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GEOPHYSICS, VOL. 73, NO. 6 �NOVEMBER-DECEMBER 2008�; P. C23–C30, 10 FIGS.10.1190/1.2978337

pectral-decomposition response to reservoir fluidsrom a deepwater West Africa reservoir

anglin Chen1, Gianni Matteucci2, Bill Fahmy3, and Chris Finn4

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ABSTRACT

We study the spectral-decomposition response to reservoirfluids from a deepwater West Africa reservoir through a sys-tematic modeling approach. Our workflow starts from select-ing the seismic data �far-angle seismic images� that showmore pronounced fluid effect based on amplitude-versus-off-set �AVO� analysis. Synthetic seismic forward modeling per-formed at the control well established the quality of the seis-mic well tie. Reservoir wedge modeling, spectral decomposi-tion of the field and synthetic seismic data, and theoreticalanalyses were conducted to understand the spectral-decom-position responses. The reservoir fluid type is a main factorcontrolling the spectral response. For this deepwater reser-voir, the amplitude contrast between oil sand and brine sandis higher at low frequencies ��15 Hz�. In addition, syntheticmodeling can help identify the possible frequency bandwhere the amplitude contrast between hydrocarbon sand andbrine sand is higher. When properly included in a comprehen-sive direct-hydrocarbon-indicator �DHI�–AVO evaluation,spectral decomposition can enhance the identification ofhydrocarbons.

INTRODUCTION

Spectral-domain seismic data attributes have been useful forome applications in hydrocarbon-reservoir characterizations. Forxample, Dilay and Eastwood �1995� analyze seismic data in thepectral domain for monitoring bitumen production by cyclic steamtimulation �steam injection� at Cold Lake,Alberta, Canada. Partykat al. �1999� discuss spectral-decomposition analysis and interpreta-ion of 3D seismic data. They show how channel details and discon-

Manuscript received by the Editor 16 November 2007; revised manuscript1ExxonMobil Upstream Research Company, Houston, Texas, U.S.A. E-m2ExxonMobil International Limited, London, U.K. E-mail: gianni.matteuc3ExxonMobil Exploration Company, Houston, Texas, U.S.A. E-mail: bill.4ExxonMobil Production Company, Houston, Texas, U.S.A. E-mail: chris2008 Society of Exploration Geophysicists.All rights reserved.

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inuities could be imaged and mapped better with spectral-decompo-ition results. Both studies used a Fourier transform over short timeindows, or short-time Fourier transform �STFT�.Chakraborty and Okaya �1995� compare different methods for

erforming frequency-time analysis on seismic data. They show thathe STFT method suffers from time-frequency resolution limita-ions. Improved spectral-decomposition results could be obtainedy methods such as discrete wavelet transform and matching pursuitlgorithm. Castagna et al. �2003� apply instantaneous spectral analy-is to seismic data and obtain high-resolution spectral-decomposi-ion images. They illustrate how spectral-decomposition results aresed to detect low-frequency shadows beneath gas-sand reservoirs.elated studies also show that spectral decomposition could be used

o image hydrocarbon sands at certain frequency bands �Burnett etl., 2003; Sinha et al., 2003�.

In this paper, we use instantaneous spectral analysis �Castagna etl., 2003� to study the spectral-decomposition response to reservoiruids from a deepwater WestAfrica reservoir �Figure 1a�. From am-litude-versus-offset �AVO� analysis, fluid effect is more pro-ounced in far-angle seismic traces �class IIp�. Our analysis there-ore focuses on far-angle stack seismic data. Spectral decompositionf far-angle stack seismic images reveals that the amplitude contrastetween the oil sand and downdip brine sand is higher at low fre-uencies �Figure 1b�. A systematic seismic forward-modeling ap-roach helps us to understand the response.

Four key factors control the spectral-decomposition response of aeservoir: thickness, stratigraphy �i.e., reflectivity series�, fluid type,nd effective attenuation. For this reservoir, the reflectivity seriesnd fluid type are the main controlling factors. We do not discuss de-ails of our work on the other two factors because the focus of this pa-er is the effect of reservoir fluids. We show that reservoir fluid types a main factor controlling spectral response. Synthetic modelingan be used to identify the possible frequency band where the ampli-ude contrast between hydrocarbon sand and brine sand is higher.

d 25 January 2008; published online 24 October 2008.lin.chen@exxonmobil.com.onmobil.com.@exxonmobil.com.xxonmobil.com.

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METHODS AND WORKFLOW

First, we performed seismic well tie at the control well. Towardhis end, wireline sonic logs and density logs were blocked �Figurea�. A far-angle synthetic seismic trace was generated through iso-ropic synthetic seismic forward modeling using a ray-tracing meth-d �Figure 2b�. The tie achieved a crosscorrelation coefficient of4% over the reservoir interval �Figure 2c�. This high-quality syn-hetic/seismic field data tie gave us confidence in the quality of logsnd input seismic data. Rock properties �P-velocities, S-velocities,nd densities� from this well were the foundation of our simulations.

We then studied in detail the spectral-decomposition response toifferent reservoir fluid fills �gas, oil, and brine� of a wedge model.ock properties of sand and shale in models were taken from the av-

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igure 1. �a� Interval average absolute amplitude �AAB� map of aeepwater West Africa reservoir. Red regions have high AAB val-es, as indicated by the color scale bar on the right. Black polygonsre fault zones. For scale, the width of the field �high AAB region� isbout 2 km. �b� Spectral-decomposition frequency slices of a seis-ic traverse �AA�: blue line in Figure 1a� showing oil-leg brighten-

ng on the 15-Hz section relative to the brine leg. The time scale isbout 600 ms for each image.

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igure 2. �a� Original and blocked logs at the control well used forodeling. �b� Gamma-ray log, P-impedance log, and far-angle seis-ic �black� to synthetic �green� plane-wave convolution well tie. �c�ample-by-sample crossplot of far-angle synthetic trace amplitudeersus far-angle field seismic stack trace with regression line thathows a correlation coefficient of 94%.

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rage of some typical deepwater WestAfrica reservoirs used in a pre-ious seismic/well-tie study �Gratwick and Finn, 2004; Gratwicknd Finn, 2005�. Figure 3a shows acoustic impedance models oftudied reservoirs. Near-angle �Figure 3b� and far-angle syntheticeismograms were generated with a plane-wave convolution ap-roach. Spectral decomposition of synthetic seismograms was per-ormed, and two spectral attributes �peak frequency and peak ampli-ude� were calculated for analyses. More than 1000 models were an-lyzed. These models examined the effect of attenuation, elastic an-sotropy, different acoustic properties for the encasing shale, andormal-moveout �NMO� stretch on far-angle synthetic traces. In ad-ition to the plane-wave convolution approach, we also used ray-racing and wave-equation modeling to examine the effect of differ-nt modeling algorithms on spectral-decomposition output.

In the second part of the study, reservoir rock-property modelsere generated by perturbing the control well logs stochastically to

pan model parameters �Vshale: shale volume fraction, porosity, andhickness� observed in logs from wells that penetrated this reservoir.

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igure 3. �a� P-impedance and S-impedance models of the schematiceservoir 30 m thick. Three bottom shale properties were modeled toxamine the effect of symmetrical and nonsymmetrical shale cas-ngs. �b� The 15°-equivalent synthetic seismograms for wedge mod-ls with symmetrical encasing shale properties.

odel parameters were adjusted based on comparisons of spectral-ecomposition attributes from the synthetic seismograms and fieldeismic images. Thousands of models were generated in each simu-ation while adjusting the model parameters. Figure 4 shows the dis-ribution of three key parameters from the final models:

Total sand thickness � �sand 1�4 Thickness, �1�

Avg net porosity ��sand 1�4�Thickness � Porosity�

Total sand thickness,

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igure 4. Distribution of average sand properties in final models forhe WestAfrica reservoir.

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Total shale thickness � �sand 1�3 Thickness. �4�

An extension of the Xu-White �Xu and White, 1995� sand/shaleodel was used to convert porosity and Vshale values to VP, VS, and

ensities as input to reservoir models to compute synthetic seismo-rams.

Two types of displays were used to examine the spectral-decom-osition response of reservoir fluids: peak frequency versus grosseservoir thickness and spectral ratios from hydrocarbon models,nd the brine model at representative sand thicknesses. The formerrovides an abstract illustration of the frequency response of the syn-hetic to the reservoir fluid changes. The latter shows the amplitudeontrast between different fluid-filled reservoirs and highlights therequency range over which the largest amplitude contrast may oc-ur.

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igure 5. �a� Peak frequency versus gross reservoir thickness of 15°-quivalent seismograms �symmetrical encasing shale�. �b� Vertical-ncidence traveltime �time thickness� of the reservoir versus grosseservoir thickness. �c, d� Peak frequency versus gross reservoirhickness for �c� 15° and �d� 40° synthetic seismograms from aedge model encased in nonsymmetrical shale. The separation be-

ween thick and thin sands is based on the crossover of the peak-fre-uency curves between the hydrocarbon scenarios and the brine sce-ario.

RESULTS AND DISCUSSION

edge-model results

Figure 5a shows results for 15°-equivalent synthetic seismogramsrom wedge models �1–35 m� encased in symmetric shale �samecoustic impedance for the shale above and below the reservoir�.otice, in this case, how peak frequencies decrease monotonicallyith increasing gross reservoir thickness as a consequence of the in-

reasing time duration for the acoustic wave to propagate throughhe reservoir sand �Figure 5b�. The small separation in peak frequen-y between different reservoir fluids is because of small time-thick-ess differences.

The situation becomes more complicated for models with non-ymmetric shale casing �acoustic impedance is different between thehale above and below the reservoir�. The spectral response is com-licated by the nonsymmetric interference effect of wavelets at theop and bottom of the reservoir, in addition to the time-thicknesshanges. Figure 5c and d shows the peak frequency versus gross res-rvoir thickness for the 15°-equivalent and 40°-equivalent models.wo regimes can be distinguished: for thin sand, the peak frequencyf the hydrocarbon sand is higher than the brine sand; for thick sand,he peak frequency of the hydrocarbon sand is lower than the brineand. In comparison with near angle, the maximum peak-frequencyeparation at far angle increases by �50% for a thin sand regime and100% for thick sand. A detailed explanation of the phenomenon is

rovided in a later section using the convolution model.The consequence of peak-frequency shifts because of different

eservoir fluid fills is demonstrated through spectral-ratio plots inigure 6. The left column of Figure 6 �Figure 6a and c� shows resultsor a 5-m sand �thin sand� model. The right column �Figure 6b and d�hows results for a 30-m sand �thick sand� model. For clarity, three

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igure 6. �a, b� Interval-averaged spectra and �c, d� their ratios for5°-equivalent synthetic seismograms of �a, c� a 5-m sand modelnd �b, d� a 30-m sand model.

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instead of five� fluid-fill scenarios were plotted: dry gas, light oil,nd brine. Figure 6a shows interval-averaged amplitude spectra for-m gas sand, oil sand, and brine sand models. Figure 6c shows thepectral ratio versus frequency. The peak-frequency shift towardigher values, as brine is replaced by hydrocarbon, causes a mono-onic increase of spectral ratios with frequency between hydrocar-on and brine scenarios. We expect that hydrocarbon sand is betterlluminated at higher frequencies. For example, at 50 Hz, the hydro-arbon-sand and wet-sand contrast is more than 30% higher than at0 Hz, the Ricker-wavelet frequency used to generate syntheticeismograms.

For thick sand �Figure 6b and d�, as brine is replaced by hydrocar-on, the peak frequency of the spectrum shifts to lower values. Thiseak-frequency shift causes a low-frequency peak in the spectral ra-io between hydrocarbon sand and wet sand �Figure 6d�. As a conse-uence, the hydrocarbon sand would be better illuminated at fre-uencies near this low-frequency peak. The contrast between gasand and wet sand is more than 40% higher at 16 Hz than at 30 HzRicker-wavelet frequency�. For oil sand and wet sand, the contrasts about 24% higher at 16 Hz than at 30 Hz.

We can explain these results in the spectral domain invoking theonvolution approach. With the convolution model, the amplitudepectrum of the synthetic seismogram is the product of the reflectivi-y spectrum with the wavelet spectrum:

Time domain: S�t� � RC�t� � Wavelet�t� �5�

Spectral domain: S��� � RC��� � Wavelet��� . �6�

In this study, a 30-Hz Ricker wavelet was used. The wavelet spec-rum peaks at 30 Hz �Figure 7b�. Reflectivity spectra for thin hydro-arbon sand increase monotonically with increasing frequenciesFigure 7a�. Multiplication of monotonic increasing-reflectivitypectra with the Ricker-wavelet spectrum leads to a higher peak fre-uency of the final spectrum than the peak frequency of the Rickeravelet �Figure 7c�. For thin brine sand, the situation is different.eflection coefficients from the top and base of the sand have the

ame sign and form an even pair. The reflectivity spectrum is a broadosine curve and decreases monotonically with increasing frequen-ies over the frequency range used in the modeling �1–80 Hz�. Mul-iplying the reflectivity spectrum with the Ricker-wavelet spectrumhifts the peak frequency of the final spectrum to a lower value thanhe peak frequency of the wavelet spectrum �Figure 7c�. Figure 7d-fhows the convolution model for thick-sand reservoirs. Examplesere serve as illustrative cases on the controlling effect of the reflec-ivity series on spectra.

The deepwater West Africa reservoir analyzed in this paper be-ongs to the thick-sand regime reservoir �see Figure 4, total sandhickness plot�. The effect of attenuation was investigated withave-equation modeling and was found to be relatively small �less

han 1 Hz� for single-cycle oil-filled reservoirs.

he West Africa reservoir

Figure 8a-d is an average absolute amplitude �AAB� map over theeservoir interval from the full-band far-angle seismic stack �Figurea�, low-frequency �13-Hz� spectral decomposition �Figure 8b�,ominant frequency �25-Hz� spectral decomposition �Figure 8c�,nd high-frequency �37-Hz� spectral decomposition �Figure 8d�.he thin white polygon outlines the oil-water contact, confirmed byell data. Low-frequency �13-Hz� spectral decomposition provides

etter separation between the oil-leg �bright� and brine-leg �dim/lue� amplitudes. The 25-Hz spectral-decomposition map �Figurec� has a very similar amplitude pattern to the input full-band seis-ics �Figure 8a� because the dominant frequency of the full-band

eismic data is about 25 Hz. The high-frequency �37-Hz� spectral-ecomposition map �Figure 8d� shows that high-amplitude patternsleed across the oil-water contact �upper-left area�. The change ofigh-amplitude patterns inside the white polygon �the reservoir� isaused primarily by the variation in the thickness of the reservoir in-erval and net-to-gross sand volume fraction. Note a dim area insidehe reservoir �upper region inside the white polygon�. This is be-ause of the interference effect of an overlying reservoir that was notnvestigated in this study.

Figure 8e and f further demonstrates the difference of the seismictack response in the spectral domain between the oil leg and brineeg. Figure 8e shows five rectangular regions over which average in-erval spectra in Figure 8f were calculated. Three regions are in theil leg, with corresponding spectra black. Two regions are in therine leg with corresponding spectra red. Two effects are clear fromrine-leg spectra to oil-leg spectra: amplitude brightening �highereak amplitude� and peak frequency shift to lower values.

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igure 7. Modification of the Ricker spectrum �middle column� byeflectivity spectra �left column� for �a-c� thin-sand models and �d-f�hick-sand models �red curves are gas sand; green curves are oiland; blue curves are brine sand�.

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To understand the spectral response of seismic images in the oilnd brine legs, we performed synthetic seismic forward modeling onogs at the control well �Figure 9a� from the oil scenario �in situ� andrine scenario �through Gassmann fluid substitution�. Figure 9bhows far-angle synthetic seismic traces. The left trace is for the oilcenario, and the right trace is for the brine scenario. Three horizon-al lines indicate the top of the reservoir �black�, the base of the oileservoir �green�, and the base of the reservoir for the brine-fill sce-ario �blue�. There is a noticeable upward time shift in the reservoirase when oil is replaced by brine because of faster velocities in therine-filled reservoir. Accordingly, the frequency content of therine scenario is higher, as shown in Figure 9c. Plotted in Figure 9cre Fourier spectra for two synthetic traces in Figure 9b and theicker-wavelet spectrum �black curve�. Notice the similarity be-

ween spectra for oil and brine scenarios in Figure 9c and Figure 8f:

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igure 8. Interval average absolute amplitude �AAB� of �a� the inputto spectral decomposition� full-band far-angle seismic stack, �b� 13Hz spectral decomposition, �c� 25-Hz spectral decomposition, andd� 37-Hz spectral decomposition. For scale, the width of the fieldhigh-amplitude region� is about 2 km. �e� 27-Hz �approximateominant frequency of the seismic data� AAB map averaged overhe top and base of the reservoir interval. Five rectangular areas wereutlined over which spectra in �f� were calculated.

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igure 9. �a� Gamma-ray, P-wave, S-wave, and density logs at theontrol well. For the P-wave, S-wave, and density logs over the res-rvoir interval ��20–60-m relative depth�, green curves show the oilcenario �in situ�, and blue curves show the brine scenario �obtainedy Gassmann fluid substitution�. �b� Far-angle synthetic seismicraces generated from the velocity and density logs in �a�. The leftrace is for the oil scenario �in situ logs�, and the right trace is for therine scenario �fluid-substituted logs�. �c� Interval averaged Fourierpectra of the synthetic seismic traces in �b�. The green curve is forhe oil-scenario trace and the blue curve is for the brine-scenariorace. The black curve is the Ricker-wavelet spectrum.

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eak amplitude reduction and peak frequency shift toward higherrequency. Thus, the spectral-response modeling at the control wellFigure 9c� explains the main features of the spectral-decompositionesponse of the field seismics �Figure 8f�.

A more elaborate modeling approach was done by stochasticallyarying the reservoir properties at the control well, based on infor-ation obtained from other wells drilled into this reservoir and seis-ic isochrons �for thickness variation�. Two spectral attributes were

xtracted from the spectral decomposition of synthetic seismic trac-s and field seismic data for comparison. These are peak amplitudesnd peak frequencies computed from averaged interval spectra overhe reservoir interval. Results are plotted in Figure 10. Figure 10and b shows results from field seismic data. Figure 10c and d showsesults from modeling. The left column is for the brine scenario, andhe right column is for the oil scenario. One polygon was drawn onhe oil-scenario field seismic data, and another was drawn on therine scenario to highlight the distribution of peak amplitudes andeak frequencies. The same polygons were overlaid on the peak-am-litude/peak-frequency crossplots from synthetic-modeling results.

Comparison of Figure 10c and 10b-d shows that spectral-decom-osition attributes �peak amplitude and peak frequency� from syn-hetic modeling reproduce the overall patterns observed from thear-angle stack seismic data. The average peak frequency for all syn-hetic models shifts to lower values when oil substitutes for brineabout 3 Hz�. Consequently, the oil leg brightens in contrast to therine leg in the low-frequency spectral-decomposition section.

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igure 10. Crossplots of peak amplitude and peak frequency frompectral decomposition of the �a, b� field seismics and �c, d� synthet-cs. The left column is for the brine scenario and the right column isor the oil scenario. �e� Analytical Fourier spectra of the oil scenariogreen� and brine scenario �blue� at the control well. �f� Spectral ratiof oil/brine.

here are some differences in details partially resulting from an im-erfect match of reservoir properties between the simulation andeld seismic data sets.The above modeling studies suggest that an analytical convolu-

ion approach in the Fourier domain potentially could serve as auick evaluation tool for examining the spectral-decomposition re-ponse to reservoir fluid. The Fourier amplitude spectrum for a re-ectivity series RCi�ti� can be represented by

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here RCi is the reflection coefficient at time ti, �tij � tj–ti is theime difference, � � 2� f is the frequency, and WRicker is the Rickerpectrum. Figure 10e and f shows spectra and the spectral ratio com-uted from this analytical expression for the reflectivity series at theontrol well �Figure 2� for the oil and brine scenarios. With oil sub-tituted to brine, the peak amplitude decreases as peak frequency in-reases. The spectral ratio shows that the amplitude contrast be-ween the oil and brine scenarios is largest ��5� at about 13.5 Hznd is near one at about 35 Hz. This result explains the oil/brine con-rast of spectral-decomposition sections at 15 and 35 Hz, illustratedn Figure 1b.

CONCLUSIONS

Synthetic seismic forward modeling explains the low-frequencyydrocarbon anomaly observed from the spectral decomposition ofhe far-angle stack seismic data from a deepwater West Africa reser-oir. We identified four main controlling factors on the spectral-de-omposition response of a reservoir: thickness, stratigraphy �i.e., re-ectivity series�, fluid type, and effective attenuation. For the reser-oir in this example, peak frequencies are lower for the oil scenarioompared with the brine scenario, leading to a larger amplitude con-rast between the oil leg and brine leg at low frequencies. This spec-ral-decomposition response is consistent with results of stochasticimulations and analytical Fourier-domain representation. Ourorkflow could be used to highlight and analyze the optimal fre-uency band at which the fluid effect shows the largest spectral-de-omposition response.

Because variations in reservoir properties �sand-shale thickness,orosity, net-to-gross, etc.� collectively affect the spectral response,esulting in ambiguities/overlaps in spectral attributes between oilnd brine scenarios, detailed modeling is needed for each reservoiro interpret spectrally decomposed seismic data correctly.

ACKNOWLEDGMENTS

We are thankful for ExxonMobil management’s support for theesearch and approval for the publication and data release. Discus-ions with many ExxonMobil geoscientists greatly benefited thisork, including Jie Zhang, Ramesh Neelamani, Dominique Gillard,ichael Payne, and Wenjie Dong. Bob Keys provided critical re-

iews to the write-up that predated this paper. We are grateful tollen Clark for arranging reviews of this paper. Dengliang Gao’s andrian P. Wallick’s detailed reviews and comments greatly improved

he manuscript. We thank a third anonymous reviewer for commentsnd John Castagna for many beneficial discussions on this topic.

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