GEOPHYSICS, VOL. 62, NO. 2 (MARCH-APRIL 1997); p. 676-689,9 FIGS., 2 TABLES.

Processing of a nine-component near-offsetVSP for seismic anisotropy

Colin MacBeth*, Xiang-Yang Li*, Xinwu Zeng*,Dale Coxs, and John Queed

ABSTRACT

A convolutional sequence of matrix operators is of-fered as a convenient deterministic scheme for process-ing a multicomponent vertical seismic profile (VSP).This sequence is applied to a nine-component near-offsetVSP recorded at the Conoco borehole test facility, KayCounty, Oklahoma. These data are corrected for toolspin and near-surface anisotropy together with sourcecoupling or imbalance. After wave-field separation usinga standard f-k filter, each source and receiver pair for theupgoing waves is adjusted to a common reference depthusing a matrix operator based on the downgoing wave-field. The up- and downgoing waves are then processedfor anisotropy by a similarity transformation, to sepa-rate the qS1 and qS2 waves, from which the anisotropicproperties are estimated. These estimates reveal a strong(apparent) vertical birefringence in the near-surface, butweak or moderate values for the majority of the subsur-face. The target zone consists of a thin sandstone anddeeper shale layer, both of which possess a strong verti-cal birefringence. The sandstone corresponds to a zoneof known fluid flow. An observed qS2 attenuation andpolarization change in the shale suggest it contains largefractures.

INTRODUCTION

Multicomponent seismic analyses of shear waves have become common owing to significant advances in acquisition,instrumentation, and seismic processing over the past decade.Such data may be used to define reservoir fractures by utiliz-ing the resultant anisotropic wave behavior. Anisotropy helpsto identify regions where natural fracture distributions con-trol the fluid storage and mobility, and has been successfullyemployed in targetting horizontal wells using surface seismics

(Mueller, 1992). Multicomponent near-offset vertical seismicprofiles (VSPs) are of particular value since the directly trans-mitted shear waves may be interpreted to give an indication ofdepth changes in the strike of subvertical fractures and in-situstress properties which can supplement wire-line logging andcore measurements in land and marine environments, whilestill fulfilling their more traditional role for depth calibrationof surface seismic data. In this study, we illustrate an analysismethod for multicomponent VSP based on matrix operatorsin a convolutional model (Zeng and MacBeth, 1993a), usinga nine-component VSP shot at the Conoco test facility in KayCounty, Oklahoma. The borehole is well characterized frompast geologic and geophysical measurements which includeBHTV images, borehole breakouts, outcrop analyses, pointload tests on core sections, and visual observation of the core.Processing reveals several zones of weak to moderate verti-cal birefringence (1.5% to 5%) overlying a thin sandstone andshale of stronger anisotropy (>15%), the sandstone being co-incident with known fluid loss during drilling.

MULTICOMPONENT CONVOLUTIONAL MODEL

Figure 1 shows the plan view of the acquisition system thatrecorded a nine-component VSP survey at the Conoco bore-hole test facility (CBTF), near Ponca City, Oklahoma. The dataare recorded between depths of 900 m and 152 m, in incrementsof 15 m, in the vertical 33-l well. Figure 2 shows the approxi-mate lithology which the well penetrates, together with detailsof the depth range for wireline measurement and ray tracingthrough the model. Although bordered by various large-scaletectonic features, the geology of the area is relatively simple andmay be accurately represented as a plane layered structure witha stratigraphy composed of shales, limestones, and sandstones(Queen et al., 1992). In-line and cross-line horizontal vibratorsare activated at near offsets of 30 m, 36 m, and 39 m and verticalvibrators at offsets of 41 m, 46 m, and 50 m, with a commonazimuth of N279”E relative to the well. The various offset po-sitions correspond to different pad locations, necessary when

Manuscript received by the Editor August 23,1995; revised manuscript received June 26,1996.*British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3 LA, United Kingdom.SExploration Research/Services Division, Conoco Inc., Ponca City, OK 74603.0 1997 Society of Exploration Geophysicists. All rights reserved.

676

Multicomponent VSP Processing 677

the baseplate digs into the ground. Additional vertical vibratorsare activated at offsets of 213 m and 457 m along a common az-

each successive operation to isolate the wave types. The dataalso show high-frequency downgoing tube waves reflected at

imuth of 155”. These offset sources were planned originally tobe part of a full walkaway survey that did not take place, and are

the transition between the cased and uncased portion of the

used instead to reorient the recording tool. Consequently, theirborehole at 500 m [see &,(t) section]. These tube waves will

positions are not optimized to take full advantage of other pos-not affect the analysis since their frequency content is higher

sible anisotropic measurements indicative of the backgroundthan the bandwidth used in subsequent processing. The lower

TIV anisotropy. More detailed recording parameters are setfrequency shear and compressional waves do not appear to beaffected by the 3 to 5 m thin washout zones in the unconsoli-

out in Table 1.The crosscorrelated near-offset data are presented in

Figure 3 in a data matrixdisplay, whereby the three-componentdisplacement vectors d:(t) excited by a source direction j =X, Y, 2, and recorded in the receiver coordinate system (x-y-z)at level i, are grouped together to form a matrix pi(t) ={d,“(t)ld:(t)ldf(t)>. me nine-component data form a 3 x 3 ma-trix of seismic sections containing up- and downgoing compres-sional and shear waves. As we shall see, this data matrix is aparticularly useful representation for the purposes of process-ing, since it provides a convenient way to visualize the effect of

dated sands which lie directly below the cased portion of theborehole. However, the coupling of the recording tool is af-fected by this zone, and as a consequence one of the traces isomitted during acquisition, being reinserted by interpolationon each component separately for display purposes only. Cas-ing ring with a frequency of 25 Hz aiso appears at depths of366 m, 411 m, and near the bottom of the receiver range.

A simple mathematical framework is now introduced in anattempt to process and interpret the data in Figure 3. This isbased upon a straightforward extension of the scalar convo-lutional model to multicomponent data (Zeng and MacBeth,

---a__

x

--z

\213mnz

hWUMUh4 REGIONALCOMPRESSIVE STRESS S H

NE-SW

N60E

N66E

I LOCAL SH RANGE

FIG. 1. Acquisition geometry for nine-component VSP shot at the Conoco test facility, Kay County, Oklahoma. Rectangles markedZ indicate vibrators with a vertical motion, and those marked X and Y give cross-line and in-line horizontal motions. Far-offsetZ vibrators are at offsets of 213 m and 457 m, and the near-offset Z vibrators at offsets between 41 m and 50 m, with the X andY between offsets 30 and 36 m (see Table 1). Large arrow gives direction of maximum compressive regional stress, with smallerarrows indicating the range limits for local stress determinations from wellbore breakouts and hydraulic fracturing with an errorof 15”.

678 MacBeth et al.

Table 1. Data acquisition parameters.

SourcesHod. vibrators x 2 AMOCO rotating baseplate

SweepAzimuthsOffsetsSweep lengthTaperNumber of sweeps stacked for each receiver position

Vertical vibrators x 3 CONOCO model YllOOSweepAzimuthsOffsetsSweep lengthTaperNumber of sweeps stacked for each receiver position

Downhole sonde DESCO 3-C receiver

Downsweep, 51-6Hz279”39m,36m,30m30 s0.5 s2

Downsweep, 102-12 Hz279” (near), 155” (far)50 m, 46 m, 41 m (near), 213 m and 457 m (far)30 s0.5 s2One level, 7% cross-talk as spec.

Depth locations 50 levels, 152 m through 900 m at 15 m intervals

Om

300t-r,

6OOrr

900m

IOOOm

TI

3.c 12 I. second source8 1 pad change

3.c I3 I bottom of.L3 I+ casing36 WASHOUTQ) 1 ZONE -SIL I

I4 first sourceI pad change

I

1.

Fort Riley Ls

Red Eagle Ls

Tonkawa Ss

VELOCITYMODEL

.

.

.

5.5km/s

200m

FIG. 2. Lithology for Conoco test well 33-1, together with the best velocity model formed as a composite of log and VSP data fromprevious studies (Queen et al. 1992), range of wireline recording, and ray coverage. Depth levels where source pad was changedand depth of the washout zone are also marked.

Multicomponent VSP Processing 679

1993a). In this model a compact convolutional matrix notationis employed for separating source, recording and mediumresponses:

J&(x, t> = g&(x, Q**&(x, t>**_S(x, 1) + N;(x, q; (1)

which is reduced to a single temporal convolution under theassumption of wavenumber independence, with all effectslumped into the frequency domain:

Q,i(t> = Gi(t>*~iS(t)*S(t> + mi(l>. (2)

The operations denoted by an asterisk are multiplication inthe transform frequency domain or convolution in the origi-nal time domain. S(t) and G;(t) are matrices representing thesource functions and geophone responses respectively, Mis(t)is the medium response, and N;(t) represents noise which weassume to be uncorrelated and random (this latter term is omit-ted in subsequent equations, although it is implicit). Each con-stituent matrix is defined with reference to a common right-handed orthogonal coordinate frame (X-Y-Z are defined inFigure 1) for both source and receivers. Z points downward,and X and Y are assigned to the cross-line and in-line direc-tions, respectively. In this particular case, the source motionsare directed along these axes in the field but the receiver axes(x-y-z) are not.

MULTICOMPONENT PROCESSING

Equation (1) is now used as a basis for further processingwhich follows as closely as possible standard scalar process-ing (Hardage, 1991) except that steps must be performed instrict accordance with the properties of the matrix quantitieswhich define an allowable direction and order for the sequenceof operations. Thus, time shifts, amplitude corrections, and de-convolution procedures are applied as matrix operators pre-or postmultiplying the data matrix in the frequency domain.The current processing sequence employs a premultiplicationby a rotation matrix to effectively align each receiver with thesource coordinate axes. This is followed by a postmultiplicationprocedure to correct for source imbalance/coupling and near-surface anisotropy. After these steps, the data can be separatedinto up- and downgoing waves. In the next stage, the upgoingwaves are then converted to a common datum level by premul-tiplying an operator derived from the downgoing waves. Thedata are now in a form whereby the qS1 and qS2 waves may beseparated by a similarity transform, which consists of both pre-and postmultiplication operations, from which the time delayscan be calculated.

Inaccuracies in acquisition components

Multicomponent VSP data are sensitive to inaccurate knowl-edge of the source and geophone responses, coupling, and

dix(t) diY(t> diz(t)

Time in seconds

FIG. 3. Nine-component data matrix recorded from the VSP with data corrected for tool spin so that the geophone axes and sourcemotion are aligned along cross-line (X), in-line (Y), and vertical down (Z) directions. The &ace notation KJ gives the geophonealong the J-axis recording the source motion along the K-axis. The traces are normalized to the maximum vector amplitude at eachdepth level.

MacBeth et al.

orientations. Great care is required to align the sources alongthe in-line and cross-line directions. Fortunately, although accu-rate control of the excitation and recording of the vector wave-field is not guaranteed in the field, recent numerical modelinginvestigations have shown that for most practicable ranges ofshear-wave splitting this does not appear to restrict resolution(Zeng and MacBeth, 1993b).

Tool spin

It is sufficient to assume that due to the hold of the sondeagainst the casing, the vertical (z = zi) geophone is directedalong the Z-axis. However, tool spin due to rotation of thesonde about the Z-axis is still possible. As a consequence, thehorizontal components can lie at an arbitrary orientation inthe horizontal plane. To correct for this effect, the horizontalgeophones are mathematically realigned along common coor-dinate axes (here it is the cross-line/in-line X-Y-Z) by premul-tiplying pi(t) by a 3-D rotation operator:

cOS($i) s in (&) 0

c(@i) = -Sin(#+) COS($j) 0 1 (3)0 0 1

applied to all displacement vectors, with the misorientationangles @i measured between the xi and X-axis by assumingthe compressional wave motion to lie solely within the sagittalplane. This approach is confirmed since we find all the esti-mated misorientations @i from the two separate offset sourcesto agree within 5”. Each pair is averaged for the final applica-tion. The data matrix in Figure 3 has already been correctedfor sonde twisting so that xi = X and yi = Y. On the assump-tion of no cross-coupling in the receiver system and equality ofresponses (see Table l), the procedure reduces $(t) to a diago-nal matrix g(t)& Past work has shown that responses differingby a scale factor of greater than 0.4 give errors in polariza-tion estimates of less than 5” (Zeng and MacBeth, 1993b). Wealso believe that the specified crosstalk also produces minimalerror. It should be noted that techniques also exist for sondereorientation in anisotropic media using shear-wave data (Liet al., 1993), although offset compressional wave data are mostcommon.

The data now have the form

pi(t) = &J&S(t)* s(t)*$?(t)-

Near-surface correction

Figure 3 displays evidence of an extended wavefield propa-gating into the subsurface, appearing longer for the horizontalsources. This long wavetrain confuses deeper strong reflectionsand obscures interpretation of the transmission behavior. Rea-sons for this may be multiples in near-surface low-velocityzones or differences between the true ground motion and mea-sured motion leading to inaccurate correlation with the vibra-tor signal. Multiples do seem likely to occur since informationfrom velocity wireline logs and core measurements show thatthe near-surface geology consists of alternating layers of high-velocity limestone and low-velocity shale, giving strong alter-

horizontal sources on the off-diagonal components d,,(t) anddr,(t), originating from above the shallowest recording level at152 m, and a slightly smaller but significant energy at shallowand deeper depths, on the dz,(t) and dZ,,(t) components. Thesedz,(t) and dZy(t) components can be explained at shallowdepths by the oblique incidence of the compressional waves.However, the increase of energy between 800 and 900 m, whereraypaths are predominantly vertical, must be associated withthe medium and is present throughout the processing stages.

Near-surface correction serves to eliminate shallow multi-ples and the effects of source interaction with the complicatedheterogeneous near-surface structure. It can be accomplishedby a multicomponent operator designed from the downgoingwavefield (Zeng, 1994; MacBeth et al., 1995), which correctsthe data to a reference level L, usually assigned as the depthof the shallowest level. This procedure can also correct forinconsistent polarities and alignments of the sources. An im-plication of this step is that it is not wholly necessary for thesources to be strictly orthogonal in the acquisition, but theymust contribute independent information on each directionalcomponent of the medium response. The exact components ofthe source matrix s(t) need not be known exactly. Equation (1)is rewritten to separate the medium response &&s(t) into thedowngoing wavefield from the near-surface l&(t), and thesubsurface response, MiL (t):

pi(t) = @IL (t>* ( MLS(t)*S(t)] - (5)

A correction is implemented as a deconvolution, postmultiply-ing Qi(t) by an estimate of the inverse downgoing wavefieldM,:(t), evaluated from a group of shallow traces. This reducesthe data to the form

Qi(t) = &hL(t)- (6)

A nine-component operator of 1.0 s duration is applied to thetotal wavefield. Figure 4 shows the best solution for applica-tion of this technique to the total wavefield in Figure 3, detailsof which may be found in MacBeth et al. (1995). It is foundnecessary to reapply the correction to each source pad change(340 m and 640 m), because the near-surface response is sensi-tive to very small spatial changes (Winterstein and Meadows,1991). By comparing this plot with Figure 3, the process appearsto work very effectively, especially for the shallowest levels,and the matrix elements dx,(t), dz,(t), dZy(t), and dyz(t) areconsiderably reduced. The original extended waveforms at theshallowest levels have now collapsed and the reflections areclearer and simpler. There is a gradual build-up of the energyon the off-diagonal components for the shear components af-ter each deconvolution, symptomatic of a uniform anisotropicmedium. Since the procedure converts the first few traces to aunit diagonal, the compressional-wave onsets initially coincidewith the shear waves at each correction.

Separation into up- and downgoing wavefields

nating impedance contrasts (Figure 2). There are1 t--L-- .-- I- -- .~ * 1

also somertunusual rearures: large compressional-wave energy rrom me

Multicomponent VSP Processing 681

We separate RyL(t) and T,:(t) by using an f-k filter, appliedindividually to each trace component of D;(r). Care is takento apply a tapered quadrilateral pass of positive or negativewavenumbers, which creates moderate intertrace mixing andend effects. Tests on synthetic data show the phenomenon ofshear-wave splitting is not affected by this procedure for a va-riety of different frequencies and geophone spacing. Once thedowngoing wavefield at the ith level ‘T:(r) is determined, itcan be converted to an equivalent upgoing transmission oper-ator TFi(t) using the reciprocity relation T:‘(t) = {Tz(f)}r .The upgoing wavefield R%(t) can then be adjusted to givea two-way response using TFi (t)*Rk(t) = RFL. Source andreceiver are now positioned on a common reference level L.R’l,(t) and T:(t) for our nine-component data are shown inFigures 5a and 5b.

INTERPRETATION OF MULTICOMPONENT RESPONSE

Wave type separation

The data matrices of Figures 5a and 5b may be explained bya TIH medium, which simulates a fractured isotropic matrix. Insuch an anisotropic medium three distinct arrivals correspond-ing to qP, qS1, and qS2 propagate if raypaths are not close tosingularities. For normal incidence the q P polarization is di-rected vertically downward and the qS1 and qS2 polarizations

>

,>

dix(t)

Time in seconds

lie in the horizontal plane. The qS polarizations are orthogo-nal, which creates symmetric transmission TiL(t) and reflectionI&(I) responses. These common assumptions mean that it isnow a simple task to separate the q P, qS1, and qS2 wavefieldcomponents by employing horizontal rotation matrices. Thewave coordinate system X-Y-Z transforms to the new X’-Y’-Zsystem, with X’ and Y’ oriented along the qS2 and qS1 polariza-tions. The similarity transformation may be calculated numer-ically (Alford, 1986) or algebraically (Li and Crampin, 1993;and as in this case, Zeng and MacBeth, 1993a). To implementthis step, the transmission response for a uniform anisotropicmaterial is written as

TiD, (t) = c(ei) &iL (t) Ceel(@i);

and the reflection response as

(8)

PyL(t) = c(&)I&‘,,lc-‘(@i); (9)

where C(@) is a 3-D rotation matrix similar to that in equa-tion (3), 0i is the rotation angle of the system from which thepolarization azimuth of qS1 may be obtained for further inter-pretation, and nil;(t) and &‘LL(t) are diagonal matrices con-taining the separated downgoing and upgoing qS2, qS1, andq P wave modes. The resultant diagonal matrices from this par-ticular processing step are shown in Figures 6a and 6b.

d;‘(t) diz(t)

0 . 6

FIG. 4. Nine-component data matrix of traces from Figure 3 corrected for corresponding near-surface operators: all traces combinedwith traces 33 to 50 using another deconvolution. Note that for display purposes the P-waves on the dz,(t) component have beenrealigned after each successive deconvolution.

682 MacBeth et al.

dix(t>

0 . 0.2 0.4 0.6 0.8 1.0 0. 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 0 . 0 . 2 0.4 0.6 0.8 1.0

b)

Time in seconds

dixN

,

0 . 4 0 . 9 1 . 4 0 . 4 0 . 9 1 . 4 u . 4 U.Y 1 . 4

Two-way time (sets) .,_(

FIG. 5. Separated up- and downgoing wavefield after near-surface correction; (a) downgoing waves; (b) upgoing wavefield afterrepositioning the each source and receiver pair to a common reference level L.

683

FIG. 6. Nine

I yul, and qP waves

684 MacEBeth et al.

Interpretation

Figures 7a, 7b, and 7c show the polarization and time-delay estimates for the qS1 and qS2 waves which are foundto give the best diagonal matrices. These diagrams indicatethat the borehole penetrates a complicated anisotropic struc-ture. There is agreement in Figure 7c between the qS1 polar-ization azimuths estimated separately from the upgoing anddowngoing wavefield, except for a departure near the casingring in the original traces. Further results from an intervalmeasurement technique (Zeng and MacBeth, 1993b; Lefeuvre

4 0 2 - t - c

702-1 4

802

et al., 1992) also match these values (Figure 7a). These indicatea roughly constant NW’E direction throughout most of thedepth range. Past work has shown the stress, microfabric, andfracture system to be complicated, with differences betweensurface and subsurface patterns. The qS1 direction from thisVSP appears to be an average of the surface mapped featureswhich were successfully correlated to shallow (10 m) RVSPmeasurements by Liu et al. (1993), and an average of the frac-ture statistics from BHTV measurements in the well (Queenand Rizer, 1990). It correlates with one of the three predom-inant fracture strikes present in the core data, particularly in

b)..

8 0 2 -8 0 2 -

902902 II II II II0 30 80 80 120 150 180 0 5 10 15 20

POLARIZATION AZIMUTH (N’E) TIME-DELAY (ms)

302.

402.

^s 502.

F4 602.n

702.

802.

0 3 0 6 0 90 120 150 180

POLARIZATION AZIMUTH (N’E)

FIG. 7. (a) qS1 polarization azimuth obtained from optimal rotation of data uof near-surface correction and also for an interval measurement technique; (bP

on each subsequent applicationsolid line-qSl-qS2 time delay

corresponding to downgoing wavefield; dotted line-corresponding time delays for synthetic seismograms ofFigure 9a. (c) qS1 polarization azimuth for optimal rotation for downgoing wavefield (solid line) of Figure 5aand upgoing wavefield of Figure 5b. Shallow dashed horizontal line marks the top of the sandstone unit, withlower lines indicating the top and bottom of the layer known to flow fluid.

Multicomponent VSP Processing 685

the shales. The direction is within the range of directions forthe maximum horizontal compressive stress determined fromborehole breakouts (Figure 1).

The qS2-qS1 time delays shown in Figure 7b are calculatedby crosscorrelation of the principal diagonal components. Al-though this time-delay profile originates from zero at 152 m,it should be noted that a delay of 4 ms is present in theoriginal data, which has been subsequently corrected by thenear-surface deconvolution. This value for the upper sand-stone/shale layers may imply a vertical birefringence as largeas 12% (based on average velocities-but this may also bea consequence of the lower surface velocities). Such a largevalue is also substantiated by previous work (Liu et al., 1993)using reverse VSP and cross-well data. The time-delay depthprofile evolves in four distinct stages: a small initial gradientbetween 152 and 377 m with no more than 1.5% vertical bire-fringence, an upward increase in slope at 377 m defining a zoneof 5% vertical birefringence continuing uninterrupted throughthe Tonkawa sandstone at 645 m, after which there is a strongslope with 15 % vertical birefringence from 677 m through 80 mof sandstone. This is followed by a time-delay decrease at thebase of this zone and then a further steep rise. The estimationroutine predicts no apparent change in the qS1 directions as-sociated with the latter time-delay variation. The results forthe first two stages are consistent with the results of Horneand MacBeth (1994) who interpret the anisotropy as a near-vertical saturated crack system with a crack density of 0.03 (3%velocity anisotropy) for raypaths to receivers in the Tonkawasandstone. The 5% zone appears to correlate with the start ofthe sandstone sequence (Horne, pers. comm.). The thin sand-stone layer of strong anisotropy is especially significant sincethis corresponds to known fluid loss during drilling in this andother wells at the test site. Such large anisotropies are a fea-ture of intense fracturing, but also weak granular contact (Runeet al., 1993) perhaps due to high pore pressure. At the base ofthe sandstone there is a general pulse broadening, increasingwaveform complexity, and an amplitude reduction for the qS2wave (see Figure 6a). The quotient of the Q-factors for qS1and qS2 is approximately 5, calculated by using a simple arith-metic average of the spectral amplitude ratios at each depth.These various observations, when combined with the time-

delay decrease mentioned above, indicate that a polarizationchange of 90” has taken place in the underlying shale. Theoff-diagonal energy on the deeper traces may indicate thatthe change is not quite 90”, and that multiple splitting occurs.The estimation technique is unable to discern this polarizationchange, which appears only as the time-delay decrease. The qS1traces below this depth should be reassigned as qS2. The qS2pulse broadening is symptomatic of a region containing verti-cal macrofractures (Ebrom et al., 1990). The pulse broadeningeventually leads to the upturn in the time-delay profile.

The most noticeable feature of the upgoing wavefield isthe weak reflectivity on the qS2 section below 800 ms (seeFigure 6b), corresponding to the zones of high fracturing.This observation is in agreement with Mueller (1992). Thelow signal-to-noise ratio is apparent by the comparable en-ergy on the off-diagonals. In the shale layer beneath the sand-stone, where large fractures are suspected, the qS1 amplitudealso appears to suffer a dimming. Although the qS1 sectionshows deeper structure below 1200 ms, the qS2 amplitudes re-main small since they are doubly attenuated upon transmissionthrough the fractured layers. Figure 8 summarizes the resultsfor the experiment.

Verification by modeling observed wavefield

To verify the results from processing, the data are now fitby full-wave synthetic seismograms computed using the aniso-tropic reflectivity method of Taylor (1991), which deals withan anisotropic, elastic or anelastic plane-layered model. This isappropriate since there is only a small regional dip (Queen andRizer, 1990), and the geologic setting is relatively free fromstructural complexities. We avoid modeling the near-surfacelayers and the consequent effects on the source radiation pat-tern by simulating the data after the near-surface corrections,so that the results are directly comparable to those in Figures 4and 5. The structure is based upon the anisotropic estimatesdetermined above, together with the background velocitymodel derived from previous studies in the area (see Table 2for details). Many of the thin shallow layers in this model weredetermined through velocity inversion using different shallowseismic methods at the test site, and were established as the

c 152

677753

FABRIC/FLAWS

N55E 5% FABRIC/FLAWS

KNOWN FLOW

FIG. 8. Outline of final results obtained from the analysis of the nine-component VSP at the Conoco testsite.

686 MacBeth et al.

best fit to that data. Here, we also include a common intrinsicQ for qS1 and qS2 of 40, and an overall 1000 for q P (essentiallylossless). This attenuation is necessary to reduce excessivemultiple reflections in the shallow layers and also to providethe requisite balance of shear- and compressional-wave energywith depth. The values are determined on a trial-and-errorbasis. Other, more direct methods for estimating the Q values

from the data were found to be unsatisfactory due to scatter.Given the high VP/V, values found in the logs, these Q valuesconform to our physical expectations of no loss attributable tothe bulk modulus. We model the subsurface anisotropy usinga TIH medium with the symmetry axis directed along N35”W,and the vertical birefringence according to the estimates inFigure 7b. The elastic constants for each material are generated

Table 2. Layered model for near-surface structure of Conoco testsite at well 33-l. Each layer thickness (Ahh) and depth to deeperinterface (h) is specified by elastic matrix compressional wave and shear-wave velocities VP and V& in addition to frequencyindependent anelastic parameters Qp and Qs. TIH anisotropy with vertical birefringence 5 is used throughout. The direction ofthe symmetry axis is specified by the horizontal azimuth 4.

LayersVP

(km/s)vs

(km/s) g/L QP4

QdQ2 Now r

:.:27

i

:i!

E

if

:;

:;2021

* 22* 23* 24* 25* 26* 27* 28* 29* 30* 31* 32* 33* 34* 35* 36* 37* 38* 39* 40* 41* 42* 4 3* 44* 45* 46* 47* 48* 49* 50* 5 1* 52* 53

z4

0.50 0.50 1.254 0.050 2.00 1000 40/4012.00 12.50 1.254 0.400 2.00 1000 40140

1.22 13.72 0.914 0.457 2.00 1000 40/404.88 18.60 1.707 0.366 2.42 1000 40/401.22 19.82 4.115 2.073 2.42 1000 401402.44 22.26 1.829 0.762 2.40 1000 40140

11.58 33.84 3.580 1.929 2.31 1000 40/409.75 43.59 2.422 0.899 2.36 1000 40/40

13.72 57.31 2.941 1.702 2.49 1000 40/409.75 67.06 4.047 2.089 2.22 1000 40/408.84 75.90 2.683 1.670 2.48 1000 40/403.35 79.25 3.520 1.859 2.24 1000 401402.74 81.99 4.867 2.552 2.25 1000 401403.05 85.04 3.273 1.833 2.31 1000 401406.10 91.14 3.289 2.298 2.37 1000 40140

11.89 103.03 3.194 1.695 2.21 1000 4014021.64 124.67 3.027 1.735 2.46 1000 40/40

1.22 125.89 6.131 2.608 2.05 1000 40/405.79 131.68 3.012 1.693 2.39 1000 401407.62 139.30 3.402 1.713 2.56 1000 40/40

10.06 149.36 4.236 2.259 2.23 1000 40/403.96 153.32 3.389 1.463 2.54 1000 40/40

28.35 181.67 4.345 1.494 2.38 1000 40/4017.07 198.74 3.048 1.463 2.45 1000 4014017.37 216.11 3.139 1.494 2.50 1000 4014021.95 238.06 3.048 1.463 2.52 1000 4014010.67 248.73 3.353 1.463 2.68 1000 401402.13 250.86 4.877 2.438 2.43 1000 40140

21.03 271.89 3.231 1.494 2.54 1000 40/4024.08 295.97 3.292 1.585 2.52 1000 40/4023.47 319.44 3.327 1.585 2.53 1000 40/4010.67 330.11 3.513 1.585 2.45 1000 40/4041.15 371.26 3.688 1.524 2.54 1000 40/4010.67 381.93 3.962 1.372 2.66 1000 40/402.13 384.06 4.877 2.438 2.57 1000 401407.32 391.38 3.749 1.432 2.36 1000 401408.84 400.22 3.593 1.524 2.54 1000 40140

26.21 426.43 3.751 1.676 2.37 1000 4014017.68 444.11 3.583 1.829 2.50 1000 4014064.92 509.03 4.877 1.829 2.59 1000 40140

5.49 514.52 3.753 2.438 1.71 1000 4014014.81 529.13 3.884 2.107 2.17 1000 40/402.44 531.57 5.594 2.919 2.35 1000 40/40

46.33 577.90 3.599 2.035 2.48 1000 40/4014.63 592.53 4.148 2.373 2.47 1000 4014050.29 642.82 3.732 2.377 2.54 1000 40/4034.18 677.00 3.525 2.245 2.18 1000 4014080.48 757.48 3.885 2.063 2.54 1000 40/4070.36 827.84 4.109 2.191 2.63 1000 40/4038.10 865.94 5.415 2.715 2.67 1000 40140

2.44 868.38 4.197 2.180 2.64 1000 4014022.85 891.23 5.618 2.906 2.63 1000 40140

9.76 900.99 4.103 2.171 2.63 1000 4014030.18 914.70 5.951 3.169 2.67 1000 40140- 944.88 3.992 2.141 2.60 1000 40/40

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Multicomponent VSP Processing

5 00

ScomPonentsYnthetic seismograms computed usin

(b) corrqmding to Figure

sb; (c) corresponding to Figure 6tp.the anisotropic reflectivity method- (a) corresponding to Figure 5a;

’

687

688 MacBeth et al.

by using the second-order formulations of Hudson (1980)for vertically aligned saturated microcracks. For the stronglyanisotropic zones this need not necessarily imply that the ori-gin of the anisotropy is in this type of fracturing, but that thecomponent of vertical birefringence that has been observedmay be adequately simulated by this system.

The final downgoing and upgoing synthetic wavefields areshown in Figures 9a, 9b, and 9c after a near-surface correctionhas been applied such that these diagrams are directly com-parable to Figures 5a, 5b, and 6b. The final synthetics confirmcertain aspects of our model since they display the characteris-tics of the processed data. Furthermore, the time-delay profileobtained by processing these seismograms also overlays theexperimental result in Figure 7b. In the comparison betweenthe synthetics and observations, it should be noted that thedata have been corrected for source coupling and there are noknown receiver problems. Both the synthetic and processed up-going data display reflectors that appear to fade upward. Thiseffect is due to the vector scaling employed in this work andhas no physical significance. The reflector positions for the syn-thetics and processed data are in good agreement. The synthet-ics also correctly simulate the decrease in qS2 energy relativeto the qS1 beyond 800 ms, corresponding to the depth of thehighly anisotropic sandstone. However, the balance of reflec-tor strengths within the qS1 section is different, particularly

dix(t>

for the region between 1000 and 1200 ms. This reduction onthe qS1 section coincides with the shale layer underlying thesandstones where the polarization change is suspected, and issymptomatic of large open fracturing. It is possible that furthervariations of the shear-wave Q values or an adequate simula-tion of the scattering from large fractures could improve this fit.Unfortunately, sonic logs are not available to further confirmand correlate the individual reflectors.

CONCLUSIONS

Acquisition and processing developments for multicompo-nent seismology continue, with potential new sources, and ac-curate and longer downhole three-component receiver arrays.However, multicomponent data must still be acquired and pro-cessed with care. Application of this technology on a routinebasis requires careful alignment and positioning of the acqui-sition components, and a robust processing scheme. In thispresent work, we have presented an example of a process-ing sequence based on a vector convolutional model which hasproven satisfactory for the analysis of a nine-component near-offset VSP, but may also be used for other multicomponentdata. Processing consists of correction for tool twisting, near-surface correction, separation into up- and downgoing waves,adjustment of upgoing waves to a common reference level foreach source and receiver pair, and finally a separation into qS2,

0.9 1.4

FIG. 9. Continued.

Multicomponent VSP Processing 689

qsl, and q P waves. The anisotropic analysis indicates that be-low the near-surface layering there is an essentially isotropicsubsurface to a depth of 377 m, followed by a region with5% vertical birefringence. This weak to moderate anisotropicbackground is in direct accord with values from various ob-servational settings (Crampin and Lovell, 1991). Underlyingthis is an 80 m thick sandstone layer of 15% vertical birefrin-gence at 645 m depth that is a known layer of fluid flow. Belowthis sandstone is a shale with large fractures, which producesa strong qS2 attenuation (and velocity) anisotropy, and a qS1polarization change of 90”. These findings indicate a need tounderstand such distinct zones of strong anisotropy and po-larization changes. Such zones may be linked to strong het-erogeneity, where wavefield kinematics may be interpreted asanisotropy even though the strict mathematical limits of equiv-alent medium theory have been exceeded (MacBeth, 1995).There is a requirement to model details of larger fractures andwavefield effects from other features such as sandstone lami-nations, and determine their relation to permeability.

ACKNOWLEDGMENTS

We thank Conoco Inc. and Amoco for the nine-componentdata set from the Conoco test facility, which was acquired aspart of a Conoco/Amoco borehole geophysics collaboration.This work was supported by the sponsors of the EdinburghAnisotropy Project (EAP) and the Natural Environment Re-search Council (NERC), and is published with the approval ofthe EAP sponsors and the Director of the British GeologicalSurvey (NERC).

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