36

In certain rocks, sound waves travel at different speeds in different directions. This characteristic, called elastic

tence of aligned features such as fractures, microcracks, fine-scale layers or mineral grains. Combining anisotropy

from petrophysics, geology and reservoir engineering may reveal a connection between these alignments and paths

The Promise of Elastic Anisotropy

Phil ArmstrongDick IresonGatwick, England

Bill ChmelaHouston, Texas, USA

Kevin DoddsLondon, England

Cengiz EsmersoyDouglas MillerRidgefield, Connecticut, USA

Brian HornbyColin SayersMike SchoenbergCambridge, England

Scott LeaneyJakarta, Indonesia

Heloise LynnLynn, IncorporatedHouston, Texas

ANISOTROPY

ANISOTROPY

ANISOTROPY

For most of this century, oilfield theory andpractice assumed that waves propagateequally fast in all directions. That is, rockshave isotropic wave velocities. But wavestravel through some rock with differentvelocities in different directions. This phe-nomenon, called elastic anisotropy, occurs ifthere is a spatial ordering of crystals, grains,cracks, bedding planes, joints or frac-tures—essentially an alignment of strengthsor weaknesses—on a scale smaller than thelength of the wave.1 This alignment causeswaves to propagate fastest in the stiffestdirection.

The existence of elastic anisotropy hasbeen largely ignored by exploration andproduction geophysicists—and for good rea-sons. The effect is often small. With stan-dard surface seismic measurement tech-niques most reservoir rocks showdirectional velocity differences of only 3 to5%, which may often be neglected. More-over, processing data under the assumptionsof an isotropic earth is already a challenge;the cost of adding the complications of

For help in preparation of this article, thanks to AustinBoyd and Stan Denoo, Schlumberger GeoQuest, Engle-wood, Colorado, USA; Alain Brie, Schlumberger Wire-line & Testing, Montrouge, France; Klaus Helbig, Han-nover, Germany; Michael C. Mueller, Amoco Exploration& Production, Houston, Texas, USA; John Walsh,Schlumberger Wireline & Testing, Houston, Texas; Jim White, Schlumberger Wireline & Testing, London,England; Don Winterstein, Chevron Petroleum Technol-ogy Company, La Habra, California, USA.In this article, DSI (Dipole Shear Sonic Imager), FMI(Fullbore Formation MicroImager) and GPIT (GeneralPurpose Inclinometer Tool) are marks of Schlumberger.

anisotropy must be justified by improve-ments in the final seismic image. At most,anisotropy has usually been considerednoise that must be filtered out, not as a use-ful indicator of rock properties.

However, with recent advances in acquisi-tion, processing and interpretation of elasticdata, the reasons for ignoring anisotropy areno longer valid. New acquisition hardwareand measurement techniques designed tohighlight anisotropy reveal highly anisotropicvelocities in ultrasonic, sonic and seismicdata. This article looks at the evidence foranisotropy, the best ways to measure it, andhow to use it to enhance reservoir descrip-tion and optimize development.

The two requirements for anisotropy—alignment in a preferential direction and ata scale smaller that of the measurement—can be understood through analogies. Forthe effect of alignment, imagine driving acar in an anisotropic city where streets inthe north-south direction have a 30-mile-per-hour speed limit, while the east-weststreets have a 50-mile-per-hour limit. East-west drivers will spend less time traveling agiven distance than north-south drivers. Anddrivers will take east-west streets wheneverpossible. In an anisotropic rock, waves dothe same thing, traveling faster along layersor cracks than across them.

For the effect of scale, a less than perfectbut interesting analogy is an insect on a leafin a forest. The insect sees leaves andbranches branching off in random direc-

Oilfield Review

anisotropy, indicates the exis-

measurements with other input

of fluid flow.

nSimple geometries assumed for elasticanisotropy. In layered rocks (top), elasticproperties are uniform horizontally withina layer, but may vary vertically and fromlayer to layer. In vertically fractured rocks(bottom), elastic properties are uniform invertical planes parallel to the fractures,but may vary in the direction perpendicu-lar to fractures, and across fractures. Theaxes of symmetry are axes of rotationalinvariance, about which the formationsmay be rotated by any amount, leavingthe material indistinguishable from whatit was before.

1. Elastic anisotropy is sometimes called velocityanisotropy, travel-time anisotropy, acoustic anisotropyor slowness anisotropy.

2. Winterstein D: “How Shear-Wave Properties Relate toRock Fractures: Simple Cases,” Geophysics: TheLeading Edge of Exploration 11 (September 1992): 21-28.

3. The axis of symmetry is an axis around which thematerial may be rotated without changing the descrip-tion of the material’s properties.

y x

z

Vertical axisof symmetry

Horizontal axisof symmetry

y

x

z

TIV

TIH

tions: up, down, left, right and everywherein between. At the scale of the insect, thereis no preferred direction of tree growth.There are heterogenieties—sharp disconti-nuities between leaf and no leaf—but at theinsect scale the forest is isotropic. However,to an insect a kilometer away from the for-est, the trees appear neatly aligned verti-cally. To it, the anisotropic nature of the for-est is revealed.

Similarly, a small wavelength wave pass-ing through a packet of thick isotropic layersof differing velocities senses the isotropicvelocity of each layer. The wave sees dis-continuities at each boundary, but if thewave is small enough to fit several wave-lengths in every layer, the layers will stillappear isotropic, and no alignment of thediscontinuities will be apparent. However, awave with a wavelength much longer thanthe layer thickness will not sample layersindividually, but as a packet. The packet oflayers acts as an anisotropic material. Theorientation of the layer boundaries is nowperceived by the wave—and as one of thefastest directions of travel. And if the indi-vidual layers are made of alignedanisotropic grains, as is the case with shales,the anisotropy is even more pronounced.

Anisotropy is then one of the few indica-tors of variations in rock that can—evenmust—be studied with wavelengths longerthan the scale of the variations. For once,using 100-ft [30-m] wavelength seismicwaves, we can examine rock structure downto the particle scale. However, seismicwaves are unable to determine whether the

October 1994

anisotropy is due to alignment at the particlescale or at a scale nearer the length of thewave. In the words of one anisotropy spe-cialist, “The seismic wave is a blunt instru-ment in that it cannot tell us whetheranisotropy is from large or small structures.”2

Two Types of AnisotropyThere are two styles of alignment in earthmaterials—horizontal and vertical—andthey give rise to two types of anisotropy.Two oversimplified but convenient modelshave been created to describe how elasticproperties, such as velocity or stiffness, varyin the two types. In the simplest horizontal,or layered, case, elastic properties may varyvertically, such as from layer to layer, butnot horizontally (left). Such a material iscalled transversely isotropic with a verticalaxis of symmetry (TIV).3 Waves generallytravel faster horizontally, along layers, thanvertically. Detecting and quantifying thistype of anisotropy are important for correla-tion purposes, such as comparing sonic logsin vertical and deviated wells, and for bore-

37

38

nWavefronts in isotropic and anisotropicmaterials. In an isotropic medium (top)waves emanate spherically from a point.In an anisotropic material (bottom) wavesspread with different velocities at differ-ent angles.

4. Most can be found in the reference list in: Helbig K:Foundations of Anisotropy for Exploration Seismics,Handbook of Geophysical Exploration,Volume 22.Oxford, England: Elsevier Science Ltd, 1994.

5. Compressional waves were originally called P for pri-mary—since they arrived first—and S for secondary.Only the P- and S-terms remain in use. Both P and Swaves are known as elastic waves. Geophysicists usethe term acoustic to emphasize wave propagation in afluid, while elastic connotes propagation in a solid.

6. Specialists have developed a new terminology forwaves in anisotropic media: P waves are called qP,and the two S waves are called qS1 and qS2. The ‘q’stands for ‘quasi-’, emphasizing the fact that inanisotropic materials, particle motion in P waves is no longer exactly parallel to propagation direction,and the particle motion in S waves is no longer exactlyperpendicular.

7. For a review of shear waves in anisotropic rocks: Winterstein, reference 2.

8. Jones LEA and Wang HF: “Ultrasonic Velocities in Cre-taceous Shales from the Williston Basin,” Geophysics46 (March 1981): 288-297.Rai CS and Hanson KE: “Shear-Wave VelocityAnisotropy in Sedimentary Rocks: A LaboratoryStudy,” Geophysics 53 (June 1988): 800-806.Hornby BE, Johnson CD, Cook JM and Coyner KB:“Ultrasonic Laboratory Measurements of the ElasticProperties of Shales,” presented at the 64th AnnualInternational Meeting, Society of Exploration Geophysicists, Los Angeles, California, USA, October 23-28, 1994.

Isotropic Water

“Anisotropic Water”

hole and surface seismic imaging and stud-ies of amplitude variation with offset (AVO).Examples appear later in this article.

The simplest case of the second type ofanisotropy corresponds to a material withaligned vertical weaknesses such as cracksor fractures, or with unequal horizontalstresses. Elastic properties vary in the direc-tion crossing the fractures, but not along theplane of the fracture. Such a material iscalled transversely isotropic with a horizon-tal axis of symmetry (TIH). Waves travelingalong the fracture direction—but within thecompetent rock—generally travel faster thanwaves crossing the fractures. Identifying andmeasuring this type of anisotropy yieldinformation about rock stress and fracturedensity and orientation. These parametersare important for designing hydraulic frac-ture jobs and for understanding horizontaland vertical permeability anisotropy.

More complex cases, such as dipping lay-ers, fractured layered rocks or rocks withmultiple fracture sets, may be understood interms of superposition of the effects of theindividual anisotropies.

Identifying these types of anisotropyrequires understanding how waves are

Particlemotion

Particlemotion

A

B

C

Particlemotion

Wave propagation directionCw

Slw

Faw

Horizontof symm

affected by them. Early encounters withelastic anisotropy in rocks were docu-mented about forty years ago in field andlaboratory experiments (see “A Brief His-tory,” page 39). Many theoretical papers,too numerous to mention, address this sub-ject, and they are not for beginners.4 How-ever, it’s easy to visualize waves propagatingin an anisotropic material. First picture theisotropic case of circular ripples that spreadacross the surface of a pool of water dis-rupted by the toss of a pebble. In “anisotropicwater,” the ripples would no longer be circu-lar, but almost—not quite—an ellipse (left).Quantifying the anisotropy amounts todescribing the shape of the wavefronts withterms such as ellipticity and anellipticity. Inanisotropic rocks, waves behave similarly,expanding in nonspherical, not-quite ellip-soidal wavefronts.

Waves come in three styles, all of whichinvolve tiny motion of particles relative tothe undisturbed material: in isotropic media,compressional waves have particle motionparallel to the direction of wave propaga-tion, and two shear waves have particlemotion in planes perpendicular to the direc-tion of wave propagation (below).

Oilfield Review

nCompressionaland shear waves.Compressional, orP, waves (top) haveparticle motion inthe direction ofwave propagation.Shear, or S, waveshave particlemotion orthogonalto the direction ofwave propagation.S-wave particlemotion is polarizedin two directions,one horizontal(middle), one verti-cal (bottom).

ompressional-ave amplitude

ow shear-ave amplitude

st shear-�ave amplitude

Time

Time

Time

al axisetry

1. Bell JF: Mechanics of Solids, vol. 1. Berlin, Germany:Springer Verlag (1973): 17.

2. For an early borehole seismic experiment: Cholet J andRichard H: “A Test on Elastic Anisotropy Measurement atBerriane (North Sahara),” Geophysical Prospecting 2, no. 3 (September 1954): 232-246.

For early photographs of noncircular wavefronts inanisotropic media: Helbig K: “Die Ausbreitung (Elastis-cher) Wellen in Anisotropen Medien,” GeophysicalProspecting 4, no. 1 (March 1956): 70-81.

nSampling anisotropic cores. To charac-terize anisotropic elastic properties ofcores, a minimum of four plugs are gener-ally taken—one perpendicular to the visi-ble layering or fracturing, two orthogonalto that, in the plane of the layering, andat least one more plug at an intermediate

In fluids, only compressional waves canpropagate, while solids can sustain bothcompressional and shear waves. Compres-sional waves are sometimes called P waves,sound waves or acoustic waves, and shearwaves are sometimes called S waves.5 Thetwo are recognized as elastic waves. In agiven material, compressional waves nearlyalways travel faster than shear waves.

When waves travel in an anisotropicmaterial, they generally travel fastest whentheir particle motion is aligned with thematerial’s stiffest direction. For P waves, theparticle motion direction and the propaga-tion direction are nearly the same. When Swaves travel in a given direction in ananisotropic medium, their particle motionbecomes polarized in the material’s stiff (orfast) and compliant (or slow) directions.6The waves with differently polarized motionarrive at their destination at differenttimes—one corresponding to the fast veloc-ity, one to the slow velocity.7 This phe-nomenon is called shear-wave splitting, orshear-wave birefringence—a term, likeanisotropy, with origins in optics. Splittingoccurs when shear waves travel horizontallythrough a layered (TIV) medium or verticallythrough a fractured (TIH) medium.

Since most geophysical applications placethe energy source on the surface, waves gen-erally propagate vertically. Such waves aresensitive to TIH anisotropy, and are thereforeuseful for detecting vertically aligned frac-tures. Any stress field can also produce TIHanisotropy if the two horizontal stresses areunequal in magnitude. Vertically traveling Pwaves by themselves cannot detectanisotropy, but by combining informationfrom P waves traveling in more than onedirection, either type of anisotropy can bedetected. One approach is to combine verti-cal and horizontal P waves—such as thosewhich arrive at borehole receivers from dis-tant sources. Another technique compares Pwaves traveling at different azimuths. Twodrawbacks to these compressional-wavemethods are that horizontal wave propaga-tion is difficult to achieve except in specialacquisition geometries, and that travel pathsfor the P waves are different, introducinginto the interpretation additional potentialdifferences other than anisotropy. Shearwaves, on the other hand, allow a differen-tial measurement in one experiment by sam-pling anisotropic velocities with two polar-

October 1994

izations along the same travel path, giving agreater sensitivity for anisotropy than Pwaves in multiple experiments.

Compressional and shear waves of allwavelengths can be affected by anisotropicvelocities, as long as the scale of theanisotropy is smaller than the wavelength.In the oil field, the scales of measurementparallel those in the analogy of the insect ina tree in a forest—the insect represents theultrasonic scale, the tree trunk radius is simi-lar to the sonic scale and the height of thetrees is the scale of the borehole seismicwavelength. The following sections describehow anisotropy is being used to investigaterock properties at each of those scales.

At the Insect ScaleWavelengths in most sedimentary rocks aresmall—0.25 to 5 mm—for 250-kHz ultra-sonic laboratory experiments, and they arefour times smaller at 1 MHz. Ultrasonic lab-oratory experiments on cores show evi-dence for both layering and fracture-relatedanisotropy in different rock types (below).While shales generally lead the pack in therelative difference between velocities of agiven wave type in fast and slow directions,experimentalists no longer deliver labora-tory results in such simple terms.8 Instead ofthe two numbers, P- and S-wave velocities,elastic properties are often characterized byplots of velocity variation around some axis

measured angle.

A Brief History

The earliest documented observation of the effect

of anisotropy on material properties is probably

that of Georges Louis LeClerc, Comte de Buffon.1

Through countless destructive experiments on 1-

to 2-inch squares of oak, Buffon discovered in

1741 that wood strength depended on how the

squares were cut relative to grain orientation.

The basic concepts regarding wave propaga-

tion in anisotropic media were expounded in the

1830s by G.R. Hamilton and J. McCullagh, inde-

pendently. The term ‘anisotropy’ was first used in

1879 by Rutledge to describe properties of light

traveling through crystals.

Laboratory and field experiments in the 1950s

detected velocity anisotropy when vertically and

horizontally traveling waves were found to have

different velocities.2 Early explanations advo-

cated an elliptical relationship for waves travel-

ing at intermediate angles. Ellipses were conve-

nient because once the vertical and horizontal

velocities are known, velocities at any other

angle can be computed. Later laboratory and field

experiments aimed at quantifying anisotropy con-

tinued to measure velocities parallel and perpen-

dicular to perceived alignments, and many publi-

cations list anisotropies of different rock types in

terms of the percentage difference between fast

and slow velocities, or the ellipticity.

However, models of wave propagation in trans-

versely isotropic (TI) media indicated that the rela-

tionship between velocities at different angles is

not an ellipse, but rather a squarish nonellipse.

And a new term, the anellipticity, was introduced

to describe the squareness. The realization that TI

materials, be they layered (TIV) or fractured (TIH),

are anelliptical, meant that experiments to quan-

tify anisotropy had to be redesigned. A measure-

ment at an intermediate angle is required to fully

characterize anelliptical elastic anisotropy.

For early shear-wave seismic experiments: Jolly RN:“Investigation of Shear Waves,” Geophysics 21 (October1956): 905-938.

For early laboratory studies: Kaarsberg EA: “IntroductoryStudies of Natural and Artificial Argillaceous Aggregatesby Sound-Propagation and X-Ray Diffraction Methods,”Journal of Geology 67 (July 1959): 447-472.

39

of symmetry (right). This variation of veloc-ity with angle of propagation has implica-tions for the validity of many empirical rela-tionships that have been established, linkingvelocity to some other rock property (see“Valid Velocities,” below).

Since ultrasonic laboratory measurementsat 0.25-to 5-mm wavelength detectanisotropy, this indicates that the spatial scaleof the features causing the anisotropy ismuch smaller than that wavelength. Themain cause of elastic anisotropy in shalesappears to be layering of clay platelets on themicron scale due to geotropism—turning inthe earth’s gravity field—and compactionenhances the effect (below right ). Theresponse of elastic waves to clay platelets ofvarying degrees of alignment has been mod-eled (next page, top left and right).9

Laboratory experiments also show theeffect of directional stresses on ultrasonicvelocities, confirming that compressionalwaves travel faster in the direction ofapplied stress.10 One explanation of thismay be that all rocks contain some distribu-tion of microcracks, random or otherwise.11

As stress is applied, cracks oriented normalto the direction of greatest stress will close,while cracks aligned with the stress direc-tion will open (next page, bottom). In mostcases, waves travel fastest when their parti-cle motion is aligned in the direction of theopening cracks.

Measurements made on synthetic crackedrocks show such results.12 And computersimulations indicate that rock with an ini-tially isotropic distribution of fracturesshows anisotropic fluid flow propertieswhen stressed. Fluid flow is greatest in thedirection of cracks that remain open underapplied stress, but the overall fluid flow candecrease, because cracks perpendicular tothe stress direction, which would feed intoopen cracks, are now closed.13

Horizontal velocity, km/sec0-2-4 2 4

0

1�

2

3

-3

-2

-1�

Vert

ical

vel

ocity

, km

/sec

qP

qS1

nWavefront veloci-ties. Laboratory-measured values of qP- and qS1-wavefront velocitiesfor a shale are plot-ted with respect to angle of propa-gation. Tick marksindicate particlemotion direction.

40 Oilfield Review

Valid Velocities

nPhotomicrograph of shale showing clay platelets distributed aroundthe horizontal. Inset graph shows the distribution of the normal to theplatelet, distributed around vertical.

Common practice calls for characterizing the

elastic properties of a rock for correlation with

other properties, such as lithology or porosity, or

for rock mechanics purposes. This characteriza-

tion determines density and P- and S-wave veloc-

ities. With those three numbers, most geoscien-

tists would say the elastic behavior of the rock is

completely described. They would be correct only

if the rock were isotropic. And since most labora-

tory experiments to characterize rock core are

done on reservoir rocks, typically isotropic sand-

stones or carbonates, anisotropy hasn’t played a

major role.

But most of the rocks surrounding reser-

voirs—75% in most sedimentary basins—are

hard-to-characterize anisotropic shales. In the

most general anisotropic case, 21 numbers are

required. In the simple layer-anisotropic rocks

described so far, five velocities—two trans-

versely polarized S, vertical P, horizontal P, and P

at 45°—plus density, are sufficient to completely

characterize the rock.

Recognizing that many rocks are anisotropic,

or may become so under stress, may have impli-

cations for any empirical relationships that

relate rock velocity as measured in one geometry

to other properties, such as strength, porosity

or lithology.

10 µm

Angle, deg

Per

cent

alig

ned

-45-90 0 45 900

4

8

nEffect of nonuniform compressive stress on microcracks. In rocks with randomly oriented microcracks (left) cracks at all orientationsmay be open. When stressed (right), cracks normal to the direction of the maximum compressional stress will close, while cracks par-allel to the stress direction will open or remain open. Elastic waves in such a rock will travel faster across closed cracks—in the direc-tion of maximum stress—than across open cracks.

9. Hornby BE, Schwartz LM and Hudson JA:“Anisotropic Effective-Medium Modeling of the Elastic Properties of Shales,” Geophysics 59, no. 10 (October 1994): 1570-1583.Sayers CM: “The Elastic Anisotropy of Shales,” Journal of Geophysical Research 99, no. B1 (January 10, 1994): 767-774.

10. Sayers CM and van Munster JG: “Microcrack-Induced Seismic Anisotropy of Sedimentary Rocks,”Journal of Geophysical Research 96, no. B10(September 10, 1991): 16,529-16,533.

11. Crampin S: “The Fracture Criticality of CrustalRocks,” presented at the Sixth International Work-shop on Seismic Anisotropy, Trondheim, Norway,July 3-8, 1994. Also, Geophysical JournalInternational 118 (1994): 428-438.

12. Rathore JS and Fjær E: “Experimental Measurementsof Acoustic Anisotropy of Rocks with OrthogonalCrack Sets,” presented at the 56th Annual Meetingand Technical Exhibition, European Association ofExploration Geophysicists, Vienna, Austria, June 6-10, 1994.

Average overdistribution function

Add silt andother minerals

Solve for aligned inclusionsof a fluid-clay compositeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a aaaaaaaaaaa a aa aUnstressedaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a aaaaaaaaStressed

41October 1994

Wavefront, m/sec Wavefront, m/sec

4000-4000

4000

2000

-4000

-2000

qP

0

qS1

qS2

4000

2000

-4000

-2000

qP

0

qS1

qS2

nWavefront velocities for synthetic shales. qP- and qS-wave velocities are computed fora shale with all clay platelets oriented horizontally (left). The shale synthesized with arealistic clay platelet distribution shows computed velocities (right) similar to those ofthe real shale depicted on the previous page.

nComponents of a shale model. Individualmodel clay platelets (top) are orientedaccording to the distribution measured inthe shale photograph on previous page(middle). Silt particles are added (bottom)to resemble real shales.

13. Sayers CM: “Stress-Induced Fluid Flow Anisotropy inFractured Rock,” Transport in Porous Media 5(1990): 287-297.

At the Tree Trunk ScaleBoth types of anisotropy, TIV and TIH, arealso detected at the next larger scale,approximately the size of a borehole radius,with the DSI Dipole Shear Sonic Imagertool. At this scale, the most common evi-dence for TIV layering anisotropy comesfrom different P-wave velocities measuredin vertical and highly deviated or horizontalwells in the same formation—faster horizon-tally than vertically. But the same can besaid for S-wave velocities (right). For years,whenever discrepancies appeared betweensonic velocities logged in vertical and devi-ated sections, log interpreters sought expla-nations in tool failure or logging conditions.Now that anisotropy is better understood,the discrepancies can be viewed as addi-tional petrophysical information. Log inter-preters expect anisotropy and look for cor-relation between elastic anisotropy andanisotropy of other log measurements, such

as resistivity (see “Oilfield Anisotropy: ItsOrigins and Electrical Characteristics,”page 48).14

Fracture-, or stress-, induced elasticanisotropy has also been detected by soniclogs through shear-wave splitting. In forma-tions with TIH anisotropy, shear waves gen-erated by transmitters on the DSI tool splitinto fast and slow polarizations (left).15 Thefast shear waves arrive at the receiver arraybefore the slow shear waves. Also, theamount of shear wave energy arriving at thereceivers varies with tool azimuth as thetool moves up the borehole, rotating on itsway (next page, top).

Detecting anisotropy in DSI waveformdata is easy, but using the data to computethe orientations of the split shear waves is abit trickier. If travel time and arrival energycould be measured for every azimuth atevery depth, the problem would be solved,but that would require a stationary measure-ment. Logging at 1800 ft/hour [550 m/hr],the DSI tool fires its shear sonic pulse alter-nately from two perpendicular transmittersto an array of similarly oriented receivers,and the pulse splits into two polarizations.As the tool moves up the borehole, fourcomponents—from two transmitters to eachof two receivers—of the shear wavefield arerecorded. The four components measured atevery level, along with a sonde orientationfrom a GPIT General Purpose InclinometerTool measurement, can be manipulated tosimulate the data that would have beenacquired in a stationary measurement.These data can determine the fast and slow

directions, but cannot distinguish betweenthe two (next page, bottom).16 Including thetravel-time difference information allowsidentification of the fast shear-wave polar-ization direction, which in turn is the orien-tation of aligned cracks, fractures or themaximum horizontal stress. In an examplefrom a well operated by Texaco, Inc. in Cal-ifornia, the fast shear-wave polarizationdirection obtained from such DSI measure-ments corresponds to fracture azimuthsextracted from an FMI Fullbore FormationMicroImager image (page 44).

Amoco Exploration and Production usedinformation about shear velocities to opti-mize hydraulic fracture design in the Hugo-ton field of Kansas, USA.17 A key parameterfor hydraulic fracture design is closurestress. Closure stress is related through rockmechanics models to Poisson’s ratio, whichis a function of the P- and S-wave velocities

42 Oilfield Review

14. White J: “Recent North Sea Experience in FormationEvaluation of Horizontal Wells,” paper SPE 23114,presented at the SPE Offshore Europe Conference,Aberdeen, Scotland, September 3-6, 1991.

15. The wave that propagates up the borehole in thiscase is more precisely called a flexural wave, but itbehaves like a shear wave for the purposes of thisexample.

16. Esmersoy C, Koster K, Williams M, Boyd A and KaneM: “Dipole Shear Anisotropy Logging,” presented atthe 64th Annual International Meeting, Society ofExploration Geophysicists, Los Angeles, California,USA, October 23-28, 1994.

17. Koster K, Williams M, Esmersoy C and Walsh J:“Applied Production Geophysics Using Shear-WaveAnisotropy: Production Applications for the DipoleShear Imager and the Multi-Component VSP,” pre-sented at the 64th Annual International Meeting,Society of Exploration Geophysicists, Los Angeles,California, USA, October 23-28, 1994.

Shale

Sand520

540

700

750

800

850

900

Slowshear Fast

shear

Gammaray

Relativebearing

50150250350 50 100 150

P

µsec/ft GAPI

Dep

th, m

deg

Dipolereceivers

Dipolesource

FastS wave

SlowS wave

Sourcepulse

nSonic logs in a60°-deviatedNorth Sea well. Inisotropic sand(top), shear-waveslownessesrecorded in twoazimuths showthe same values(black and bluecurves). In deeperanisotropic shale(bottom), twoshear slownessesare recorded.Other curves indi-cate P-wave slow-ness, gamma rayand the receiverbearing relative tothe vertical planecontaining theborehole.

nShear wave splitting in borehole. The DSIDipole Shear Sonic Imager tool records fastand slow shear waves. Data are analyzedfor orientation and degree of anisotropyindicated by the amount of birefringence.

nChanges in shear-wave arrival timesand arrival amplitude with changingdipole azimuth in TIH-anisotropic layers.Shear-wave arrival times, recorded whenreceiver and transmitter are aligned—called inline—vary with tool orientation(left). Inset “compasses” show orientationof a pair of DSI receivers relative to frac-tures. At 490 ft, the receiver aligned withfracture direction (blue) records fast sheararrival before the receiver oriented per-pendicular to fractures (red) records theslow. The wave amplitude recorded onthe crosscomponent (middle)—blue trans-mitter to red receiver or vice versa—isminimal. At 487 ft, receivers are mis-aligned, and the arrival times arebetween fast and slow. Crosscomponentamplitude is maximum. At 485 ft, arrivaltimes separate and crosscomponentamplitude decreases again. Absolutebearing of red receiver azimuth (right)shows that tool has rotated 90° relative toits orientation at 490 ft.

43October 1994

nSimulation of sta-tionary multiaz-imuth data fromone four-compo-nent DSI measure-ment. Inline (left)and crosscompo-nent (right) wave-forms computedfrom four mea-sured traces (red).Maximum inlineand minimumcrosscomponentamplitudes (blue)indicate a fastshear-wave direc-tion of 54° for thisexample.

485

495

Dep

th, f

t

Arrival time, msec Time, msec N deg E4.6 4.7 4.8 4.9 5.0 3 4 5 6 7 110 200 290

Inline Travel Time Cross Receiver Dipole Azimuth

180

0

4 5 6 7 4 5 6 7

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Time, msec

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ole

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ntat

ion,

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Time, msec

of the rock. But in an anisotropic rock, it isdebatable whether the fast or slow S-wavevelocity should be used—a slow velocitywould give a higher closure stress, thereforea higher volume of pumped fluids. The DSItool indicated about 8% anisotropy in theshale. Amoco engineers designed a fracturejob around the fast shear-wave velocity, pre-dicting lower closure stress, and reducingpumped fluid costs from $100,000 to$35,000 per well. Pump-in closure stresstests confirmed the lower stress value indi-cated by the faster S-wave velocity from theDSI tool. Amoco anticipates saving $10,000to $65,000 per well on the remaining 300infill wells to be drilled in the field.

At the slightly larger scale of a few feet tometers, crosswell seismic surveys also senseelastic anisotropy. But while most oilfieldexperiments employ vertically travelingwaves to study elastic properties, crosswellseismic surveys harness horizontally travel-ing waves. In such a survey at the BritishPetroleum test site in Devine, Texas, USA, aseismic source was fired in one well to 56receiver positions in a well 100 m [330 ft]away (next page). Then the experiment wasrepeated at 55 other source positions. Dataprocessing called tomography divided thearea between the wells into 56x56 cells andsolved for the P-wave velocity in eachsquare, to create a tomogram. Typicaltomography, solving for isotropic velocities,reconstructed an image with layer bound-aries that correspond to boundaries seen ingamma ray logs. However, allowing thevelocities to be anisotropic enhances theresults with a clearer tomographic imagebetween wells.18

44 Oilfield Review

Calculation Window

Fast Waveform

Stress AzimuthFrom Breakout

FMI Fracture Strike

1000

Off-axisEnergy

Fast Shear Slowness

Slow Shear Slowness

Slowness-based Anisotropy

Time-based Anisotropy

Fast Shear Azimuth

Azimuth Uncertainty

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nComparison of fracture anisotropy from fast shear-wave azimuth and from boreholeimages. Shear-wave logs from a California well operated by Texaco, Inc. were pro-cessed using four-component rotation to extract the azimuth and amount of anisotropyindicated by shear-wave birefringence. Minima in the crosscomponents (green filled log,first track) indicate anisotropy. Waveforms of the fast (solid line) and slow (dotted line)shear waves appear in the second track. The time window for calculations is shadedpink. Azimuthal information appears in the third track, with fast shear direction (blackcurve), hydraulic fracture azimuth from tiltmeter records (blue bar) and fractureazimuths seen in FMI Fullbore Formation MicroImager displays (colored squares). Theamount of birefringence, here equated with anisotropy, is plotted in the fourth track,with slowness-based percentage anisotropy (green), slow shear slowness (dotted blue),fast shear slowness (red) and time-based percentage anisotropy (solid blue).

nCrosswell seismic experiment at British Petroleum’s Devine Test Site. The downhole source was fired at 56 positions, each recordedby 56 receivers (top). Travel time data were processed for slowness—the inverse of velocity—in the layers between the two wells.Assuming isotropic slownesses (bottom left), diagonal smears contaminate the tomographic image. Processing with anisotropic slow-nesses yields two images, horizontal (bottom middle) and vertical (bottom right) slownesses.

18. Miller DE and Chapman CH: “Incontrovertible Evi-dence of Anisotropy in Crosswell Data,” presentedat the 61st Annual International Meeting of the Soci-ety of Exploration Geophysicists, Houston, Texas,USA, November 10-14, 1991.

19. For a review of the VSP method: Belaud D, ChristieP, de Montmollin V, Dodds K, James A, Kamata Mand Schaffner J: “Detecting Seismic Waves in theBorehole,” Technical Review 36, no. 3 (July 1988):18-29.

20. Queen JH and Rizer WD: “An Integrated Study ofSeismic Anisotropy and the Natural Fracture Systemat the Conoco Borehole Test Facility, Kay County,Oklahoma,” Journal of Geophysical Research 95,no. B7 (July 10, 1990): 11,255-11,273.Winterstein DF and Meadows MA: “Shear-WavePolarizations and Subsurface Stress Directions atLost Hills Field,” Geophysics 56 (September 1991):1331-1348.

21. Walsh J: “Fracture Estimation from Parametric Inver-sion of SV Waves in Multicomponent Offset VSPData,” presented at the 63rd Annual InternationalMeeting of the Society of Exploration Geophysicists,Washington DC, USA, September 26-30, 1993.

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At the Tree and Forest ScalesMost of the experiments designed to capturein-situ elastic properties have been verticalseismic profiles (VSPs), at the 10-m [33-ft]wavelength scale.19 Specially planned VSPsreveal elastic anisotropy of both types, TIVand TIH, but mostly fracture-related TIHanisotropy via shear-wave splitting.20 Thesestudies show a good correlation betweenfracture azimuth inferred from VSPs andfrom other measurements, such as boreholeimager tools, regional stress data, surfacemapping and experiments on cores. Con-ducting such studies in the marine settingoffers a special challenge, because shearwaves can not be generated in nor propa-gate through water. VSPs can, however,record waves that have been converted fromP to S by reflection or refraction.21 Such ver-tically propagating shear waves then behavepredictably by splitting into fast and slowshear waves when they propagate throughfractured rock to borehole receivers.

October 1994

As desirable as fractures may be forenhancing fluid flow, they are undesirablein caprock shales, where vertical fracturescould diminish their integrity as reservoirseals. Geophysicists are looking into waysto identify fractured and unfractured shalecaprock, hoping not to see fracture-relatedanisotropy in them.

More sophisticated walkaway VSPs, calledwalkaways for short, can measure elasticproperties of layer-anisotropic TIV rocks in away that no others can. Most VSPs rely onnear-vertical wave propagation. But withoutnonvertical travel paths, the elastic proper-ties of TIV materials, such as shales, cannotbe measured in situ. The walkaway, with itslarge source-receiver offsets and horizontaltravel paths, is able to deliver vital informa-tion about shale properties.

A walkaway survey in the South ChinaSea sampled a compacting shale sequencethrough more than 180° of propagation

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nAcquisition geome-try for walkawayvertical seismic pro-file (VSP). A singleborehole receiverarray recorded sig-nals from 200 sur-face source positions,100 on each side ofthe well. Wavearrival angles at the receiversspanned 180°.

nCompressionaland shear wave-front velocities for aTIV material withthe same propertiesas the shale sam-pled by walkawayVSP in the SouthChina Sea. Tickmarks indicate par-ticle motion direc-tion. Superimposedare two ellipses fit toangles 0 to 30°(blue) and 0 to 90°(black), but neitherellipse fits well.

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angles, usually impossible in all but labora-tory experiments (right, top). The datarevealed fine-scale layering-inducedanisotropy with horizontal P-wave velocities12% greater than vertical (right, middle).22

The elastic properties of this highly anel-liptic anisotropic shale were used to under-stand the effects of anisotropy on seismicreflection amplitude variation with offset(AVO) analysis. Surface seismic surveys andVSPs typically involve reflections of wavesthat propagate within 30° of vertical. Evenin TIV-anisotropic shales, these near-verticalwaves would not sense much anisotropy.But in surveys designed to highlight AVOeffects, waves often travel at larger reflectionangles. Reflection amplitude depends on theangle of reflection, or offset between sourceand receiver, and the contrast between P-and S-wave velocities on either side of thereflector. In isotropic rocks, some reflec-tors—especially those where hydrocarbonsare involved—have amplitudes that varywith angle of reflection. Some operators usethis property as a hydrocarbon indicator.23

In anisotropic rocks, there is the additionalcomplication that the P- and S-wave veloci-ties themselves may vary with angle of prop-agation, again causing AVO. If a propitiousAVO signature is encountered, it is vital toknow how much is due to hydrocarbon andhow much to anisotropy. This dilemma canbe resolved by modeling, which simulatesthe seismic response to a given rock or fluidcontrast. Modeling requires knowledge ofelastic properties, and correct modelingshould include anisotropy (right, bottom).But anisotropy is a scale-dependent effect,and it is best measured at a scale similar tothe VSP or surface seismic experiment beingmodeled, such as with a VSP. Most exam-ples of AVO modeling use sonic-scale elas-tic parameters— sonic log data. But it is pos-sible to envision an anisotropy, especially ifit is fracture-related, at a scale larger thanthe sonic wavelength but smaller than theVSP wavelength. In this case, the anisotropymay be felt by seismic waves but not bysonic waves.

Another walkaway, by British Petroleumin the North Sea, measured anisotropic

46 Oilfield Review

nModeled amplitude variation with offset (AVO) response to isotropic andanisotropic shales overlying an oil-bearing sand. For an isotropic shale overly-ing the sand (left), the modeled response shows an increase in AVO. If the shaleis highly anelliptic (middle), the AVO response is diminished. For a mostly ellipticshale (right), the AVO response is enhanced. Elastic properties for the isotropicshale were taken from borehole logs. Properties for the anisotropic shales weremeasured from walkaway VSPs.

Isotropic Shale South China Sea Shale Java Sea Shale1.8

AVO Modeling Caprock Over Oil Sand

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nSeismic reflectionamplitude varia-tion with offset at ashale-sand inter-face. The AVOcurve modeledassuming an oilsand overlain byan isotropic shale(red) does not fitthe observed AVOresponse from thewalkaway data(black). Using theanisotropic elasticproperties mea-sured by the walk-away VSP gives anAVO model curvethat fits theobserved walka-way data (blue).

22. Miller D, Leaney WS and Borland W: “An In SituEstimation of Anisotropic Elastic Moduli for a Sub-marine Shale,” Journal of Geophysical Research 99,no. B11 (Nov. 10, 1994): 21,659-21665. Armstrong P, Chmela B and Leaney S: “AVO Calibra-tion Using Borehole Data,” presented at the 56thAnnual Meeting and Technical Exhibition, EuropeanAssociation of Exploration Geophysicists, Vienna,Austria, June 7-11, 1994.

23. Chiburis E, Franck C, Leaney S, McHugo S and Skid-more C: “Hydrocarbon Detection with AVO,” Oil-field Review 5, no. 1 (January 1993): 42-50.

24. Farmer P, Gray S, Hodgkiss G, Pieprzak A, Ratcliff Dand Whitcomb D: ”Structural Imaging: Toward aSharper Subsurface View,” Oilfield Review 5, no. 1(January 1993): 28-41.

25. Turning rays are seismic rays that travel down, thenturn up toward the surface, and reflect off the under-side of a structure before returning to the surface.They show promise in imaging features below saltand other occlusive materials.

26. Heffer KJ and Dowokpor AB: “Relationship BetweenAzimuths of Flood Anisotropy and Local EarthStresses in Oil Reservoirs,” in Buller AT, Berg E,Hjelmeland O, Kleppe J, Torsaeter O and Aasen J(eds): North Sea Oil and Gas Reservoirs-II. London,England: Graham & Trotman (1990): 251-260.

27. Lynn HB: “Opening Address of the 6th InternationalWorkshop on Seismic Anisotropy,” presented inTrondheim, Norway, July 3-8, 1994.

28. See references 16, 17 and 20. Also: Mueller MC:“Prediction of Lateral Variability in Fracture IntensityUsing Multicomponent Shear-Wave Surface Seismicas a Precursor to Horizontal Drilling in the AustinChalk,” Geophysical Journal International 107(1991): 409-415.

properties in a shale overlying a reservoirwith an anomalous AVO signature. Theelastic properties were used to model theAVO response at the interface between theshale caprock and the oil sand reservoir(right). The AVO signature seen in the walk-away data fits the anisotropic model. If thecaprock had been assumed to be isotropic,a different AVO response to the oil sandwould have been seen, and the sand mightnot have been identified as oil-bearing. Theeffect of the anisotropy on the interpretationof the AVO anomaly had an importantbearing on conclusions drawn from a con-current study based on 3D surface seismicdata in the area.

Velocity anisotropy is also beginning tofind a home in another corner of the surfaceseismic world, that of processing surveys toobtain images. This process, called migra-tion, requires knowledge of the velocities ofthe seismic waves to assign a correct spatialposition to reflections recorded in time.24 Inthe absence of measurements of anisotropicelastic properties, conventional migrationschemes include a 5% fudge factor andassume elliptical anisotropy to convertstacking velocities— results from a prior pro-cessing step—to migration velocities. Aknowledge of velocity anisotropy beyondthe 5% fudge factor, essentially knowing theanellipticity, will become more important inturning ray seismics, as seismic waves spendmore time in horizontal travel paths.25

Harvesting the ForestThese two types of elastic anisotropy, TIVand TIH, impact the oilfield geoscientist aswell as the anisotropist. Measurements oflayer-induced anisotropic elastic propertiesare used to refine processing and produceclearer images or to create better modelsthat lead to more accurate interpretation. Inthe long run, measuring TIV elasticanisotropy improves reservoir description,which in turn promotes efficient hydrocar-bon recovery.

Measuring fracture- and stress-inducedTIH anisotropy may have a more direct andfar-reaching impact. Just as elastic waves arebound to travel in the direction of maximumstress or open fractures, so are reservoir flu-ids.26 The same forces that induce elasticanisotropy give rise to permeabilityanisotropy (see “Measuring PermeabilityAnisotropy: The Latest Approach,” page 24).But the tie between these two is not maderoutinely, nor is it fully understood.

October 1994

Establishing the elastic-permeability tie foranisotropy requires geophysicists, reservoirengineers, geologists and petrophysicists toexperiment with such a tie, documentingsuccesses and failures. Today, the most basiclevel of anisotropic description involvesonly the geophysicist.27 The descriptioncomprises the azimuth of fracture or stressanisotropy, the degree of anisotropy in rela-tive velocity difference, and the velocities ofthe two shear waves.

At a more sophisticated level the geologistand petrophysicist add the following infor-mation to make further links in the rock-fluid tie: lithology from core or logs; age ofthe reservoir; history of hydrocarbon matu-ration; azimuth and aperture of fracturesseen in image logs; stress direction in thevicinity of the borehole from caliper logs orhydraulic fractures; and the effect of fluidsaturation on resistivity anisotropy.28

The ultimate level of integrated interpreta-tion brings the reservoir engineer into thepicture. This level adds measurement of fluidflow magnitudes and direction at the scaleof the reservoir, in the region sampled by theelastic measurements. Achieving such anintegrated interpretation will promote elasticanisotropy as a tool for better reservoirdescription and reservoir management. —LS

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