borehole acoustic waves

34 Oilfield Review

Borehole Acoustic Waves

Jakob B.U. HaldorsenDavid Linton JohnsonTom PlonaBikash SinhaHenri-Pierre ValeroKenneth Winkler Ridgefield, Connecticut, USA

For help in preparation of this article, thanks to Jeff Alford,Houston, Texas; and Andy Hawthorn and Don Williamson,Sugar Land, Texas.

Borehole acoustic waves may be as simple or as complex as the formations in

which they propagate. An understanding of wave-propagation basics is essential

for appreciation of modern sonic-logging technology.

Everyday sounds come from many sources.Keyboards click, crickets chirp, telephones ringand people laugh. Understanding the informa-tion contained in these sounds is something that most people do without thinking. For most,deciphering the sounds they hear is much moreimportant than knowing what sound waves areand how they travel.

However, for geoscientists and others whomust understand the information contained insound waves traveling in the Earth, it is essentialto know what sound waves are and how theytravel. This article reviews the basic types ofacoustic sources and the sound waves that travelin rocks near a borehole. We also discuss theeffects that variations in rock properties have onacoustic waves.

The acoustic waves recorded by a sonic-logging tool depend on the energy source, thepath they take and the properties of theformation and the borehole. In wireline logging,there are two primary types of sources, monopoleand dipole. A monopole transmitter emits energyequally in every direction away from its center,while a dipole transmitter emits energy in apreferred direction.

From a monopole transmitter located in thecenter of the borehole, a spherical wavefronttravels a short distance through the boreholefluid until it meets the borehole wall. Part of theenergy is reflected back into the borehole, andpart of the energy causes waves to propagate inthe formation (next page, top). The direction ofwave propagation is always perpendicular to the

wavefront. This simple case also assumes theformation is homogeneous and isotropic, andthat the sonic tool itself has no other effect onwave propagation.1

The 3D cylindrical setting of the wellborecomplicates this explanation, which can besimplified by examining a vertical plane throughthe axis of a vertical borehole. In the resulting 2Dsystem, spherical wavefronts become circles andpropagate in one plane. In a 3D world, wave-fronts propagate everywhere outward from thesource and surround the borehole symmetrically.

In the 2D simplification, when the wavefrontin the borehole mud meets the borehole wall, itgenerates three new wavefronts. A reflectedwavefront returns toward the borehole center atspeed Vm. Compressional, P-, and shear, S-, wavesare transmitted, or refracted, through theinterface and travel in the formation at speeds Vp

and Vs, respectively. In this simplest case of ahard, or fast, formation, Vp > Vs > Vm.

Once the refracted P-wave becomes parallelto the borehole wall, it propagates along theborehole-formation interface at speed Vp, fasterthan the reflected borehole-fluid wave.According to Huygens principle, every point onan interface excited by a P-wave acts as asecondary source of P-waves in the borehole aswell as P- and S-waves in the formation. Thecombination of these secondary waves in theborehole creates a new linear wavefront called ahead wave.2 This first head wave in the mud isknown as the compressional head wave, and its

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arrival at the receivers is recorded as the Parrival. The P-wave takes longer to arrive atreceivers that are farther from the source. Thetime difference between P arrivals divided by thedistance traveled is known as ∆ t , or slowness,and is the reciprocal of speed. This is the mostbasic sonic-logging measurement.3

The P-wave that continues into the formationis known as a body wave, and travels on deeperinto the formation unless a reflector sends itback toward the borehole, at which time it iscalled a reflected P-wave. Standard sonic loggingignores reflected P-waves, but special applica-tions, such as those described near the end ofthis article, take advantage of the extrainformation contained in reflected P-waves.

The behavior of refracted S-waves is similarto that of refracted P-waves. When the refractedS-wave becomes parallel to the borehole wall, itpropagates along the borehole-formationinterface as a shear disturbance at speed Vs andgenerates another head wave in the boreholefluid. Its arrival at the receivers is recorded asthe S-wave. In this way, shear slowness of a fastformation can be measured by a tool surroundedby borehole fluid, even though S-waves cannotpropagate through the fluid.

In cases when the shear-wave speed is lessthan the mud-wave speed—a situation known asa slow formation—the shear wavefront in theformation never forms a right angle with theborehole. No shear head wave develops in thefluid. In both fast and slow formations, an S bodywave continues into the formation.

Another way of visualizing how P and S headwaves and body waves travel near the borehole isthrough ray tracing. Strictly speaking, ray tracingis valid only when the wavelength is muchsmaller than the diameter of the borehole, orwhen the wavefronts can be approximated asplanes rather than spheres or cones. Mostborehole acoustic modes, especially those at lowfrequencies, do not meet these conditions, butray tracing can still be useful for visualization. Aray is simply a line perpendicular to a wavefront,showing the direction of travel. A raypathbetween two points indicates the fastest travelpath. Changes in raypath occur at interfaces andfollow Snell’s law, an equation that relates theangles at which rays travel on either side of aninterface to their wave speeds (right). Amongother things, Snell’s law explains the conditionsunder which head waves form and why none formin slow formations.

Ray tracing is useful for understanding wherewaves travel and for modeling basics of sonic-tooldesign, such as determining the transmitter-receiver (TR) spacing that is required to ensurethat the formation path is faster than the directmud path for typical borehole sizes andformation P and S velocities. This ensures thatthe tool will measure formation properties ratherthan borehole-mud properties. Ray tracing alsohelps describe the relationship between TR

> The first few moments of simplified wavefront propagation from a monopole transmitter in a fluid-filled borehole (blue) and a fast formation (tan). Bothmedia are assumed homogeneous and isotropic. Tool effects are neglected. Time progression is to the right. Numbers in the upper left corner correspondto time in µs after the source has fired. Wavefronts in the mud are black, compressional wavefronts in the formation are blue, and shear wavefronts in theformation are red. The compressional head wave can be seen at 90 µs, and the shear head wave can be seen at 170 µs.

40 70 80 110 17090

Compressionalhead wave

Shearhead wave

>Wavefront reflection and refraction at interfaces,and Snell’s law. θ1 is the angle of incident andreflected P-waves. θ2 is the angle of refracted P-waves. θs is the angle of refracted S-waves.Vm is mud-wave velocity. Vp is P-wave velocity inthe formation, and Vs is S-wave velocity in theformation. When the angle of refraction equals90°, a head wave is created.

Reflected P

Refracted P

Refracted S

Incident P-wave

Source

Mud velocity, Vm P velocity, Vp > Vm

Borehole Formation

S velocity, Vs

=Vm

Sin θ1

Vp

Sin θ2 =Vs

Sin θs

θs

θ1

θ1

θ2

1. A homogeneous formation is one with uniform velocity.In other words, the velocity is independent of location.An isotropic formation is one with velocity independentof direction of propagation.

2. The head wave has a conical wavefront in 3D.3. Slowness typically has units of µs/ft.


spacing and near-wellbore altered-zone thick-ness and velocity contrast (above). In addition,ray tracing is used in inversion techniques suchas tomographic reconstruction, which solves forslowness models given arrival-time information.

After the P and S head waves, the next wavesto arrive at the receivers from a monopole sourceare the direct and reflected mud waves. Theseare followed by trapped modes and interfacewaves that owe their existence to the cylindricalnature of the borehole. Trapped modes arisefrom multiple internal reflections inside theborehole. Wavefronts of particular wavelengthsbouncing between the walls of the boreholeinterfere with each other constructively andproduce a series of resonances, or normal modes.Trapped modes are not always seen on logs andmay be affected by borehole condition. In slowformations, trapped modes lose part of theirenergy to the formation in the form of waves that

radiate into the formation. These are called leakymodes, and propagate at speeds between P and Svelocities. Leaky modes are dispersive, meaningtheir different frequency components travel atdifferent speeds.

Stoneley WavesThe last arrivals from a monopole source areinterface, or surface, waves. Surface waves werefirst suggested by Lord Rayleigh in 1885.4 Heinvestigated the response at the planar surface ofan elastic material in contact with a vacuum andfound that a wave propagated along the surfacewith particle motion that decreased in amplitudewith distance from the surface—a propertycalled evanescence. Rayleigh’s findingspredicted the existence of waves that propagatealong the Earth’s surface and give rise to thedevastating shaking caused by earthquakes. The

same effect at a much smaller scale leads to“ground roll” noise in surface seismic surveys.

In 1924, Stoneley looked at waves propa-gating at the interface between two solids andfound a similar type of surface wave.5 Theparticular case corresponding to a fluid-filledborehole, that is, the interface between a solidand a liquid, was described not by Stoneley, butby Scholte.6 The waves traveling at the fluid-borehole interface are nonetheless known asStoneley waves. In other areas of geophysics,such as marine seismic surveys, waves travelingat a fluid-solid interface are called Scholte orScholte-Stoneley waves.7

A Stoneley wave appears in nearly everymonopole sonic log. Its speed is slower than theshear- and mud-wave speeds, and it is slightlydispersive, so different frequencies propagate atdifferent speeds.

The decay of Stoneley-wave amplitude withdistance from the interface is also frequency-dependent; at high frequencies, the amplitudedecays rapidly with distance from the boreholewall. However, at low frequencies—or at wave-

36 Oilfield Review

> Ray tracing using Snell’s law to model raypaths. Here,rays are traced through a formation that has radiallyvarying velocity in a zone of alteration. Velocity is lowernear the borehole and grows larger with distance, asituation that arises when drilling induces near-wellboredamage. Rays traveling to the receivers nearest thetransmitter travel only through the altered zone (darkbrown), and rays traveling to distant receivers sense thevelocity of the unaltered formation (light brown).

Transmitter

Receiverarray

Zone ofalteration

Unalteredformation

> The Stoneley wave, traveling at the interfacebetween the borehole and the formation. TheStoneley wave is dispersive and its particlemotion is symmetric about the borehole axis. Atlow frequencies, the Stoneley wave is sensitiveto formation permeability. Waves traveling pastpermeable fractures and formations lose fluid,and viscous dissipation causes attenuation ofwave amplitude and an increase in waveslowness. At open fractures, Stoneley waves are both reflected and attenuated. Red arrows in the center of the borehole symbolizeStoneley-wave amplitude.

Fracture

Receiver

Permeableformation

Stoneleywave

Transmitter

Condition Effect

Attenuated

Attenuatedand sloweddown

Reflected

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Spring 2006 37

lengths comparable to the borehole diameter—the Stoneley amplitude decays very little withdistance from the borehole wall. At sufficientlylow frequencies, the amplitude is nearly constantfrom one side of the borehole to the other,creating what is known as a tube wave. Anexample of a tube wave is the water-hammereffect that can sometimes be heard in plumbingpipes when flow is suddenly disrupted.

The low-frequency Stoneley wave is sensitiveto formation permeability. When the waveencounters permeable fractures or formations,the fluid vibrates relative to the solid, causingviscous dissipation in these zones, whichattenuates the wave and slows it down (previouspage, right). The reductions in Stoneley-waveenergy level and velocity vary with wavefrequency. Stoneley-wave dispersion data over awide bandwidth of frequencies can be inverted toestimate formation permeability.8 Open fracturescan also cause Stoneley waves to reflect backtoward the transmitter. The ratio of reflected toincident energy correlates with fractureaperture, or openness. This technique for thedetection of permeable fractures works well inhard formations.9

All of the above waves propagate symmetri-cally up and down the borehole, and can bedetected by monopole receivers—typicallyhydrophones. Hydrophones are sensitive topressure changes in the borehole fluid, and haveomnidirectional response, meaning that theyrespond equally to pressure changes from any direction.

Waveforms recorded at a given depth areinitially displayed as a time series from the arrayof receivers (above). In some recordings, the

P-, S- and Stoneley-wave arrival times can beseen clearly, but often, data-processingtechniques are used to pick times accurately. Thedifference in arrival times divided by thedistance between receivers yields the slownessfor each mode. However, in many recordings,high noise levels, bad hole conditions or otherfactors can cause these arrivals to be indistinctor mixed with each other. In such cases, visual orautomated picking of arrival times fails to yieldtrue slownesses.

4. Strutt JW, 3rd Baron Rayleigh: “On Waves PropagatedAlong the Plane Surface of an Elastic Solid,” Proceedingsof the London Mathematical Society 17 (1885): 4. Rayleigh waves on the Earth’s surface have vertical and horizontal components of motion. Other surfacewaves discovered by A.E.H. Love have two horizontalmotion components.

5. Stoneley R: “Elastic Waves at the Surface of Separationof Two Solids,” Proceedings of the Royal Society,Series A 106 (1924): 416–428.

6. Scholte JG: “On the Large Displacements CommonlyRegarded as Caused by Love Waves and SimilarDispersive Surface Waves,” Proceedings of theKoninklijke Nederlanse Akademie van Wetenschappen51 (1948): 533–543.

7. Bohlen T, Kugler S, Klein G and Theilen F: “Case History1.5D Inversion of Lateral Variation of Scholte-WaveDispersion,” Geophysics 69, no. 2 (March–April 2004):330–344.

8. Winkler KW, Liu HL and Johnson DJ: “Permeability andBorehole Stoneley Waves: Comparison BetweenExperiment and Theory,” Geophysics 54, no. 1(January 1989): 66–75.

9. Hornby BE, Johnson DL, Winkler KW and Plumb RA:“Fracture Evaluation Using Reflected Stoneley WaveArrivals,” Geophysics 54, no. 10 (October 1989):1274–1288.

> Typical waveforms from a monopole transmitter in a fast formation, showing compressional, shearand Stoneley waves. The pink dashed lines are arrival times. A sonic-logging tool receiver array isshown at left.

Rece

iver

num

ber

13

11

9

7

5

3

1

Time, µs

1,0000 3,000 5,000

Compressionalwave

Shearwave

Stoneleywave

2

4

6

8

10

12


Slownesses can be estimated in a robust waywith minimal human intervention using a signal-processing technique that looks for similarity—known mathematically as semblance, orcoherence—in waveforms across the receiverarray.10 The method starts with an assumedarrival time and slowness for each wave type andsearches the set of waveforms for the time andslowness that maximize coherence. The graph ofcoherence for different values of slowness andtime is called a slowness-time-coherence (STC)plot, from which local maxima of the coherencecontours can be identified (above). Maxima

corresponding to compressional, shear andStoneley slownesses plotted for each depthcreate a slowness log. The two dimensions of anSTC plot are compressed into a single dimensionby projecting the coherence peaks onto theslowness axis. This vertical strip of color-codedcoherences, when plotted horizontally at theappropriate depth, forms an element of an STC-projection log, a standard sonic-logging output.The slowness of each mode is plotted on top ofthe STC projection.

Dipole SourcesSo far, the discussion has focused on wavesgenerated by monopole sources, but for someapplications, a different type of source isrequired. For example, in slow formations, wheremonopole sources cannot excite shear waves, adipole source can be effective. The dipole sourceprimarily excites flexural waves, along withcompressional and shear head waves. The motionof a flexural wave along the borehole can bethought of as similar to the disturbance thattravels up a tree when someone standing on theground shakes the tree trunk. The analogy worksbetter if the tree trunk is fixed at the top and hasconstant diameter.

Typically, a tool designed to generate flexuralwaves will contain two dipole sources orientedorthogonally along the tool X- and Y-axes. Thedipole transmitters are fired separately. First,the X-dipole is fired, and a flexural waveform isrecorded. Then, the Y-dipole is fired, and aseparate measurement is taken. The flexuralwave travels along the borehole in the plane ofthe dipole source that generated it. The particlemotion of the flexural wave is perpendicular tothe direction of wave propagation, similar to S-waves, and flexural-wave slowness is related toS-wave slowness. Extracting S-wave slownessfrom flexural-wave data is a multistep process.

Flexural waves are dispersive, meaning theirslowness varies with frequency (below). In manysets of flexural waveforms, it is possible to seethe wave shape change across the receiver arrayas different frequency components propagate atdifferent speeds. Because the wave shape

38 Oilfield Review

> Flexural-mode waveforms, showing a changein wave shape across the receiver array. In thiscase, the wave shape stretches out in time fromnear receiver (bottom) to far receiver (top). Thechange in wave shape is caused by dispersion.

Wav

efor

m n

umbe

r

1

13

11

9

7

5

3

Time, μs1,000 3,500 6,000

> Slowness-time-coherence (STC) processing for monopole arrivals. Waveformsat a given depth (top left) are scanned over time windows and over a range ofangles—called moveouts, which are related to slowness. When the signals onthe waveforms within the window are best correlated, coherence is maximum.An STC plot for that depth (bottom left) displays color-coded coherence in theslowness-time plane, with maximum coherence in red. The coherence valuesare projected onto a vertical strip along the slowness axis and then displayedas a thin horizontal strip at the appropriate depth on the STC projection log(right). A slowness log for each wave is generated by joining the coherencemaxima at all depths.

Compressionalwave

Shearwave

Stoneleywave

13

11

9

7

54

1

12

10

23

6

8

Wav

efor

m n

umbe

r

1,000 2,000 3,000 5,000Time, µs

300

200

100

2,000 3,000 4,000 5,000

Slow

ness

, µs/

ft

Waveforms from 3,764.89 ft

4,000

1,000

Time, µs

µs/ft40 340

Slowness

STC Coherence

3,760

3,770


Spring 2006 39

changes across the receiver array, standardmethods for estimating slowness, such as STCprocessing, which relies on wave-shapesimilarity, must be adapted to handle dispersivewaves. Dispersive STC processing identifies theslowness of individual frequency components.11

A plot of flexural-wave slowness versusfrequency is called a dispersion curve (below).Dispersion-curve analysis compares modeledacoustic dispersion curves for homogeneousisotropic formations with curves measured byborehole sonic tools.12

The radial depth of investigation of flexuralwaves is approximately one wavelength. Low-frequency flexural waves probe deep into theformation, and high-frequency flexural waveshave shallower depths of investigation. Analysisof flexural-mode slowness as a function offrequency can therefore provide detailedinformation about the formation near and farfrom the borehole.

At zero frequency, flexural-wave slowness isthe true formation shear slowness. Plottingflexural-wave slowness versus frequency andidentifying the zero-frequency limit of the curveallow estimation of formation shear slowness. Inthis way, analysis of flexural-wave dispersionallows estimation of shear slowness in fast orslow formations.13

Up to now, this article has concentrated onthe simplest case of a homogeneous isotropicformation and monopole and dipole sources.Such a formation has one P-wave slowness, oneStoneley-wave slowness and one S-waveslowness. Most of the applications for usingsonic-logging results to infer formation porosity,permeability, fluid type, elastic moduli, lithologyor mineralogy have been developed forhomogeneous isotropic formations. Additionalcomplexities arise in inhomogeneous oranisotropic formations. The rest of this articleaddresses anisotropy first, then looks atinhomogeneous formations.

AnisotropyThe spatial alignment of mineral grains, layers,fractures or stress causes wave velocity to varywith direction, a property called anisotropy.14 Inseismic surveys, the anisotropy of the overburdenshales is known to cause imaging difficulties thatneed to be corrected to place reservoir targets atthe correct location. Information about aniso-tropy is also needed whenever an understandingof rock mechanics is required. Directionaldrilling, drilling in tectonically active areas,designing oriented-perforating jobs, planninghydraulic-fracturing operations and developingpressure-supported recovery plans all benefitfrom knowledge of elastic anisotropy.

The natural processes that cause anisotropyalso cause it to have one of two mainorientations: horizontal or vertical. To a firstapproximation, horizontal layers create ananisotropic medium that may be consideredisotropic in all horizontal directions, butanisotropic vertically. Such a medium is knownas transversely isotropic with a vertical axis ofsymmetry (TIV) (above right). Similarly, verticalfractures create a simplified anisotropic mediumthat may be considered isotropic in any directionaligned with fracture planes, and anisotropic inthe direction orthogonal to fracture planes. Thismedium is known as transversely isotropic with ahorizontal axis of symmetry (TIH).

Sonic waves are sensitive to these directionaldifferences in material properties. Waves travelfastest when the direction of particle motion,called polarization, is parallel to the direction ofgreatest stiffness. Compressional waves haveparticle motion in the direction of propagation,so P-waves travel fastest in directions parallel tolayering and fractures, and travel more slowlywhen perpendicular to layering and fractures.

10. Kimball CV and Marzetta TL: “Semblance Processing ofBorehole Acoustic Array Data,” Geophysics 49, no. 3(March 1984): 274–281.

11. Kimball CV: “Shear Slowness Measurement byDispersive Processing of the Borehole Flexural Mode,”Geophysics 63, no. 2 (March–April 1998): 337–344.

12. Murray D, Plona T and Valero H-P: “Case Study ofBorehole Sonic Dispersion Curve Analysis,”Transactions of the SPWLA 45th Annual LoggingSymposium, June 6–9, 2004, Noordwijk, TheNetherlands, paper BB.The key parameters required for dispersion-curvemodeling are formation slowness, formation density,borehole-fluid velocity, borehole-fluid density andborehole diameter.

13. Sinha BK and Zeroug S: “Geophysical Prospecting UsingSonics and Ultrasonics,” in Webster JG (ed): WileyEncyclopedia of Electrical and Electronic EngineersVol. 8. New York City: John Wiley and Sons, Inc. (1999):340–365.

14. This holds for alignments on scales that are smaller thanthe wavelength of the waves in question.Armstrong P, Ireson D, Chmela B, Dodds K, Esmersoy C,Miller D, Hornby B, Sayers C, Schoenberg M, Leaney Sand Lynn H: “The Promise of Elastic Anisotropy,” Oilfield Review 6, no. 4 (October 1994): 36–47.

> Dispersion curves characterizing slowness at different frequencies in an isotropicformation. Shear waves are not dispersive; alltheir frequency components travel at the sameslowness. Stoneley waves are only slightlydispersive. Flexural modes excited by a dipolesource exhibit large dispersion in this formation.At the zero-frequency limit, flexural-waveslowness tends to the shear-wave slowness(dotted line).

Slow

ness

, µs/

ft

400

300

200

100

00 2 4 6 8

Frequency, kHz

Stoneley

Dipoleflexural

Shear

> Simplified geometries in elastic anisotropy. Inhorizontal layers (top), elastic properties may beuniform horizontally, but vary vertically. Such amedium may be approximated as transverselyisotropic with a vertical axis of symmetry (TIV),meaning that the formation may be rotated aboutthe axis to produce a medium with the sameproperties. In formations with vertical fractures(bottom), elastic properties may be uniform invertical planes parallel to the fractures, but mayvary in the perpendicular direction. This mediummay be approximated as transversely isotropicwith a horizontal axis of symmetry (TIH).

Vertical axisof symmetry

TIV

x

z

y

Horizontal axisof symmetry

x

z

y

TIH


Shear waves have particle motion perpen-dicular to the direction of propagation (above).In isotropic media, S-wave particle motion is contained in the plane containing the Pand S raypaths. In anisotropic media, an S-wave will split into two shear waves withdifferent polarizations and different velocities.The S-wave polarized parallel to the layering or

fractures is faster than the S-wave polarizedorthogonal to layering or fractures. Flexuralwaves behave like S-waves, and so they split inthe same ways. In the discussion that follows, S-waves and flexural waves are usedinterchangeably.

Sonic logging can be used to detect andquantify the direction and magnitude ofanisotropy if the tool geometry and theanisotropy axis are properly aligned. In a TIHmedium, such as a formation with alignedvertical fractures, S-waves propagating along avertical borehole split into two waves, and thefast wave is polarized in the plane of the

40 Oilfield Review

> Particle motion and direction of propagation in compressional and shear waves.Compressional waves (A) have particle motion in the direction of wave propagation. Shearwaves have particle motion orthogonal to the direction of propagation. In a TIH anisotropicmaterial (bottom), a shear wave propagating parallel to fractures splits. The S-wave withvertically polarized particle motion, parallel to the fractures (C) is faster than the S-wavewith particle motion polarized orthogonal to fractures (B).

Particlemotion

Particlemotion

Particlemotion

A

B

C

Horizontal axisof symmetry

Time

Time

Time

Compressional-wave amplitude

Slow shear-waveamplitude

Fast shear-waveamplitude

Wave propagation direction


Spring 2006 41

fractures (above). Similarly, in a TIV medium,such as a shale or a finely layered interval, S-waves propagating in a horizontal borehole split,and the fast wave becomes polarized in thebedding plane.

The polarization of S-waves split byanisotropy cannot be detected by a singlemonopole receiver. Directional receivers arerequired. A suitable directional receiver can becreated by substituting a single monopolereceiver with two or more pairs of monopolereceivers. Each pair of monopole receivers actsas a dipole reciever. For adequate recording offlexural waves, at least one dipole receiver isaligned with each dipole transmitter. At eachfiring of the dipole source, signals are recordedby the dipole receiver oriented “inline” with thatsource and also by the dipole receiver oriented“offline” (above right).15 This example showsrecording of flexural waves at 13 receiverstations with eight receivers distributed in a ringat each station.16

In isotropic formations, flexural wavesgenerated by a dipole source remain polarized inthe plane of the source and are detected only onthe dipole receiver aligned in that plane.However, in anisotropic formations, the flexuralwave splits into fast and slow componentsaligned with the formation anisotropy. Unless thetool axes are fortuitously aligned with the

formation’s fast and slow directions, flexural-wave energy will be recorded by the offline aswell as the inline receivers.

The directions, or azimuths, of fast and slowshear or flexural waves can be seen in a crossed-dipole log. Creating a crossed-dipole log is amultistep process. The first step is decompo-sition and recombination of the waveforms

> Inline and offline response on azimuthally distributed receivers from aborehole flexural wave in an anisotropic formation. The flexural wavewas excited by firing of the X-dipole transmitter, Tx, shown at the bottom.In this TIH medium, the flexural wave splits into fast and slow waves withcomponents of particle motion on all receivers, not just those alignedwith the tool X-axis.

Tool axis

x

x’y

θ y’Tool orientationrelative to formation

Formation fastshear-wave axis

Ty

Tx

Dipoletransmitter

pair

Undisturbedborehole

Low-frequencyboreholeflexural wave(exaggerated)

R5x

R6x

R7x

R8x

R9x

R10x

R11x

R12x

R13x

R4x

R3x

R2x

R1x

R13y

R12y

R11y

R7y

R6y

R5y

R4y

R3y

R2y

R1y

R10y

R9y

R8y Receiver-8 ring

Receiver-9 ring

Receiver-10 ring

Receiver-11 ring

Receiver-12 ring

Receiver-13 ring

Receiver-7 ring

Receiver-6 ring

Receiver-5 ring

Receiver-4 ring

Receiver-3 ring

Receiver-2 ring

Receiver-1 ring

Receiver array

15. Offline is sometimes referred to as crossline.16. Pistre V, Kinoshita T, Endo T, Schilling K, Pabon J,

Sinha B, Plona T, Ikegami T and Johnson D: “A ModularWireline Sonic Tool for Measurements of 3D (Azimuthal,

Radial, and Axial) Formation Acoustic Properties,”Transactions of the SPWLA 46th Annual LoggingSymposium, New Orleans, June 26–29, 2005, paper P.

> Shear-wave splitting in a vertical borehole in a TIH medium with vertical fractures. No matterhow the dipole source is oriented relative to thefast and slow directions of the medium, the shearwave will split into fast and slow components.The fast component aligns parallel to the plane of the fractures, while the slow component alignsperpendicular to the plane of the fractures.

Dipolereceivers

Dipolesource

FastS-wave

SlowS-wave

Sourcepulse


acquired on all sensors at each receiver stationto yield four waveforms corresponding to theinline and offline responses at every depth to thetwo orthogonal dipole transmitters. Next, thesewaveforms are mathematically rotated to putthem in a coordinate system consistent with thedirections of maximum and minimum offlinewaveform energy.17 Then, the waveforms corre-sponding to fast- and slow-shear orientationsundergo semblance processing to obtain the fastand slow shear-wave slownesses.18 Zones withequal fast and slow shear-wave slownesses areisotropic, while zones with large differencesbetween fast and slow shear-wave slownesses arehighly anisotropic.

The slownesses of the fast and slow S-wavesand the P- and Stoneley waves—the four slow-nesses that can be measured by sonic logging inan anisotropic medium—are transformed intofour anisotropic moduli. These four moduli canalmost characterize the simplest of anisotropicmedia. TIV and TIH media require five moduli to

be fully characterized. For more complex types ofanisotropy, more measurements are required,such as P-waves propagating in differentazimuths or inclinations, or S-waves travelingvertically and horizontally. Surface seismic andborehole seismic surveys often can provide thisinformation.

InhomogeneityFormation properties may vary not only withmeasurement direction, as in anisotropic forma-tions, but also from place to place, in what arecalled inhomogeneous, or equivalently, hetero-geneous, formations. As with anisotropy,detecting and quantifying inhomogeneity usingacoustic waves will depend on the type offormation variation and its geometry relative tothe borehole axis.

Standard sonic logging can characterizeformation properties that vary along theborehole. Early sonic-logging tools run in vertical

boreholes identified inhomogeneities in the formof boundaries between horizontal layers (see“History of Wireline Sonic Logging,” page 32).Other heterogeneities, such as high-permeabilityzones or open fractures that intersect theborehole, can be detected using Stoneley waves,as described earlier.

Formation properties that vary away from theborehole, or along the radial axis, are evidence ofthe drilling process and are more difficult toassess. The drilling process removes rock andcauses the in-situ stresses to redistribute, orconcentrate, around the borehole in a well-knownelastic manner.19 In addition, drilling not onlybreaks the rock that is removed to form theborehole, but also may mechanically damage avolume of rock surrounding the hole.20 This type ofdamage is called plastic deformation, in contrastto elastic, or reversible, deformation. In additionto plastic deformation, drilling fluid may reactwith clays, causing swelling and altering near-wellbore velocities. Mud that invades pore spacedisplaces formation fluids that probably havedifferent properties, also altering sonic velocities.Drilling-induced variations may be more gradualthan variations across layer interfaces.

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17. Alford RM: “Shear Data in the Presence of AzimuthalAnisotropy: Dilley, Texas,” Expanded Abstracts, 56th SEGAnnual International Meeting, Houston (November 2–6,1986): 476–479.Brie A, Endo T, Hoyle D, Codazzi D, Esmersoy C, Hsu K,Denoo S, Mueller MC, Plona T, Shenoy R and Sinha B:“New Directions in Sonic Logging,” Oilfield Review 10,no. 1 (Spring 1998): 40–55.

18. Esmersoy C, Koster K, Williams M, Boyd A and Kane M:“Dipole Shear Anisotropy Logging,” Expanded Abstracts,64th SEG Annual International Meeting, Los Angeles(October 23–28, 1994): 1139–1142.Kimball and Marzetta, reference 10.

19. Winkler KW, Sinha BK and Plona TJ: “Effects ofBorehole Stress Concentrations on Dipole AnisotropyMeasurements,” Geophysics 63, no. 1(January–February 1998): 11–17.

20. Winkler KW: “Acoustic Evidence of Mechanical DamageSurrounding Stressed Borehole,” Geophysics 62, no. 1(January–February 1997): 16-22.

21. Zeroug S, Valero H-P and Bose S: “Monopole RadialProfiling of Compressional Slowness,” prepared forpresentation at the 76th SEG Annual InternationalMeeting, New Orleans, October 1–3, 2006.

22. Sinha B, Vissapragada B, Kisra S, Sunaga S,Yamamoto H, Endo T, Valero HP, Renlie L and Bang J:“Optimal Well Completions Using Radial Profiling ofFormation Shear Slownesses,” paper SPE 95837,presented at the SPE Annual Technical Conference andExhibition, Dallas, October 9–12, 2005. Sinha BK: “Near-Wellbore Characterization Using RadialProfiles of Shear Slownesses,” Expanded Abstracts, 74th SEG Annual International Meeting, Denver (October 10–15, 2004): 326–329.

23. Chang C, Hoyle D, Watanabe S, Coates R, Kane R,Dodds K, Esmersoy C and Foreman J: “Localized Mapsof the Subsurface,” Oilfield Review 10, no. 1 (Spring1998): 56–66.

24. Hornby BE: “Imaging of Near-Borehole Structure UsingFull-Waveform Sonic Data,” Geophysics 54, no. 6 (June 1989): 747–757.

> Compressional and shear radial profiles in an anisotropic inhomogeneousformation. The profile of variation in compressional slowness (Track 4) is created bytomographic reconstruction based on tracing rays through a modeled formationwith properties that vary gradually away from the borehole. The percentagedifference between observed slowness and slowness of the unaltered formation isplotted on color and distance scales to indicate the extent of difference away fromthe borehole. In these sandstones, identifiable from the gamma ray log in Track 2,compressional slowness near the borehole varies by up to 15% from far-fieldslowness, and the variation extends to more than 12 in. [30 cm] from the boreholecenter. The borehole is shown as a gray zone. Shear radial profiles show thedifference between fast shear-wave slowness and far-field slowness (Track 1) andthe difference between slow shear-wave slowness and far-field slowness (Track 3).Large differences in shear slowness extend out to almost 10 in. [25 cm] from theborehole center. The radial variation in compressional and shear velocities isdrilling-induced.

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Alteration in near-wellbore properties cancause velocities to increase or decrease relativeto the unaltered, or far-field, formation. Usually,drilling-induced damage reduces formationstiffness, causing velocities to decrease near theborehole. However, when drilling fluid replacesgas as the pore-filling fluid, the resultingformation is stiffer, so compressional velocityincreases near the borehole.

Radial alteration of rocks and fluids affectscompressional and shear velocities differently.Alteration that reduces stiffness of the rockfabric, such as drilling-induced cracking orweakening, causes both P and S velocities todecrease. However, a change in pore fluid haslittle effect on S velocity, while P velocity maychange dramatically. For example, when drillingfluid replaces gas, P-wave velocity increases, butS-wave velocity is relatively unaffected.Complete characterization of radial inhomo-geneity requires analysis of radial variation ofcompressional and shear slownesses.

A radial compressional-slowness profile isgenerated by collecting P-wave data for multipledepths of investigation, from near the wellbore tothe unaltered, far-field formation. This requiresrecordings from a wide range of transmitter-

receiver spacings. Ray-tracing techniques invertthe refracted compressional arrivals to yieldcompressional slowness versus distance from theborehole.21 The difference between near-wellbore compressional slowness and far-fieldcompressional slowness can be plotted alongwith depth of radial alteration (previous page).In this example, radial variations of shearslownesses are also plotted.

Radial variations in shear slowness arequantified through inversions of the broadbanddispersions of flexural and Stoneley modes.22 Athigh frequencies, these dispersive modesinvestigate the near-wellbore region, and at lowfrequencies, they probe the unaltered formationfar from the borehole. Dispersion data from awide range of frequencies help produce the most reliable radial profiles of variations in shear slowness.

Some of the most challenging inhomo-geneities to characterize are those that do notintersect the borehole. These may be verticalfractures or faults near a vertical borehole orsedimentary interfaces near a horizontal well.Detecting such inhomogeneities requires amethod that looks deep into the formation andthat is able to detect abrupt changes information properties.

The sonic-imaging technique, sometimescalled the borehole acoustic reflection survey,provides a high-resolution directional image ofreflectors up to tens of feet from the borehole(left).23 Consequently, this technique hassignificant potential application in horizontalwells. To create an image, the tool recordswaveforms of relatively long duration from themonopole transmitters. Receivers must bedistributed around the tool to allow the azimuthsof the reflections to be distinguished.

Complex data processing similar to thatdesigned for surface seismic surveys is applied ina multistep process. First, a compressional-velocity model of the region in the vicinity of theborehole is created using the P head waves.Then, to extract reflected energy, the traditionalsonic arrivals, including P and S head waves andStoneley waves, must be filtered from thewaveforms for each shot. The filtered traces areinput to depth migration, a process that positionsreflections in their correct spatial location usingthe velocity model.

The migration process formally converts a setof amplitude and traveltime measurements intoa spatial image of the formation. This can beviewed as a triangulation process in which thedistance and the dip of a reflector relative to theborehole are determined by the signals recordedat receivers at different TR spacing. Thereceivers at different azimuths around theborehole measure different distances to areflector depending on the azimuth and the dipof the reflector relative to the borehole.

The sonic-imaging technique was developedin the 1980s, but results have improved withadvances in sonic tools and processingmethods.24 The technique has been used to imagesteeply dipping beds from near-verticalboreholes and sedimentary boundaries fromhorizontal wells. For examples of sonic imagingand other applications of sonic measurementssee “Sonic Investigations In and Around theBorehole,” page 14. –LS

> Sonic-imaging data-acquisition geometry. Designed to detect layerboundaries and other inhomogeneities roughly parallel to the borehole, thesonic-imaging technique records reflected signals (red rays) from interfacestens of feet away. Borehole signals (black rays) must be filtered out.

Coal bed

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