Quantitative seismic analysis of a thin layer of CO2 in the Sleipnerinjection plume

Gareth Williams1 and Andrew Chadwick1

ABSTRACT

Time-lapse seismic reflection data have proved to be the keymonitoring tool at the Sleipner CO2 injection project. Thinlayers of CO2 in the Sleipner injection plume show striking re-flectivity on the time-lapse data, but the derivation of accuratelayer properties, such as thickness and velocity, remains verychallenging. This is because the rock physics properties arenot well-constrained nor are CO2 distributions on a small scale.However, because the reflectivity is dominantly composed ofinterference wavelets from thin-layer tuning, the amplitudeand frequency content of the wavelets can be diagnostic of theirtemporal thickness. A spectral decomposition algorithm basedon the smoothed pseudo Wigner-Ville distribution has been de-veloped. This enables single frequency slices to be extractedwith sufficient frequency and temporal resolution to provide

diagnostic spectral information on individual CO2 layers. Thetopmost layer of CO2 in the plume is particularly suitable forthis type of analysis because it is not affected by attenuationfrom overlying CO2 layers and because there are areas in whichit is temporally isolated from deeper layers. Initial application ofthe algorithm to the topmost layer shows strong evidence ofthin-layer tuning effects. Analysis of tuning frequencies onhigh-resolution 2D data suggests that layer two-way temporalthicknesses in the range 6 to 11 ms can be derived with an ac-curacy of c. 2 ms. Direct measurements of reflectivity from thetop and the base of the layer permit calculation of layer velocity,with values of around 1470 ms−1, in reasonable agreement withexisting rock physics estimates. The frequency analysis can,therefore, provide diagnostic information on layer thicknessesin the range of 4 to 8 ms. The method is currently being ex-tended to the full 3D time-lapse data sets at Sleipner.

BACKGROUND

Thin layers of CO2 in the Sleipner injection plume show strikingreflectivity on the time-lapse data, but the derivation of accuratelayer properties, such as thickness and velocity, remains very chal-lenging.It is well known that geologic strata produce characteristic fre-

quency tuning of propagating seismic waves, such that thin bedscause enhancement or suppression of preferred frequencies withinthe seismic spectrum depending on their temporal (traveltime)thickness. Spectral decomposition is a signal processing techniquethat allows the seismic signal to be decomposed into discrete fre-quency components, allowing spectral tuning effects to be evaluated(Partyka et al., 1999). Several authors have used spectral decompo-sition qualitatively and quantitatively to characterize stratigraphicalsequences on the basis of their frequency content (e.g., Chakraborty

and Okaya, 1995; Partyka et al., 1999; Sinha et al., 2005; Wang,2007; Chen et al., 2008). In many cases, certain of the decomposedfrequency components allow enhanced imaging of fine-scalestratigraphical and depositional features (e.g., Partyka et al., 1999;Laughlin et al., 2003).In this paper, we examine the possibility of using spectral decom-

position in a quantitative manner to assess the thickness and velo-cities of thin layers of dense-phase carbon dioxide in the injectedCO2 plume at Sleipner in the Norwegian North Sea. Early work onthe Sleipner time-lapse 3D seismic data used seismic amplitudesand time-shift analysis to estimate layer thicknesses (e.g., Artset al., 2004; Chadwick et al., 2004, 2005; Ghaderi and Landrø,2009), but this depended on deriving velocities from rock physics,with significant uncertainty. An alternative approach used structuralanalysis of the reservoir topseal topography to determine the thick-ness of the topmost CO2 layer (Chadwick et al., 2009; Chadwick

Manuscript received by the Editor 7 November 2011; revised manuscript received 7 June 2012; published online 24 September 2012.1British Geological Survey, Keyworth, Nottinghamshire, U. K. E-mail: gwil@bgs.ac.uk; rach@bgs.ac.uk.

© 2012 Society of Exploration Geophysicists. All rights reserved.

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GEOPHYSICS, VOL. 77, NO. 6 (NOVEMBER-DECEMBER 2012); P. R245–R256, 18 FIGS., 1 TABLE.10.1190/GEO2011-0449.1

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and Noy, 2010), but this gave no information on layer velocities. Preand poststack inversions have been used to derive layer properties(e.g., Delépine et al., 2011; Rubino and Velis, 2011; Velis andRubino, 2011), but these are not highly constrained and cannotproperly account for the strong modulation of reflection amplitudesby the thin layers. More recently, a constrained AVO technique hasbeen tested in which forward modeling was used to extract layerthicknesses from offset raypaths, again with inconclusive results(Sturton et al., 2010).This paper describes some initial findings from detailed analysis

of the seismic waveforms associated with the thin layers, in parti-cular by analyzing their spectral content. We look at the 3D time-lapse data and also some of the high-resolution 2D data acquiredover the Sleipner CO2 plume.

TIME-LAPSE SEISMIC IMAGING OF THESLEIPNER CO2 PLUME

Carbon dioxide separated from natural gas produced at the Sleip-ner field (Norwegian block 15/9) is being injected into the UtsiraSand, a regional saline aquifer of late Cenozoic age, in excess of200 m thick in the Sleipner area (Figure 1a). The aquifer comprisesmostly clean, unconsolidated sand of high porosity (>30%) andpermeability (>1 Darcy). Several thin intrareservoir mudstones,typically 1–2 m thick, are evident from geophysical logs acquiredin wells around Sleipner (Figure 1b).The CO2 is injected in a dense phase via a deviated well at a depth

of 1012 m below sea level, approximately 200 m beneath the topof the saline aquifer. Injection commenced in 1996 at a roughlyconstant rate, with around 13 million tons of CO2 stored by2011. A comprehensive deep-focused monitoring program has beendeployed, using several geophysical methods (Arts et al., 2008). Ofthese, time-lapse seismic has proven to be the key monitoring tool.A baseline 3D survey was acquired in 1994, with repeat surveys in1999, 2001, 2004, 2006, 2008, and 2010. In addition, a 2D high-resolution survey was acquired over the plume in 2006.The plume is imaged on the seismic data as several high-

amplitude subhorizontal reflections within the aquifer (Figure 2).Most of this reflectivity is thought to represent tuned responses fromthin layers of CO2 trapped beneath the intrareservoir mudstones,which are partially but not wholly sealing. The reflective layeringhad formed by 1999 with each individual reflection traceable on allof the subsequent surveys. As a general rule, the middle and upperreflections in the plume have increased in amplitude and lateralextent on successive time-lapse surveys, whereas the lower layershave ceased growing and in some cases have shrunk and dimmed.The plume is around 200 m in height and markedly elliptical in planview (Figure 2).A key objective of the Sleipner monitoring project is to demon-

strate that geologic storage of CO2 is a safe and verifiable technol-ogy. This requires that quantitative constraints can be placed ondynamic flow simulations of the injection process. The injection

well is near-horizontal at the injection point,so no wellbore penetrates either the CO2 plumeor the stratigraphy that the plume now occupies.Quantitative analysis is therefore challenging.Early work based on detailed interpretationand mapping established amplitude-thicknesstuning relationships for the reflective layers(e.g., Arts et al., 2004; Chadwick et al., 2004,2005). This was a reasonable approach for theearly surveys when layers were thin, but loca-lized decreases in layer reflectivity on morerecent vintages suggest that, in places, the tuningthickness is now being exceeded. In addition, re-flections from the lower layers have becomestrongly attenuated. This is thought, at least inpart, to reflect more fundamental seismic ima-ging problems in the deeper plume, in whichclassical poststack time migration is unable toadequately focus seismic energy. A furtherlimitation of simple amplitude — thicknessmodeling is that it requires reasonably accurateknowledge of layer velocities. This is not readilyavailable. Velocities can be obtained from rock

Figure 1. (a) Isopach map of the Utsira Sand. (b) Geophysical welllog from the vicinity of Sleipner. The reservoir sand has character-istically low gamma-ray (GR) readings and higher neutron porosity(NPHI). The gamma-ray peaks (neutron porosity troughs) withinthe sand denote thin mudstones.

Figure 2. Top panels show a cross section from the time-lapse 3D seismic data at Sleip-ner showing the baseline (1994) data set and a selection of the repeat surveys. Notestrong reflections corresponding to the CO2 plume with the topmost layer arrowed. Bot-tom panels show map views of the plume expressed as total reflection amplitude. Blackpolygons mark the extent of the topmost CO2 layer within the overall plume footprint.

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physics and tomographic inversion (e.g., Broto et al., 2011; Rossiet al., 2012), but in the absence of any independent constraints(no wellbore penetrates any of the CO2 layers), the rock physicsis uncertain. The properties of CO2 in the Utsira reservoir (in whichconditions are close to the critical point for CO2) are very sensitive

to temperature and pressure, and the former in particular is some-what uncertain (Alnes et al., 2011).

The topmost CO2 layer

Much of the recent quantitative analyses have focused on the top-most CO2 layer in the plume (Figure 3). There are two main reasonsfor this. First, the layer lies directly beneath the reservoir topseal,and due to the lack of overlying CO2, it is clearly and stably imagedwith no progressive signal attenuation through time. Second, thelayer spreads by buoyancy-driven lateral CO2 migration and pond-ing beneath the topseal topography. The latter can be mapped withreasonable accuracy because uncertainties largely reside with over-burden velocities, which are constrained by nearby wells.By 2006, the topmost layer was well-developed, forming an

irregular-shaped accumulation some 3 km from south to northand about 0.8 km from east to west (Figure 3). Layer thicknessescan be estimated directly on a trace-by-trace basis by taking thedifference in elevation between the topseal relief, and the spatiallyinterpolated CO2 — water contact on the same trace, with no re-quirement to know the velocity of the CO2 layer itself (Chadwicket al., 2009; Chadwick and Noy, 2010). In this study, topseal reliefwas calculated using a constant overburden velocity of 1857 ms−1

(as found in the nearby well 15/9-13). Computed values weresmoothed using a 50 × 50 m spatial filter to remove traveltime fluc-tuations induced by local noise (Figure 4a). Reflection amplitudescorrespond broadly but not exactly to the calculated thicknesses(Figure 4b). A prominent north-trending prolongation correspondsto northward migration of the CO2 beneath and along a linear ridgein the topseal surface (Figures 3 and 4).This paper investigates the potential application of time-

frequency analysis to further improve understanding of layer thick-nesses and velocities in the Sleipner plume, with particularreference to the topmost CO2 layer. We focus on the 2006 time-lapse seismic data because a high-resolution 2D data set is alsoavailable.

Figure 4. Map views of the topmost layer of CO2 in 2006. (a) Layerthickness calculated trace-by-trace from difference in elevation ofthe CO2 — water contact and the overlying base topseal (smoothedon 50 × 50 m spatial filter). (b) Reflection amplitudes.

Figure 3. Three-dimensional views of the top of the Utsira reservoirlooking northwest. (a) Shaded relief display of the reservoir top.(b) Reservoir top with superimposed reflection amplitude of top-most layer of CO2 in 2001. (c) Reservoir top with superimposedreflection amplitude of topmost layer of CO2 in 2006. Note the pro-minent north-trending tongue of CO2, which migrates beneath alinear ridge in the basal topseal surface. The white scale bar is1 km in length.

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ESTIMATING THE THICKNESS OF THIN LAYERSUSING TIME-FREQUENCY ANALYSIS

For a thin layer sitting in a homogeneous background medium,peak seismic amplitude of the tuned reflection wavelet occurs whenthe reflection from the layer top exhibits maximum constructive in-terference with the (reverse polarity) reflection from the layer base.This occurs when the layer two-way thickness corresponds to halfof the dominant seismic wavelength. The two way temporal tuningthickness T corresponds to half of the dominant seismic period. Ifthe velocity V of the layer is known, the tuning thickness can also beexpressed as a true (one-way) depth thickness (t). Tuning also oc-curs when the layer thickness is 3∕2, 5∕2, 7∕2, etc. times the seis-mic wavelength (corresponding to the second, third, fourth, etc.tuning peaks).Thus, for a wavelet of dominant frequency Fdom and a layer

velocity V,

T ¼ 1

2 � FDOM

(1a)

and

t ¼ V4 � FDOM

. (1b)

Tuning thickness is therefore a function of the dominant fre-quency in the seismic wavelet. Of more specific interest here isthe fact that discrete frequencies within the wavelet frequency spec-trum will be preferentially enhanced by thin-layer tuning. Thisprovides us with a potential diagnostic tool.This is illustrated by synthetic seismic modeling of a simple

wedge model of varying temporal thickness (Figure 5). The seismicwavelet is extracted from the Sleipner 3D data, with a frequencyrange roughly between 15 and 55 Hz, centered on 35 Hz. At layer

temporal thickness greater than the tuning thickness (∼14 ms), thelayer is resolved as two separate reflections from the top and bottominterfaces. Beneath the tuning thickness, the wavelet side lobes fromthe top and base interfaces interfere and the wedge is imaged as aninterference wavelet whose amplitude and frequency content varywith layer thickness (Figure 5a). The frequency response of thesynthetic seismogram (Figure 5b) shows the seismic response atdiscrete frequencies. For example, on the first tuning peak, temporalthicknesses of 10 and 25 ms produce tuning at frequencies of 50 and20 Hz, respectively. For this particular wavelet fdom ¼ 35 hz (seelater), the second tuning peak T ¼ 3∕2fdom only starts to influencethe signal at wedge thicknesses above about 24 ms, with the thirdtuning peak only significant at even greater thicknesses.It has been shown that the amplitude spectrum of the layer reflec-

tion computed over a short time window is a composite of the wa-velet spectrum and the tuning effect of the layer (Partyka et al.,1999). The temporal thickness of a layer can therefore be estimatedby identifying the tuning frequency from the discrete frequencycomponents extracted from the time-windowed seismic trace, givenappropriate spectral balancing to remove wavelet overprint (Partykaet al., 1999; Mahendra et al., 2006). With accurate layer velocityinformation, the true (depth) thickness of the layer can also be es-tablished.

The Wigner-Ville distribution (WVD)

To extract spectral information from single reflections from in-dividual layers in the Sleipner plume, it is necessary to analyze verynarrow traveltime windows (25 ms or less). Conventional lineartime-frequency analysis techniques such as the windowed Fouriertransform and continuous wavelet transform suffer from resolutionproblems. A narrow analysis window localizes the spectrum in timebut provides poor frequency resolution, whereas a broader windowloses temporal accuracy. The WVD (Wigner, 1932; Ville, 1948) —a member of the quadratic Cohen’s class of time-frequency trans-forms — can potentially overcome some of the limitations inherentin these techniques (Li and Zheng, 2008). The improved resolutionoffered by quadratic transforms (Figure 6) make them particularlysuitable for calculating the thickness of individual CO2 layers in theSleipner plume, which can only be satisfactorily isolated using ashort time window.Although less popular than the various linear transforms, the

WVD has been applied to the spectral decomposition of activeand passive seismic signals (Prieto et al., 2005; Wu and Liu,2006; Li and Zheng, 2008). The WVD function (see Wigner[1932] and Ville [1948] for a complete formulation) is calculatedby computing the power spectrum of a signal (the Fourier transformof the local autocorrelation function) and removing the integrationover time (equation 2). In effect, the WVD is constructed by com-puting the autocorrelation over all possible lags at each time sample(the local autocorrelation function) and transforming into Fourierspace;

Wxðt;vÞ ¼Z þ∞

−∞x

�tþ τ

2

�x��t −

τ

2

�e−i2πvτdτ; (2)

whereWx is theWigner distribution of a function x, t is time, τ is thelag, ν is the frequency, and * represents complex conjugation.The result is a quadratic function. As a consequence of this,

discrete events in a time series will produce cross terms in the

Figure 5. Seismic response of a simple low velocity wedge. (a) 2Dseismic section showing reflectivity tuning where wedge temporalthickness is less than 14 ms. (b) 2D seismic section as in (a), butshowing reflectivity as a function of frequency. Lines show the first,second, and third tuning peaks computed from equation 1a.

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time-frequency distribution (Figure 6d). The cross terms can be re-duced by smoothing with an appropriate filter kernel along the timegðx-tÞ and frequency hðτÞ axes (equation 3) to give the smoothedpseudo Wigner-Ville distribution (SPWVD).

SPWVDxðt;vÞ ¼Z þ∞

−∞hðτÞ

Z þ∞

−∞gðx − tÞx

�tþ τ

2

�x�

×�t −

τ

2

�dt e−i2πvτdτ. (3)

Smoothing leads to reduced resolution in thetime and frequency planes (Bradford et al., 2006;Wu and Liu, 2006; Ralston et al., 2007) forcing atrade-off between resolution and interference ef-fects (Figure 7).

Synthetic data example

To investigate the potential of the SPWVD tomap thin-layer tuning effects comparable tothose observed on the Sleipner seismic data, a2D synthetic seismic model was created. Rockphysics data based on core measurements andgeophysical well logs from the Utsira Sand wereused to calculate the key seismic properties(Table 1). Velocities for the sand — water— CO2 system were calculated for uniformand patchy fluid mixing, using, respectively,the Reuss and Hill averages (Figure 8).The model comprised a thin sand layer-

saturated with CO2 trapped beneath mudstonecaprock in a simple 2D domal closure (Figure 9),and assuming uniform fluid mixing at 100% CO2

saturation. The geometry of the CO2 layer ismodeled as a 2D dome (or ridge) increasing in thickness from zeroat the edges to 10 m at the apex (the latter corresponding to a two-way temporal thickness of about 14 ms for high CO2 saturations).The seismic section was generated by 1D convolution with a

Ricker wavelet of dominant frequency 60 Hz, similar to thehigh-resolution 2D data from Sleipner. Strong tuning is evidenton the flanks of the structure with maximum tuning of the full wa-velet at a layer thickness of 6 m (corresponding to a temporal thick-ness of 8.4 ms) which is consistent with the 60 Hz dominantfrequency (equation 1a). In the central part of the model, the tuningthickness is exceeded and the CO2 layer is explicitly imaged as se-parate negative and positive reflections from the top and base of thelayer, respectively.A set of isofrequency sections through the model were computed

using the SPWVD to demonstrate thin-bed effects on the time-fre-quency spectrum (Figure 10). The tuning thickness, correspondingto the peak amplitude of the power spectrum and highlighted with ablack arrow, clearly decreases with increased frequency. Thus, at adiscrete frequency of 35 Hz, tuning occurs at the layer crest(t ¼ 10 m), whereas at progressively higher frequencies the tuningpeak migrates down the flanks of the dome as the layer progres-sively thins, with the 70 Hz section showing tuning at about5 m layer thickness. It is clear therefore, that given sufficient band-width in the input data, the SPWVD is capable of quantifying bedthickness within the expected range for the CO2 layers at Sleip-ner (<10 m).

APPLICATION TO SLEIPNER SEISMIC DATA

In the following section, we present preliminary observationsfrom the spectral decomposition applied to the Sleipner 3D and2D high-resolution seismic data sets from 2006. This is not a sys-tematic or exhaustive analysis of the results but rather an insight intosome of the preliminary findings.The 3D data occupy a rectangular area some 6 × 3 km, covering

the current footprint of the CO2 plume (Figure 11a). The 2D linesare arranged in a radial configuration centered on the plume, plus

Figure 6. (a) Synthetic trace comprising four Ricker wavelets with peak frequencies of80, 60, 40, and 20 Hz. The sampling rate is 1 ms. Frequency decomposition using (b) thewindowed Fourier transform (computed in a 128-point Hanning window), (c) the con-tinuous wavelet transform, and (d) the WVD.

Figure 7. (a) Synthetic trace comprising four Ricker wavelets withpeak frequencies of 80, 60, 40, and 20 Hz. The sampling rate is1 ms. Frequency decomposition using (b) the WVD and (c) theSPWVD (smoothed using a 24-point Hanning window). Note thatthe obvious interference cross terms present in (b) have beensmoothed out at the expense of time-frequency resolution in (c).

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several parallel lines NNE–SSW and one E–W. Comparison of the3D and 2D data (Figure 11b and 11c) show the higher resolution ofthe latter, but at the expense of rather higher noise levels. Thesedifferences are confirmed by the frequency spectra (Figure 12a).The 3D data have a dominant frequency of around 35 Hz with use-ful frequencies up to around 75 Hz or so, whereas the 2D data peakis around 50 Hz, but with useful energy above 100 Hz. It is notablethat the low noise levels of the 3D data allow even its upper fre-quency limits to be usefully exploited.

Table 1. Parameters used to calculate the velocity anddensity of layers in the synthetic model shown in Figure 9.Initial values (of VP, VS, and density) for brine-saturatedUtsira Sand and the mudstone caprock were averaged fromselected well logs close to Sleipner.

Parameter Value

VP (mudstone caprock) 2270 ms−1

VS (mudstone caprock) 850 ms−1

Bulk density (mudstone caprock) 2100 kgm−3

VP (brine-saturated Utsira Sand) 2050 ms−1

VS (brine-saturated Utsira Sand) 620 ms−1

Bulk density (brine-saturated Utsira Sand) 2050 kgm−3

Porosity (brine-saturated Utsira Sand) 0.37

Brine density 1.040 kgm−3

CO2 density 690 kgm−3

KMATRIX 36.9 GPa

KFLUID 2.305 GPa

KCO20.088 GPa

Figure 8. Calculated rock physics parameters (VP and density) forthe rock-water-CO2 system for the Utsira Sand using the Reuss andHill averages for the uniform and patchy mixing bounds, respec-tively. Values of VP derived from layer reflection ratios are shownas a black line.

Figure 9. Synthetic model of a thin layer with 100% CO2-saturatedsand trapped beneath a 2D domal closure, and enclosed by water-saturated strata. Model assumes a Ricker wavelet of dominant fre-quency 60 Hz. (a) Velocity/density model. (b) Synthetic seismicsection from 1D convolution. The thick black traces on both flanksshow the tuning thickness for the seismic wavelet used in the con-volution. The values displayed on the horizontal axis represent thethickness of the rock-water-CO2 system. The zone between 0.4 and0.5 s has been decomposed into a sequence of time-frequency slicesshown in Figure 10.

Figure 10. Isofrequency sections at 35, 40, 50, 60, and 70 Hz com-puted using the SPWVD with a 24-point Hanning window for the2D domal model shown in Figure 9. The values displayed on thehorizontal axis represent the thickness of the rock-water-CO2 sys-tem. Arrows indicate the tuning thickness (for a layer velocity of1428 m∕s) at the extracted frequency.

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Evidence of frequency tuningon the 3D data

Full spectral analysis of the 3D data sets is on-going and beyond the scope of this initial paper.Here, we restrict discussion to preliminary ana-lysis that does show clear evidence of frequencytuning associated with changes in CO2 layerthickness.Discrete frequency cubes were generated from

the 3D data from 30 to 80 Hz at 5 Hz intervals.To correct for the fact that the frequency spec-trum of the seismic wavelet is not flat, spectralbalancing was required. For the purposes of thispreliminary analysis, a simple normalizationscheme was adopted — for each frequencyslice, the maximum amplitude seen across allof the seismic traces was scaled to a com-mon value.Particularly distinctive tuning effects on the

topmost layer are evident at the southern endof the prominent north-trending ridge of CO2

(Figure 13a). Discrete frequency slices (com-puted using the SPWVDwith a 24-point Hanningwindow) along a west-east section (Figure 13b)show low frequency tuning (∼40–50 Hz) at theridge crest, with higher frequency tuning peaksprogressively migrating down the ridge flanks.This tuning behavior is strikingly similar to thatof the synthetic 2D domal model shown inFigures 9 and 10. Reference to the tuning curves(Figure 13c) suggests therefore that theCO2 layerhas a temporal thickness of around 12 ms at theridge crest, thinning to around 6 ms at the 80 Hztuning peak. Characterization of the even thinneroutermost flanks of the ridge would require frequencies above80 Hz, which are beneath the noise floor of the data set.

Estimating CO2 layer temporal thickness throughspectral analysis

The 2D data are significantly higher frequency than the 3D datawith a relatively flat spectrum in the 10–75 Hz range and usefulfrequencies beyond 100 Hz (Figure 12a). As a consequence, it isreasonable to use a simple amplitude normalization procedure tobalance each spectral slice. Two intersecting seismic sections(STO698-07001 and STO698-06006) traversing the topmostCO2 layer from north to south and northeast to southwest, werechosen for spectral analysis (for location, see Figure 11a). Coinci-dent sections were extracted from the 3D data for comparison. The3D sections were balanced using wavelet spectra extracted over alarge time window through the 3D volume (Figure 12a).

2D seismic line STO698-07001 and coincident 3D data

The wavelet trough (blue on Figure 14a) marking the negativeimpedance contrast at the top of the topmost CO2 layer was pickedand also the corresponding peak (red on Figure 14a) marking thebase of the layer. It is clear that the layer has a somewhat variabletemporal thickness. In the north and the south, where the layer

Figure 11. (a) Map showing coverage of the 2006 3D survey (rectangle) and the 20062D high-resolution lines (black lines), with the reflection footprint of the 2006 plumeshown for reference. The areal extent of the top layer of CO2 is shown by a black line.The locations of the seismic profiles in Figures 14 and 16 are shown as thick white lines.(b) Three-dimensional seismic section through the upper plume. (c) Two-dimensionalhigh-resolution data along the same line of section as (b).

Figure 12. Plot of the smoothed power spectrum (a) and truncatedautocorrelation (b) for the 3D (dashed line) and 2D (solid line) seis-mic data sets. The truncated autocorrelation of a trace provides theamplitude characteristics of the wavelet’s Fourier transform. Powerspectra were extracted over a large time window (800–1500 ms) fortraces outside the plume and averaged to produce an estimate of thewavelet spectrum. Note that the peak-to-trough separations of the3D and 2D wavelets are ∼13 and ∼7 ms, respectively.

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thickens progressively from zero at its edges, the measured trough-to-peak temporal separation is notably consistent at ∼7 to 8 ms(Figure 14b), indicative of a tuning wavelet closely matching thetrough-to-peak separation of the seismic wavelet (Figure 12b). Here,in the tuning region, changes in layer thickness are manifest princi-pally as changes in reflection amplitude. Where the CO2 is thickesthowever (at 250–600 m distance in Figure 14), the tuning thicknessis exceeded and the high frequency content of the data has allowedthe top and base of the CO2 layer to be imaged explicitly. In theseregions, we can measure the true peak-to-trough time separation thatranges up to 10.5 ms; the systematic nature of these changes in tem-poral thickness can be clearly seen when plotted (Figure 14b).The SPWVD was used to compute a time-frequency volume in a

24-sample Hanning window about the topmost CO2 reflector and asequence of isofrequency sections were extracted from the time-frequency distribution (Figure 15). Tuning frequencies increasefrom the center of the section where layer thickness is greatest,out to the northern and southern ends of the section where layer

thicknesses decrease. Thus, tuning frequencies around 40–50 Hzdominate in the central parts, around 65–70 Hz on the midflanks,and around 75 Hz toward the ends of the section. This situation isdirectly comparable with the synthetic 2D dome model (Figures 9and 10), in which CO2 has accumulated in a topographic culmina-tion, with a roughly flat CO2–water contact.The tuning frequencies (the frequency with the highest amplitude

at each trace) extracted from the SPWVD can be converted intolayer temporal thicknesses via equation 1a. There is a goodcorrelation between the calculated (solid for 2D and broken linefor 3D) and measured (solid black circles) temporal thicknesses(Figure 14b), although discrepancies of some 1–2 ms (balanced3D) and 3–4 ms (2D) occur between 300 and 500 m distance. Thisdiscrepancy probably reflects frequency smoothing inherent in theSPWVD, although inaccuracies in time picking and residual wave-let overprint could also contribute to the mismatch.

2D seismic line STO698-06006 and coincident 3D data

Spectral decomposition (using the SPWVDwith a 24-sample Hanning window) was also ap-plied to 2D line STO698-06006, which images aculmination of the top reservoir surface (Fig-ure 16). For passive infill of caprock topography,the CO2 layer will be thickest at this point, at adistance of about 500 m (Figure 16b). The mea-sured trough-to-peak temporal separation (filledblack circles on Figure 16b) increases from thetuning value of about ∼7 ms at the southwesternend of the profile to ∼10 ms at 500 m. Again,there is a good correlation between the measuredtemporal thicknesses and temporal thicknessestimates based on the spectral analysis fromthe 2D data (solid black line in Figure 16b).Thickness estimates derived from the spectrallybalanced coincident 3D section also show areasonable match with the observed temporalseparations.The sequence of isofrequency sections along

the 2D line (Figure 17) again show that the tun-ing frequency increases from the center of the to-pographic high (at ∼500 m distance) to itsflanks.Both of the examples indicate that tuning fre-

quencies extracted from the SPWVD can providea direct measure of the temporal thickness of theCO2. Where the CO2 layer is thickest, the 2Dhigh-resolution data allow the frequency-derivedvalues to be compared with direct trough-to-peakmeasurements. It is clear that the lower frequency3D data can also provide useful information withthis technique, provided an appropriate spectralbalancing procedure is adopted.

CO2 LAYER VELOCITY

Temporal thickness estimates can be convertedto layer thickness provided the velocity of theCO2-saturated layer is known (see equation 1b).Velocity can be estimated from rock physics

Figure 13. Tuning at the southern end of the CO2-filled ridge. (a) Map view (lookingnorth) of the top of the Utsira reservoir, showing the outer extents of the topmost CO2layer in 2006 (black line) and the line of cross section. (b) Discrete frequency slices fromthe 3D data on a west–east cross section through the north-trending ridge of CO2 (com-puted using the SPWVD with a sliding 24-point Hanning window). (c) Tuning curvesshowing the relationship between frequency and two-way temporal thickness calculatedusing equation 1a.

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(Figure 8), but seismic parameters can be subject to significant un-certainty. For the high-resolution 2D seismic data, velocity can bederived directly from the reflectivity of the topmost CO2 layer inwhich the top and base reflections show temporal separation. Thisexploits the fact that the CO2 layer is overlain by caprock (water-saturated mudstone) with different acoustic properties to those ofthe underlying rock (water-filled sand) (Figure 18).For reflection at the top of the layer

RTOP ¼ A1 − A2

A1 þ A2

(4)

and for reflection at the base of the layer

RBASE ¼ A2 − A3

A2 þ A3

; (5)

where

RTOP ¼ reflection coefficient at the layer top;

RBASE ¼ reflection coefficient at the layer base;

A1 ¼ acoustic impedance of the caprock;

A2 ¼ acoustic impedance of the CO2 saturated sand in the layer;

and

A3¼acoustic impedance of water-saturated sand beneath the layer:

Equations 4 and 5 rearrange into a quadratic equation solving forA2 in terms of A2, A3, and the ratio RTOP∕RBASE. The latter is ap-proximately equal to the ratio of the reflection amplitudes from thetop and base of the reflector and so can be measured directly fromthe seismic data. The acoustic impedances of the caprock and virginaquifer are also available from well-logs and so A2 can be calcu-lated. The coefficients (A, B, C) in the quadratic are given by

A ¼ 1 −RTOP

RBASE

; (6)

B ¼ ðA3 − A1Þ ��1þ RTOP

RBASE

�; (7)

and

C ¼ A1 � A3 ��RTOP

RBASE

− 1

�: (8)

The ratio of the amplitudes of the reflections from the top andbase of the layer was measured for the central part of STO698-07001, where the tuning thickness is exceeded. It varies betweenapproximately 1.05 and 1.8, but with a well-defined mode of∼1.35 and a mean of 1.37 (Figure 18b). The variation will likely

Figure 14. Part of 2D line STO698-07001. (a) Seismic sectionshowing picks on the top and base of the top CO2 layer (for locationsee Figure 11a). (b) Plots of temporal thickness and reflection am-plitudes for the seismic section. The blue and red lines show rmsamplitudes extracted from a 4 ms window about the top and basereflector, respectively. The filled black circles show the measuredpeak-trough time separation, whereas the solid black line and bro-ken black line show temporal thickness estimates derived fromspectral decomposition of the 2D and a coincident (spectrally ba-lanced) 3D seismic profile. Spectral decomposition employed theSPWVD with a sliding 24-point Hanning window.

Figure 15. Normalized isofrequency sections extracted from thetime-frequency distribution computed in a 24-point Hanning win-dow about the topmost CO2 reflector shown in Figure 14b. Blackarrows indicate prominent examples of tuning: Reflection at thecrest of the structure (430 m) tunes at ∼50 Hz, on midflank(200 m) at ∼60 Hz and on the far flanks (50 and 760 m) at 70–75 Hz.

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reflect minor lateral changes in acoustic properties but is principallydue to noise. Taking this ratio as approximating to RTOP∕RBASE, wecan say

RTOP∕RBASE ¼ 1.37:

Measured values of VP and density (Table 1) give acoustic im-pedances for the caprock and water-saturated Utsira Sand as follows

A1 ¼ 4.88 × 106 ms−1:kgm−3

and

A3 ¼ 4.20 × 106 ms−1:kgm−3.

From these, the acoustic impedance of the CO2-saturated sand isgiven by the positive solution of the quadratic

A2 ¼ 2.85 × 106 ms−1:kgm−3:

To derive VP for the CO2-saturated sand, it is necessary to knowits density, which depends on the CO2 saturation. Core experimentson the Utsira Sand (E. Lindeberg, personal communication, 2003)indicate very low residual water saturations under drainage condi-tions, with layers greater than 2 m thick having average CO2 satura-tions in the range 0.8 to 0.9 (Chadwick et al., 2005). Again using theparameters from Table 1, CO2 saturations of 0.9 and 0.8 givewhole-rock densities of 1934 and 1947 kgm−3, respectively. Thesetranslate into VP values for the CO2-saturated sand of 1474 and

1464 ms−1, respectively. This is in good agreement with the valuesdetermined from the rock physics (Figure 8) and traveltime tomo-graphy (c. 1600 m∕s; see Broto et al., 2011) and provides an inde-pendent calibration of the rock physics velocity calculation. It is thecase, however, that derived velocities are very sensitive to the inputproperties of the overlying and underlying strata, and we believethat uncertainties are currently too high for firm conclusions tobe drawn regarding fluid mixing scales. More robust assessmentsof the key velocity and density parameters of the virgin sandand the immediately overlying caprock are required. This is plannedfor the next phase of work.

CO2 LAYER THICKNESSES

The CO2-saturated layer velocity values derived above can becombined with the results of the spectral analysis to estimate truethicknesses in the topmost CO2 layer. Along the 2D seismic lines,temporal layer thicknesses approach 10 ms around the structuralculmination of the layer. This converts to a layer true thicknessof ∼7 to 7.5 m. This is in good agreement with the 7 to 8 m rangederived from structural analysis of the topseal (Figure 4a). It is im-portant to stress that the latter does not use the CO2 layer velocityand so is a wholly independent estimate. Away from the structuralculmination a reasonable match is maintained down to thicknessesof 4 to 5 m, with temporal thicknesses of about 6 ms. The lattercorresponds to a frequency of 80 Hz (Figure 13c), which roughlymarks the maximum usable frequency in the data. Thicknesses less

Figure 16. Part of 2D line STO698-06006. (a) Seismic sectionshowing picks on the top and base of the top CO2 layer (for locationsee Figure 11a). (b) Plots of temporal thickness and reflection am-plitudes for the seismic section. The blue and red lines show rmsamplitudes extracted from a 4 ms window about the top and basereflector, respectively. The filled black circles show the measuredpeak-trough time separation, wheareas the solid black line and bro-ken black line show temporal thickness estimates derived fromspectral decomposition of the 2D line and a coincident (spectrallybalanced) 3D seismic profile, respectively. Spectral decompositionemployed the SPWVD with a sliding 24-point Hanning window.

Figure 17. Normalized isofrequency sections extracted from thetime-frequency distribution computed in a 24-point Hanning win-dow about the topmost CO2 reflector shown in Figure 16. As fre-quency increases, the zone of high spectral amplitude moves fromthe culmination at ∼500 m from the origin out to the margins. Blackarrows indicate tuning.

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than about 4 or 5 m cannot be characterized by the peak tuning/frequency content.

CONCLUSION

Thin layers of CO2 in the Sleipner injection plume are domi-nantly imaged as tuned wavelets and are potentially suitable forthe use of spectral analysis in assessing their temporal thickness.A spectral decomposition algorithm based on the SPWVD enablessingle frequency slices to be extracted with sufficient frequencyand temporal resolution to provide diagnostic spectral informationon an individual CO2 layer. The algorithm has been tested on 2Ddata but is equally applicable to 3D data. Initial investigationssuggest that for the topmost layer in the plume temporal thicknessescan be derived with an accuracy of 1–2 ms. On high-resolution2D data the layer is locally above the tuning thickness and measure-ment of top and base layer reflectivity permits direct calculation oflayer velocity. These values are in close agreement with the rockphysics.The work illustrates the potential, but also the significant chal-

lenges of deriving reliable properties for these thin layers. The top-most layer of the plume is rather suitable for this type of analysisbecause, as it spreads beneath the topseal, there are large areas onseveral of the time-lapse data sets in which it is not closely underlainby a deeper reflective layer. This enables the pure wavelet to beisolated for frequency analysis. Deeper in the plume the layersare very closely spaced. Their wavelets doubtless interfere, aboveand below, significantly affecting the accuracy of the method. On-going work is concentrating more on quantitative analysis of the 3Ddata sets, looking at time-lapse changes in frequency signature andhow these can be related to changing layer thicknesses. This is po-tentially a powerful approach because the independent informationon topmost layer thicknesses based on structural analysis of the top-seal topography gives the possibility of deriving true layer velocitieswithin the tuning domain.

ACKNOWLEDGMENTS

This publication has been produced with support from the CO2R-eMoVe Project and the BIGCCS Centre, whomwe thank for permis-sion to publish. CO2ReMoVe is funded by the EU 6th FrameworkProgramme and by industry partners BP, ConocoPhillips, ExxonMo-bil, Statoil, Schlumberger, Total, Vattenfall, and Wintershall.

BIGCCS is part of the Norwegian research pro-gram Centres for Environment-friendly EnergyResearch (FME) and is funded by the ResearchCouncil of Norway and an industrial consortium:Aker Solutions, ConocoPhilips, Det Norske Ver-itas AS, Gassco AS, Hydro Aluminium AS, ShellTechnology AS, Statkraft Development AS, Sta-toil Petroleum AS, and TOTAL E&P Norge AS.The authors publish with the permission of theExecutive Director, British Geological Sur-vey (NERC).

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