For many years geophysicists have attempted to exploitattenuation measurements in exploration seismology, becauseattenuation is perhaps the seismic property most closely relatedto the saturating fluid. The routine application of such ideashas proven elusive, however, largely because of the difficultyexperienced when we attempt to measure attenuation in reflec-tion data. Recent developments in the application of spectraldecomposition methods to seismic data have opened the pos-sibility of making further progress in this direction.

It is certainly the case that a wide range of evidence sug-gests that hydrocarbon zones are associated with abnormallyhigh values of seismic attenuation and, in view of theKramers-Kronig relations, we might expect that this atten-uation would be associated with significant velocity dis-persion. Consideration of the “drift” between velocitiesmeasured in VSP and log data over thick sections of theearth’s crust has suggested that velocity dispersion in seis-mic wave propagation is generally small, but this still leavesthe possibility that certain zones, such as hydrocarbon reser-voirs, exhibit significant magnitudes of velocity dispersionand attenuation. Consideration of indirect dispersion mea-surements, particularly the frequency dependence of shear-wave splitting and other anisotropic attributes, furthersuggests that this is the case.

It can be difficult to explain the link between fluid satu-ration and attenuation using poroelastic models; straightfor-ward application of the Biot equations will lead to attenuationvalues which are far too small. A recent paper (Chapman etal., 2005) showed how to implement ideas from squirt-flowtheory to model hydrocarbon-related attenuation anomalies.Abnormally high attenuation can be produced as result of gassaturation, but this attenuation must be accompanied by sig-nificant velocity dispersion in the reservoir layer. This leadsnaturally to the view of the reservoir as a “dispersion anom-aly” and under these circumstances the reflection coefficientbecomes strongly frequency dependent. Synthetic modelingsuggests that this effect is rather important and would usu-ally dominate the traditional effect of attenuation thought ofas a continuous and cumulative loss of energy during prop-agation. The nature of the frequency response dependsstrongly on the AVO behavior at an interface.

The effect of the frequency-dependent reflection coefficientis essentially instantaneous in character. This makes moderninstantaneous spectral analysis techniques the ideal tool fordetecting such variations. Such an approach has a number ofpotential advantages over the traditional methods which relyon the comparison of the spectral properties of two windowsseparated in time, and which inevitably contain different com-binations of events.

This article applies the spectral decomposition techniquesto two field data sets in an attempt to detect the type of dis-persion anomalies suggested by the modeling. Within thecontext of a standard AVO analysis, we find that reflectionsfrom the hydrocarbon-saturated zone appear to display sys-tematic frequency anomalies. These anomalies can be repro-duced with synthetic reflectivity modeling which is alsoconsistent with the AVO analysis. In general, the study leadsus to believe that the study of systematic frequency variations

can potentially help provide additional information on fluidsaturation.

Spectral decomposition and balancing. Spectral decompo-sition techniques help us to understand scale and frequency-dependent phenomena, essentially by allowing us to studythe data one frequency at a time. Specifically in this paper,given a trace f(t), we form the Stockwell, or S-transform:

which mean that, for each choice of frequency, we have a newtrace corresponding to that particular frequency. With such a

Application of spectral decomposition to detection of dispersion anomalies associated with gas saturationEMEKA ODEBEATU, Leeds University, U.K.JINGHUA ZHANG, MARK CHAPMAN, ENRU LIU, and XIANG-YANG LI, Edinburgh Anisotropy Project, U.K.

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Figure 1. Isofrequency stacked sections for example 1 for 15 Hz and 30Hz. The reservoir zone, indicated, is bright at the lower frequencies butcannot be observed on the higher frequency sections.

concept and given a collec-tion of traces we can form a“frequency gather,” consist-ing of each trace’s represen-tation at the specifiedfrequency. While such anarrangement may seembeguiling, it is very impor-tant to remember that perfectspectral decomposition is alogical impossibility onaccount of the Heisenberguncertainty principle.

When we wish to com-pare the traces at different fre-quencies, we should expectto find markedly differentamplitudes because neitherthe source nor the earth’sreflectivity have white spec-tra. The procedure for com-pensating for these effects is to use spectral balancing. In oursynthetic data, because we know the input wavelet, we canbalance the different traces exactly, a step which is similar todeconvolution. In real data we attempt to equalize the aver-age amplitudes between the various traces across a particu-lar time window, or reference horizon. Our preference is tobalance over a wide time window, because this makes localfrequency anomalies particularly clear.

The main use of spectral decomposition has been in delin-eating tuning phenomena. Nevertheless, there have been sug-gestions that it can be used for direct hydrocarbon detection.This paper attempts to develop this aspect of the techniquein conjunction with rock physics modeling.

Example 1. Our first example is a 2D line of streamer datafrom a gas field in the North Sea. The main point of our

approach is that interpreta-tion has to begin with a stan-dard AVO analysis. Such ananalysis indicated that thedata showed zones of strongclass III AVO anomalies at thereservoir level; this was con-firmed by gradient and inter-cept crossplotting as well asconsideration of product,fluid-factor, and scaledPoisson ratio stacks.

Following the work ofCastagna et al. (2003), weformed “isofrequency sec-tions” from the stacked data.From these it is immediatelyapparent that significant fre-quency anomalies are associ-ated with the class III AVOanomalies at the reservoir

level. Figure 1 highlights such a region, which is bright on a15-Hz section, but no bright spot is visible on the 30-Hz sec-tion. The effect was consistent for other frequencies; the reser-voir was bright at low frequency, but did not stand out on thehigher frequencies. This highlights the fact that in practice theconcepts of amplitude and AVO anomalies are typically fre-quency-dependent phenomena.

We performed an extensive synthetic modeling study todetermine if the frequency and AVO anomalies could be sys-tematically related to gas saturation. We used a commercialreflectivity code (ANISEIS) which permits the use of materi-als with frequency-dependent velocities and attenuations.Our interest had three components; the simple Gassmanneffect, the Gassmann effect with tuning, and the full dynamicmodeling with attenuation and associated dispersion.

When we considered the simple single-layer case, it was

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Figure 2. AVO curves for various frequencies for our first model, undergas saturation. The low-frequency curve corresponds to the traditionalGassmann case.

Figure 3. Reflectionsfrom the single inter-face for our modelunder gas saturation.Left diagrams are forthe Gassmann case;right diagrams arethe dispersive case.Spectral balancingbased on the inputwavelet has beencarried out. For theGassmann case,similar energyappears on eachisofrequency section.In the dispersive case,the low-frequencysections havemarkedly moreenergy.

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Figure 4. Isofrequency sections from the multilayer model. Left diagrams correspond to the dispersive case, but with a thick reservoir layer of 420 m forwhich no tuning occurs. Right diagrams are for the Gassmann case, but with a thin reservoir of 90 m which is close to the tuning thickness. Spectralbalancing has been applied in both cases, but the lower-frequency sections appear brighter.

Figure 5. PP stacked sec-tions from example 2, band-passed into low- (top) andhigh- (bottom) frequencysections. Note how thereservoir level (around 2 s)appears dim in the high-frequency section but not inthe low-frequency section.

easy to model the standard AVO attributes with Gassmann,under straightforward assumptions. We performed spectraldecomposition to produce balanced isofrequency sections. Asmight be expected, these sections showed similar energy ineach isofrequency section, and so we could not model the effectseen in the data with a simple one-layer model. When we intro-duced dispersion into the reservoir layer, however, the fre-quency dependence of the reflection implied that theisofrequency sections were no longer balanced, and the lowfrequencies appear to have much more energy. Figure 2 showsthe gas-saturated reflection coefficients for a range of fre-quencies for the model while Figure 3 shows a comparisonbetween the balanced isofrequency sections for the single-layercase, assuming both the purely elastic case (left) and the casewith a dispersive reservoir layer (right).

In practice we know that we never deal with reflectionsfrom single layers; tuning and multiples are always impor-tant issues. To address these issues, we formed a blockedmodel with 10 layers from velocity data from the field in ques-tion. We also varied the thickness of the reservoir layer to sim-ulate tuning phenomena, and we did this both for the simpleGassmann modeling as well as the modeling with dispersion.In general we found that the dispersion effect is still strongeven in the multilayer case, but, for certain reservoir layer thick-nesses, tuning can give a similar effect to that arising from thedynamic modeling. Figure 4 shows a comparison for the mul-tilayer case between a dispersive reservoir layer without tun-ing and an elastic reservoir layer with tuning. We concludethat without detailed information on the velocity model it canbe difficult to distinguish between the effects of dispersion andtuning.

Example 2. We applied similar ideas to a gas field from OrdosBasin, onshore China. The potential reservoirs in the area areprimarily in the fluvial sandstone in the Permian. The sub-surface has a flat-layered structure with gas reservoirs typi-cally below 3000 m. The targeted gas beds are thin and havea small P-wave velocity difference between the gas sand andthe overlaid shale, giving rise to a weak amplitude on the

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Figure 6. “Difference traces” formed by stacking the synthetic data, per-forming spectral decomposition, consistent spectral balancing, and sub-tracting the 30-Hz trace from the 15-Hz trace. The reservoir layer is 10-mthick, and we consider water and gas saturation in both the dispersive andGassmann cases. Note that the Gassmann modeling gives small absolutevalues, but that gas saturation is associated with a strong positive ampli-tude when we perform dispersive modeling.

Figure 7. Theresults of balanc-ing and differ-encing thesections fromFigure 5. Noticethat the gasreservoir showsas a positiveanomaly (ringed)in accordancewith our syn-thetic modeling.

PP-wave reflection.Standard AVO analysis suggested that the top of the reser-

voir was in principle a class III interface, but that the reser-voir reflection itself was a composite event, which led to anapparent negative reflection coefficient whose absolute ampli-tude declined with increasing angle of incidence, resemblingthe behavior of a class IV interface. Based on log data, we cre-ated an idealized multilayer model, with a 10-m thick gas sandand 10-m thick shale layer encased in a half space of higherimpedance. This arrangement was able to effectively modelthe observed AVO behavior within the reservoir.

Application of spectral decomposition techniques to thestacked field data revealed an unexpected anomaly. Figure 5shows the results of filtering the final stack into low- andhigh-frequency bands. It is clear that in the high-frequencysection the reservoir appears as a low-amplitude anomaly, butthis is not the case in the low-frequency section. Because thereservoir is only 10-m thick, it proved difficult to model thiseffect as being due either to a traditional attenuation mecha-nism or fluid-related changes in the tuning-thickness. Toexplain the behavior, we turned to our dispersive modeling.

As before we ran two sets of models, the standard elasticGassmann case as well as the dispersive modeling, and foundthat as expected, for a class III interface, the gas saturation wasassociated with a systematic boost to the low frequencies rel-ative to the high frequencies in the dispersive case. To illus-trate this point we ran four models corresponding to waterand gas saturation for both Gassmann and the dispersivecase, stacked the data, formed isofrequency traces, and per-formed consistent spectral balancing on each trace. We thensubtracted the resulting 30-Hz trace from the 15-Hz trace, andwindowed around the main arrival to compensate for the dif-ferent time durations of the signals. The results are illustratedin Figure 6. For each Gassmann trace there is little residualenergy, implying that the traces were well balanced. In the dis-persive case there was residual energy for both saturations,but it was much stronger in the gas-saturated case. A similarprocedure was carried out on the data shown in Figure 5. Thetwo sections were balanced and a difference was taken; Figure7 shows the result. As can be seen, in the vicinity of the reser-voir we have a response very similar to the gas response wesaw in our synthetics.

Discussion. In this paper we have applied the spectral decom-position techniques to reflection data from hydrocarbon-sat-urated zones. Sharp changes in the spectral behavior associatedwith gas saturation have been noted elsewhere; the noveltyof this paper lies in the attempt to model the behavior in termsof well-defined poroelastic effects. The understanding of sucheffects builds on the standard AVO analysis, since our inter-pretation is within the extended Rutherford-Williams classi-fication outlined by Chapman et al. (2005). We emphasize thatour work is an adjunct to the standard AVO methodology; wedo not believe that it is possible to robustly interpret the spec-tral response in the absence of a thorough AVO analysis.

In our data examples, the gas saturation can be associatedwith a clear spectral signature, and the effect can actually bemodeled in terms of a simple single-layer model, providedwe account for velocity dispersion. Nevertheless, we knowthat in practice we always deal with more complicated geo-logic models. In particular, tuning is always present to a cer-tain degree. When we perform fluid substitution withGassmann in such a thin-layer case, we change the velocityand hence the effective tuning thickness. This provides a nat-ural explanation as to why gas-saturated zones should appearas spectral anomalies. In our first example, we cannot dis-criminate whether the observed spectral anomaly is caused

by tuning or dispersion, but in the second example the reser-voir is only 10-m thick, and the tuning effect is not sufficientto produce a significant spectral response for such thin reser-voirs at seismic frequencies.

Paradoxically, the fact that spectral anomalies often occurfor such very thin reservoirs has often been cited as a reasonwhy attenuation cannot be the responsible mechanism,because it was thought that attenuation, being primarily apropagation phenomenon, could only accumulate a signifi-cant impact for waves traveling over longer distances. Ouremphasis on the frequency-dependent reflection coefficientarising from the attenuation-related dispersion anomaly pro-vides an explanation to this point. The framework also answersanother common argument against attenuation mechanismsbeing responsible for spectral anomalies which is that thehigh frequencies are commonly observed to return for reflec-tions from below the reservoir, which would be impossible ifwe viewed attenuation as a simple cumulative loss duringtransmission mechanism. This phenomenon is reproduced inour synthetics. The deeper reflections occur at interfaces whichare not associated with a strong attenuation and dispersioncontrast and so are governed by a relatively frequency inde-pendent reflection coefficient. The spectral properties of suchreflections therefore are those of the background trend, withthe energy loss associated with passing twice through theattenuating layer being generally only a secondary effect.

Unfortunately, many processing and other artifacts cangive rise to spectral anomalies which correlate with gas satu-ration, as has been eloquently pointed out by Ebrom (2004),and we are consequently conscious of the danger in overin-terpreting such observed features. The purpose of this paperis simply to show that it is in fact possible to quantitativelymodel observed spectral anomalies in seismic data associatedwith gas saturation in terms of dispersion. Whether in factvelocity dispersion is the true cause of the spectral anomaliesmust be considered an open question; but nevertheless if thesuccess of the modeling is maintained in other data sets, thenit may be possible to develop an extension of the current AVOmethodology which will include consideration of the disper-sion effect and might give better access to fluid-saturation infor-mation.

Suggested reading. “Instantaneous spectral analysis: Detectionof low-frequency shadows associated with hydrocarbons” byCastagna et al. (TLE, 2003). “Direct detection of oil and gas fieldsbased on seismic inelasticity effect” by Rapoport et al. (TLE, 2004).“The influence of abnormally high reservoir attenuation on theAVO signature” by Chapman et al. (TLE, 2005). “Application ofspectral decomposition to gas basins in Mexico” by Burnett et al.(TLE, 2003). “The low-frequency gas shadow on seismic sections”by Ebrom (TLE, 2004). TLE

Acknowledgments: Emeka Odebeatu was sponsored throughout this researchby the Shell Centenary Scholarship Fund, and the work was carried out atthe Edinburgh Anisotropy Project (EAP) as part of the course MSc inExploration Geophysics at Leeds University, UK. This work is presentedwith the permission of the executive director of the British Geological Survey(NERC) and is supported by the sponsors of the EAP: BG, BGP, BP, Chevron,CNPC, ConocoPhillips, Eni-Agip, ExxonMobil, GX Technology, Hydro,Kerr-McGee, Landmark, Marathon, PetroChina, PDVSA, Schlumberger,Shell, Total, and Veritas DGC. Our particular gratitude to David Taylor ofMacroc Ltd., for his help with the computation of synthetic seismograms inthe ANISEIS software package. For information on ANISEIS contactmacroc@blueyonder.co.uk. All other calculations were carried out using theEAP’s rock unix (RU) software package.

Corresponding author: mhch@bgs.ac.uk

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