how accurate is w4ll tie

There appears to be a body of opin-ion among geophysicists that well-log synthetic seismograms andseismic data cannot be expected tomatch one another very closely. Forexample, Simmons and Backus(GEOPHYSICS, 1996), in a paper onimpedance estimation, state “...as ismost often true, well-log-based synthetic seismograms do not agreewell with observed seismic data.”Norman Neidell, in conjecturing onthe conditions that generate coher-ent multiple reflections (TLE,November 1993) comments thatexplorationists often encounter syn-thetic seismogram fits that are lessthan satisfactory. That may be true,but it is not inevitable. We wish tocounter these pessimistic views byshowing an example of how good awell tie can be.

It would be a misfortune for seis-mic exploration, and especially forreservoir geophysics, i f poormatches between synthetic seismo-grams and seismic data became anaccepted fact of life. Although thereis more to validating an interpreta-tion than producing a close well tie,a poor tie invariably diminishesone’s confidence in an interpreta-tion. And the ability to model seis-mic data accurately in the vicinity ofa well must always be the primaryconcern in establishing the scientificcredentials of transformations toimpedance.

By any measure, the well tie wepresent is a very accurate one, but itis exceptional only in the duration(900 ms) over which it closelymatches the seismic data. It also givesa reasonably good match over theremaining 400 ms of logged section.With the advent of 3-D seismic dataacquisition and continuing improve-ments in acquisition and processing,examples of comparable accuracy canbe found in other areas of the NorthSea, although they would more typ-ically extend over 500 ms. Some ofthese were shown in a poster (“Theaccuracy of well ties: practical pro-cedures and examples”) at SEG’s1997 Annual Meeting in Dallas.

Phase errors from the best tieswere of the order of 7°. When one ofus (REW) began measuring well tieaccuracy in the late 1970s for BP,phase errors were rarely less than 15°.

At the very least, well ties with datafrom most marine surveys should beroutinely satisfactory. And they canoften be very good indeed.

The seismic data. The well tie comesfrom a dip line shot through well44/29-1A in the southern North Sea.Figure 1 shows part of the migratedseismic section, in the center of whichare spliced three identical syntheticseismogram traces. The explorationtarget was a sequence of sands,shales, and coals marked by thereflections beginning at 2.4 s. Thesands are gas bearing, although notin commercial quantities at this loca-tion. Above them is the LowerPermian Rotliegendes shale, whichunderlies 220 ft of Zechstein evapor-ites, marked by the flattish reflectionsjust before 2.3 s. The quiet zone abovethis corresponds to a firmly com-pacted Lower Triassic shale, theBunter shale, on top of which at 2.05-2.10 s is the Bunter sandstone, a fine-to medium-grained sandstoneinterbedded with thin layers of shale.

This sandstone is overlain uncon-formably by 45 ft of shale followedby a 210-ft layer of salt (2.02 s). Thewell is on the wing of a synclineformed between two salt features,one of which appears on the right ofFigure 1. Above the salt is a sequenceof Lower-Middle Triassic shales. TheSpeeton clay formation lies uncon-formably on these shales, abovewhich is the Upper Cretaceous chalk.The dipping reflection at 1.87 s marksthe base of the chalk, which is morethan 3000 ft thick. The reflectionswithin the chalk above 1.73 s corre-spond to variations in porosity (seeFigure 4).

The seismic data were acquiredfrom a water-gun array shooting intoa 132-group cable at offsets rangingfrom 199 to 2236 m. A source signa-ture was supplied for this array. Aninitial study starting from a stack tapeproduced in 1983 showed a goodmatch with the well-log syntheticseismogram. Because we wanted toanalyze the data before stack, the datawere reprocessed from the field tapes.

0000 THE LEADING EDGE AUGUST 1998 AUGUST 1998 THE LEADING EDGE 1065

How accurate can a well tie be?ROY E. WHITE, Birkbeck College, University of London, U.K.TIANYUE HU, Chinese Academy of Sciences, China

Figure 1. Part of the migrated seismic section through well 44/29-1A. Threesynthetic seismogram traces are spliced into the data at the location of bestmatch over the interval 1.4-2.0 s.

Downloaded 12 Jan 2011 to 201.222.2.2. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/

Figure 2 outlines the processingsequence.

The main effort went into velocitycontrol and the production of a goodquality prestack migration. Theprestack migration was a Stolt timemigration that used an average veloc-ity field centered on the well. This wasintended to produce a volume of datathat was sufficiently well focused onCRPs for subsequent refinement ofthe velocity field.

Following signature deconvolu-tion, water-bottom multiples wereattenuated by 80-ms gap predictivedeconvolution. After prestack migra-tion a beam-forming technique,applied to enhance the primaries onthe CMP gathers, was found to bebeneficial to the prestack well tie.Figure 3 shows a prestack CMPgather close to the well on the linebefore and after DMO plus prestackmigration, and after beam-formingmultiple attenuation. The benefitfrom the beam former was no longerevident in the stacked data, however.The final section of Figure 1 was pro-


Figure 2. Outline of processing sequence.

Figure 3. A prestack CMP gather close to the well on the line showing the data (left) before and (center) after DMOand prestack migration and (right) after beam-forming multiple attenuation.



duced by stacking, demigrating withthe velocity function applied duringprestack migration, and then remi-grating with a laterally varying veloc-ity function using a finite-differencetime migration.

The well logs. Figure 4 shows the welllogs used in constructing syntheticseismograms. The display runs fromnearly the top of the chalk down to theLower Permian Rotliegendes shale (11200 ft); the other formations describedearlier can be readily identified on it.Some spikes were identified and

edited on the sonic and density logs.To highlight possible discrepancies inthe logs, we employ a petrophysicalmodel (see “Anew velocity model forclay-sand mixtures” by Xu and White,Geophysical Prospecting, 1995) to pre-dict the P-wave sonic from lithologyand porosity estimates and then com-pare the measured and predicted logs(DT and PDT, panel 4, Figure 4).

Apart from two obvious errorsfrom the tool sticking, the logs wereof good quality. The model was veryuseful in automating the identifica-tion of coals beneath 11 600 ft, where

no density log was recorded. In con-structing synthetic seismograms, it ismost important that coals areassigned the correct density.

The sonic and density logs werecalibrated using first arrival timesfrom a VSP and blocked using theprocedure described in Walden andHosken (Geophysical Prospecting,1985). A suite of broadband planewave normal incidence syntheticseismograms was computed from theblocked logs, including the primaryreflection coefficients, the attenuatedprimaries (p), the primaries plusinternal multiples (p+im), and thesurface multiples.

Matching procedure. If the syntheticseismogram is to model the wave-forms observed in the seismic data,some form of matching is required inorder to estimate the effect of the over-burden on the seismic wavelet. Toachieve reasonable accuracy, it isessential to match a seismic data seg-ment having a bandwidth-durationproduct of 25 or more and containinga number of reasonably coherentreflections. In the North Sea, this typ-ically means using 500 ms of data,which must of course be accompaniedby a corresponding length of goodquality logs. There is no real likeli-hood of a good fit being forced on thismuch data, and in any case there arediagnostics to flag this likelihood.What is more important, and cannotbe emphasized too strongly, is that theaccuracy of the tie is measured andmonitored throughout the testing ofthe tie (see the cited poster paper inSEG’s 1997 Expanded Abstracts). Apartfrom quality control of the testing,quantifying the accuracy of well tiesallows their utility to be assessed rel-ative to, say, the accuracy required forinversion to impedance, and, with theaccumulation of results, the signifi-cance of improvements in techniquecan be put into perspective.

What if one simply does not havethe required 500 ms of data and logs?If there are several wells within thesurvey, it may be possible to workwith shorter segments, althoughwell-to-well validation becomesmore questionable. With just onewell, it may be possible to start froma model wavelet and estimate a verysimple trimming filter to representthe overburden. In either situation,the case for monitoring accuracybecomes even stronger. For example,there is not much point in compar-ing wavelets from well ties, or anyother approach, without some mea-sure of their accuracy. Similarly rou-

Figure 4. The logs used in constructing synthetic seismogram at well 44/29-1A. Panel 1: gamma-ray; panel 2: deep (ILD) induction log; panel 3: density;panel 4: porosity estimates; panel 5: P-wave sonic log and the P-wave logpredicted using the Xu-White model. Depths are in feet.



tine monitoring of accuracy wouldimmediately reveal the unsatisfac-tory nature of the many well ties onesees based on data segments that aretoo short (e.g., 200 ms) to yield reli-able results.

The first step in making the welltie is to run pilot analyses, the pur-pose of which is to establish the para-meters needed for estimating thewavelet as accurately as possible. Akey step is to scan time gates andtraces around the well for the bestmatch location. Figure 5 shows howthe goodness-of-fit of the tie at 44/29-1A varies with CMP location in twodisjoint time gates. The well is atCMP 1110. In the 1.4-2.0 s gate, thebest-fit location is 380 m away atCMP 1087; in a 2.0-2.5 s gate, it movesto CMP 1076, and in a 2.3-2.8 s gateto CMP 1071. Much of the bulk shiftis likely to be positioning error. Thesystematic drift is caused by raypatheffects in time-migrated data: Thebest match location is tracking the

starting point at the surface of imagerays that end on the well bore. Imageray tracing from a simple depthmodel (Figure 6) shows how the driftoriginates. A depth of 2000 m at thewell corresponds to a two-way reflec-tion time of 1.66 s. The surface loca-tions of image rays emerging fromthe well move systematically in anupdip direction. Although the driftfrom this crude model does not agreeexactly with that observed, they aresimilar. It is generally observed thatthe best match location moves updipfrom the well when tying time-migrated sections in which velocityincreases with depth.

Once the best-fit location has beenfound, other analysis parameters canbe tested. In the interests of brevity weskip the details of this. In addition onecan test, for example, whether internalmultiples should be included with pri-maries in the synthetic seismogram,and whether surface multiples are con-tributing significantly to the data.

These are often not critical decisions formodern data from the North Sea.

Well tie. The most accurate tie at44/29-1A was obtained from match-ing the 1.4-2.3 s segment at CMP 1087with the (p+im) synthetic seismo-gram. Within this time gate, the syn-thetic seismogram predicts 85% ofthe trace energy; that is, the meansquare of the residuals is 15% of themean square value of the trace seg-ment. This translates into an esti-mated normalized mean squareenergy in the wavelet of 0.015, or astandard error in phase within theseismic bandwidth of about 6˚. Thetie is shown in detail in Figure 7.

The best match location varieswith two-way time. Matching overshorter time windows, such as 1.4-2.0s and 1.5-2.1 s, produces virtually thesame wavelet and predicts the sameproportion of trace energy in the 1.4-2.3 s gate. Although the predictabil-ities rise to 87% and 88% respectivelyin the 600-ms intervals, the estimatedwavelet accuracies are slightly less.

Reflections from 2.4 s to near theend of the log at 2.8 s originate withinthe sand-shale-coal sequences. Theties of Figures 1 and 7a do not matchthis sequence well. The best tie loca-tion is really 16 CMPs updip, but themain change appears to be that thewavelet has become more narrowband and phase shifted by approxi-mately 40˚.

Figure 7b shows the tie over theinterval 2.3-2.8 s at CMP 1071, thebest match location. This is still arespectable tie. The normalized meansquare energy in the wavelet is 0.08;the standard error in phase is 12˚. The(p+im) synthetic was significantlybetter than a simple primaries-onlysynthetic in matching the 2.3-2.8 sdata. Within the 1.4-2.3 s interval, itmade little difference which syntheticwas used.

The wavelet of Figure 7b has lostboth high- and low-frequency energyrelative to the one in Figure 7a. Theattenuation is not consistent with aconstant-Q loss. It is doubtfulwhether our log blocking was goodenough to model a finely layeredsand-shale-coal sequence and thewavelet could be compensating forthat. However, frequency attenuationis also detectable within the 1.4-2.3 sinterval, and this too deviates from aconstant-Q model by more than theerrors of estimation. Without goinginto details, it is clear that testingwhether the wavelet varies with timehas to take account of image rayeffects (and the log calibration). While

Figure 5. Results fromscanning the migratedseismic sectionthrough well 44/29-1Afor the location of bestfit with the broadbandwell-log syntheticseismogram over twotime intervals: 1.5-2.0 s(dashed line) and 2.0-2.5 s (solid line).The vertical axis is Pthe proportion of traceenergy predicted by matching; the horizontal axis is CMP number.

Figure 6. Image ray tracing of a depth model constructed from the migratedseismic section through well 44/29-1A showing the reflection points corre-sponding to CMP locations at the surface. The separation of the starting pointsof the rays at the surface is 16.67 m.


parsimonious modeling of the time-varying spectral decay improves thetie, the gain is not great, and it raisesother issues that we leave for dis-cussion elsewhere.

The section of Figure 1 was zero-phased and whitened using the seis-mic wavelet from Figure 7a. Figure 8shows the resulting zero-phase sec-tion. Improved resolution of this kindhad not been seen before from thesedata.

Wavelets from the prestack data. Afterbeam forming was applied to attenu-ate multiples, various weighted andunweighted substacks of the moveoutcorrected CMP gathers were matchedwith the normal incidence syntheticseismogram. Figure 9 is a contour plotof goodness-of-fit over a 1.5-2.0 s timegate from six simple disjoint 11-tracesubstacks. It appears that the CMPgather at the well is focused on thewell over the first four offset bands.Muting (Figure 3) affects the fifth andsixth offset bands.

The prestack wavelets are verysimilar to the wavelet in Figure 7a,except that they become increasinglystretched with increasing offset.

Conclusions. In general, data fromthe North Sea yield reasonable-to-good well ties. Why is this and why,in other places and other situations,are well ties often poor? Because manyfactors contribute to the making of awell tie, there is no simple answer tothese questions, but Neidell wassurely right in emphasizing that geol-ogy plays an important role. In theNorth Sea, well ties in the Tertiary areusually poorer than those from theCretaceous and below. It is unlikely tobe a coincidence that the Tertiary rocksare softer and more prone to generateAVO anomalies and nonhyperbolicmoveouts. These last two factors wereraised by Denham, in his response toNeidell’s conjecture, together with therequirements of strong multipleattenuation and precise migration.

We also regard multiple attenua-tion and migration, preferably start-ing prestack, as key concerns of theprocessing. In the 44/29-1A examplepresented here, most of the repro-cessing effort went into the attenua-tion of multiples and to building anaccurate velocity field for migration.The result was that a good well tiefrom production processing, whichpredicted 65% of the trace energy,became an exceptionally good onethat predicted more than 80%.Migration is beneficial for several rea-sons beyond its improved position-

Figure 7. The match between the trace at (a) CMP 1087 from the remigratedsection and the primaries-plus-internal-multiples synthetic seismogram atthe well over the time interval 1.4-2.3 s, and at (b) CMP 1071 over the timeinterval 2.3-2.8 s.

Figure 8. Part of the whitened zero-phase seismic section. Three syntheticseismogram traces are spliced into the data at the location of the best matchover the interval 1.4-2.0 s.

a)

b)

IMPEDANCE BROADBAND ESTIMATED FILTERED DATA RESIDUALSLOG SYNTHETIC WAVELET SYNTHETIC SEGMENT (DIFFERENCE)




ing of events. It contracts the Fresnelzone, reduces timing and raypatheffects relative to the stack and, whenapplied prestack, approximates CRPdata and aids velocity control. Inprinciple, depth migration shouldbring a further benefit. The practicalquestion is whether it can be madeaccurate enough to yield this benefitwithout seriously distorting the seis-mic waveforms.

The basic ingredients of a goodwell tie are high quality seismic andlog data, and near-vertical wells.Geologic factors that can stand in theway of a good tie are structural com-plexity, rapid lateral variations invelocity or reflectivity, seriouslyunconformable dips within the matchgate, and finely layered sequenceshaving severe impedance fluctuations.

To these physical factors we wouldemphasize the importance of an ana-lytical approach to well ties with quan-titative measures of accuracy (and notjust goodness-of-fit). By providingobjective quality controls, an analyti-cal approach provides a consistentbasis for testing options and forimproving well ties as a matter of rou-tine. Whenever possible, analysis forsignal and noise spectra and forwardmodeling should be a complementarypart of the exercise. Although thiseffort may bring only incrementalimprovements, experience invariablyshows that following up details in thepreparation of the seismic and log databears fruit. An analytical approachbrings rigor to any detailed investi-gation of the data. Details of imple-

mentation also need attention: optimalalignment of the synthetic and data,minimizing effects from the trunca-tion of data segments, allowing fornoise in the data, and errors in thesynthetics. Sonic log calibration andtiming are another area obviously

deserving close attention. Of well ties,it is definitely true that “the devil is inthe details.”

Suggestion for further reading. Thetheory for estimating the accuracy ofwell ties was described by Waldenand White in “On errors of fit andaccuracy in matching synthetic seis-mograms and seismic traces”(Geophysical Prospecting, 1984). LE

Acknowledgments: We thank Fina ExplorationLtd. for permission to publish its data, P.Anderton of Fina for helpful discussions on theresults, Shiyu Xu for his work on the well logs,and Tudor Davies for his help and advice in pro-cessing the seismic data. We also thank BrianBarley of BP, who has seen many more well ties,good and bad, than either of us, for his com-ments on what makes for a good well tie.

Corresponding author: R. E. White, 44-171-380-7332, [email protected]

Figure 9. Contour plot from the scanof substacks of the prestack migratedCMP gathers for best fit with the nor-mal incidence synthetic seismogramover a 1.5-2.0 s time gate. The quan-tity contoured is the proportion oftrace energy predicted by matchingthe synthetic seismogram.


how accurate is w4ll tie

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