roger_Q.pdf

GEOPHYSICS, VOL 63, NO, 6 (NOVEMBER-DECEMBER 1998); P.2120-2128, 5 FIGS., 4 TABLES.

Estimation of Q from surface seismic reflection data

Rahul Dasgupta* and Roger A. Clark!

INlRODUC1l0NABSlRACT

Reliable estimates of the anelastic attenuation factor,Q, are desirable for improved resolution through inverseQ deconvolution and to facilitate amplitude analysis, Qis a useful petrophysical parameter itself, yet Q is rarelymeasured. Estimates must currently be made from bore-hole seismology. This paper presents a simple techniquefor determining Q from conventional surface seismiccommon midpoint (CMP) gathers, It is essentially theclassic spectral ratio method applied on a trace-by-tracebasis to a designatured and NMO stretch-corrected CMPgather. The variation of apparent Qversus offset (QVO)is extrapolated to give a zero-offset Q estimate. Studieson synthetics suggest that, for reasonable data quality(S/N ratios better than 3:1,shallow 50) dips, and stack-ing velocity accuracy

Q fromSurfaceSeismicData 2121

Procedure

THE Q VERSUS OFFSET METHOD

which is the classic spectral ratio method (e.g., Tonn, 1991) ofestimating Q.

We now describe a new and simple application of the spec-tral ratio method to surface seismic reflection data that recov-ers apparent Q (i.e., intrinsic Q plus stratigraphic Q inducedby effects such as thin-bed tuning and scattering). We thendemonstrate that apparent Q remains a useful parameter.

(4)

(3)

AU) ~ kB(kf),

Q = 2nj(1 - e47fPc/x),

where

If NMO-corrected data are used, this correction is an impor-tant factor which, empirically, we find sufficiently accurate upto 20% NMO stretch. Beyond this point, we discard the data.

Each trace then has its corresponding source spectrum re-moved. [Individual shot signatures are often not available, andboth source and receiver have frequency-dependent directivi-ties (e.g., Loveridge et al., 1984)].

To improve the SIN ratio, corrected complex spectra arestacked over an offset-range window of a few traces only,whichis rolled across the CMP gather (Figure 2b).

The resultant corrected spectra are effectively spectral ra-tios, whose attenuation signature is that of the overall source-to-reflector two-way path. The spectral ratio slope and its un-certainty bound for each offset window is determined by aleast-squares regression, which acknowledges errors in bothabscissa and ordinate (Williamson, 1968). Because the spectralratios are stacked, their range provides an uncertainty bound;the bandwidth of each fast Fourier transform (FFT) harmonicgives an uncertainty bound for frequency. The spectral ratiointercept expresses elastic losses [equation (2)].

Finally, spectral ratio slopes vary with offset because of dif-fering raypath geometries, the consequent change in travel-times, and hence in accumulated attenuation. If traveltime

The Q versus offset method is summarized as a flowchart inFigure 1 and illustrated with real data in Figure 2. First, a CMPgather ispreprocessed, preserving true relative amplitudes andspectra. Then the gather is NMO corrected (Figure 2a) for easeof recognition of events.

First, spectra are computed of the reflection event of inter-est on each trace of the gather individually. To contain the en-tire event if significant nonhyperbolic moveout and/or NMOstretch are present, the time window used (typically two tothree times the dominant period) may require adjustment fromtrace to trace.

Next, the wavelet spectra will contain NMO stretch effects,especially at longer offsets. Each trace's complex spectrum af-ter NMO correction, A(j), is restored to its pre-NMO formB(j) using a formulation by Dunkin and Levin (1973) andBarnes (1992). Where x is source-receiver offset, to is zero-offset travel time, and v(to), v'(to) are rms velocity and itsderivative with respect to to,

function of Q, where

where G is the geometric spreading factor. Rearranging equa-tion (1) to form a spectral ratio, with wavelength in terms offrequency and velocity, then taking logarithms, we have

In[A(w)jAo(w)] = In(RG) + [(xj4nc)ln(1- 2njQ)]w.(2)

Hence, plotting the logarithm of the spectral ratio as a func-tion of (angular) frequency should yield a linear trend whoseintercept on the ordinate is a measure of elastic losses (energypartitioning and geometric spreading) and whose slope, p : is a

a wider bandwidth than for an equivalent surface seismicreflection. However, a longer depth interval is needed to im-pose a measurable amount of attenuation. Furthermore, only asingle vertical Q profile is obtained without any areal coverage.

A stacked trace from surface seismic reflection data might beconsidered for estimation of Q because of its optimum SINratioand an apparent analogy with a zero-offset VSP. It could de-liver in-situ, cost-effective values with greater lateral coveragethan a VSP,and Q could be mapped in a manner similar to theway that velocity is now. However, its use is incorrect, even dis-regarding migration effects, for several reasons. Consider theindividual traces combined in a stacked trace. Except at zerooffset, virtually every sample in a trace represents a differentraypath. For a given reflection event, path lengths (hence accu-mulated attenuation), spectral distortions from NMO stretch,and reflectivity-transmissivity effects vary from one trace to thenext. Thus, the spectral amplitude of a stacked trace has a dis-torted attenuation signature. These effects, together with theobvious influences of noise and multiples, conspire to make es-timation of Q from stacked traces of surface seismic reflectiondata both difficult and potentially erroneous. Several attemptsto estimate Q from surface seismic data, either unsuccessful(Raikes and White, 1984) or without details of methodology(Prohl et al., 1995), have been reported.

In this paper, we present a simple technique for determin-ing Q from surface seismic common midpoint (CMP) gathers,where the variation of apparent Q versus offset (OVO) is ex-ploited to give a zero-offset Q estimate. Observations on thesensitivity and capability of the OVO method inferred frommodel studies are noted. The method is validated by com-paring Q versus offset surface seismic results to those fromconventional VSP methods. Two successful applications of themethod are then presented. In the first, Q estimates in a fron-tier area have been used as a predictor/discriminant betweentwo very contrasting lithological interpretations. In the sec-ond, the effect of hydrocarbons is shown; in-situ Q is found todecrease markedly in a gas-charged unit. This second findingis both qualitatively and quantitatively consistent with labo-ratory studies, showing the potential of Q as a risk-reductionparameter prior to drilling.

A(w) = Ao(w)RG exp[- (- l j2A) ln(1 - 2n j Q)x], (1)

METHODS OF DETERMINING Q

The underlying theory of Q and associated measurementmethods is well established (Futterman, 1962). For frequency-independent Q in the bandwidth of interest, a seismic waveletof wavelength Awillhave its spectral amplitude Ao(w) modifiedto A(w) after traveling a distance x at phase velocity c. If withinx there is reflection from a boundary of reflection coefficientR, then

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2122 Dasgupta and Clark

Validation and sensitivity analysis

The algorithm itself was validated using simple horizon-tal structures simulating typical UK North Sea sections, withnoise-free data, perfectly known velocities, and single-trace

variations are given by the classical NMO equation, spectralratio slopes should, for small-spread conditions, vary linearlywith the square of offset. Regression therefore yields the zero-offset spectral ratio slope (Figure 2c) and hence Q,the averagesource-to-reflector Q.Again, the Williamson (1968) algorithmis used with uncertainty bounds based on regression-deriveduncertainties in slopes and the offset range window width.

Elastic, rather than anelastic, amplitude changes across thegather (i.e., offset-dependent reflectivity and any uncorrectedgeometric spreading) will appear as variation of spectral ratiointercepts with offset. Thus, given we assume AVO is frequencyindependent, AVO effects do not modify our apparent source-to-receiver Q or our extrapolation of it to zero offset.

This procedure can be applied to further reflector(s) in theCMP gather. From Q and two-way traveltime t at the (n - 1)thand nth reflectors, the Q value for intervening interval Qi isreadily derived:

Table 1. Uncertainties in source-to-reflector Q from variouscauses, as inferred from synthetics.

offset windows (i.e., synthetic seismograms generated usingray-based methods in 2D-AIMS). These conditions werethen perturbed to assess their effects on attenuation estimates.Examples of error in source-reflector average Q are shown inTable 1. They are not exhaustive [see Dasgupta (1994) for fur-ther details] but indicate the general performance expected,i.e., Q estimates should be obtained to within about 3%.

The error in Qi is estimated from the error (Do) on each ofthe two Q values needed to derive it, such that

{.6.(Qi1)}2 = (tn-l/T) {.6.(Q;;-~1)}2 + (tn/T){ .6. (e,') }2,(6)

using the variables of equation (5) and where T = (fn - fn- l ).The value Qi can only be recovered for a given interval if it

0.991.71.21.5

Consequentuncertainty in Q (%)Error source

White noise, SNR 6:1White noise, SNR 3:1Stacking velocity errors up to 5%Dipping reflector, dip up to 5

(5)Qi = [tn - tn-l]/[tn/Qn - tn-l/Qn-l],which yields interval Q down the section.

A

for ea

NMO-corrected traces of atrue-relative-amplitude

eMP gather

ch individual trace: -

FFT for a time windowcontaining the reflector

frequency-domain NMOstretch compensation

deconvolution ofcorresponding source's

sianatureI

horizontal stacking infrequency domain for anoffset-range window of

several traces

I repeat acros~1eMP gather

determine slope of ~spectral ratio

Bfor each reflector of interest

zero-offset source-to-reflector avera e

repeat or re ectorsbounding all intervals

of interest

use successive pairs ofsource-to-reflector Q, Q,

to determine Q forintervening interval, Qi

FIG. 1. A flowchart of the QVO method. (A) Processes applied to a single given reflection event within a CMP gather. (B) Howthis is extended to give Q value(s) for desired two-way time interval(s).

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Q from Surface Seismic Data 2123

65.0Frequency [Hz]

- Offset range 54 - 174 m- - 174 294m- 354 - 474m-- 534 - 654m- 714 834m- - 894 -1014m

I- I

II I\ I '\

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-, '.~r,\ 1 ~, I

I, ,I -I /

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45.0

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,

I ~ v\ I,

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8.0

7.0

0i 6.0II:et) 5.01Ila.enClo 4.0.J

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-0.0350..en-0

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0en

-0.055

-0.065O.Oe+OO

I I II

5.0e+05Square of Offset [m**2]

I

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1.0e+06

FIG. 2. The key elements of the QVO process illustrated with a real data example. (a) Preprocessed CMP gather, preservingtrue relative amplitudes and spectra and then NMO corrected. (b) Designatured and NMO-stretch-corrected spectra-effectively,spectral ratios-for several separate offset-range windows across the CMP gather. (c) Spectral ratio slopes plotted against offset,termed a QVO plot, together with a linear regression to derive the spectral ratio slope at zero offset and hence the averagesource-to-reflector Q. The additional points in (c) derive from intermediate positions of the rolling offset-range window.

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imposes a detectable amount of attenuation (more precisely,of t* or traveltimelQ) on the wavelet. Error in Qi will clearlybe inversely proportional to interval two-way time thicknessbut will increase with absolute depth of the interval. For 3%uncertainty in Q, the uncertainty of Qi for a 500-ms-thick in-terval between 1000 and 1500 ms two-way time is 11%, but a200-ms-thick interval would have uncertainty in Qi of 21%. Toobtain an uncertainty of 20% in Qi, at 500 ms two-way timethe interval could be as thin as 100 ms; but at 1500ms two-waytime, it would need to be 300 ms thick.

On real data, rather than compute errors in Q estimates an-alytically,as done by White (1992), we take a simple empiricalapproach. We find the bounds on zero-offset, spectral ratioslope, and thus on Q, obtained by regression of spectral ra-tio slope against the square of each offset (Figure 2c). Theseare then propagated into Qi values through equation (6).The general conclusion of the modeling study-that Q, val-ues are recovered to an accuracy of 20% or so-appears to besupported.

APPLICATIONS TO REAL DATA

We assumed that a source signature was available, but of-ten it is not. Analytically, it is simple to show and confirm withmodeling that use of an incorrect signature corrupts all the Qestimates, but it corrupts the Qi value for only the shallowest(i.e., surface downward) interval. Thus, for an interval at depthrather than at surface, use of an alternative source signature(such as a sea-bottom or other strong shallow event from aclose-offset trace of the appropriate shot gather) is acceptable.With a reasonable choice of close offset, for which the take-off angle matches that of the deep event, source directivity isincorporated into the QVO process. However, even if a singlemeasured or modeled source wavelet is used and the sourceis treated as isotropic, we feel the method is adequately ro-bust for two reasons. First, for a given event at a given offset,frequency-dependent directivity will be expressed as a distor-tion to spectral ratio slope. This distortion will indeed vary withoffset, but extrapolation to zero offset (Figure 2c) avoids its in-fluence. Second, and even without the preceding argument,for most practical situations where Q of an interval is sought,directivity effects will be virtually identical for both top andbottom events. In the case study below on effects of gas, forexample, the range of take-off angles corresponding to the off-sets used is ~3.2-22.5 and ~3.6-23.3 for reflectors 1 and 2,respectively (Figure 5). Nevertheless, if it were desired and atthe expense of adding a ray-tracing stage to the QVO process,source and receiver directivity could of course be accountedfor deterministically.

A further difficulty is interference by multiples causing spec-tral scalloping and nulls. Provided that (1) a wide bandwidth(40 Hz or more) is available, (2) care is taken to removeas much multiple activity as possible during preprocessing,and (3) the bandwidth used for regression is chosen withcare, then multiples need not degrade the accuracy of the Qresults.

In the following case studies, all seismic data were acquiredwith marine air gun for conventional 2-D acquisition param-eters (i.e., without specific requirements or constraints forthis study). Exact locations are not given, but their absencedoes not prejudice our conclusions. Source signatures were not

available, so alternatives were used. An offset-range windowof three traces (Figure 2b) was used throughout.

Validation against a VSP

To validate the method against real data, a southern NorthSea seismic line associated with a VSP was investigated. Fig-ure 3 shows the true-relative-amplitude surface seismic sec-tion. It identifies the four reflectors (Top Chalk, Base Chalk,Top Bunter, and Top Rotliegendes) to which Q was estimatedand the reference reflector used, instead of a source signa-ture. We did not separate the Zechstein from the Bunter be-cause the former did not appear to warrant much attenuation[Ziolkowski (1994) reports Q values of around 1000 in salts].With the exception of strong water-bottom multiples that de-graded the Base Chalk event, the data were of high quality.Trace spacing in the CMP gather was 53 m, and offsets from

~100 to ~1000 m were used. Available bandwidth was from10 to 70 Hz at shallow depth, reducing to 10-55 Hz at depth.The VSP was at a deviated well some 3 km from the surfaceseismic line, the closest CMP being 420.Shots (typically at leastfive for each depth) were vertically over receiver positions, soall raypaths were treated asvertical with effective 15-mreceiverdepth spacing. Each individual source signature was availableand deconvolved from the direct-arrival spectra, which werethen stacked in the frequency domain and Q estimates madeusing simple spectral ratios.

The QVO surface seismic and VSP estimates of Q (Table 2)differed by some 13-23%, while the uncertainties on QVOestimates were 11-17%, consistent with the level anticipatedfrom model studies. In addition to internal consistency withinthis data set, there was adequate agreement with the resultsofTonn (1991), who obtained Q values of 80-150 and 100-200using a range of methods on a deeper southern North Sea VSPfor Keuper-Mushelkalk and Zechstein, respectively, comparedto 38-60 and 135-182 at this location.

Lithology discrimination

With this data set (Figure 4), we investigated whether Qcan serve as a lithology discriminator in a frontier area withsparse well control. It was reasonable to anticipate that thesection down to reflector 1 is sedimentary. However, between

Table 2. Q estimates for the four intervals (range of thick-nesses as noted) in data set 1. Ranges ofindividual Qestimatesare given. Averaging of six CMPs' surface seismic estimates isdone on Q-t, not Q. Average Q values are [average Q-l]-1; theratio [standard deviation on Q-l]:[average Q-l] is multipliedwith [average Q-l]-1 to give the quoted uncertainty bounds.Those on VSP estimates are from regression on stacked di-rect-arrival spectral ratios.

twtthickness Surface seismic

Unit (ms) Average Range VSPTo top Chalk 420-500 468 36-60 N/AChalk 460-480 130 15 112-150 1154Mushelkalk -Keuper 160-180 478 38-60 587Bunter-Zechstein 420-500 156 18 135-182 184 20

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Q from Surface Seismic Data 2125

Effects of gas

Table 3. Average interval Q estimates at four CMPs (250,300,350,400) for four intervals in the seismic line of data set 2.Averaging and uncertainty bounds are found as for Table 1.

An attractive application of Q estimation is as a gas indicator,to reduce risk when used in conjunction with flat spots, brightspots, and AVO anomalies. Laboratory evidence (Frisillo and

while a layer within it (e.g., a sill) had a Q of 2000, the high-Q layer would need to be some 200 ms thick. Some expres-sion of this would be expected in the seismic section, wherewe saw no such prominent features. We therefore suggestedthe target interval was not a young sedimentary unit but per-haps old sediments possibly metamorphosed to some degreeor igneous rocks possibly fractured in some way to producelower-than-expected Q. Subsequent to this analysis, a well wasdrilled nearby. Within the exploration block, the target intervalwas found to be metamorphic.

133-146684-778142-172694-820

Q estimatesAverage Range

1406731 40157 13759 58

Interval

To reflector 1Reflector 1 to reflector 2Reflector A to reflector 1Reflector 1 to reflector B

reflectors 1 and 2, at roughly 1000 and 2000 ms two-way time,respectively, projections based on regional tectonics suggestedcrystalline basement could be expected; from reflection char-acter and pattern, this interval could be interpreted as sedi-mentary. Sedimentary rocks are usually relatively low Q (e.g.,between 10 and 450; Hamilton, 1972), whereas the igneous andmetamorphic rocks comprising basement will be higher (e.g.,100 up to several 1000 s; Tittman et aI., 1981). The target inter-val for Q estimation was thus between reflectors 1 and 2.

The structure was generally near flat, fault free, and con-tinuous. Preprocessing excluded multiple suppression, as thereflections studied (A, 1, B, 2, in order of increasing depth; fig-ure 4) were strong and apparently undistorted. The sea-floorreflection was used as the reference wavelet. CMP trace spac-ing was 50 m. Signal bandwidth was some 15-95 Hz, and offsetsup to 1000 m were used.

The QVO method was applied at four well-separated CMPsfor the source-to-reflector 1 and reflector-l-to-reflector 2 in-tervals. These returned Q values of 140 6 and 731 40,respectively (Table 3). It was possible that since the deeperinterval was very thick (::::;900 ms two-way time), its high Qarose from a low-Q succession of potentially prospective sed-iments with some interbedded higher Q layers. Hence, the in-tervals were subdivided using the strong reflectors A and B.The average Q for the upper part of the target interval was75958, in very close agreement with its overall Q of731 40.Furthermore, if the target interval had an average Q of 800

Well & VSP

o

500

'"'0 1000c:0u(l)'"-

E(l)E

f= 1500

2000

FIG. 3. A true-relative-amplitude seismic section from the southern UK North Sea, for which Q has been estimated at six CMPsand for the four geological intervals shown. Q values are given in Table 1.

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Stewart, 1980) suggests that Q changes drastically in the pres-ence of gas, falling to some 20% of its ambient value for only30-40% pore fluid saturation. This effect has been confirmedin-situ with VSP Q estimates (e.g.,Ryjkov and Rapoport, 1994)and was studied here with surface seismic data from a high-porosity ( =0.23)hydrocarbon reservoir in the UK North Sea.The key part of the seismicsection isgiven in Figure 5,where anobvious target interval containing the reservoir is highlighted.As for data set 1, multiple activity necessitated careful pre-processing. Trace spacing in the CMP gathers was 107 m. Abandwidth of 20 to 70 Hz and offsets up to 1800m were used,and the sea-floor reflection was taken as the reference wavelet.The OVO method was applied at 40-CMP intervals along thetarget interval in and beyond the coverage of Figure 5, whichalso shows the interval Q results (Table 3).

A clear and systematic reduction in Q was seen for the tar-get interval. The lowest Q values (50 11) were coincidentwith the anticline crest (and, as later recognized, the reservoir)compared with Q of ~100 on and beyond its flanks. Whereappropriate, a Q value for the reservoir only was calculatedby assuming a bilithological model of host rock and hydro-carbon reservoir, each of known two-way time thickness. Theformer was assigned a Q of 93, the average overall intervalQ outside the reservoir. The implied reservoir Q values (13-33, Table 4) were some 20-25% of the host rock Q values-in excellent agreement with the results from laboratory data(Frisillo and Stewart, 1980) and VSPs (Ryjkov and Rapoport,1994). Note that, conversely, if the same bilithological modeland host rock Q were assumed together with the laboratory

measurements of gas effects, then the two-way time thick-ness of the hydrocarbon column would have been estimatedaccurately.

DISCUSSION

We recognize that the OVO method presented is a proto-type, but, as the case studies demonstrate, it has been success-ful in recovering useful Q estimates. Further OVO analyses wehave undertaken revealed features such as the low-Q hydro-carbon reservoir in more data sets. We note in passing that our

Table 4. Interval Q estimates for the fuD interval of data set 3(see Figure 5) and for the reservoir interval alone at somelocations.

Q estimatesCMP Overall Reservoir only160 9520 N/A240 9620 N/A320 10522 N/A400 10221 N/A440 9220 N/A480 84 17 N/A560 61 13 136600 7314 33 12640 5912 208680 5011 146720 78 15 N/A800 93 19 N/A

Q)E

F=

CMP 150

o

500

1500

2000

230 310 390 470 550

REFLECfOR I

REFLECTOR B

REFLECfOR 2

FIG. 4. The true-relative-amplitude seismic section, from a frontier area, of data set 2; Q has been estimated for the intervalshighlighted and at the four CMPs shown. Results are listed in Table 2.

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Q from Surface Seismic Data 2127admittedly small data set did not indicate any common [intervalvelocity):[interval Q) relation. Interpretation of such results isunderdeveloped, and there are few reported in-situ Q values,largely from well data. Larger scale application of this methodto investigate features such as lithology correlation, overpres-sure effects, and sand-shale ratios is now desirable.

Developments to the QVO method, we anticipate, includealgorithm refinements such as spectral ratio slope estima-tion, e.g., an M-norm method [Oliver (1992) notes that least-squares fits are not ideal; Gao (1997) proposes use of Bayesiannonlinear methods]. Source and receiver directivity could beexplicitly accounted for. The difficulties of NMO stretch could

140

120

100tIS)='-eIS> 8001'0)...

60 Qof entire interval -eISe.......rn

UJ40

20Q of pay-zone

850800700 750550 600 650eM? Number

O'----...l..---'----'---'----....L...---L..._--L_----'L...--_...L-_-l350 400 450 500

FIG. 5. A portion of a true-relative-amplitude seismic section from the UK North Sea, showing the classic antiform structurecontaining gas; with it are Q values measured for the whole of the interval highlighted and inferred for the hydrocarbon reservoironly (see also Table 3). The effect of the hydrocarbons on Q is very clear.

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be circumvented by using a pre-NMO time-variant window tocapture the reflection, The method is capable of further exten-sion. It is in principle as applicable to 3-D data as AVO meth-ods are, and strategies to isolate intrinsic Q might be developed(e.g., Neep et al., 1995).Well control will still be important. Forexample, we make the assumption that the reflection eventsare from single, isolated interfaces. This may not be so; tuningwill modify wavelet spectra, propagate into Q estimates, andform part of the interval Q signatures.

In practice, we found that many actual QVO signatures(Figure 2c) depart from linearity in a number of ways, bothrandomly and systematically. Because they express (in part)traveltime moveout, some nonlinearities may be ascribed tofocusing and other nonhyperbolic moveout effects. Integratedwith ray tracing and modeling, QVO signatures may prove tohold information on properties such as anisotropy of Q. Appli-cations of accurate Q values are numerous, ranging from theroutine (e.g., AVO inversion; Hampson, 1991) to the experi-mental (e.g., combined inverse Q deconvolution and prestackmigration; Sollie et al., 1994).

ACKNOWLEDGMENTS

Shell UK, Enterprise Oil, and Cairn Energy kindly pro-vided the data used here. R. Dasgupta was funded by the UKgovernment through a Nehru Centenary Fellowship while onleave from Oil India Ltd. R. Clark held a Shell UK Lectureshipduring the course of this work. Bernhard Hustedt assisted withpreparation of figures.Graham Stuart offered useful commentson the first draft of the manuscript, which was much improvedby the comments of both reviewers. We thank them all.

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