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AbstractThe data set provided for amplitude versus off-

set (AVO) inversion has been subjected to the threesteps which are involved in the DELPHI consortiumprogram: preprocessing, structural imaging, and litho-

logic characterization.In the preprocessing step, a major problem is thepresence of strong surface-related multiples. With anintegrated surface-related and Radon multiple elimi-nation procedure, it was possible to remove the mul-tiples in a satisfactory way without distorting the pri-mary AVO characteristics.

Once the multiples were removed, structural im-aging could be done in a fairly straightforward way,in which prestack migration techniques were used toget a good macro velocity depth model for thepoststack depth migration.

In the lithologic inversion stage, anomalies in the

compressional to shear wave velocity c p / cs ratio,which are related to hydrocarbons, were detected byinversion of prestack data. The inversion result showsthat the shallower reservoirs have larger anomaliesthan the deeper (Jurassic) reservoirs. This is in agree-ment with the provided well data.

Finally, using wave equation-based depth ex-trapolation, a shot record at the well was transformedinto a pseudo vertical seismic profile (VSP). The

DELPHI Stepwise Approach toAVO Processing

Dirk Jacob Verschuur, Aart-Jan van Wijngaarden,and Riaz Alá’iDelft University of Technology, Delft, The Netherlands

pseudo VSP facilitates an accurate comparison be-tween real VSP data and surface data. Integration ofreal and pseudo VSP data may provide a new way topredict lateral reservoir variations.

IntroductionThe DELPHI consortium at the Delft University

of Technology is carrying out a research program onthe stepwise inversion of seismic data. The three prin-cipal steps are:

1) Preprocessing2) Structural imaging3) Lithologic characterization

As such, the Mobil AVO data set is a good candi-date to test the application of the DELPHI processing

approach.For this data set, preprocessing is an important

step, as the data suffer from distortions due to sur-face multiple energy. The DELPHI surface-relatedmultiple elimination method (including the latest de-velopments on integration with the parabolic Radonmethod) will be applied to supply the best possibleprimaries-only data set for the imaging and charac-terization steps. The amplitudes of the primary events

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Verschuur, van Wijngaarden, and Alá’i

140

should be preserved after this preprocessing stage.Because of moderate dips, the structural imaging

step is accurately performed with conventional stack-ing and poststack depth migration. However, the ini-tial depth model derived from stacking velocities has

been updated using the prestack areal shot record

migration method described by Berkhout andRietveld (1994) and Rietveld and Berkhout (1994) toobtain a consistent depth model.

In the lithologic characterization step, a gradientsection was derived to get an overview of the generalAVO behavior of the data. After that, the preprocesseddata were used as input for our linear constrainedinversion process to estimate the seismic contrast pa-rameters. Well information was used to constrain theinversion. The contrast parameter section was thentransformed to lithology/hydrocarbon information.The final section of this paper describes how the seis-mic shot records around one of the wells were trans-formed to pseudo VSP data for comparison with thereal VSP data.

PreprocessingTo process the Mobil line, shots 354 to 1053 were

selected, with 1024 samples per trace. The preprocess-ing consisted of the following steps:

1) Direct wave mute. Careful direct wave mutingwas performed so that the reflection data wereundisturbed.

2) 3-D to 2-D spherical correction. A simple timegain was applied to simulate line source insteadof point source responses.

3) Replacement of bad traces. On careful inspec-tion of the shots it appeared that several chan-nels in each shot contained data that are not con-sistent with their neighboring traces (phase andamplitude distortions). They were killed andreinterpolated from the good traces using arough normal moveout (NMO) correction andspline interpolation.

4) Wavelet deconvolution. Predictive decon-volution was applied with a gap of 20 ms and a

filter length of 240 ms.5) Receiver sensitivity correction. Even after in-

terpolation to replace bad traces, the receiversappeared to show a consistent sensitivity be-havior throughout the shot records. Least-squares inversion techniques were used to cor-rect these amplitude fluctuations. Also thesources showed a fluctuating amplitude behav-

ior. These fluctuations are not as strong as thereceiver amplitude fluctuations and, therefore,they were left in the data.

6) Interpolation of missing shots and near offsets,Application of the surface-related multiple-elimination method requires full coverage of the

shots and receivers up to zero offset. Amongthe selected shots from the line, six shot recordsare missing (shots 549-551 and 859-861). Theywere interpolated in the common offset plane.As the nearest offset was 263 m, approximatelyten near-offset traces are missing in each shot.They were created using a parabolic Radontransform to extrapolate the data to zero offsetin the CMP domain (see Kabir and Verschuur,1993).

In Figure 1, five shots (503, 603, 703, 803 and 903)are displayed without any processing (except for di-rect-wave mute). For display purposes, NMO correc-tion is applied to the shots. This gives some idea aboutthe structure of the primary reflections. The down-ward curving events can be considered to be mul-tiples.

In Figure 2, the same five shots (503, 603, 703, 803and 903) are displayed after the five basic preprocess-ing steps. Deconvolution has done a good job withrespect to sharpening the events. Note that near traceshave been created up to zero offset. Actually, due tothe many multiples, the interpolation results are a littlenoisy for the larger times (larger than 2 s). Later we

will see that we fail to do a good job of multiple re-moval on the interpolated near offsets. However, theyare only meant to yield a better multiple estimationand will be omitted in the later processing (i.e., stack-ing and migration).

Multiple Elimination

MethodAfter the basic preprocessing sequence, the data

are ready for the most important preprocessing step:multiple elimination. As can be seen in Figure 2, a lot

of multiples are present in the data, especially in thedeeper part of the sections. Therefore, effective mul-tiple elimination that preserves the primary ampli-tudes is necessary to obtain reliable AVO inversionresults. We will compare and integrate two methods,the surface-related multiple-elimination method andthe parabolic Radon tranform multiple-eliminationmethod.

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DELPHI Stepwise Approach to AVO Processing

141

Fig. 1. Shot records 503, 603, 703, 803, and 903 before preprocessing (NMO correction applied).

Fig. 2. Shot records 503, 603, 703, 803, and 903 after basic preprocessing and interpolation ofmissing shots and traces (NMO correction applied).

Q)

E

Q)

E:0::

3.b..L,;==

503 603

503 603

shot number

703

shot number

703

803

803

903

903

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Surface-related and Radon multipleelimination

The surface-related multiple elimination method,described by Verschuur et al. (1992), is based on wavetheory. It can be proven that by taking temporal and

lateral auto-convolutions of the seismic data, an ac-curate prediction of the surface-related multiples isobtained. Subsurface information is not needed, butinformation on the free surface reflectivity (assumedto be –1 for marine data) and the source wavefield isrequired. As the latter is not known in practice, themethod is applied adaptively. By eliminating themultiples, the source signature is estimated as well.

The generalized Radon transform multiple sup-pression method originally was described byHampson (1986). By adding the events in a seismicrecord (e.g., a CMP gather) along curved paths, eachevent maps to a restricted area in the transform do-main. In the case that primaries and multiples havedifferent moveouts, they map to different parts in theRadon domain. In this domain, the multiples are se-lected and an inverse transform is applied. Next, thepredicted multiples are subtracted from the inputdata, yielding the primary gather. From an implemen-tation point of view, the parabolic Radon transformis more efficient than a hyperbolic transform since theprocedure can be applied in the Fourier domain foreach individual frequency component (see also Kabirand Verschuur, 1993). By applying a partial NMO cor-rection to the input data, the residual moveouts often

can be assumed to be approximately parabolic. Us-ing least-squares matrix inversion to transform thedata to the Radon domain, optimum resolution can

be achieved. If the offset geometry of the subsequentdata gathers is (approximately) constant, a very effi-cient implementation of the Radon transform can beachieved (Kelamis and Chiburis, 1992.)

Integration of surface-related andparabolic multiple elimination

Following the theory of surface-related multipleelimination (Verschuur and Berkhout, 1994), it can be

shown that the adaptive surface-related multipleelimination procedure can be written as an iterativeprocess. For this iterative procedure, an initial esti-mate of the multiple free data is used as multiple pre-diction operator. The iterative formulation has twomajor advantages:

1) The iteratitive procedure begins with a betterguess for the multiple free data, e.g., the out-

put of another multiple elimination method.This makes the method more efficient.

2) Each iteration is carried out as a linear least-squares optimization step, yielding faster and

better results (i.e., no local minima). In addi-tion, the restrictions on the estimated wavelet

deconvolution filter can be relaxed. Therefore,varying signatures for different sources or evensource directivity are included in a more con-venient way (Verschuur and Berkhout, 1993).

In conclusion, we propose to make use of an effi-cient multiple removal procedure to get an initial guessof the multiple free data and use that as input for aniterative formulation. Then only one or two iterationswill be needed for the final surface-related multipleelimination result. The examples will show that theRadon multiple elimination method provides a verygood initial guess for the multiple free data.

Multiple Elimination

ResultsThe initial multiple elimination results obtained

with the parabolic Radon transform method are dis-played in Figure 3. (Note that the Radon transformmethod is applied on CMP gathers, although shotsare shown here). Comparing the results with the in-put data of Figure 2 shows that the Radon transformmethod does a very good job in the shallow data

(above 2 s) but below 2 s some multiples still remain.Using more severe muting in the Radon domain maydistort primary reflection energy.

This result was used as an initial multiple predic-tion operator (as the upper part is multiple free) forthe surface-related multiple-elimination method. Onlyone iteration had to be applied. The surface-relatedmultiple-elimination method also provides an esti-mate of the residual source signature deconvolutionoperator. This filter was applied to the output to simu-late zero-phase results. The remaining distortions ofthe wavelet are due to propagation and absorptioneffects only; (i.e., subsurface-related effects). Addition-

ally, a dip filter was used to remove those dips fromthe data that do not contribute at the target.

For the shots under consideration, Figure 4 showsthe final result. It appears that, partly due todeconvolution, the result has higher frequencies andis noisier than the Radon result. But in the deeper data,it was possible to predict and remove the multiplesthat were left by the Radon method. For the upperpart, the Radon result might even be better, although

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Fig. 3. Shot records 503, 603, 703, 803, and 903 after parabolic Radon multiple elimination(NMO correction applied).

Fig. 4. Shot records 503, 603, 703, 803, and 903 after surface-related multiple elimination andwavelet deconvolution.

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at stack level this difference was not visible. Both theRadon and the surface-related method have some dif-ficulties at the very near offsets. Therefore, a near-off-set mute was applied before stacking. Figure 5 shows

the stacked section after basic preprocessing, but be-fore multiple elimination. Figure 6 shows the stackafter multiple elimination and application of the esti-mated residual wavelet deconvolution filter. Figure 6

Fig. 5. Stacked section after basic processing.

800

900

1000

_. 1111100

l -Q)

.0

E:: l 1200c

Q .

"0u

1300

1400

1500

1600

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shows an improvement in the multiple removal for both shallow (e.g., first-order multiples at 1.1 s) anddeeper multiples (e.g., around CMP 1300 at 2.8 s). The

effect of multiple removal after migration is shownin Figure 7. Deeper structures are better imaged.

Fig. 6. Stacked section after multiple elimination and residual wavelet deconvolution.

800

900

1000

1100

....

(])

.0E:::l 1200c0-"0( )

1300

1400

1500

1600

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Fig. 7. Poststack depth migration of stack after multiple elimination and residual waveletdeconvolution.

800

900

1000

1100

....

Q)

.£ l

E::J 1200c

0. .

-0u

1300

1400

1500

1600

depth (m)

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Constrained Linear

InversionAfter preprocessing and multiple elimination, we

used linearized inversion on CMP gathers to estimate

the relative elastic contrast parameters. We assumeda locally flat and low contrast medium. In our algo-rithm, the nonlinear Zoeppritz equation for the elas-tic angle dependent plane-wave P-P reflection coeffi-cient R(φ ) is linearized. Following Aki and Richards(1980), R(φ ) is written as a weighted sum of the rela-tive contrasts in the elastic parameters P-wave veloc-ity c

p, S-wave velocity c

sand density ρ

R(φ ) =1

2sec2φ

∆c pc p

− 4cs

2

c p2 sin2φ

∆cs

cs + (

1

2 − 2

cs2

c p2 sin2φ )

∆ρ

ρ

( 1 )

where φ equals the angle of the incident P-wave, ∆c p

equals contrast in the P-wave velocity over an inter-face and c

p equals the average P-wave velocity over

the interface. Similar definitions apply for ∆cs, c

s, ∆ρ

and ρ. This can also be written in terms of tan2φ andsin2φ :

R(φ ) =1

2

∆Z

Z+

1

2

∆c

c p

p

tan2φ − 2 γ 2 ∆µ

µ sin2 (2)

with

Z = c pρ , µ = ρ cs2 and γ =

cs

c p . (3)

Available well data can be used to estimate therelation between the P-wave velocity and the S-wavevelocity γ .

In the inversion algorithm, the NMO-correctedCMP data are converted to the reflection coefficients(scaled with the wavelet) for a number of angles us-ing the P-wave macro model.

The relative contrasts can be found by least-squares inversion. Using Equation (2) we estimatedthe relative contrast in acoustic impedance Z, in P-wave velocity c

pand in the shear modulus µ at each

time sample by minimizing the difference betweenR(φ ) given by Equation (2) and the NMO-correctedCMP data. The output of the inversion consists ofthree time sections: one for each estimated contrast.

In our algorithm, a Bayesian approach is used inthe statistical inversion. The available well data areused in the following relations to stabilize the inver-sion:

∆ Z

Z = Γ 1

∆c pc p

(4)

and

∆c pc p

= Γ 2 ∆µ

µ . (5)

Lithology and hydrocarbonindicators

Since the estimates are derived from a linear combination of the data, any linear combination of theoriginal parameters can be taken. This means that wecan, for example, estimate the relative P-wave veloc-ity contrast∆c

p /c

pand the relative shear modulus con-

trast ∆µ/µ and compute, from a linear combination ofthose two, a contrast deviation factor

∆ D = ∆c pc p

− k ccs

p

ρ µ µ 2

∆ . (6)

The contrast deviation factor ∆D shows deviationsfrom an empirical linear relation between P-wave andS-wave velocities (Castagna et al., 1985),

c p = (k ρ ) cs + c (7)

where k [(kg/m3)-0.5] and c [m/s] are constants.Well-log velocities are used to determine the con-

stants k and c. Differentiating this relation to obtain a

relation in relative contrasts gives∆c pc p

=

k c

cs

p

ρ µ

µ 2

∆. (8)

Note that interfaces satisfying Equation (7) willshow a contrast deviation factor ∆D equal to zero.

Equation (6) needs the trend in the relation

k ρ (ρ )[cs /c

p] at every point in the subsurface to com-

pute deviations from Equation (7).In our algorithm, we compute the ratio Γ from

the data using the relation

∆c pc p( x,t ) = Γ( x,t ) ∆µ µ ( x,t ) (9)

and average the ratio in time and in lateral directionto get <Γ (x,t)>.

This averaged ratio is used to compute deviationsfrom the trend in the ratio between the P-wave veloc-ity contrast and in the shear modulus contrast. This

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anomaly indicator or contrast deviation factor sectionis defined by

IND( x,t ) = ∆c pc p

( x,t ) − < Γ ( x,t ) >∆µ

µ ( x,t ) . (10)

Inversion resultsThe depth migrated section was interpreted to

show the main fault structures. The large reflector nearthe base Cretaceous or ‘X’ unconformity as well asthe large fault blocks in the Jurassic section are easilyrecognized in Figure 8. We also tried to follow themain reservoir sands.

At well A, we made crossplots of the P-wave ve-locity c

pand the shear modulus µ around the three

hydrocarbon bearing sands at 2000 m, 2300 m and2600 m. The crossplots are shown in Figures 9 and 10.From these figures we conclude that the relation be-

tween c p

and µ is approximately linear for shalesand nonhydrocarbon sandstones. The oil-bearing

sandstones have a slightly lower c p/ µ ratio. The

gas-bearing sandstones have a larger deviation in

c p/ µ ratio from the trend, which is clearest in Figure

9. From this well data analysis we conclude that itshould be possible to detect the gas sands as ananomaly in the ratio of the relative P-wave and µ con-trasts (Equation 10).

The first output section from the inversion is theestimated contrast in acoustic impedance. A poststackdepth migrated section from 900 m to 4000 m is shown

in Figure1. The estimated relative contrasts in cP andµ are combined as stated in Equation(10), and the re-sult is shown in Figure 12. The overlaid interpreta-tion is the same as in Figure 8.

The indicator (Figure 12) shows clearly the strongAVO anomalies in the area below the X-reflector be-tween well A and B. From well data, we know that atwell B, this layer does not contain any hydrocarbons.The gas and oil sands at well A around 2600 m are notclearly present as an anomaly in the indicator. Com-paring the crossplots of the well data in Figures 9 and10, we could already have concluded that it would bedifficult to see this reservoir as an anomaly.

The area indicated by Q at 2000 m around CMP1375 shows also a very strong anomaly. The NMOcorrected CMP data are shown in Figure 13. Here wesee a strong increase in amplitude versus offset, whichmight be related to a gas–filled sandstone. The areaindicated by P at 3100 m around CMP 1234 shows ananomaly in the same layer, in which at Well B a gassand has been found. The NMO-corrected CMP datais again shown in Figure 14. Here we can see a small

acoustic impedance contrast with a polarity reversalin amplitude versus offset of about 2.7 s.

The highly faulted area at CMP 1100 at 2800 mshows also anomalies. One should note that the as-sumptions of a (locally) flat layered medium are vio-lated here.

VSPThe Mobil data also contained three-component

zero-offset vertical seismic profiles recorded in wellsA and B. We used the VSP data for Well B to investi-gate how they tie to the surface data. In this section,we address:

• Preprocessing of the raw VSP data (Well B)• Pseudo VSP generation from a shot record along

the line near Well B• Comparison of the Pseudo VSP data with the

preprocessed real VSP data

VSP preprocessingSome results will be shown on the preprocessing

of the raw three-component VSP data (Well B—start-ing at the sea bottom at 500 m depth). Here we intro-duce a fast and efficient method to suppress the noisyand spiky parts in the VSP data registrations. Themethod will be applied to the zero-offset vertical seis-mic profile for Well B. The registration tool used torecord Well B consisted of four detectors each mea-suring three-component data. Figure 15 illustrates the

raw VSP data registrations for the four detectors. Onlythe vertical component is shown. Figure 16 showsagain the registrations for detector1 together with a

blowup of a selected part of the data. The blowup ofthe data registrations is shown here to give a betterview of the noise in the VSP data. As can be seen fromthe raw VSP data registrations, there are many badtraces.

Furthermore, one can see that several registrationswere made at each depth level, in which many tracesare noisy. The objective is to remove the bad traces ina fast and efficient way before common depth levelstack so that we obtain only one clean trace per depth

level. In the following, we illustrate an efficient sort-ing and stacking method, the so-called alpha-trimstack. For an extensive discussion and applicationsof this process, the reader is referred to Scheick andStewart (1991) and Frinking (1994). Figure18 illus-trates the alpha-trim stack procedure of sorting andstacking at a certain depth level. For each time sample,the data are sorted in ascending order of amplitude.This is repeated for all time samples. Next a window

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well A

900

1000

1100

....

(] )

.cE

1200::)

c::

Q."'0()

1300

1400

1500

well 8

1600


Fig. 8. Interpreted depth migration.

149

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Fig. 9. Crossplot of the P-wave velocity versus µ at Well A around 2000 m and 2300 m.

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Fig. 10. Crossplot of the P-wave velocity versus µ at Well A around 2600 m.

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Fig. 11. Depth migration of acoustic impedance contrast (from 900 m).

800

1000

1200

1400

1600

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Ii.... ....

§ §

I !

§ §

§ §

§ §.. ..

§.. ..

8 8.. .... ..

51.. .... ..

8 8.. ..

... ...

51.. ..

... ...

i i.. po

5! 51... ..

... ..

i i.. ...

Q

... ...

§ §... ...

Q::!... ...

§..

IQ

I... ...

I I..

Fig. 12. AVO anomaly indicator (in depth) with structural interpretation and well locations overlaid.

153

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154

Fig. 13. NMO-corrected CMP gather at CMP 1375 showing event

Q at 2 s.

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155

Fig. 14. NMO-corrected CMP gather at CMP 1222 showing event

P at 2.7 s.

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Fig. 15. Raw VSP data registrations (Well B—vert. component; detectors 1 to 4).

depth[m]

a) b)

c) d)

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Fig. 16. (a) Data registrations fordetector 1 and (b) partial blowup.

Fig. 17. Alpha-trim sorting and stacking procedure applied to VSP data (several registra-tions at one depth level).

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158

Fig. 18. VSP data after alpha-trim stacking for different α values: (a) α = 0, (b) α = 0.7, (c) α = 1, (d)VSP data after manual trace editing.

depth [m]

~ ~ Ql QlE E+= +=

a)

depth [m]

500 1500 2500 3500

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is selected within which the data are stacked. Thewidth of the window depends on the value of α, whichvaries between α = 0 and α = 1.α = 0 selects all tracesat each depth level before stack (i.e., a mean stack ofall traces per depth) and α=1 corresponds to select-ing only 1 trace (the median filtering technique). In-

creasing the parameter a reduces the number of traces(data points) used for stacking. The value of α must

be chosen such that the stacked result contains at leastone clean trace per depth level. Figure 18 shows theresult of applying the alpha-trim stacking for a val-ues 0, 0.7, and 1 (Figures 18a, b and c, respectively).Afterward we regularized the data in depth and weinterpolated missing traces. With increasing values ofα we remove more and more noisy data points. Wechose α = 0.7 (Figure18b) as optimal for removingnoisy data points and preserving the amplitudes ofthe useful data.

The lower part of Figure 18 compares the alpha-trim stacking procedure forα (Figure18c) with a con-ventional method for VSP preprocessing (Figure 18d).The conventional method for VSP preprocessing ismanual removal of noisy traces before common depthlevel stacking. This is a very time consuming method.Finally the alpha-trim method is compared with themedian filtered version, which shows that the alpha-trim method looks even better. Note that with manualtrace editing, a complete trace is removed and usefulinformation within this trace is lost. The alpha-trimstacking procedure determines for each time slicewhich samples will be rejected. In this way useful in-

formation will be preserved that would otherwise berejected as a bad trace. The same procedure for sup-pressing the noisy parts of the raw VSP data was ap-plied on the two horizontal components recorded inWell B. Figure 19 illustrates the result of alpha-trimstacking on the horizontal-1 and horizontal-2 com-ponent of the data. The optimal value for αwas foundto be α = 0.6. The conversion from the direct P- to anS-wave can be clearly identified, although reflectionsare very difficult to distinguish.

Pseudo VSP generation from

surface dataSo far we have described the preprocessing of thereal VSP data. In the following, we will show the gen-eration of pseudo VSP data from a real shot record(shot point 822; CDP No. 1572) at Well B. To avoid theinfluence of interpolated near-offset traces, the pseudoVSP was generated at 200 m offset. For an extensiveoverview and discussion on the generation of pseudoVSP data from surface data, see Alá’i and Wapenaar

(1994). First we will show the result of the pseudoVSP generation from the shot record with all multiplesincluded (Figure 20). Acoustic two-way wavefieldextrapolation operators are used in this pseudo VSPgeneration. (Only reflected wavefields in the shotrecord are used as input; the direct source wavefield

is not included.) The seismic data are affected by verystrong multiples, and the primaries are not clearly vis-ible because of these strong multiples. Therefore thepseudo VSP was also generated from the same shotrecord after adaptive surface multiple elimination wasapplied. A blocked version of the true velocity logused for the generation of the pseudo VSP is displayednext to the pseudo VSP to show its relation in depthwith the migrated section. Figure 21 shows the pseudoVSP generated from the same shot record (822, i.e., atWell B) after surface-related multiple elimination. Theprimaries are more identifiable compared to thepseudo VSP in Figure 20. Note the downgoing mul-tiple reflections from the sea bottom (at 500 m depth).The transformation of the surface data into pseudoVSP data provides a better understanding of complexevents (e.g., internal multiples). Reference arrowsshow the relation of the different data sets in the dif-ferent planes (x-t, z-t, x-z). This facilitates followingan event from the shot record to the VSP data andtracing it back to the intersection with the direct sourcewavefield at the original reflector depth. In fact thepseudo VSP data can be used as a tool to map a timeevent in the shot record into depth. The generation ofthe pseudo VSP data provides an unambiguous tie

between seismic events on a time section and theirgeologic interface in depth.

Comparison pseudo VSP and realVSP

Here we give some final remarks regarding thevalue of the pseudo VSP data. First we would like todiscuss the comparison between real VSP and pseudoVSP data (generated after surface-related multipleelimination). Note that only primaries should be com-pared. Because the acquisition of the real VSP data iscompletely different from the surface data, the data

have different frequency content. The pseudo VSPdata have a lower frequency band, and therefore alower resolution, than the real VSP data. On the otherhand, after proper preprocessing (this may include athorough study of the sources and detectors that areused in both situations), the pseudo VSP may have a

better signal-to-noise ratio. Hence, in practical situa-tions, both VSPs may enhance each other significantly.Of fundamental importance in the pseudo VSP gen-

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Fig. 19. (a) Original VSP data (Well B—hor. 1-component) and (b) after alpha-trim stacking (α–TS) α = 0.6. (c) hor. 2-component) and (d) after α–TS α = 0.6.

depth [m]

500 1500 2500 3500

a) b)

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Fig. 20. Integrated shot record /pseudo VSP / migrated section (all multiples included).

III 11111I I , ..

'I I

depth [m]

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Fig. 21. Integrated shot record / pseudo VSP / migrated section (after surface-related multiple elimination).

depth [m]

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163

eration method is that we can walk away from thewell with the optimally determined matching param-eters at the well and extend our geologic knowledgelaterally in all directions. We expect that the inherentsimplicity of pseudo VSP data will allow a more de-tailed interpretation of lateral variations in the reser-

voir.

Discussion and

ConclusionsThe anomaly indicator used in this article shows

AVO anomalies in the data. This means that anoma-

lies in c p/ µ ratio, which are related to hydrocarbons,

can be detected by inversion of prestack data, butnonhydrocarbon-related AVO anomalies are alsopresent. The general trend in the relation between c

p

andcs must be determined to find the anomalies. Butthe trend can be estimated from the data. For AVO

inversion of the deeper data, it is important to removemultiple reflections, to obtain the correct angle de-pendent reflectivity.

We demonstrated the generation of pseudo VSPdata. The pseudo VSP facilitates an accurate compari-son between real VSP data and surface data. In addi-tion, pseudo VSPs can be used for lateral prediction.

AcknowledgmentsThis research was performed under the direction

of the international DELPHI consortium project. Theauthors would like to thank the participating compa-nies for their financial support and the stimulatingdiscussions at the DELPHI meetings.

ReferencesAki, K., and Richards, P. G., 1980, Quantitative seis-

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