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Tuning Phenomenain Reservoirs

Widess (1973) demonstrated the interaction of closely-spaced reflections. In his classicpaper, “How thin is a thin bed?,” he discussed the effect of bed thickness on seismic signature.For a bed thickness of the order of a seismic wavelength or greater there is little or no interfer-ence between the wavelets from the top and the bottom of the bed and each is recorded withoutmodification. For thinner beds these wavelets interfere both constructively and destructively.Considering wavelets of opposite polarity, the amplitude of the composite wavelet reaches amaximum for a bed thickness of one-quarter wavelength (one-half period) and this is known asthe tuning thickness. For beds thinner than this the shape of the composite wavelet stays thesame but its amplitude decreases. Clearly, the bed thicknesses at which these phenomena occurdepend on the shape of the wavelet in the data and hence on its frequency content.

These tuning phenomena are of considerable importance to the stratigraphic interpreter.They must be recognized as effects of bed geometry as opposed to variations in the acousticproperties of the medium. Figure 6-1 shows a sedimentary pod. As the reflections from the top

and the base come together (within the black square) the amplitude abruptly increases; this isinterpreted as tuning between the top and base reflections.Convergence of reservoir reflections around the periphery of reservoirs is commonplace. Fig-

ure 6-2 illustrates the tuning phenomena in amplitude and time that occur between a top reser-voir reflection and a fluid contact reflection near the downdip reservoir limit. At the tuningthickness the amplitude maximizes (for a given acoustic contrast), and for the parts of the reser-voir thinner than this the amplitude will decrease. The tuning thickness is also the closest possi- ble approach of the two seismic wavelets, so that, as the reservoir thins, the seismic reflectionsno longer will coincide with the reservoir interfaces. For zero-phase data this divergence will bedisposed symmetrically between the top and fluid contact reflections, as shown in Figure 6-2.

The limit of seismic visibility indicated on Figure 6-2 is considered in more detail in Figure 6-3. For reservoirs with a higher acoustic contrast with the embedding medium, thinner parts of the reservoir will be visible, the exact thickness depending on the noise level in the data and the

nature of the wavelet. Considering a common situation in Tertiary clastic reservoirs where thetop and fluid contact reflections are equal in amplitude and opposite in polarity, the actualdowndip limit is invisible but can be found by extrapolating to zero the amplitude gradientobserved between the tuning thickness and the limit of visibility.

Figure 6-4 shows some bright spots which are reflections from the top and base of gas sandsof variable thickness. The base of the gas sands (the bright red events) are fluid contacts atmost of the downdip limits. Hence the top and base reflections in many places constitute thin-ning wedges. Close inspection of Figure 6-4 reveals several local amplitude maxima close tothe downdip limits of brightness. At these points the apparent dip also changes. The interfer-ing wavelets are unable to approach each other more closely than a half period. Therefore, thecomposite bed signature for each of these thin beds assumes a dip attitude which is the mean

Effect of Tuningon StratigraphicInterpretation

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of the real dips of the top and the base of the interval. Because the base gas is flat at thedowndip pinchout, it is easy to see the dip of the composite wavelet turning to assume thisintermediate value.

Tuning amplitudes are easily recognized on horizon slices. Figure 6-5 is a horizon slice overthe reflection from the top of a Gulf of Mexico gas reservoir. Dip is to the north, which is to theright in this figure. Horizon tracking was stopped at the limit of visibility, which is the edge ofthe various shades of blue along the north. Close to that edge and parallel to it is a lineation oflocally higher amplitudes, visible as locally darker blues and indicated by a red arrow. This is

the tuning thickness trend along which the reservoir thickness is equal to one-half of the seismicperiod, namely about 15 m (49 ft).Tuning effects are not always a nuisance; in fact, they can be used to increase the visibility of

thin beds. Amplitude tuning occurs for a layer thickness of one-half period of the dominant seis-mic energy, as already discussed. Frequency tuning, on the other hand, occurs for layer thick-nesses of one-quarter period or less. Robertson and Nogami (1984) used instantaneous frequencysections to study thin, porous sandstone lenses based on this phenomenon.

Tuning phenomena are usually described by graphs such as those of Figure 6-6. In thissimple form the principles of tuning are well understood and widely published (for example,see Neidell and Poggiagliolmi, 1977). Figure 6-6 shows that measured thickness, indicated by

Fig. 6-1. Amplitudeincreases as reflectionsconverge because oftuning. (CourtesyPetroleo Brasileiro.)

DeterministicTuning Curves

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Fig. 6-2. Tuning effects inboth amplitude and time

applicable to zero-phasewavelets for a thinningwedge such as occursbetween reservoir top andfluid contact reflectionsnear a downdip reservoirlimit.

Fig. 6-3. Limit of seismicvisibility depends onacoustic contrast ofreservoir interfaces, noiselevel and wavelet shape.(After Meckel and Nath,1977.)

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Fig. 6-4. High-amplitude

reflections from gassands of variablethickness showing tuningeffects in amplitude andtime as events converge.The two panels are thesame data with differentgains to aid theobservation of some ofthe subtle amplitudeeffects on the printedpage. (Courtesy ChevronU.S.A. Inc.)

the time separation of the reflections from the top and base of a bed, is only an acceptablemeasure of the true thickness of the bed for thicknesses above the tuning thickness. Also attuning thickness the amplitude of the reflections reaches a maximum due to constructiveinterference between the reflected energy from the top and bottom of the bed.

The upper diagram of Figure 6-7 shows how the wavelets from the top and the base of asand bed must be aligned to produce the principal tuning amplitude maximum; here it isassumed that the reflection coefficients are equal in magnitude and opposite in polarity. It isapparent that the shape of the tuning curve is dependent on the shape of the side lobes of thewavelet. Constructive interference occurs when the central peak of the wavelet from the baseof the sand is aligned with the first negative side lobe of the wavelet from the top of the sand.

The lower diagram of Figure 6-7 shows how a second tuning maximum is caused. In this

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Fig. 6-5. Horizon slice

over reservoir top wherestructural dip is to thenorth (right). Close to thedowndip limit running top-to-bottom, an amplitudelineation in locally darkerblues (in line with the redarrow) indicates the trendalong which the reservoirthickness is equal to thetuning thickness.(Courtesy Chevron U.S.A.Inc.)

case the central peak of the wavelet from the base of the sand is aligned with the second nega-tive side lobe of the wavelet from the top. Hence multiple wavelet side lobes generate multi-ple maxima in the tuning curve. Kallweit and Wood (1982) studied the resolving power of zero-phase wavelets and reported multiple maxima in their tuning curves (Figure 6-8).

Figure 6-9 illustrates deterministic tuning curves derived from four different wavelets. At thetop of the page the Ricker wavelet has no side lobes beyond the first and consequently the tun-ing curve determined from it has only one maximum. This is the classical type of tuning curve,similar to that illustrated in Figure 6-6 and to that published by Meckel and Nath (1977).

The second wavelet in Figure 6-9 is a zero-phase wavelet derived from four corner frequen-cies defining a band-pass filter. It has, as can be seen, the same width of central peak as the Rick-er wavelet but otherwise was randomly selected. This wavelet simply illustrates that multiple

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side lobes in the wavelet generate multiple maxima in the tuning curve. In fact it is interestingto note the similarity in shape between the tuning curve and half of the wavelet upside-down.

The third wavelet is again zero phase. Its simpler shape generated only two maxima in thetuning curve.

The fourth wavelet in Figure 6-9 was extracted from zero-phase data by a cross-correlationtechnique between the processed seismic trace and the synthetic seismogram at a well. Thewavelet is seen to be almost, but not quite, zero phase. The deterministic tuning curve derivedfrom the extracted wavelet shows some complexity but principally two maxima.

An amplitude spectrum was generated from this tuning curve. By interpreting this spec-trum in terms of four corner frequencies it was possible to compute an ideal zero-phase equiv-

alent wavelet and its tuning curve. For the extracted wavelet at the bottom of Figure 6-9 theideal zero-phase equivalent wavelet is shown directly above as the third wavelet on the page.In a practical situation the interpreter may be striving for a tuning curve applicable to the

zone of interest over some broad area of a prospect. Inevitably, the interpreter will wonderwhether a deviation from zero-phaseness such as that shown by the extracted wavelet at the bottom of Figure 6-9 is applicable to the whole area. He may reasonably consider the idealzero-phase equivalent wavelet and its tuning curve to be more universal.

Tracked horizon data in time, amplitude and other attributes are normally mapped beforedrawing conclusions from it. It is also possible to crossplot one attribute against another fromthe same subsurface position. Crossplotting operates within a user-specified subsurface area

Statistical TuningCurves

Fig. 6-6. Basic conceptsof tuning for thin beds.

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With this capability statistical analysis of horizon data can be an important part of interactiveinterpretation.

In studying the detailed character of bright spots and the tuning phenomena therein, it may

 be desirable to make the simplifying assumption that lateral variations in amplitude are dueto lithologic changes in the reservoir or to tuning effects, and not due to changes in the acousticproperties of the embedding media. Figure 6-10 shows a crossplot of the top sand amplitudesagainst the base sand amplitudes for a particular reservoir. The general proportionality between the two as indicated by the extension of the points along the diagonal yellow lineindicates that, to a first approximation, the lateral changes in amplitude do result from lateralchanges within the reservoir rather than in the encasing material.

In pursuing the more quantitative study of reservoirs (Chapter 7), the absolute value sum-mation of top and base reservoir amplitudes accentuates the properties of the reservoir, litho-logic or geometric, relative to those of the encasing material. This absolute value summation isreferred to as composite amplitude. Figure 6-11 shows a crossplot of composite amplitudeagainst gross isochron (that is, measured thickness). These are the parameters for studyingtuning (Figure 6-6), so Figure 6-11 is a statistical approach to the determination of tuning

effects.The principal maximum in composite amplitude (Figure 6-11) occurs at 16 ms, the tuningthickness. In addition there is a second maximum evident at about 35 ms. The meaning of these two maxima in terms of wavelet interaction was explained schematically in Figure 6-7.The first interpretation of a statistical tuning curve from this crossplot is then the envelope of the plotted points (Figure 6-12). This is based on the assumption that the highest amplitudepoints all indicate the maximum acoustic response of the interval under study and thereforethat the variable shape of this envelope with isochron indicates geometric effects alone.

The horizontal blue line to the right of Figure 6-12 is the baseline and indicates the maximumuntuned amplitude. The ratio of the amplitude of the tuning maximum to this baseline value iscontrolled by the side lobe levels of the interfering wavelets. On this basis the tuning maxima as

Fig. 6-8. Tuning curves for two zero-phase wavelets showing multipleamplitude maxima (after Kallweit andWood, 1982).Fig. 6-7. Constructive interference of zero-phase

wavelets to produce tuning maxima.

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Fig. 6-9. Various waveletsand their correspondingdeterministic tuningcurves.

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drawn in Figure 6-12 are too high. Considering the very large number of points plotted forisochrons in the 10-40 ms range, it is reasonable that some amplitudes are spuriously high because of constructive interference of the already-tuned reflections with nonreservoir interfaces,multiples or noise. In Figure 6-13, 99th percentile points computed over 2 ms isochron gates areplotted as blue asterisks. They fall at more reasonable levels relative to the untuned baseline.

Hence the existence of two maxima in the tuning curve was indicated by the raw crossplot, but a statistical analysis of the points guided by the knowledge of the deterministic tuningcurve was required to establish the shape of the final curve. This final interpreted curve isshown in yellow in Figure 6-13.

Figure 6-14 shows the deterministic tuning curve points and the final interpreted curvesuperimposed on the same crossplot. Deterministic tuning curves have arbitrary verticalscales. Hence it was necessary to interpretively judge the factor by which the deterministicpoints must be scaled so that they could be plotted on the same composite amplitude axis as

the crossplot points. This was done by matching the deterministic points to the crossplot enve-lope at the greater thicknesses where little or no tuning effect exists, and was confirmed byplotting the model response at a control well. The yellow curve in Figures 6-13 and 6-14 is thesame. It is repeated to demonstrate how the final interpreted tuning curve for the area understudy tied both the statistical and deterministic inputs.

Interpreters sometimes try to explain as reservoir tuning effects amplitude phenomenawhich really cannot be explained that way. Understanding wavelet shape is the key to under-standing what reasonably can or cannot be interpreted as a tuning effect.

Figure 6-15 shows four zero-phase wavelets of different bandwidths. The lowest frequencyin the band is held the same while the highest frequency is progressively increased by a full

Fig. 6-10. Interactivecrossplot of base sandamplitudes against topsand amplitudesdemonstratingapproximateproportionality.

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Fig. 6-11. Interactivecrossplot of compositeamplitude against grossthickness of a reservoirinterval for all theinterpreted data points ina prospect.

Fig. 6-12. Same crossplotas Figure 6-11 with upperenvelope drawn as a firstinterpretation of astatistical tuning curve.

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Fig. 6-13. Same crossplotas Figure 6-11 analyzedto yield 99th percentilepoints which show a morerealistic peak-to-baselineratio as required bydeterministic studies.

Fig. 6-14. Same crossplotas Figure 6-11 withdeterministic tuning curvepoints computed from anextracted wavelet. Theyellow final interpretedtuning curve is the sameas in Figure 6-13 toprovide comparisonbetween statistical anddeterministic tuningpoints.

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Tuning andCharacterMatching in

ReservoirEvaluation

octave from one wavelet to the next. The center lobe of the wavelet narrows considerably butwhat we are concerned with here is the size of the first side lobe. Notice that the first side lobe isabout the same size as the center lobe for the one octave wavelet; the first side lobe is about halfthe center lobe for two octaves; it is about a third of the center lobe for three octaves; and it is

about a quarter for four octaves. Thus we can establish a generalized rule-of-thumb, that the first side lobe as a fraction of the center lobe of a zero-phase wavelet is the reciprocal of the octave band-width. Furthermore a typical bandwidth for good but not exceptional seismic data today is two-and-one-half octaves; this gives a side lobe level of 40% relative to the wavelet’s center lobe.

I call this the “40% rule”; it is an approximate but very useful rule-of-thumb. Figure 6-7demonstrates that the size of the wavelet side lobe controls the magnitude of the tuning effects.Thus the 40% rule means that 40% is a common increase in amplitude at tuning for zero-phasewavelets reflected from the top and base of a reservoir layer. Increases in amplitude muchgreater than this must be explained some other way. A lateral amplitude increase of 40% is notdramatic even when using the highest dynamic range color scheme. It follows that dramaticamplitude changes which we observe in our data are unlikely to be simple tuning effects.

The mispositioning of reflections by tuning effects in time was discussed above andillustrated in Figure 6-2. Even after phase errors have been corrected and accuratevelocities obtained, these tuning issues remain. They need to be considered in matchingseismic information to geologic information in the course of reservoir characterizationor evaluation.

Consider Figure 6-16. The reservoir has a good log response but is thinner than one-quarter wavelength, so the exactly corresponding interval on the seismic data (AB) con-tains no peaks or troughs. This seismic interval will yield, at best, very poor informationabout the reservoir. The reflection caused primarily by the top reservoir interface (P) is

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Fig. 6-15. Four zero-phase wavelets ofdifferent bandwidthsdemonstrating the effectof bandwidth on side lobesize and hence themagnitude of tuningeffects.

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moved up a few milliseconds by tuning, and the reflection caused primarily by the basereservoir interface (T) is moved down. Crestal reflection points yield more reliable ampli-tudes and attributes than points on the flank of the waveform. Thus the best seismic infor-mation about this reservoir lies at P and T, both out-of-place because of tuning, and this is

the information that should be used. The interpreter should match the seismic response tothe well response on character taking account of this tuning mispositioning.In general the interpreter should recognize that the best information in amplitude and

other attributes lies on the waveform crest. Thus, to a first approximation, the number of reflections dictates the number of reservoir units that may be characterized. If two reser-voir units lie within the same quarter wavelength, then those two units should be studiedtogether as one. Seismic reservoir studies need to be guided by the resolution of the data.Even with excellent data the analysis of one reservoir unit per reflection is probably the best we can hope to do.

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Fig. 6-16. Poroussand, with or withouthydrocarbons,typically has a sonicor impedance logsimilar to that on left.Correspondingseismic response inEuropean polarity is

shown on right. Theamplitudes thatshould be used tocharacterize thisreservoir are to befound at P and T, andnot over the directlycorrespondinginterval AB.

P

A

B

T

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Kallweit, R. S., and L. C. Wood, 1982, The limits of resolution of zero-phase wavelets: Geo-physics, v. 47, p. 1035-1046.

Meckel, L. D., Jr., and A. K. Nath, 1977, Geologic considerations for stratigraphic modelingand interpretation, in C. E. Payton, ed., Seismic stratigraphy — applications to hydrocar- bon exploration: AAPG Memoir 26, p. 417-438.

Neidell, N. S., and E. Poggiagliolmi, 1977, Stratigraphic modeling and interpretation —

geophysical principles and techniques, in C. E. Payton, ed., Seismic Stratigraphy —applications to hydrocarbon exploration: AAPG Memoir 26, p. 389-416.

Robertson, J. D., and H. H. Nogami, 1984, Complex seismic trace analysis of thin beds:Geophysics, v. 49, p. 344-352.

Widess, M. B., 1973, How thin is a thin bed?: Geophysics, v. 38, p. 1176-1180.

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References