anzi_ an2 60 [0053] Let us now focus on the part Ece, _001 (t, mki m k2 m2)e-27i(mk1+Tn1)e1 [0054] By using the version of the Poisson sum formula above, we can rewrite the expression above as co sf' (co, Mkt + m1, Mk2 + m, )e-27n(mk +nti = --cc f (6),e, + -ki Mk2 + m2)e2rtmilci/M [0055] Using a similar argument for the sum over k2 we obtain +miXi-F(Mk2Y) -27n(Wki h (a), el, 2) = Ek"' Zee' f Go, Mk + Mk + - k2--00 2 m2ie /L, k2 _22ri(rni +7712k2)1M+M20

A

V00 V00 = Lik2=-oo Lici=-on f (a), G S2 1-A4) (3) [0056] It is now important to note that the periodicity of ft with respect to C2 is (1/M) and not 1 as it is for the (3) periodicity with respect to el. To see this, note that for any CD integer k2' it holds that ('Si C:) h (co, el, e2 k21/M) = Ew von k2=-Go tact =-en f (co, + e2 k2+:2f)euri((mikr+m2k2)/m+m2(e+k21)) = Ecc co ± k2+k2() 2Tri((mikr+m2(k2+k20)/M+m20 = ke=-Go (6), -, t2 e (co, 6} 2).

[0057] It now follows that

M

D (a), = Emm1-iEmm2=111 (w, TriA c2)e -1,-yr7 2(0 will have period 1 in the el-direction and period 1/M in the e2-direction. It is now possible to choose the time delays 1m1.m2 such that the periodicity of D(w, el,e2) in the el direction is larger than 104 (where we in the definition of periodicity use a requirement of independence of f, discarding degenerate cases such as 1=0), and typically such that the periodicity becomes 1 (using the normalized setup with Ar= 1 as mentioned earlier on).

[0058] Let us now consider what happens for fixed values of w. Since the support of f lies inside a cone whose width is determined by the spatial sampling parameters and the propagation medium velocity, it follows that the footprint of f(w-2) will be a disk in the 2)-plane. Fig. 2 illustrates such a disk with two particular features marked "*" and "+". From the derived expression above it follows that D(w,e1A2) consists of the union of several, possibly overlapping, such disks. Whereas the information that is recoverable in a regular sampling scheme would only be parts of disks that do not overlap (see Fig. 3 where the "*" and "+" features are reproduced identically in all overlapping regions), it is possible to recover information even when the disks are overlapping in the case illustrated in this application, because of the fact that there are several disks with Odifferent information content overlapping (see Fig. 4 where CD the "*" and "+" features are now not reproduced identically in the horizontal direction but reproduced identically in the vertical direction). This implies that it is possible to design a set of linear equation to recover information well beyond what would be feasible in a standard sampling setup. It also allows for trading sampling information in the different sampling directions.

[0059] Fig. 5 and Fig. 6, show the part of the data that is used to solve for delineating the overlapping parts. In the case of regular sampling this will not be possible since the overlapping parts are all identical (Fig. 5). However, in the case of applying the sampling strategy in the inline direction as described in the present invention we see that the overlapping parts are different such that it is possible to determine where the marked features in the overlapping domains belong, provided that we know how the data were sampled in the inline direction (e.g., what time delay pattern that was used for the simultaneous source acquisition). As described above, the sampling in the inline direction can for instance be carried out using time-delays that vary periodically or randomly for instance in the inline direction. The sampling does not need to be identical in the crossline direction (the case illustrated in Fig. 4 and Fig. 6). However, it will be important to know what time delays that were used along the parallel sail-lines.

[0060] One such scenario would be a vessel travelling along a sail-line, where it is possible to collect information along that line fairly densely. To collect information not only along single lines, the vessel will have to travel along several sail lines. To obtain a dense sampling, these sail lines would therefore have to be laid out close to each other, and this results in that the total measurement scenario takes a long time.

[0061] Instead, the vessel could carry sources spread out in the direction perpendicular to the sail line. By using the (,) properties described above it is possible to obtain a sampling CD that provides full resolution up to a certain frequency too where the overlapping of disk does not prohibit perfect recovery, at an (more) equally spaced sampling lattice than what is obtained by acquiring data along individual sail lines.

Brief summary of the invention

[0062] The invention relates to methods for acquiring and separating contributions from three or more different simultaneously or near simultaneously emitting sources in a common set of measured signals representing a wavefield. In particular, the present invention relates to methods for first estimating at least two blends of contributions from at least two or more sources in at least one spatial direction. These blends are then interpolated or reconstructed in the at least one spatial direction. Finally the contributions from the three or more sources are separated in the horizontal plane from the interpolated or reconstructed estimated blends. The method of signal apparition or random dithering can be used to encode the sources in one or both horizontal directions. However, in a preferred embodiment the method of signal apparition is used to encode the sources in the at least one horizontal direction. In this embodiment, an encoding sequence is used that results in a number of lozenge-shaped or diamond-shaped regions that is smaller than the number of simultaneous sources such that the response of the sources cannot be fully separated until the resulting data blends have been interpolated or reconstructed to a denser sampling interval in the at least one horizontal direction and then fully decoded in the horizontal plane. The invention would apply equally to onshore and offshore seismic surveys, and for implosive, explosive or vibratory type sources.

[0063] Advantages, aspects and novel features of the present invention, as well as details of an illustrated embodiment (,) thereof-, may be more fully understood from the following

CD description and drawings. ('Si

CD Brief Description of the Drawings

[0064] In the following description reference is made to the attached figures, in which: Figs. 1A,B illustrate how in a conventional marine seismic survey along a single shot line all signal energy of sources typically sits inside a "signal cone" bounded by the propagation velocity of the recording medium and how this energy can be split in a transform domain by applying a modulation to a second source; Fig. 2 shows an illustration of a frequency plane for a receiver gather with sources shot on a 2D (x,y)-grid. The example illustrates a well-sampled case without any aliasing or interference of contributions from different sources during simultaneous source acquisition. The "*" and the "+" mark two features of interest within the signal cone; Fig. 3 shows an illustration of a frequency plane for a receiver gather with sources shot on a 2D (x,y)-grid. The example illustrates an under-sampled case where a single source was shot on a four times as sparse grid as that in Fig. 2, generating overlapping regions of replicated and shifted signal cones; Fig. 4 shows an illustration of a frequency plane for a receiver gather with sources shot on a 2D (x,y)-grid. The example illustrates a case of under-sampling in the y-direction but where apparition encoding has been carried out in the x-direction; Fig. 5 shows a zoom in of the region of interest in 1-- Fig. 3., where we would like to remove overlap between cones; a) CD Fig. 6 shows a zoom in of the region of interest in C)J Fig. 4., where we would like to remove overlap between CD cones; Fig. 7 shows a flowchart describing a preferred embodiment of the present invention; Fig. 8 shows a frequency slice at 6.48Hz through a 3D frequency-wavenumber transform (dimensions corresponding to temporal frequency, inline horizontal wavenumber and cross-line horizontal wavenumber) of the quad-source simultaneous source data recorded at a single receiver; Fig. 9 shows a frequency slice at 6.48Hz through a 3D frequency-wavenumber transform (dimensions corresponding to temporal frequency, inline horizontal wavenumber and cross-line horizontal wavenumber) of the contribution of source 1 at a single receiver; Fig. 10 shows a frequency slice at 6.48Hz through a 3D frequency-wavenumber transform (dimensions corresponding to temporal frequency, inline horizontal wavenumber and cross-line horizontal wavenumber) of the contribution of source 2 at a single receiver; Fig. 11 shows a frequency slice at 6.48Hz through a 3D frequency-wavenumber transform (dimensions corresponding to temporal frequency, inline horizontal wavenumber and cross-line horizontal wavenumber) of the contribution of source 3 at a single receiver; Fig. 12 shows a frequency slice at 6.48Hz through a 3D frequency-wavenumber transform (dimensions corresponding to temporal frequency, inline horizontal wavenumber and cross-line horizontal wavenumber) of the C) contribution of source 4 at a single receiver. (3)

O Detailed Description ('Si

CD [0065] A flowchart illustrating preferred embodiment of the present invention is shown in Fig. 7.

[0066] In a first step 701, a seismic survey with at least 3 simultaneous sources is acquired. The sources are encoded with respect to each other along at least one source line. That is the sources are excited at shot points along trajectories and fire with some distance in between shot points.

[0067] Under certain conditions the sources could be encoded relative to each other using signal apparition. However, instead of encoding the sources such that the sources can be separated from each other, in the present case we deliberately choose modulation sequences with a periodicity pattern that is smaller than the number of sources. This has the apparent disadvantage that the sources cannot be fully separated from each other. Instead, in a second step 702, it will only be possible to fully separate certain combinations of source contributions within the lozenge-shaped or diamond-shaped regions. However, it is seen as an advantage that these regions may be larger compared to a case where the periodicity of the modulation function would have been the same as the number of simultaneous sources.

[0068] In a third step 703, certain combinations of source contributions can now be reconstructed throughout the full frequency band for instance by means of analytic reconstruction as outlined above and in the prior art.

[0069] In a fourth step 704, the certain combinations of source contributions is interpolated or reconstructed to a finer shot point spacing along at least one of the trajectories. This step can be done as an integral part together with the reconstruction to the full bandwidth for instance using analytic reconstruction. (3)

CD [0070] Finally, in a fifth step 705, with the finely sampled C)J certain combinations of source contributions available along CD multiple adjacent shot lines, a full reconstruction in the horizontal place of individual source contributions can be carried out by considering sampling the same wavefield along a plurality of parallel sail-lines to unambiguously delineate regions of overlap in a Fourier-wavenumber plane of at least two spatial dimensions as described above and by Andersson and Robertsson (2018).

[0071] We note that the at least 3 simultaneous sources can be actual sources or (virtual) self-induced sources, also referred to as residual shot noise, or combinations thereof.

Example

[0072] A synthetic example was created using an acoustic 3D finite-difference synthetic data set mimicking a seabed seismic acquisition geometry over a complex sub surface model.

[0073] In the example a 25m by 25m shot grid was generated over a single seabed node receiver. The source had a spectrum up to 30Hz. An example was generated from the synthetic data mimicking a quad source acquisition where 4 sources towed next to each other are excited near simultaneously at every shot point. An apparition-style modulation sequence with periodicity 2 was used along each sail line using time shifts less than 50ms. Note that when the data is viewed from a single sail line, a modulation sequence of periodicity 2 is insufficient to separate the response from four sources. Instead, two different mixes of the four sources can only be obtained from such data rendering the separation problem underdetermined throughout the data bandwidth. (3)

CD [0074] In the simulated quad-source acquisition we use a different modulation sequence of periodicity 2 along the Nadjacent sail lines. In this example we simply shifted the CD modulation sequence by one spatial position from sail line to sail line.

[0075] Fig. 8 shows a frequency slice at 6.48Hz through a 3D frequency-wavenumber transform (dimensions corresponding to temporal frequency, inline horizontal wavenumber and cross-line horizontal wavenumber) of the data recorded at a single receiver. Again, if the data are only viewed along a single inline (i.e., imagine a line through cross-line wavenumber 0), it is only possible to see the intersection of two of the circles. However, when viewed in the full horizontal plane enabled by the acquisition of non-identical modulation sequences for adjacent shotlines as described above, the data are revealed to comprise 4 different regions bounded by circles (cones when viewed in the full 3D representation as a function of frequency).

[0076] It is instructive to note that whereas signal apparition is usually described as a partial shifting operation. However, Fig. 8 shows that it is the support of the data that changes when a modulation sequence is introduced.

[0077] Revisiting Fig. 8, it is now apparent that we have a well-posed problem that can be solved as we have four circle shaped regions and 4 unknown source contributions that contribute in different mixes in the four regions. Fig. 9, 10, 11 and 12 show the individual source contributions to all four regions.

[0078] The example demonstrates that the inline shotpoint interval can be made coarser without reducing the frequency below which the separation of sources is exact if multiple parallel shotlines are acquired. Conversely, if the inline and crossline shotpoint intervals are the same, a greater number of sources can be simultaneously activated. For Oexample, in the case of 25m shotpoint interval and 3 sources CD in a survey with a single acquisition line, if a full 3D survey with 25m inline and 25m crossline shotpoint interval was acquired, 9 sources instead of 3 could be simultaneously activated to obtain exact separation up to the same frequency as in the 3 source 2D single line survey.

[0079] Following the flowchart in Fig. 7, it is advantageous to for instance reconstruct two mixes of data on a line by line basis before the separation of the four sources. That will double the frequency below which the separation is exact. Methods in the prior art as the one using analytic quaternion reconstruction will benefit greatly from a bandwidth of exact separation that is twice as large. Once the reconstruction have been carried out in a line by line basis so that two mixes of four sources are available along each line, the data can be transformed in 3D to separate the contribution of each individual source from 4 mixes as illustrated in Fig. 8.

List of cited References [Abma et al., 2015] R. Abma, D. Howe, M. Foster, I. Ahmed, M. Tanis, Q. Zhang, A. Arogunmati and G. Alexander, Geophysics. 80, WD37 (2015).

[Akerberg et al., 2008] Akerberg, P., Hampson, G., Rickett, J., Martin, H., and Cole, J., 2008, Simultaneous source separation by sparse Radon transform: 78th Annual International Meeting, SEG, Expanded Abstracts, 2801-2805, doi:10.1190/1.3063927.

[Andersson et al., 2016] Andersson, F., Eggenberger, K., van Manen, D. J., Robertsson, J. 0. A., and Amundsen, L., 2016, Seismic apparition dealiasing using directionality regularization: 2016 SEG annual meeting, Dallas.

O[Andersson et al., 2017a] Andersson, F., Robertsson, J. 0. A., CD van Manen, D. J., Wittsten, J., Eggenberger, K., and Amundsen, L., 2017, Express Letters: Flawless diamond separation in simultaneous source acquisition by seismic apparition: Geophysical Journal International, 209 (3), 1735-1739.

[Andersson et al., 2017b] Andersson, F., van Manen, D. J., Wittsten, J., Eggenberger, K., and Robertsson, J. 0. A., 2017, Quaternion dealising for simultaneous source separation: 2017 SEG annual meeting, Houston.

[Andersson and Robertsson, 2018] Andersson, F., and Robertsson, J. 0. A., 2018, Method for acquisition and processing of seismic data: UK Patent Application GB1803535.2 [Beasley et al., 1998] Beasley, C. J., Chambers, R. E., and Jiang, Z., 1998, A new look at simultaneous sources: 68th Annual International Meeting, SEG, Expanded Abstracts, 133136.

[Bracewell, 1999] R. Bracewell, The Fourier Transform & Its Applications (McGraw-Hill Science, 1999).

[Halliday et al., 2014] Halliday and Laws, Seismic acquisition using phase-shifted sweeps: US Patent application US20140278119A1 (2014).

[Hager, 2016] Hager, E., 2016, Marine Seismic Data: Faster, Better, Cheaper?: GeoExpro, Vol. 13.

[Ikelle, 2010] L. T. Ikelle, Coding and Decoding: Seismic Data: The Concept of Multishooting. (Elsevier, 2010), Vol. 39.

[Kumar et al., 2015] R. Kumar, H. Wason and F. J. Herrmann, Geophysics. 80, WD73 (2015).

[Lynn et al., 1987] Lynn, W., Doyle, M., Larner, K., and Marschall, R., 1987, Experimental investigation of interference from other seismic crews: Geophysics, 52, 1501-(3) 1524.

[Moldoveanu et al., 2008] Moldoveanu, N.,Kapoor, J., and Egan, M., 2008, Full-azimuth imaging using circular geometry acquisition: The Leading Edge, 27(7), 908-913. doi: 10.1190/1.2954032 [Mueller et al., 2015] M. B. Mueller, D. F. Halliday, D. J. van Manen and J. 0. A. Robertsson, Geophysics. 80, V133 (2015).

[Robertsson et al., 2012] Robertsson, J. 0. A., Halliday, D., van Manen, D. J., Vasconcelos, I., Laws, R., Ozdemir, K., and Gronaas, H., 2012, Full-wavefield, towed-marine seismic acquisition and applications: 74th Conference and Exhibition, EAGE, Extended Abstracts.

[Robertsson et al., 2016] Robertsson, J. 0. A., Amundsen, L., and Pedersen, A. S., 2016, Express Letter: Signal apparition for simultaneous source wavefield separation: Geophys. J. Int., 206(2), 1301-1305: doi: 10.1093/gji/ggw210.

[Shipilova et al., 2016] Shipilova, E., Barone, I., Boelle, J. L., Giboli, M., Piazza, J. L., Hugonnet, P., and Dupinet, C., 2016, Simultaneous-source seismic acquisitions: do they allow reservoir characterization? A feasibility study with blended onshore real data: 86th Annual International Meeting, SEG, Expanded Abstracts.

[Stefani et al., 2007] Stefani, J., Hampson, G., and Herkenhoff, E. F., 2007, Acquisition using simultaneous sources: 69th Annual International Conference and Exhibition, EAGE, Extended Abstracts, B006.

[Wittsten et al., 2019] Wittsten, J., Andersson, F., Robertsson, J. 0. A., and Amundsen, L., 2019, Perfect partial SO, reconstructions for multiple simultaneous sources: Geophys. (3)

CD [Ziolkowski, 1987] Ziolkowski, A. M., 1987, The determination C)J of the far-field signature of an interacting array of marine CD seismic sources from near-field measurements: Results from the Delft Air Gun experiment: First Break, 5, 15-29.

Prosp, DOI: 10.1111/1365-2478.12761.

Claims (20)

1. Claims 1. Wavefield acquisition and/or processing method including the steps of (a) Obtaining wavefield recordings by at least one receiver of an underlying continuous wavefield that has a conic support in the temporal-spatial frequencywavenumber domain, based on the synchronous activation of at least three separate sources, being moved from shotpoint to shotpoint along a first spatial direction and repeating the activation along two or more activation lines, wherein the activation lines are distributed along a second spatial direction, and where each activation line comprises separate lines corresponding to the at least three separate sources; (3) (b) varying at least one parameter between the sources from one activation to the following along at least (,) one of the at least two spatial directions selected CD from one or more of a group consisting of source signal amplitude, source signal spectrum, source activation time, source location at activation time and source depth, such that the varying causes the support of the frequency-wavenumber representation of the obtained wavefield to be the union of at least two shifted replicas of the support of the frequencywavenumber representation of the continuous wavefield in at least one of the at least two spatial directions; (c) wherein the number of shifted replicas of a frequencywavenumber representation of the data from a single activation line is smaller than the number of sources such that only combinations of source contributions can be separated along each activation line when considered in isolation; (d) using the wavefield recordings from at least one additional activation line to separate the response from the individual sources from the combinations of source contributions obtained from single activation lines.
2. 2. The method of any of the preceding claims in which the varying of at least one parameter is periodic.
3. 3. The method of claim 1 in which the varying of at least one parameter comprises the superposition or a product of at least two varying functions where at least one of the functions is periodic.
4. T11
5. 5. The method of any of the preceding claims in which the CD varying of at least one parameter comprises time delays that are smaller than 100ms when comparing the firing time of individual sources.
6. 6. The method of any of the preceding claims where methods of dealiasing and/or reconstruction are used to recover the response due to the combinations of source contributions at a finer sampling interval along each activation line beyond the temporal frequency below which an unambiguous separation of the combination of sources along each activation line can be directly obtained.
7. 7. The method of claim 6 wherein dealiasing and/or reconstruction comprises the steps of forming the analytic part of recorded wavefield information, extracting a nonaliased representation of a part of the recorded wavefield, forming a phase factor from a conjugate part of an analytic part of the non-aliased representation, combining the analytic part of the recorded wavefield 4. The method of any of the preceding claims in which the varying of the at least one parameter between the sources from one activation to the following is different from each other along at least two activation lines.information with the phase factor to derive an essentially non-aliased function, applying a filtering operation to the non-aliased function, and recombining the filtered non-aliased function with the non-conjugated phase factor to reconstruct a representation of essentially dealiased recorded wavefield information.
8. 8 The method of claims 6 and 7 wherein dealiasing and/or reconstruction comprises the steps of iteratively forming analytic parts from parts of the dealiasing and/or reconstruction and using these parts in solvers of linear systems to increase the range of the dealiased and/or reconstructed part.
9. 9. The method of claims 6 to 8 wherein the quaternion analytic part is used instead of the analytic part.
10. 10. The method of claims 1 to 9 applied to marine seismic data or seabed seismic data where the sources are towed by (,) the same vessel.
11. 11. The method of claims 1 to 9 applied to marine seismic data or seabed seismic data where the sources are towed by at least two different vessels.
12. 12. The methods of claims 10 and 11 where airguns are used as seismic sources.
13. 13. The methods of claims 10 and 11 where marine vibroseis devices are used as seismic sources.
14. 14. The method of claims 1 to 9 applied to land seismic data where the sources belong to the same vibroseis source array.
15. 15. The method of claims 1 to 9 applied to land seismic data where the sources belong to at least two different vibroseis source arrays.
16. 16. The method of any of the preceding claims in which at least one of the at least two sources is towed at a greater depth than the other sources such that the source exhibits different notch frequencies to provide a broadband source effect for all of the at least two sources for wavelengths corresponding to and below the certain frequency.
17. 17. The method of any of the preceding claims wherein the wavefield is obtained at locations corresponding to a Bravais grid.
18. 18. The method of any of the preceding claims wherein the number of activation lines is eight or more.
19. 19. The method of any of the preceding claims wherein the number of shot points along an activation line is eight or more.T11
20. 20. The method of any of the preceding claims wherein the CD at least three simultaneous sources can be actual sources, self-induced source contributions resulting in residual shot noise, or combinations thereof.