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`special topic
`Data Processing
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`Wide azimuth imaging and azimuthal velocity
`analysis using offset vector tile prestack migration
`
`Alexander Calvert,1* Edward Jenner,1 Robert Jefferson,1 Robert Bloor,1 Nicola Adams,2
`Rosemarie Ramkhelawan2 and Chris St. Clair3 make the case for the application of vector
`offset binning to many of today’s wide azimuth surveys. They say the approach is a natural
`complement to the surface-fitting method for azimuthal anisotropy analysis and used together
`allow efficient post-migration analysis for velocity anisotropy, providing insights into subsur-
`face fracturing and stress.
`
`T he industry is acquiring increasing numbers of
`
`wide azimuth surveys. In soft rock settings, such
`as the Gulf of Mexico, the objective is usually to
`improve illumination and imaging of obscured or
`structurally complex targets (e.g., Michell et al., 2007). In
`hard rock settings, the presence of significant azimuthal
`velocity anisotropy can actually degrade the image qual-
`ity of wide azimuth surveys when ignored (Williams and
`Jenner, 2001). If the anisotropy is measured and corrected
`for, the result is not only an improved image, but also
`valuable information related to the fracture and stress
`characteristics of the overburden and reservoir. Knowledge
`of fracture densities and orientations in tight rocks, where
`fractures are the dominant source of porosity and perme-
`ability, may allow improved well positioning and perform-
`ance. Understanding of the principal stress orientation may
`also permit more efficient planning and prediction of well
`fracturing.
`Traditional signal processing techniques often smear
`or ignore this azimuthal information and it is certainly
`lost in poststack or common offset prestack migration.
`Increasingly, more care is being taken to preserve and use
`this information through imaging to produce migrated
`azimuthal attributes for interpretation. In this paper we
`review field data experiences preserving, measuring and
`correcting for azimuthal velocity effects with prestack
`vector offset imaging.
`
`Measuring azimuthal velocity anisotropy
`The presence of azimuthal velocity anisotropy results in
`an elliptical variation of the measured NMO velocity with
`azimuth (Grechka and Tsvankin, 1998). When caused by a
`single set of aligned vertical fractures, the fast NMO veloc-
`ity direction is orientated along the fracture strike and the
`slow direction perpendicular to fracture strike. A number
`
`of approaches are currently being used in the industry to
`analyze for azimuthal velocities. These fall into three broad
`categories:
`(cid:78) Sectoring (e.g., Lynn, 2007). NMO velocity analysis is per-
`formed independently on azimuth sectored migrated sub-
`sets of the data, and then an azimuthally varying elliptical
`velocity is fit to these velocities. Lynn (2007) has suggested
`that sectoring approaches may suffer from accuracy issues
`related to the instability of independent velocity analysis
`and the limited data points available for velocity fitting.
`To obtain usable images the design of land surveys often
`requires large sector sizes (600, 450, or 300) providing few
`velocity points for ellipse fitting.
`(cid:78) Scanning (e.g., Sicking et al., 2007). Azimuthal velocity per-
`turbations from an isotropic or VTI background model are
`scanned over a 2D grid of test parameters (e.g., fast orienta-
`tion and % anisotropy). This approach is attractive when
`applied in conjunction with an azimuthally anisotropic
`migration, but requires compute intensive migration scan-
`ning and layer stripping with an inherent trade off between
`precision and compute time/cost.
`(cid:78) Surface-fitting (e.g., Jenner et al., 2001). An azimuthal
`NMO ellipse is simultaneously fit to the measured travel
`times as a function of offset and azimuth. A valuable fea-
`ture of the surface-fitting method is that it does not require
`the data to have any particular distribution as long as the
`offset/azimuth space is sufficiently sampled to constrain the
`anisotropic velocities.
`
`Measured elliptical NMO velocities should be converted
`to interval parameters using a generalized form of the Dix
`equation (Grechka et al., 1999). Attempting to determine
`interval parameters as a function of azimuth directly from
`picked NMO velocities using conventional Dix will result
`in an incorrect answer unless the anisotropy is weak or
`
`1 ION Geophysical, GXT Imaging Solutions, 225 E. 16th Ave., Suite1200, Denver, CO 80439 USA.
`2 BP America, 501 Westlake Park Blvd., Houston, Texas 77079, USA.
`3 VGS Seismic, Suite 306, 1117-1st Street SW, Calgary AB, T2R 0T9, Canada.
`*Corresponding author, Email: Alex.Calvert@iongeo.com.
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`one is fortunate enough to measure the velocities close to the
`principal directions of the interval of interest.
`Sectoring and scanning approaches have historically been
`applied to migrated data whereas surface-fitting approaches
`have predominantly been applied to unmigrated data. None
`of these approaches is inherently limited to either of these
`domains. Although surface-fitting has been applied to migrated
`data (Kappius, 2006), it has been more widely used for
`pre-migration analysis owing to the low fold and irregular
`design of many land surveys which makes them unsuitable for
`sectoring using prestack migration. As survey densities continue
`to increase, they become more suitable for prestack migration
`and post migration analysis. When possible, azimuthal velocity
`analysis after migration is preferred because structural dip can
`potentially bias measurements on unmigrated data resulting in
`artifacts that can be difficult to distinguish from anisotropy.
`
`Summary of offset vector tiling (OVT)
`The concept of using vector offset bins was proposed almost
`simultaneously and independently by Vermeer (e.g., 2002)
`under the name offset vector tile (OVT) and by Cary (1999)
`under the name common offset vector (COV). Until recently
`the approach has experienced limited usage perhaps related to
`the limited availability of surveys perceived to be suitable and
`awareness of the value of azimuthal information. The approach
`consists of defining vector offset migration bins (vs. the stand-
`ard scalar offset bins) with the two vector offset components
`aligned along the CMP grid axes. For a number of standard
`survey designs, the vector offset bin dimensions can be chosen
`such that each bin defines a single fold cube over the survey
`area populated with traces of similar offset and azimuth.
`To understand how these bin dimensions are chosen, it
`is useful to view an orthogonal land survey as a collection of
`single fold sub-surveys each acquired by a source-receiver line
`pair (Figure 1a and 1b). These sub-surveys are often referred
`to as ‘cross-spreads’. Traces from adjacent CMPs within a
`cross-spread have similar offsets and azimuths (Figure 1c&d).
`Selecting traces that fall within a range of inline and crossline
`offset defines a rectangular ‘tile’ of CMPs. If these vector offset
`ranges are chosen such that the tile width perpendicular to
`the shot lines matches the shotline spacing and the tile width
`perpendicular to the receiver lines matches the receiver line
`spacing, the corresponding ‘tile’ from an adjacent cross spread
`will be located next to the original tile with no gap or overlap
`(Figure 1e). If the shot and receiver station and line spacings are
`regular, collecting all of these tiles from all of the cross-spreads
`that make up the survey results in a volume of single fold data
`with similar offsets and azimuths (Figure 1f).
`Selection of the appropriate vector offset ranges to produce
`a tile with the required dimensions is best explained by start-
`ing in 2D. Consider a 2D survey with shots spaced every Δ(cid:0)S
`into a static spread of regularly spaced receivers. The CMPs
`from a shot located at x=0 recorded by receivers located from
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`first break volume 26, September 2008
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`0 <= x < 2Δ(cid:0)S will fall in the range 0 <= x < Δ(cid:0)S. The CMPs
`from the next shot located at x=Δ(cid:0)S from the same offset range
`are located at Δ(cid:0)S <= x < 2Δ(cid:0)S. They lie next to the CMPs from
`the previous shot with no gap or overlap. This relative CMP
`positioning will be true for all subsequent shots located at
`nΔ(cid:0) S. Selecting data with an offset range equal to twice the
`shot spacing selects a single fold data subset with no gaps
`in CMP coverage. This is the standard approach for offset
`binning 2D data to obtain single fold ‘common’ offset profiles
`(perhaps ‘similar’ offsets might be more accurate). To extend
`to 3D, if the shots have the same x coordinates but are now
`arbitrarily displaced in the y-direction, as they would be for a
`shot line orthogonal to the receiver line, the CMPs still have
`the same x-coordinates so the optimal vector offset range
` parallel to the receiver line is twice the shot line spacing.
`Similarly the appropriate range for the vector offsets parallel
`to the shot lines is twice the receiver line spacing.
`Although originally conceived for orthogonal survey
`designs, the OVT approach can be extended to survey designs
`
`Figure 1 An orthogonal land survey may be viewed as the sum of subsurveys
`acquired by each ‘cross-spread’ (a source-receiver line pair) (a). CMPs from a well
`behaved cross-spread fall on a single fold grid (b). Offsets increase progressively
`from the source-receiver line intersection. A rectangular ‘tile’ of CMPs have
`similar offsets (c) and azimuths (d). If the tile size is chosen to match the source
`and receiver line spacing, the same tile from the cross-spread associated with
`the adjacent shot line (dotted and cyan) will lie adjacent to the first tile (e).
`Collecting all the tiles from all the cross-spreads results in coverage of the full
`survey area with single fold data that has similar offsets and azimuths (f).
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`that exhibit 2D periodicity along the CMP grid axes (e.g., slant
`designs). For non-orthogonal designs the required vector offset
`ranges will not be twice the perpendicular distance between
`shot and receiver lines but twice the repeat period of the
`geometry along the CMP grid axes. The tiles defined by vector
`offsets in non-orthogonal geometries may not be rectangular.
`For example, the tiles for a slant design will be parallelograms
`but still tessellate.
` In summary, the OVT approach is a natural extension
`of the binning used for 2D surveys to 3D. It uses a Cartesian
`coordinate system of vector offsets aligned appropriately with
`the survey CMP grid. Conventional sectoring attempts to use
`a polar coordinate system of offset and azimuth for bin defini-
`tion which inherently cannot fit the 2D periodicity of most
`land survey designs (Figure 2). Such polar coordinate binning
`schemes will inevitably produce holes and/or overlaps requir-
`ing careful fold compensation to minimize migration artifacts
`and potentially reduce attribute quality. See Vermeer (2002)
`for a more detailed review of the theory and applications of
`cross-spreads and vector tiling.
`
`Azimuthal velocity analysis after OVT Migration
`The CIP gathers produced by OVT prestack time migration
`(PreSTM) are quite different from conventional offset gathers.
`In OVT gathers, scalar offsets are not linearly sampled and
`often duplicated so they cannot be processed or analyzed with
`tools that assume a constant offset spacing. This may also be
`a reason why the industry has historically favoured sectored
`migrations. Sectored migrations are usually parameterized to
`produce gathers with regularly spaced offsets within the sec-
`tors allowing standard scalar offset velocity analysis tools to be
`applied to each sector. Fortunately the surface-fitting approach,
`developed to deal with arbitrary offset/azimuth distributions in
`unmigrated data, is directly applicable to the OVT binning
`scheme. A similar workflow to that for pre-migration analysis
`may be used but the nominal OVT centre offset and azimuth
`now define the geometry of each trace.
`In an effort to understand the practical differences between
`sectored and OVT migration on azimuthal attributes, both
`migration approaches were applied to a reasonably dense
`survey in Canada (210 m receiver line spacing, 240 m shot line
`spacing at a 450 slant). Apart from some gaps in shot coverage,
`the slant design survey is very regular with excellent data
`quality over relatively flat structure. Figure 3 shows the fast
`and slow NMO velocity difference derived by surface-fitting
`both the sectored and OVT PreSTMs. Both approaches identify
`similar first order anomalies but also contain subtle differences.
`It is important to emphasize that as surface-fitting was used to
`obtain both results this is a comparison of the impact of the
`migration differences alone. We expect that application of the
`full sectored approach described above, including independent
`velocity analysis of sectors, would result in more significant
`differences. The standard error estimate, which accounts for
`
`Figure 2 The vector offset locations (red dots) of traces from nine adjacent
`CMPs drawn from a slant design survey in Canada illustrating the natural 2D
`periodicity of the vector offset sampling. An OVT binning approach (left) natu-
`rally fits the data distribution unlike a sectored binning scheme (right).
`
`both data distribution and misfit, implies that the OVT result is
`significantly more constrained. Examination of the velocity fit
`to the data confirms the increased scatter of the sectored result.
`As Figure 2 illustrates, the sectored migration has many CIP
`locations that did not contain a trace before migration. During
`migration these locations are populated by swinging data in
`
`Figure 3 Vfast-Vslow anisotropy results (top) and associated standard error esti-
`mate (middle) from post migration surface-fitting of OVT (left) and sectored
`(right) PreSTMs. Although similar, the OVT result appears better constrained.
`The velocity fit to the data at a higher anisotropy location (top, white arrow)
`suggests less migration noise is present in the OVT result (bottom).
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`from nearby traces resulting in subtle timing errors even for flat
`events. These observations are expected to be true in general
`but differences may diminish with increased survey density.
`
`Including azimuthal anisotropy in migration
`Once the azimuthal velocities have been determined, the data
`can be remigrated with a model and travel-time calculation
`that includes azimuthal anisotropy effects (Kappius, 2006).
`These azimuthal travel-times are calculated by using the
`appropriate velocity for the source to image point and image
`point to receiver azimuths. Figure 4 shows azimuth (0−1800)
`sorted gathers from applying this workflow to another dataset
`acquired in Wyoming, USA. Some of the events imaged using
`an isotropic PreSTM velocity model contain a consistent varia-
`tion in timing with azimuth which can be corrected for with an
`azimuthal RMO derived using surface-fitting. The azimuthal
`RMO partially corrects the gathers but some azimuthal resi-
`dual moveout remains. However, when the data are remigrated
`using the same azimuthally anisotropic velocity field that was
`used for the azimuthal RMO, the resulting gathers are flatter
`than the RMO result. This result was unexpected. Our expla-
`nation and hope is that the inclusion of azimuthal effects in
`migration results in subtle improvements in relative positioning
`of the wide azimuth prestack images, resulting in gathers that
`more accurately represent the relative timing and amplitude of
`events as a function of offset and azimuth.
`
`Some practical aspects
`The OVT approach fundamentally assumes a regular survey
`geometry with consistently spaced and parallel shot and recei-
`ver lines. In practice, obstructions or exclusions often require
`significant deviations from this ideal. We have found that the
`OVT approach is surprisingly robust even in the presence of
`significant but randomly distributed survey irregularities. In
`these situations additional steps need to be taken to compen-
`sate for fold variations and to remove large pre-migration gaps
`
`Figure 4 Example pair of azimuth sorted gathers (0-180 degrees) from isotropic
`OVT PreSTM (left), OVT PreSTM + azimuthal RMO (middle) and OVT PreSTM
`using the same azimuthal velocities used for the azimuthal RMO (right). The
`fast direction is approximately N-S. Note slight further gather flattening by
`accounting for azimuthal velocities in PreSTM.
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`that are populated by migration swing. Consistent or progres-
`sive differences in line spacing are problematic. This situation
`will probably most often arise when attempting to merge two
`or more surveys with different line spacings or orientations.
`These surveys cannot be imaged using a single set of OVT
`parameters. The surveys either need to be imaged separately
`with different OVT parameters or some form of regularization
`needs to be applied to transform the surveys to a common
`acquisition grid. A simplistic approach is to do this by trace
`borrowing and trace header manipulation but higher dimen-
`sional regularization and interpolation (e.g., Liu and Saachi,
`2004) is a better solution.
`Even if the survey is very regular, the line spacings and
`associated vector offset ranges can be so large that using the
`standard OVT binning scheme described above may produce
`only a few unique scalar offsets for velocity analysis. It is
`valuable to understand that although the tile must have certain
`dimensions, there is no constraint on the absolute location of
`the tile. One can define overlapping or random brick patterns
`of tiles to broaden the range of available offsets or even focus
`on a particular azimuth of interest.
`A first step to assessing the suitability of a survey for
`azimuthal analysis using OVT migration is to determine the
`nominal fold for offsets less than or equal to the depth of
`interest. As azimuthal NMO analysis is usually constrained
`to approximately this offset range, where moveout is approxi-
`mately hyperbolic, this is the approximate number of unique
`non-overlapping tiles available for analysis. The number of
`tiles required to obtain a robust result will depend on the data
`quality. Thirty to 40 unique tiles should provide sufficient sta-
`tistics for inversion of event travel-times for three anisotropic
`velocity parameters but we continue to test increasingly sparse
`surveys to understand where these limits lie practically.
`Cross-spread gathers and OVT volumes also offer an
`opportunity for data conditioning and regularization before
`migration. Both data subsets, when sorted by inline and
`crossline, produce 3D volumes with adjacent CMPs sampling
`the subsurface with similar offsets and azimuths. The
`progressive variation in offset and azimuth in a cross-spread
`gather make them a suitable domain for applying 3D
`algorithms such as F-Kx-Ky for coherent noise attenuation
`or FXY deconvolution for attenuation of incoherent noise.
`FXY has also proven very effective for attenuating incoherent
`noise in OVT volumes. Even though the full dataset is wide
`azimuth, perhaps leading one to believe that 5D interpolation
`is required for prestack interpolation, lower dimensional
`interpolation (2D or 3D) can be effective if the data is sorted
`to cross spreads or OVT volumes. Missing stations result
`in the loss of a single line or line segment of CMPs in these
`domains, so even simple 2D interpolation can be quite
`effective. OVT volumes also offer one further opportunity
`when large acquisition holes are present. As source-receiver
`reciprocity is rarely a bad assumption for P-wave data,
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`traces can be shared between reciprocal tiles to fill holes. If
`the survey is particularly ill-behaved, we have even found it
`advantageous to stack traces from reciprocal tiles after apply
`residual NMO to the nominal tile offset.
`The examples shown have all been drawn from onshore
`prestack time imaging projects where azimuthal anisotropy
`can be significant. OVT has also been proven very effective for
`isotropic depth imaging and velocity model building for wide
`azimuth marine streamer surveys (e.g., Michell et al., 2007).
`Areas of ongoing research include extending the techniques
`described in this paper to increasingly irregular surveys and
`more challenging imaging environments.
`
`Conclusions
`OVT and cross spreads offer many practical opportunities for
`today’s modern wide azimuth surveys. PreSTM using vector
`offset binning provides data well suited to azimuthal analysis
`when used in conjunction with surface-fitting. The resulting
`attributes appear better constrained than those produced by
`conventional sectoring. The azimuthal analysis results can
`be used for a further migration including azimuthal anisot-
`ropy in the travel-time calculations that may produce addi-
`tional improvement in gather flatness and stack quality. OVT
`appears effective for a greater variety of survey geometries
`than perhaps previously thought. Sorts into cross-spread and
`OVT gathers also offer many opportunities for data condi-
`tioning and regularization prior to migration.
`
`Acknowledgements
`The authors would like to thank BP America and VGS
`Seismic for permission to show these data, Craig Cooper
`at BP for his ongoing support of our work, and the many
`people at GX Technology who helped with this work and
`the associated software. We also thank Gijs Vermeer for the
`
`informative discussions and references as well as his sugges-
`tions to improve the paper..
`
`References
`Cary, P.W. [1999] Common-offset-vector gathers: an alternative to cross-
`spreads for wide-azimuth 3-D surveys. 69th SEG Annual Meeting, 18,
`1496-1499, Expanded Abstracts.
`Grechka, V. and Tsvankin, I. [1998] 3-D description of normal moveout in
`anisotropic inhomogeneous media. Geophysics, 63, 1079–1092.
`Grechka, V., Tsvankin, I. and Cohen, J. K. [1999] Generalized Dix equation
`and analytic treatment of normal-moveout velocity for anisotropic
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`Jenner, E., Williams, M. and Davis, T. [2001] A new method for azi-
`muthal velocity analysis and application to a 3D survey, Weyburn
`field, Saskatchewan, Canada. 71st SEG Annual Meeting, 20, 102-105,
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`Kappius, R. [2006] Prestack time migration with azimuthal veloc-
`ity anisotropy. In Grechka, V., Helbig, K. and Pšenčík, I. (Eds) The
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`Liu, B. and Sacchi, M.D. [2004] Minimum weighted norm interpolation of
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`Sicking, C., Nelan, S. and McLain, W. [2007] 3D azimuthal imaging. 77th
`SEG Annual Meeting, 26, 2364-2367, Expanded Abstracts.
`Vermeer, G. J. O. [2002] 3-D seismic survey design. SEG, USA.
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`Meeting, 20, 126-129, Expanded Abstracts.
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