4_Rock_Physics.pdf

Chapter 4

Rock Physics Introduction Rock ph Rock phys ysics ics is an es essen sentia tiall par partt of mu multi lticom compo pone nent nt se seism ismic ic tec techn hnol olog ogy. y. Kn Know owled ledge ge of rock-physics principles is required to understand the behavior of P and S reflections at targeted interfaces and to explain why a P-wave image across a stratigraphic interval might look different from an S-wave image although both are correct descriptions of geologic properties that affect P- and S-wave propagation. This chapter considers two sources of rock-physics information — principles found by doing physical measurements on rock samples sam ples in a labo laborato ratory ry and pri princi nciples ples developed developed by ana analyzi lyzing ng theo theoreti retical cal mod models els of rock and fluid systems. The objective is to understand how rock and fluid properties affect P- and S-wave propagation in real rocks.

Laboratory measurements of V P and in nonfractured rock

V S

When George Pickett was a researc researcher her at Shell Oil Company in the 1960s 1960s,, he amassed the early data that demonstrated demonstrated how compre compressional ssional and shear velocities, V P and V S, when used together, segregate into distinct numerical ranges according to rock type (Pickett, 1963). Pickett continued this line of investigation for several years during his post-Shell career as an industry consultant and as a professor at Colorado School of Mines. His most often cited laboratory results were made at frequencies on the order of 100 kHz on small rock samples (3 to 4 cm) (Figure 1). This format, in which P-wave slowness DtP and S-wave slowness DtS are crossplotted, is referred to now as a Pickett plot. Each straight line drawn through the data points of this figure represents a constant V P/V S ratio. Rock porosity increases as the data points move toward the lower right of the crossplot domain. The important point is that although V P and V S vary with porosity, the velocity ratio V P/V S tends to stabilize into a narrow, distinct numerical range for each distinct rock type across a wide range of porosity. This behavior causes the V P/V S ratio to be a more reliable rock-typing parameter than velocity value V P or V S is when either velocity is used alone. The data displayed in Figure 1 were collected using clean shale-f shale-free ree rock samples, and no measurements are displayed for shales. When rocks have a shale component, investigators have found that the V P/V S velocity ratio can exhibit shale-dependent variations. That is demonstrated by the laboratory measurements published by Domenico (1984),

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Multicomponent Seismic Technology

Figure 1. Laboratory data generated by Pickett (1963) show that rock types can be differentiated if V V P and V S velocities are known. Lines of constant slope represent constant velocity ratios V P/V S. Each rock type tends to segregate into a distinct subspace of this ( V P, V S) crossplot domain. All measur mea sureme ements nts were were made on cle clean an (nonsha (nonshaley ley)) samples samples and sho show w tha thatt clea clean n limeston limestones es tend to have a V P/V S ratio of about 1.9, clean dolomites cluster along a value of approximately 1.8, and clean sand sa ndst stone oness ex exhi hibi bitt a wi wide derr but se sepa para rate te rang rangee of 1.6 1.65 5 to 1.7 1.75. 5. Fo Forr eac each h rock rock ty type pe,, al alth thou ough ghV P and V S vary according to porosity, with porosity increasing toward the lower right corner of the crossplot, the V P/V S ratio remains approximately approximately constan constant. t.

whose results are shown in tabular form in Table 1. Even Ev en th thou ough gh th thee ma magn gnit itud udee an and d ty type pe of sh shal alee cont co nten entt ca caus usee th thee ve velo loci city ty ra rati tio o to va vary ry,, th thes esee Rock type V P/V S dataa su dat supp ppor ortt the co conc ncep eptt in intro trodu duced ced by Pi Pick ckett ett (1963) (19 63) tha thatt V P/V S ratios ratios segr segregat egatee into dist distinct inct Sandstone 1.59 – 1.76 numeric num erical al ran ranges ges for dif differ ferent ent roc rock k typ types. es. Not Notee Dolomite 1.78 – 1.84 also that the the numeric numerical al ranges of of V V P/V S that DomeLimestone 1.84 – 1.99 Shale 1.70 – 3.00 nico found for sandstone, dolomite, and limestone aree cen ar center tered ed on the V P/V S values values pub publish lished ed by Pickett (1963). Like Pickett’s work, Domenico’s (1984) measurements also were done on small rock samples in the 100-kHz frequency range. Two important observations provided by Domenico are that V P/V S behavior in shales is quite variable and that the V P/V S ratio for shales is generally larger than it is for sandstones. A third example of a high-frequency laboratory investigation of P- and S-wavefield propagation that needs to be noted is the work reported by Gregory (1976). Some of Gregor Gre gory’s y’s meas measure uremen ments ts on well well-co -conso nsolida lidated ted sed sedimen imentar tary y roc rocks ks are sum summar marized ized in Figure 2, and those data provide several important insights. Table 1. Ranges of V V P/V S in typical rocks. After Domenico, 1984.

Chapter 4: Rock Physics

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For a fixed rock matrix matrix and pore fluid, fluid, the V P/V S rati ratio o te ten nds to in incr crea ease se slightly as porosity increases. This deviati vi ation on fr from om th thee str straig aight ht-l -lin inee tr trend endss sugg su gges este ted d by Pi Pick cket ett’ t’ss (1 (196 963) 3) da data ta appears to occur because S-wave velocity (the denominator in the V P/V S ratio) rati o) ten tends ds to decr decreas easee mor moree rap rapidl idly y than does P-wave velocity as porosity increases. For sed sedimen imentary tary roc rocks, ks, V P/V S values segregate segreg ate into two distinct populations, populations, onee fo on forr fa faci cies es th that at ha have ve br brin inee-fil fille led d pores and a second for the same rock type when its pores contain gas. The V P/V S value in a brine-filled pore system consistently exceeds the V P/V S value in a gas-filled pore system (for thee sa th same me ro rock ck ma matri trix x an and d pr pres essu sure re/ tempera temp erature ture con conditi ditions ons)) whe when n matr matrix ix porosity is greater than 25%. Although the V P/V S value valuess fo forr ga gass-sat satur urate ated d and an d wa water ter-s -satu atura rated ted ro rocks cks co conv nver erge ge at low porosities, the V P/V S value for a br brin inee-sa satu tura rate ted d ro rock ck st stil illl te tend ndss to exceed the gas-saturated value by several percen percentage tage points points..

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Figure 2. Behavior of V V P/V S ratio with porosity for various well-consolidated well-consolidated,, brinebrine-satusaturated, and gas-s gas-saturat aturated ed sedime sedimentary ntary rocks (Gregory, (Grego ry, 1976). The confining pressu pressure re ranged from fr om 0 to 10 10,0 ,000 00 ps psii (6 (689 89 MP MPa) a) fo forr se seve vera rall of th thee measurements. The V P/V S ratio for gas-saturated sedimentary rocks never exceeded 1.7 for the types of rocks that were tested. For a fixed porosity, the V P/V S value for brine-saturated rocks always exceeded the value for gas-saturated rocks. However, the difference might not be statistically significant or measurable at low porosities.

This evid This evidenc encee that V P/V S in a gassatu sa turat rated ed ro rock ck is co cons nsis isten tently tly les lesss th than an V P/V S in a brine-saturated version of that samee roc sam rock k giv gives es seis seismic mic inte interpr rpreter eterss an impor imp ortan tantt too tooll fo forr exp exploi loitin ting g ga gass re rese serrvoirs if multicomponent seismic data are acquired across a prospect so that V P and V S interval velocities can be estimated. Examples of this wave-propagation principle being applied to P and S seismic data acquired in several geologic environments are provided in Chapters 7 and 8.

Rock properties that affect

V P/V S

Numerous rock properties affect V P and V S velocities and consequently might affect a V P/V S ratio. Among those properties are porosity, pore shape, cementation, clay content, fractu fra ctures, res, dif differ ferenti ential al str stress, ess, temp temperat erature ure,, and typ typee of por poree flui fluid. d. Non Nonee of tho those se roc rock k parameters except porosity is accounted for rigorously in the Pickett (1963) crossplot

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(Figur (Fig uree 1) be becau cause se th thee da data ta in tha thatt fig figur uree we were re ge gene nera rated ted us usin ing g on only ly cl clean ean (n (non onsh shale aley) y),, we wellllconsol con solidat idated ed sand sandston stones, es, limestone limestones, s, and dol dolomi omites, tes, and meas measure uremen ments ts wer weree mad madee at roo room m temperature using only dried samples. Gregory’s (1976) work (Figure 2) differs in that he varied the type of pore fluid (brine or gas) and allowed the differential stress to vary from zero (Pickett’s [1963] data) to 10,000 psi (689 MPa). An observation that should be made about all these experimental data is that if a variation in a certain rock property — porosity, for example — induces a quasi-linear change rather than a dramatic, nonlinear change in V P and V S, then that particular rock property ofte of ten n ha hass mi mini nima mall ef effe fect ct on th thee V P/V S rat ratio io be becau cause se th thee in indu duced ced va varia riatio tions ns in th thee nu nume mera rator tor and denominator tend to be proportional and to have a ratio close to one. The essential principle that these selected laboratory studies provide is that V P/V S ratios tend to segregate into distinct numerical ranges according to rock type and type of pore fluid. Some of those numerical behaviors might be linear (such as the Pickett [1963] crossplot shown in Figure 1), and others might be nonlinear (such as the Gregory [1976] plot shown in Figure 2 and the Domenico [1984] data shown in Table 1). The fact that the quantity V P/V S changes according to rock type and type of pore fluid — not that the change cha nge has a sim simple ple linear linear behavior behavior or a more complex complex nonlinear nonlinear behavio behaviorr — makes the availability of both V P and V S data very important to interpreters of multicomponent seismic data. The term rock type is used generically here not only to indicate distinct lithologic units, such as sandstone and limestone, but also to distinguish among subgroups within a lithology class, for example, to distinguish between clean sandstone and shaley sandstone.

Geomechanical properties that affect P and S wavefields Elastic constants for a specific rock type determine the magnitudes of V V P and V S velocities for that rock. For an isotropic medium, the relationships among those velocities and vari va riou ouss ela elast stic ic co cons nstan tants ts ar aree su summa mmari rized zed in Tab Table le 2, tak taken en fr from om Bi Birc rch h (1 (196 966) 6).. An imp impor orta tant nt relationship that can be developed from this table is that in an isotropic medium the velocity ratio V P/V S can be defined as





1

4 2 = + , m 3 V S V P

K

(1)

where K is th thee bu bulk lk mo modu dulus lus (o (orr in inco compr mpress essib ibili ility ty)) of th thee pr prop opag agati ation on med mediu ium, m, an and d m is th thee shea sh earr mo modu dulu luss (o (orr ri rigi gidi dity ty)) of th thee me medi dium um.. Th This is re rela lati tion onsh ship ip is im impo port rtan antt be beca caus usee it he help lpss to explain why the ratio V P/V S decreases in a gas-saturated rock. Gas is much more compressible than liquid; thus, a gas-saturated rock is more compressible than is a brine-saturated or oi oill-sat satur urate ated d ro rock ck.. Be Beca caus usee bu bulk lk mo modu dulu luss K is th thee in inve vers rsee of co comp mpre ress ssib ibil ilit ity, y, th thee va valu luee of for a porous rock can decrease significantly when pores change from brine saturated to K for gas saturate saturated. d. In co cont ntra rast, st, the sh shea earr mo modu dulu luss m is re relat lativ ively ely un unaf affec fected ted by va vari riati ation onss in po pore re flu fluid id.. Th This is reduction in bulk modulus, coupled with little or no change in shear modulus, causes the

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Relationship onshipss among elasti elasticc constants of an isotropic medium. From Birch, 1966. Table 2. Relati K

l + 2m /3

m

E

l

3l + 2m l+m

··

− l K −

··

9K

··

9K m + m 3K +

··

− l 3K −

E m

3(3m − E ) ··

K 2 2m /3 − 2m E −

··

m

··

3K − E 3K 9K − E

3m − E

l

1 + s 3s

l

m

2(1 + s ) 3(1 − 2s )

2m(1 + s )

m

3K (1 (1 2 2s )

3K

··

(1 + s )( )(1 − 2s )

E

··

3(1 − 2s ) r (V P

2

− 43 V S 2 )

9r V VS 2 R2 2 2

3 R2 + 1

l

2 ( l + m) l − l 3K − − 2m 3K − 2(3K + m)

− E 3K −

6K

2s 1 − 2s s

1 + s s E s

(1 + s )( )(1 − 2s )

r (V P 2 − 2V S 2 )

r V VS 2 = m

l + 2m

··

3K 2 2l

3(K 2 l)/2

+ 4m /3 K +

··

4m − E 3m − E

··

E /(2m) 2 1 m

··

s

r V VP 2

s

+ E 3K + 3K − E 9K −

3KE − E 9K −

··

l

1 − s s

··

m

2 − 2s 1 − 2s

··

1 − s 3K 1 + s

··

E E (1 − s ) (1 + s )( )(1 − 2s ) 2 + 2s

See below.

l

1 − 2s 2s ··

1 − 2s 3K 2 + 2s

··

··

= ( R1 2 − 2)/( R1 2 − 1) = (3 R2 2 − 2)/(3 R2 2 + 1) = 2 (3 R3 2 − 1)/(3 R3 2 + 1). 2s = K bulk modul modulus; us; E Young’ Young’ss modul modulus; us; m shear modulu modulus; s; l Lame´ ’s consta constant; nt; s 2 2 2 2 R1 = V P /V S ; R2 = K /(r V VS ); R3 = K /(r V V P ); b = compressibility = 1 /K . ¼

¼

¼

¼

¼

Poisson’s Poisson ’s ratio ratio;; r

¼

density;

velocity velocit y rati ratio o V P/V S to ha have ve re redu duced ced va value luess in ga gass-sa satu turat rated ed zo zone ness co comp mpar ared ed wi with th the velocity ratio in laterally equivalent brine-saturated units. This concept will be an important interpretation principle in some of the case histories given in Chapters 7 and 8 of this book. P and S wavefields reflect from boundaries where there is a change in the elastic impedance of the rock layers. Two types of petrophysical properties control the value of elastic elas tic imp impedan edance ce in ind individ ividual ual roc rock k laye layers: rs: (1) elastic properties properties related related to the roc rock k matrix and (2) petrophysical properties related to the fluid that occupies the pore spaces of the rock. P-waves travel through both elastic material and fluids; thus, any variation in either the rock matrix (such as a change in mineralogy or porosity) or in the type of fluid occupying the pore spaces can create a discontinuity in the P-wave impedance of the rock system. A

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Figure 3. Relationships between petrophysical conditions that can occur at an impedance boundary and the existence of P and S reflections at that boundary. P-wave reflections are created at boundaries where a change occurs in rock matrix or pore fluid. In contrast, S-waves are affected only weakly by changes in pore fluid. An S-wave reflection occurs at some pore-fluid interfaces because the bulk density changes across those boundaries. Rock matrix 1 = rock matrix 2; pore fluid 1 = pore fluid 2.

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P-wave refl P-wave reflecti ection on thu thuss occu occurs rs at boun bo unda dari ries es at wh whic ich h th ther eree is a change in either the rock matrix or th thee po pore re flu fluid id or bo both th (Fi Figu gurre 3). S-waves S-w aves,, in con contra trast, st, pro propapagate ga te th thro roug ugh h el elas asti ticc me medi diaa bu butt not through fluids. Consequently, a variation in the properties of the rock matrix can create a reflecting boundary for S-waves, but a variation in pore fluid will create only a small (often negligible) Swave wa ve re refle flect ction ion bo boun unda dary ry.. If an S-wavee reflectio S-wav reflection n coef coefficient ficient occurs at a fluid bound boundary, ary, that coef coef-ficient usually exists because the bulk bu lk de dens nsity ity of the ro rock ck sy syst stem em varies across the fluid boundary. Those Tho se obs observ ervatio ations ns pro provid videe valuabl valu ablee geo geolog logic ic ins insigh ights ts whe when n both P and S reflection data are acquired across a prospect area:

When P an When and d S re reflec flectio tions ns oc occu curr at th thee sa same me de dept pth h coo coord rdin inate ate,, th thee pr prefe eferr rred ed in inter terpr preta etatio tion n is that the reflecting boundary at that depth is associated with a variation in the rock matrix. A variation in the pore fluid at that boundary might or might not occur. When a P reflection occurs at a boundary but but there is no S reflectio reflection, n, a plausible interpretation is that the boundary marks a variation in pore fluid and not a change in rock matrix. An equally plausible interpretation is that the bulk modulus changes across the boundary, but the variation in shear modulus is negligible. Using that premise, there can be interfaces between different rock matrices that P-waves see but S-waves do not. When there is an S reflectio reflection n but no corres correspondin ponding g P reflectio reflection, n, the boundary might be one at which mineralogy, cementation, and porosity conditions cause significant variations in V S but negligible changes in V P.

Laboratory measurements of velocity behavior in fractured rock Shear-wave splitting is an elegant theory, and it is important to verify the theory with physical tests. An investigation by Rathore et al. (1995) is helpful in that regard. Two labora rato tory ry st stud udie iess — on onee by So Son nde derg rgel eld d an and d Rai (1 (19 992 92)) an and d on onee by Xu an and d Ki King ng (1 (198 989) 9) — ar aree particularly informative for understanding the physics of fast-S and slow-S propagation in fractured rock samples and are considered in this chapter.


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The test-sample setup used by Sondergeld and Rai (1992) is illu illustra strated ted in Fig Figure ure 4. A piez piezocer oceramic amic elemen elementt was secured secured to one end of a cylindr cylindrical ical volume of laminated shale to serve as an S-wave source. A similar element was positioned at the oppo op posi site te en end d of th thee cy cylin linde derr as an an SS-wa wave ve sen senso sor. r. Th This is la layer yered ed propagation medium and the fact that the source-receiver geometry caused S-waves to propagate parallel to the embedded interfaces interf aces of the rock sample combined to make a good simulation of S-wave propagation through a system of vertical fractu fra ctures. res. Bot Both h the sou source rce and the rec receive eiverr elemen elements ts were were vector-type sensors, and the polarity of the data depended on the orientations of the positive-polarity end of each element. The vector nature of these piezoceramic elements replicates the vector sources and receivers used in actual S-wave seismic field-data acquisition. In several key tests, the source remained in a fixed orientation relative to the plane of the simulated fractures, and the receiver element was rotated at azimuth increments of 10 to determine the azimuth dependence of S-wave propagation through the sample. The test results are illustrated in Figure 5 as an end-on view of the test sample from the source end. The objective was to simulate the propagation propagation of a fast-S (or S1) mode, in which the source-displacement source-displacement vector is parFigure 4. Laboratory alle al lell to th thee fr frac actu ture re pl plan anes es (F (Fig igur uree 5a 5a), ), an and d th then en to si simu mula late te th thee measurements measur ements of S-wave propagation of a slow-S (or S2) mode, in which the displacepropagation propaga tion through a ment me nt ve vecto ctorr is pe perp rpen endi dicu cular lar to the fr fract actur uree pl plan anes es (F (Fig igur uree 5b 5b). ). simulated simula ted fractu fractured red meAs will be emphasized later in this chapter, the difference dium. In most tests, an between S1 and S2 velocities is small when fracture density S-wave source element (number of fractures per unit length or unit volume) is small, remained at a fixed azbut the difference in velocities can be rather significant when imuth while an S-wave fracture density is large. receiver element was The positive-polarity end of the source is oriented in the rotated at azimuth incredire di rect ctio ion n in indi dica cate ted d in Fi Figu gure re 5 by th thee ar arro rowh whea ead d on th thee ments of 10 to determine the azimuth indepensource vector. For response A, the positive polarity of the redence of S-wave propaceiver is oriented the same as the source. For response C, the gation through a fracture receiver has been rotated, as shown in Figure 4, so that its system. positive-polarity end points in an opposing direction. Thus, the polarity of wavelet C is opposite to the polarity of wavelet A. In actual seismic fieldwork with S-wave sources and receivers, the positive polarities of all receivers are oriented in the same direction across a data-ac data-acquisitio quisition n template so that wavelet polarities are identical in all quadrants around a source station, as illustrated in Figure 17 of Chapter 1. At receiver orientations B and D in Figure 5, the receiver is orthogonal to the source vector, which produces zero-amplitude responses. 8

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Figure 5. Data acquired using the test arrangement illustrated illustrated in Figure 4 to simulate S-wave propagation propag ation through a fractu fractured red medium.. (a) The illumi medium illuminating nating S-wavee displ S-wav displacement acement vector is parallel parall el to the test-sample fractures fractu res to simula simulate te fastfast-S S propagation. As the source stays fixed, the posit positive-pol ive-polarity arity end of the receiver is rotated at angular increments of 10 relative relati ve to the posit positive-pol ive-polarity arity orientation of the sourcedisplacement displ acement vector. Every transmitted response is a fast-S wavelet. The dashed circle labeled T0 defines time zero. Arrowheads Arrow heads define the posit positiveivepolarity ends of the source and receiver elements. (b) The same test is repeated with the illuminating S-wave displa displacement cement vector oriented perpendicular to fractures to simulate the propagation of a slow-S mode. After Sondergeld and Rai, 1992, Figures 4 and 6.

a)

Transmitted fast-S wavelets B

90° To

C

R e c e i v e r o r i e n t a t i o n

180°

0°

A

8

270°

Source vector

D

Fractured sample Receiver orientation

Transmitted slow-S wavelets

b)

B

90° To

R e c e i v e r o r i e n t a t i o n

C 180°

0°

A

The experimental data illustrated in Figure 6 simulate thee ge th gene nera rall cas casee of SS-wa wave ve illumination of a fracture sys270° tem in which the illuminating illuminating source vector is polarized at an ang angle le F relat relativ ivee to th thee Source vector aligned fractures. The waveFractured sample D fields that propagate through Receiver orientation thee me th medi dium um ar aree now now a co comb mbiinatio na tion n of fa fastst-S S and slo sloww-S S wavelets and not S1-only or S2-only wavelets as were generated in the experimental data displayed in Figure 5. Wavelets A, B, C, and D are again the responses observed when the receiver is parallel to or orthogonal to the illuminating source vector. The observed data contain both S1 and S2 arrivals. The length of the propagation path through throu gh the sample is such that the dif differenc ferencee in S1 and S2 traveltimes causes the S1 and S2


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Transmitted wavelets wavelet wave letss to no nott ov overl erlap ap.. In re real al B S2 seismic data when a fracture interval is thin and the differA¢ S1 B ¢ ence in S1 and S2 traveltimes is not too large, the response R e c 90° e i will wi ll be a co comp mplic licate ated d wav waveev e To r o r form representing the sum of i e n t a t i o n partial par tially ly ove overla rlappi pping ng S1 and f A S2 wavel wavelets. ets. The wav wavele elets ts at C 180° 0° positions A′ , B′ , C′ , and D′ illustrate lustr ate impor important tant S-wa S-wave ve phys phys-ics.OnlyanS1 mode modeprop propagates agates paralle par allell to the fra fractu cture re pla planes nes 270° ′ ′ (responses A and C ). Only an D¢ S1 S2 mode mode pr propa opagat gates es per perpen pen-C¢ dicula dic ularr to the fr fractu acture re pla planes nes S2 Source vector (responses B′ and D′ ). Fractured sample D The experiment documenReceiver orientation ted in Figure 7 illustrates the results that should be observed Figure 6. End-on view of the fractured test sample from the when S-wave dat ataa are ac ac-- source end. The source vector is polarized at an angle F relative to the azimuth of the fracture planes. As the source quire qu ired d acr acros osss a fr frac actur turee sy syssremains fixed, the receiver again is rotated 360 at angular tem as a 3D survey in which increments of 10 relative to the orientation of the positivethere is a full azimuth range polarity of the S-wave source vector. These test data show that bet etw wee een n sele lect cted ed pai airrs of only a fast-S (or S ) mode propagates parallel to fracture 1 sources and receivers. In this planes (responses (responses A′ and C′ ), and only a slow-S (or S2) mode test, tes t, the so sour urce ce an and d rec receiv eiver er propagates perpendicular to the fracture planes (responses B′ are rotated in unison so that and D′ ). A mixtur uree of S1 and S2 is ob obse serv rved ed at al alll ot othe herr az azim imut uth h orientations. ations. Amplit Amplitude ude behavio behaviorr is aff affected ected by the continua continually lly the pos positiv itive-p e-pola olarity rity end endss of orient changin ging g ang angle le bet betwee ween n the vec vector tor ori orient entatio ations ns of the pos positi itiveveboth always point to the same chan azimuth. This source-receiver polarity ends of the source and receiver elements. After geom ge ometr etry y is wh what at is ac accom com-- Sondergeld and Rai, 1992, Figure 7. plis pl ishe hed d wh when en fie field ld da data ta ar aree conver con verted ted fro from m inl inline ine/crossline data-acquisition space to SV-SH coordinate space, as discussed in Chapter 3. The test data show convincing proof that only a fast-S mode propagates parallel to fractures and an d on only ly a sl slow ow-S -S mo mode de pr prop opag agate atess pe perp rpen endi dicul cular ar to fr fract actur ures es.. At all int inter ermed mediat iatee azi azimu muth thss between those two directions, S-wave propagation involves a mixture of fast-S and slow-S wavefields. The experimental results of Xu and King (1989) are presented in Figure 8. In this test, P, S1, and S2 modes propagated through a test sample before and after the sample was cracked to create a series of internal fracture planes. Wave transit times through the sample were measured to determine the effect of cracks on each wave mode. For both the cracked and uncracked samples, transit-time measurements were made for a series 8

8

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of co confi nfini ning ng pr pres essu sure re co cond nditi ition onss vary va ryin ing g fr from om 1. 1.4 4 MP MPaa to al almo most st 21 MPa. P-wave traveltime behavS2 S2 iorr is de io desc scri ribe bed d in Fi Figu gure re 8a 8a.. S1 S 1 S1 and S2 traveltimes are summarized in Figure 8b and 8c, respectively. R e c 90° e i To v e On each data panel, the transit r o r i e n time for uncracked rock is marked t a t i o n as A. Point B indicates the traveltimee thr tim throug ough h the cra cracke cked d sam sample ple.. 180° 0° The traveltimes for P and S1 modes exhib exh ibit it litt little le pre pressu ssure re dep depend endenc encee through a fracture system Figure 7. S-wave propagation through over the applied pressure range for observed observ ed when the source and receiver are aligned in the cracked or uncracked media. There same azimuth. S1 is the fast-S mode. S2 is the slow-S is a no notice ticeabl ablee dec decrea rease se in tra transi nsitt mode. The azimuth angle in this graphic defines the time for the S2 mode as confining orientation of the positive-polarity end of both the source pressure is increased. This behavior and receiver relative to the fracture planes, whereas the is in ind dic icat ated ed by th thee da dasshe hed d li line ne angle in previous figures defines the orientation of the receiver relative relative to the source. Only S1 propagates pardrawn across the S2 waveforms in alle al lell to fr frac actu ture res, s, an and d on only ly S2 pro propag pagates ates perp perpend endicul icular ar to Figure 8c. fractures. After Sondergeld and Rai, 1992, Figure 10. The wave physics confirmed by this test is that P and S1 velocities decrease by only a small amount, if any, when the propagation medium changes from nonfractured rock to an aligned-fracture condition. The observed delay in transit time is less than 2 ms for each of those wave modes when fractures are present. In contrast, the delay in traveltime for the S2 modes exceeds 5 ms, more than twice the transit-time delays of the P and S1 modes. Data point B for the S2 mo mode de pr prop opag agati ating ng in the cr crack acked ed ro rock ck is sel select ected ed ar arbi bitra trari rily ly fr from om th thee wav wavef efor orm m observed at the midpressure range used in the test. Transmitted wavelets

Reflectivity from fractured rock Severall roc Severa rock-p k-phys hysics ics mod models els hav havee been pro propos posed ed for ana analyzi lyzing ng fra fractu ctured red med media ia (Nishizawa, 1982; Schoenberg and Douma, 1988; Jakobsen et al., 2003; Hu and McMechan, 2009) and for describing interactions between fractures and porosity (Thomsen, 1995; Hudson et al., 1996). A model proposed by Hudson (1981) has proved to be valuable for analyzing elastic wavefield propagation in a vertical-fracture medium such as the rock samples in the tests conducted by Sondergeld and Rai (1992) and by Xu and King (1989). Hudson’s (1981) theory allows the elastic stiffness matrix of a fractured medium to be defined in terms of crack density, aspect ratio of the cracks, bulk modulus and density of fracture-filling fluid, Lame´ constants (l, m ) of the isotropic host rock, and type of fracture distribution (isotropic, single fracture set, multiple fracture sets). The coefficients of the


a)

Confining pressure (MPa)

A B Time delay < 2 ms B

20.7

g n i k c a r c r e t f A

13.8 6.9 1.4

135

A

P-wave propagation

P

20.7

g n i k c a r c e r o f e B

13.8 6.9 1.4 10

20

30

Test sample

40

Traveltime (ms)

b)

A B


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13.8 6.9 1.4

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A

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13.8 6.9 1.4 10

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c)

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20.7


B 13.8 6.9 1.4

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13.8 6.9 1.4 10

20

30

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40

Traveltime (ms)

Figure 8. Traveltime measurements through a test sample before (data point A) and after (data point B) cracking the sample to create a propagation medium of quasiquasi-aligned aligned fractures. fractures. Confining pressure was varied as labeled between measurements. (a and b) A principal finding is that P and S1 react weakly to the presence of fracture, but (c) S2 reacts strongly. After Xu and King, 1989. Courtesy of M. S. King. Used by permission.

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stiffness matrix then can be used to calculate V P and V S, which allows P and S reflectiv reflectivities ities to be analyzed across fracture targets. One application of Hudson’s (1981) model is illustrated in Figure 9. Fracture planes 1 through 6 shown in this model are part of a single set of vertical fractures that form a horizont zo ntalal-tr tran ansv sver erse se iso isotr trop opic ic (H (HTI TI)) med mediu ium m tha thatt ha hass a ho hori rizo zont ntal al sy symm mmetr etry y ax axis is AA (w (with ith th thee shaded vertical plane passing passing through AA being a symmetr symmetry-axis y-axis plane) and a vertical isotropy plane BB. The top of this fracture system is horizontal interface CCDD. Some of the log data used to investigate P and S reflectivity across an area of interest in west Texas using this Hudson (1981) model are displayed in Figure 10. Interface CCDD from Figure 9 is represented by the dashed line separating layer 1 and layer 2 on the log curves. For modeling purposes, layer 1 above interface CCDD is assigned properties: 4000 m/s, V S 2200 m/s, and r b 2.4 gm/cm3. V P In this modeling, downward-traveling elastic waves are constrained to arrive at interface CCDD from only two azimuth directions: (1) in the direction of vertical symmetryaxis plane AA or (2) in the directio direction n of vertical isotropy isotropy plane BB. From log data, the fracture layer (layer 2) is assigned properties: ¼

†

†

†

†

†

¼

¼

fast V P 5390 m/s; slow V P 5385 m/s fast V S 2970 m/s; slow V S 2618 m/s r b 2.59 gm/cm3 fracture density 0.1 aspect ratio ratio of fractures fractures 0.0001 ¼

¼

¼

¼

¼

¼

¼

Those petrophysical petrophysical properties, combined with the anisotropic reflectivity analyses of Ru¨ ge gerr (2 (200 001) 1),, re resu sult lt in th thee re refle flect ctiv ivit ity y re resp spon onse sess pl plot otte ted d in Fi Figu gure re 11 11.. In th thee no nota tati tion on us used ed in

B D

D

A

f

C

C A

f

1

2

3

4

5

6 B

AA = symmetry axis = Raypath

BB = is isot otro rop py pl plan ane e

f = = angle of incidence

= Parti Particlecle-disp displac laceme ement nt vect vector or

CCDD CCD D = top int interf erface ace

1 = fr frac actu ture re pl plan ane e

Figure 9. Model used to describe elastic wave propagation in an HTI medium.

Chapter 4: Rock Physics Velocity (km/s)

GR API 0

Grayburg

50

100

2

4

137

Density (g/cm3) 6

1.5

2

2.5

3

1350

1400

1450

San Andres

) t f ( h t 1500 p e D

V S

Layer 1

V P

1550

Layer 2

1600

1650

Figure 10. Log data used to define rock properties used in an application of Hudson’s (1981) model of fractured rock.

a)

b)

0.15

P-PB

P-PA

0.1

0.15

0.1

0.05

0.05

t n e i c i f f 0 e o c n o i t –0.05 c e l f e R

t n e i c i f f 0 e o c n o i t –0.05 c e l f e R

–0.1

SV-SVB SH-SHB

–0.1

P-SVA P-SVB

–0.15

SV-SVA

–0.15 SH-SHA

–0.2

–0.2 0

10

20

30

40

P-wave angle of incidence (°)

50

0

5

10

15

20

25

S-wave angle of incidence (°)

A, B = axis of raypath direction

Figure 11. (a) P-P and P-SV reflectivities and (b) S-S reflectivities for waves propagating in a brine-filled HTI medium, as defined in Figure 9. Subscript A indicates that the incident raypath is confined to symmetry plane AA. Subscript B indicates that the incident raypath is confined to isotropy plane BB (Figure 9).

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this plot, subscripts A and B are the symmetry and isotropy directions shown in Figure 9. These reflectivity curves show several principles: †

†

†

†

For this particular fracture layering, P-P reflectivity does not change with azimuth (curves PPA and PPB are identical). Some fractured-layer systems create measurable azimuth azim uth-de -depen penden dentt var variati iations ons in P-P refl reflecti ectivit vity y and velo velocity city.. (Tw (Two o suc such h exam examples ples are included in this chapter in Figures 20 through 23 below). However, in numerous fracture systems, such as the one modeled in Figure 11, azimuth-dependent variations in P-P seismic attributes are negligible or are below resolution. P-SV reflectivity reflectivity does vary with the azimuth-approach azimuth-approach direction of the incident P-wave P-wave relative to vertical fractures (curves P-SVA and P-SVB differ). P-SV PSV refl reflec ectiv tivity ity is les lesss wh when en the in incid ciden entt PP-wa wave ve ap appr proa oache chess no norm rmal al to fr fract actur ures es (s (slo lowwS direction; curve P-SVA) than when the P-wave approaches parallel to fractures (fast-S direction; curve P-SVB). Because SV-SV and SH-SH modes have orthogonal particle-displacement vectors, they react re act to or orien iented ted fr fract actur ures es in op oppo posin sing g way wayss fo forr ea each ch azi azimu muth th di dire recti ction on of ra rayypath pa th ap appr proa oach ch.. If the ill illum umin inati ating ng ra rayp ypath ath is ali align gned ed alo along ng sy symme mmetr try y ax axis is AA (F (Figu igure re 9) 9),, an SH-SH mode propagating through through the fractu fracture re layer is a fast-S wave because its particle-displacement vector is parallel to fracture planes, but an SV-SV mode is a slow-S wave because its particle-displacement vector is orthogonal to fracture planes. If the illuminating raypath approaches along isotropy plane BB, then an SH-SH mode is a slow-S wave, and an SV-SV mode is a fast-S wave. Thus, as shown in Figure 11, SH-SH waves propagating along symmetry axis AA have a larger reflectivity amplitude than do SH-SH waves traveling along isotropy axis BB. The reflectivity curves shown for an SV-SV mode have the opposite behavior, with reflectivity SV-SVB being larger than reflectivity SV-SVA.

The mo The mode dell re resu sult ltss sh show own n in Fi Figu gure re 11 as assu sume me th that at fr frac actu ture ress ar aree fil fille led d wi with th br brin inee an and d th thee fracture density in Hudson’s (1981) model is fixed at 0.1. Hudson and Liu (1999) and Liu et al. (2000) extend this model to higher fracture densities. Different reflectivities occur if the fracture-filling fluid is gas rather than brine and/or if fracture density varies. For complete pl etene ness ss of th thee an analy alysi sis, s, th thee cu curv rves es in Fig Figur uree 12 ill illus ustra trate te th thee typ types es of re refle flecti ctivi vity ty va varia riatio tions ns that can be encountered when fracture density varies and when fractures are filled with brine or gas.

Slow-S velocity and fracture density Physical measurements of S-wave transit time through fractured media, such as those documented in Figure 8, and numerical modeling of velocity-based S-wave reflectivity, such as that described in Figure 12, establish the relationship between slow-S velocity and fracture density illustrated in Figure 13. This model simulates a seismic profile traversing an earth system consisting of blocks of anisotropic rock bounded by blocks of isotropic rock. Anisotropic conditions in blocks B, C, and D are caused by aligned fractures which have different fracture density (FD) and fracture azimuth (F) from block to block.

139

Chapter 4: Rock Physics Fracture density (FD) from 0 to 0.1 in steps of 0.02 Gas-filled fractures

a)

0.1

0.1

0.1

SH-SH

0.1 P-SV 0.05

FD

0.09

0 FD

0.08

t n e i c i f f e 0 o c n o i t c e l f e –0.05 R

FD 0 P-P

0

SV-SV

t n e 0.07 i c i f f e 0.06 o c n o i t 0.05 c e l f e 0.04 R

0.1 0.1

SV-P

0.03

0 FD

0 FD

0.02

–0.1

0.01

0.1

0 0

10

20

30

40

50

0

P-wave incidence angle (°)

10

20

30

40

50

S-wave incidence angle (°)

Fracture density (FD) from 0 to 0.1 in steps of 0.02 Brine-filled fractures

b)

0.1

0.1 SH-SH

0.1 P-SV

0.1 0.09

0 FD

0.05

FD

0.08

t n e i c i f f e 0 o c n o i t c e l f e –0.05 R

t n e 0.07 i c i f f e 0.06 o c n o 0.05 i t c e l f e 0.04 R

P-P

FD 0 0.1

0.1 0.1

0.03

SV-P

0.02

–0.1

0

SV-SV

0 FD

0 FD

0.01 0

10

20

30

40

P-wave incidence angle (°)

50

0

0

5

10

15

20

25

S-wave incidence angle (°)

Figure 12. Eff Effects ects of fractu fracture re density and fractu fracture-fil re-filling ling fluid on reflectivity reflectivity of each componen componentt of a seismic elastic wavefield from an isotropic-fractured layer. (a) Reflectivities for gas-filled fractures. (b) Reflectivities for brine-filled fractures. Fracture density FD is defined as FD N(Q3/V), where V is a unit volume, Q is the effective radius of a fracture, and N is the number of fractures in volume V. Gas-filled and brinebrine-filled filled fractures fractures have essentially essentially the same P-SV, S-S, and SV-P reflecti reflectivities vities,, but P-P reflect reflectivity ivity differs. differs. ¼

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Figure 13. Relationship between betwee n slowslow-S S velocit velocity y (S2) and fracture density (FD). As fracture fractu re densit density y increas increases, es, S2 velocity decreases. In contrast,, fasttrast fast-S S velocity velocity S1 and Pwave velocity V P do not change, or they change by only minor amounts across Blocks A through E. In isotropic Blocks A and E, there is no S-wave splitting and only one S-wave velocity V S. In all blocks (A through E), fast-S velocity V S, the velocity veloci ty in the nonfra nonfractured ctured rock. Mineralogy, porosity, and pore fluid do not change across the profile. The only earth properties that vary from block to block are fracture fractu re densit density y and orientation.

c o p i c r o s o t r I s

X

S e i s m i c p r o of i l e A B

Z

1 o n e z e ) u r e 1 c t u F 1 F a a r F F D 1, 2 ( n e o z e ) 3 u r e 2 c t u F 2 F a a r o n e F F D 2, z e ) ( u r e F 3 c t u a a r c c F ( F D 3, o p i r o r Is o t s C D E X

¢

¼

y t i c o l e v S w o l S

V S

V S

V 1 V 2

V 3

FD1 < FD3 < FD2 V 1 >V 3 >V 2 Profile coordinate

When th When this is ea eart rth h sy syst stem em is il illu lumi mina nate ted d wi with th an el elas asti ticc wa wave vefie field ld,, sl slow ow-S -S ve velo loci city ty ha hass th thee generalized behavior diagrammed below the earth model shown in Figure 13. As fracture dens de nsity ity FD in incr creas eases es,, slo sloww-S S ve veloc locity ity (S2) de decr crea ease ses. s. Th Thee ma magn gnit itud udee by wh whic ich h S2 decreases is a qualitative, not quantitative, indicator of fracture density. S2 velocity behavior can be used to predict fracture density in a quantitative manner only if fracture density can be determined determi ned independently independently at severa severall calibrat calibration ion points across seismic image space. Establishi lis hing ng su such ch cal calib ibra ratio tion n is dif diffic ficult ult.. Re Restr strict ictin ing g th thee us usee of S2 ve velo loci city ty be beha havi vior or to th that at of on only ly a qualitative predictor of fracture density is still most important and valuable for understan st andin ding g fr fract actur uree dis distr trib ibuti ution on acr acros osss are areas as ima image ged d wit with h mu multi ltico comp mpon onent ent sei seism smic ic da data. ta. Va Variriations in fracture azimuth F affect only the polarization direction of the slow-S mode, not the magnitude of S2 velocity. Fast-S velocity in a fractured medium is the same as in an unfractured sample of that same medium (Figure 8b). S1 velocity might decrease by a small amount if fracture density is su sufffic ficie ient nt to al alte terr bu bulk lk de dens nsit ity; y; ot othe herw rwis ise, e, it is re reas ason onab ably ly co corr rrec ectt to as assu sume me th that at S1 ha hass th thee same magnitude in fractured rock as in nonfractured sections of the same rock.

Fast-S and slow-S amplitudes in fractured rock The rock-physics studies of S1 and S2 propagation in fractured rock that have been documented by Sondergeld and Rai (1992) provide valuable insights into the physics of S-wave propagation in media that have aligned fractures. The research findings of Son-


141

dergeld and Rai (1992) are particularly important for understanding azimuth-dependent variations in S1 and S2 wavelet amplitudes when multicomponent seismic data are used to int interp erpret ret fra fractur cturee pro proper perties ties.. To illu illustr strate ate the wav wavee phy physics sics,, the lab labora orator tory y dat dataa of Sondergeld and Rai (1992) displayed in Figure 6 are presented again in Figure 14 with theoretical S-wave radiation patterns from Figure 17 of Chapter 1 superimposed on the data. Using the notation for isotropy and symmetry axes introduced in Hudson’s (1981) model (Figure 9 above), the S1 mode expands in opposing directions as circular radiation patterns centered on isotropy axis BB, and the S2 mode expands in opposing directions as two circular radiation patterns centered on symmetry axis AA. Thee ra Th radi dial al di dista stanc ncee fr from om the intersection of isotropy and symmetr try y ax axes es AA and BB to th thee boundary of any of the four circular rad radiati iation on patt pattern ernss defi defines nes the S2 amplitude amplitu de of the S-wave mode traA B S1 veli ve ling ng in th thee ra radi dial al di dire rect ctio ion n in whic wh ich h th that at li line ne is dr draw awn n. Th This is radialrad ial-dis distanc tancee con concept cept exp explain lainss T=0 S1 the azimuthazimuth-depend dependent ent amplitud amplitudee S2 variations of S1 and S2 wavefields obser ob served ved to pr prop opag agate ate thr throu ough gh fr fracactured media in laboratory tests. In Figure 14, the two S1 circles define thee am th ampli plitu tude de be beha havio viorr of th thee in inne nerr ring of wavelets (the fast-S waveS2 S1 lets) observed in laboratory measurements, and the two S2 circles defi efine ne th thee am ampl plit itu ude beh ehav avio iorr S1 A of the outer ring of wavelets (the B S2 slow-S wavelets). Source vector The rock samp mple less used in Fractured sample thiss lab thi labora orator tory y test testing ing wer weree con con-Figure 14. Ra Radia diati tion on pat patter terns ns fro from m Fi Figur guree 17 of Cha Chapte pterr stru st ruct cted ed so th that at th thee tr trav avel el pa path th 1 are combined with azimut azimuth-depend h-dependent ent variations of S1 from source to receiver was long and S2 wavelet amplitudes observed in laboratory meaenou en ough gh to ca caus usee S1 and S2 wavelets surements of Sondergeld and Rai (1992) taken from to be separated in time and to not Figure 6 of this chapter. AA is the symmetry axis of the overla ove rlap. p. In real mul multico ticompo mponen nentt fracture system; BB is the isotropy axis. A radial line field data, the thickness of a fracdrawn from the intersection of AA and BB to the cirtured-rock interval might be such cumference cumfere nce of any radiation circle defines the amplitude thatS1 andS2 wav wavelet eletss that tra traver verse se of the S-wave mode propagating in the azimuth of that thee int th inter erval valsep separ arate ate by on only ly a sm small all radi ra dial al li line. ne. Ci Circ rcle less la label beled ed S1 de defin finee th thee amp ampli litu tude dess of th thee time interval and create complex inner ring of wavelets (fast-S wavelets). Circles labeled waveforms formed by overlapping S2 define the amplitudes of the outer ring of wavelets (slow-S wavelets). S1 and S2 wavelets.

142


Fast-S and slow-S wavelet phase in fractured rock The pr The prece ecedi ding ng an analy alysi siss es estab tablis lishe hess the pr prin incip ciples les of azi azimu muth th-d -dep epen ende dent nt va varia riatio tions ns in S1 and S2 amplitudes in fractured media, but it does not address azimuth-dependent variations in S1 and S2 wavelet phases. The wavelet phases observed in the laboratory rock-physics studies of Sondergeld and Rai (1992) are not the same as those observed in seismic field data because the receivers used in those authors’ laboratory work pointed in a different azimuth for each data trace that was recorded. In contrast, horizontal sensors used to acquir acq uiree mu multi ltico comp mpon onen entt da data ta in act actua uall fie fieldw ldwor ork k ha have ve to be de depl ploy oyed ed in the sam samee azimuth orientation at every receiver station (Figure 8 of Chapter 2) or at least in known azimuths that can be adjusted to a consistent orientation. Thee di Th diag agra ram m in Fig Figur uree 15 wil willl be us used ed to ad adjus justt th thee ph phase asess of lab labor orato atory ry-m -meas easur ured ed S1 and S2 wave wavelet letss to th thee wavelet wavelet ph phase asess ob obser serve ved d in real fiel field d data. data. In thi thiss dia diagra gram, m, BB is again again the the isot is otro ropy py ax axis is of th thee fr frac actu ture re sy syst stem em,, an and d AA is th thee sy symm mmet etry ry ax axis is.. Th Thee in inte ters rsec ecti tion on of ax axes es AA andBBrepresentsastackingbin,eitherasuperbinoraconventionalcommon-midpoint(CMP) bin in,, in se seis ismi micc im imag agee sp spac ace. e. Th Thee da data ta ar aree se segr greg egat ated ed in into to fo four ur qu quad adra rant ntss la labe bele led d 1, 2, 3, an and d4 surrou sur roundi nding ng the stac stackin king g bin whe where re azim azimuth uth-de -depen penden dentt tra traces ces will be gath gathere ered d and sum summed med.. To define wavelet phase, a whit wh itee tr trou ough gh wi will ll be de defin fined ed as positive polarity, and a black 1 peak will be defined as negative S2 polarity. Using those definitions, A B S1 the polarities of the laboratorymeasured S1 and S2 wavelets in each of the four azimuth quadT0 rant ra ntss ar aree su summ mmar arize ized d in Tab Table le 3 using P to indicate positive polari la rity ty an and d N to re repr pres esen entt ne nega gati tive ve Stacking bin polarit pol arity. y. This tabu tabulati lation on sho shows ws 4 2 that th at if th thee lab labor orato atory ry wav wavele elets ts aree su ar summ mmed ed to ma make ke a si sing ngle le stacked trace at the central stacking bin, the wavelet sum is zero, and an d nei eith ther er an S1 nor an S2 waveS1 lett wi le will ll be ob obse serv rved ed in th thee st stac acke ked d B A trace. S2 If the data-pr data-processin ocessing g objecSource vector Fractured Fractur ed sample tive is to extract the fast-S mode 3 Receiver orientation from fr om rea reall se seism ismic ic fie field ld da data, ta, the these se labo la bora rato tory ry da data ta ca can n be ph phas aseeFigure 15. Data from Sondergeld and Rai (1992) segreadju ad just sted ed to re repr pres esen entt ho how w th thee gated into azimuth quadrants for phase analysis. BB is the mode-extractio mode-e xtraction n proces processs works isotropy axis of the fracture system; AA is the symmetry with wi th fie field ld da data ta ac acqu quir ired ed wi with th axis. Circle T0 defines time zero.


143

constant-azimuth sensors. The required phase adjustments are summarized in Table 4. In this analysis, the positive-polarity S1 wavelets in data quadrants 1 and 2 are defined as being in the positive-offset domain for the central stacking bin. Thus, data acquired with sensors stationed in data quadrants 3 and 4 are in the negative-offset S1 domain, and trace polarities in those latter two quadrants have to be reversed to represent field data acquired with constant-azimuth sensors, as illustrated in Figures 23 through 25 of Chapter 3. When the these se dat data-p a-polar olarity ity rev reversa ersals ls are made, the summed result is a high-fold Table 3. Polarities of S1 and S2 wavelets in stack of the S1 mode and a cancellation of laboratory data. the S2 mode (Table 4). Quadrant S1 polarity S2 polarity If th thee da datata-pr proc ocess essin ing g ob objec jectiv tivee is to extract the slow-S mode, the phase adjust1 P N ments that need to be made to the labora2 P P tory-measured data are summarized in Ta3 N P ble 5. In this tab tabulat ulation ion,, pos positiv itive-p e-pola olarity rity 4 N N S2 wavelets in data quadrants 2 and 3 are Sum 0 Sum 0 defined as being in the positive-offset domain. Data in quadrants 1 and 4 are thus in the negative-offset S2 domain, and trace Table 4. Extraction of fast-S mode (assume polar po lariti ities es in th thos osee two qu quad adra rant ntss ha have ve to data quadrants 1 and 2 are the positive-offset be re reve vers rsed ed to rep repres resen entt da data ta ac acqu quir ired ed in domain). the field with constant-azimuth sensor orientatio ent ation. n. Whe When n tho those se pha phasese-adju adjusted sted data Quadrant S1 polarity S2 polarity are summed in the stacking bin labeled in 1 P N Figure 15, the S2 mode is emphasized, and 2 P P the S1 mode is canceled (Table 5). R 3 P N If mu mult ltic icom ompo pone nent nt se seis ismi micc da data ta ar aree R 4 P P acquir acq uired ed acr across oss a fra fractur ctureded-roc rock k pro prospe spect ct Sum 4P Sum 0 with wi th a so sour urcece-re recei ceive verr geo geomet metry ry th that at al al-R polarity of laboratory data is reversed. lows lo ws ri rich ch-a -azi zimu muth th SS-wav wavee da data ta to be su summ mmed ed in stacking bins, then as shown by these tables, tab les, a ful full-az l-azimut imuth h stac stack k is a pow powerf erful ul Table 5. Extraction of slow-S mode (assume procedure for isolating S1 wavefields from data quadrants 2 and 3 are the positive-offset S2 wavefields. Separation can be achieved domain). even if S1 and S2 wavelets (1) have small Quadrant S1 polarity S2 polarity time delays and (2) overlap to create complex waveshapes. The success of S1 and S2 1R N P wavefield segregation by stacking requires 2 P P that fast-S and slow-S azimuths be deter3 N P mined min ed with reas reasona onable ble accu accurac racy y so that pos pos-R 4 P P itive-offset and negative-offset domains for Sum 0 Sum 4P S1 and S2 data are known during the conR polarity of laboratory data is reversed. struction of trace gathers. ¼

¼

¼

¼

¼

¼

¼

¼

144


Determining fast-S and slow-S azimuths with 3C data The processing of 3C 3D data across a fracture system involves a source-receiver geometry identical to that used by Sondergeld and Rai (1992) to produce Figure 7 of this chapter. After 3C 3D data are rotated from field-coordinate space to radial/transverse spac sp acee (e (equ quat atio ion n 6 of Ch Chap apte terr 3) 3),, 3C 3D da data ta po pola lari riti ties es ar aree de desc scri ribe bed d in Ta Tabl blee 4. Th Thee po pola lari rity ty of data recorded by the radial geophone is identical to the polarity convention listed in thee “S1 po th pola lari rity ty”” co colu lumn mn of th that at ta tabl blee an and d ha hass a po posi siti tive ve al alge gebr brai aicc sign sign in al alll fo four ur data data qu quad ad-rants surrounding the stacking bin. The polarity of data recorded by the transverse geophone is the same as the polarities listed in the “S2 polarity” column. In contrast to the constant-posit constan t-positive ive polarit polarity y of radial-c radial-compon omponent ent data, the polarit polarity y of transve transverse-co rse-componen mponentt data reverses algebraic sign when source-to-receiv source-to-receiver er raypat raypaths hs move across either the isotropy axis or the symmetry axis of the fracture system. Examples of radial-geophone and transverse-geophone trace gathers constructed at a stacking bin in 3C 3D image space are displayed in Figure 16. The radial-geophone data

a)

0

Radial component

Transverse component

Azimuth (°)

Azimuth (°)

120

240

360

b)

0

120

240

360

1.0

Azimuthal velocity variation ) s ( e 1.5 m i T

Azimuthal polarity reversals

2.0

Fast

Slow

Fast

Slow

80

170

260

350

Phase flip azimuth (°)

Figure 16. (a) Radial-sensor data and (b) transverse-sensor data constructed at a 3C 3D stacking bin. Fast-S and slow-S azimuths defined by interpreting radial-component arrival times are verified by phase reversals occurring in transverse-component data at the same azimuths. Data example from Todorovic-Marinic et al., 2005. Used by permission of the Canadian Society of Exploration Geophysicists.


145

8

have a constant polarity as the trace gather progresses in a 360 circle around the stacking bin,, but the pol bin polarit arity y of the tra transv nsvers erse-g e-geop eophon honee dat dataa cha change ngess whe when n the data analysis analysis swings across an isotropy axis or a symmetry axis of the fracture system. The arrival time of radial-sensor data can be used to determine which polarity reversal is associated with which fracture-system axis because the isotropy axis corresponds to the azimuth of fast-S polarization, polarization, and the symmetry axis is oriente oriented d in the same azimuth as slow-S polarization. Any interpretation of the azimuths in which fast and slow arrival times appear in radial-component data can be verified by determining if transverse-component data have a phase reversal at that same azimuth. Interpretations of fast-S and slow-S azimuths are illustrated in the trace gathers.

Determining fast-S and slow-S azimuths with 9C data When a fracture system is illuminat illuminated ed with 9C 3D data, two orthog orthogonal onal dipole sources sources have to be deployed at each source station. The resulting orthogonal particle-displacement vectors that propagate through a fractured interval are represented in Figure 17. In this display, wavelet phases are presented as they would be if field data were acquired with consistently oriented horizontal sources and receivers ((Figure 8 of Chapter 2) and then transformed to radial/transverse data space (Figure 10 of Chapter 3). When those conditions are satisfied, SV and SH wavelets propagate in all azimuth directions with the same polarity polarity.. Because of the orientations of their particle-displacement vectors (Figure 3 of Chapter 1), SH and SV modes have oppos opposing ing velocity behavior behavior when SH and SV raypaths align with wi th sy symm mmet etry ry pl plan anee AA an and d is isot otro ropy py pl plan anee BB BB.. Wh When en an SV ra rayp ypat ath h is po posi siti tion oned ed in sy symmmetry plane AA, the SV mode is the slow-S mode because the SV particle-displacement vector is perpendicular to fracture planes. In contrast, the SH mode is the fast-S mode because SH particle displacement is parallel to fracture planes. When SH and SV raypaths alig al ign n wi with th is isot otro ropy py pl plan anee BB BB,, SV is th thee fa fast st-S -S mo mode de an and d SH is th thee sl slow ow-S -S mo mode de.. As a re resu sult lt,, when SH and SV full-azimuth trace gathers are constructed at a stacking bin, arrival times of SH and SV reflections from a fractured interval have an oscillating, azimuth-dependent behavior similar to that illustrated in Figure 18. A previously unpublished example of this wave physics is shown in Figure 19.

P-wave propagation in fractured rock When SWhen S-wa wave ve sp spli litt ttin ing g is ob obse serv rved ed acr acros osss a fr frac actu ture redd-ro rock ck ar area ea,, it is com commo mon n th that at no az aziimuth-dependent variations are observed for P-waves. When encountering a fractured interval, a P-wave does not split into daughter P-waves that have different polarizations as Swave wa vess do do.. Ho Howe weve ver, r, if co comp mpre ress ssib ibil ility ity (t (the he re reci cipr proc ocal al of bu bulk lk mo modu dulu luss [T [Tab able le 2] 2])) is di difffe fere rent nt parallel to fractures than it is normal to fractures, P-wave velocity can vary in a “slow” and “fast” manner in directions parallel and perpendicular to oriented fractures, as S-wave velocity does. The challenge is that V P velocity varies in a more subdued way than V S

146


Figure 17. Fracture-system illumina mi nati tion on wi with th (a (a)) SV so sour urce ce an and d (b (b)) SH source. Using the definiti definitions ons of SH and SV particl particle-disp e-displacement lacement vectors illustrated in Figure 3 of Chapterr 1, when SH and SV modes Chapte propagate in symmetry plane AA, SH is the fast-S mode and SV is the slow-S mode. When SH and SV modes propagate in isotropy plane BB, SH is the slow-S mode and SV is the fast-S mode. Subscript 1 indicates indica tes “fast “fast,” ,” and 2 represents “slow.”

1

a) B SV1

A SV2 T0

4

2 SV source

SV2 A

SV1B

does, and azimu does, azimuth-d th-depen ependent dentvarvariations of V P are often difficult 3 to detect or measure. Two ex1 ampl am ples es ar aree in incl clu uded her eree to demonstrate that by implement- b) A B SH2 ing proper data-acquisition and SH1 data-proce dataprocessin ssing g proc procedur edures, es, fracture-s tur e-sens ensiti itive ve beh behavi avior or can be T0 detected detec ted with seismic P-wav P-waves es in some instances. Exam Ex ampl plee 1 in invo volv lves es da data ta acquired and analyzed by Lynn 4 2 (200 (2 004a 4a,, 20 2004 04b) b).. Ke Key y PP-wav wavee velocity behavior is illustrated in SH source Figures 20 and 21. The superbin gather gat her illu illustr strated ated in Figu Figure re 20 show sh owss de defin finit itee az azim imut uth h va vari ri-atio at ion n of PP-wa wave ve ar arri riva vall ti time me SH1 A for reflections related to a tarSH2 B geted ge ted fr frac actur turee int inter erva val. l. Th These ese Source vector data da ta al allo low w fa fast st an and d sl slow ow az aziiFractured sample 3 muths to be interpreted with a rigo ri gorr tha thatt is us usua ually lly av avail ailabl ablee only on ly wi with th SS-wa wave ves. s. Th This is va variriation in P-wave traveltime translates into distinctive fast and slow V P velocities that are, respectively, parallel to and orthogonal to oriented fractures. To achieve this azimuthdependent traveltime effect, the data assembled into this particular superbin gather were


147

restricted to an offset range of 5000 to 7000 ft (1500 to 2100 m). In other geologic environments, different offset ranges will have to be used. The CMP gathers displayed in Figure 21 were made using source-receiver pairs that were constrained to orientations in azimuth corridors that trended parallel to and perpendicular to fractures. The residual moveouts remaining on the north-south gathers after applying applyi ng velocity moveouts that flatten east-west gathers confirm that V P velocity parallel to fractures is faster than V P velocity perpendicular to fractures.

e m i t l a v i r r a n o i t c e l f e RT

Fast velocity

T SH-SH SV-SV + DT

Slow velocity

0

90 180 270 Source-to-receiver azimuth relative to fracture plane (°)

360

Figure 18. Generalized depiction of SH and SV arrival times for reflections from a fractured interval. Azimuth is defined as the angle between the S-mode raypath and the plane of the aligned fractures.

a)

SV-SV 3.2

) s ( e m i T

3.3 0

90

b)

1 80

270

180

27 0

SH-SH

) 3.2 s ( e m i T

3.3 0

90

Source-to-receiver Source-to-receiv er azimuth relative to fracture plane (°)

Full-azimuth zimuth (a) SV-SV and (b) SH-SH trace gathers exhibiting fast-S and slow-S Figure 19. Full-a behavior at a stacking bin across a fractured-rock prospect.

148


Example 2 is illustrated in Azimuth (°) Figures 22 and 23. This analy5 60 185 245 siss wa si wass do done ne by Al Al-H -Haw awas as et al. (2003) across a prospect in Saudi Sau di Arab Arabia. ia. The vel velocit ocity-s y-sememblance bla nce an analy alyse sess ill illus ustra trated ted in Figure 22 show that a P-wave stacking velocity that is appropriate for data trending parallel 1.1 to fractures is not correct across a frac fracture ture-ta -target rget inte interval rval when raypaths travel perpendicular to ) fractures. That is the same prin s ( e cipl ci plee de demo mons nstr trat ated ed by Ly Lynn nn m i T (200 (2 004a, 4a, 20 2004 04b) b).. In th this is Sau Saudi di 1.2 Arab Ar abia ia ex examp ample le (A (All-Haw Hawas as et al., 200 2003), 3), V P interval interval velocity acros acr osss th thee fr fract actur uree tar targe gett re redduced by 80 to 120 m/s when Pwave wa vess pr prop opag agat ated ed no norm rmal al to alig al igne ned d fr frac actu ture res, s, wh whic ich h is a 1.3 reduction of 2% to 3%. Examplesofstackedprofiles of P-P data across this prospect are shown in Figure 23. Profiles Demonstration ration of azimuth variation of P-wave Figure 20. Demonst parallel to aligned fractures exvelocity across a fractured-rock interval. These data are a hibit good reflection continuity superbin gather with offsets restricted to 5000 to 7000 ft wit ithi hin n th thee fr frac actu ture re in inte terv rval al,, (1500 to 2100 m). Fast and slow velocity behaviors are whereas profiles normal to fracdefinitive. After Lynn, 2004a, Figure 6. tureshavebroken,discontinuous reflections. The poststack amplitud lit udee di dimmi mming ng exh exhibi ibited ted by thes th esee da data ta wh when en PP-P P ra rayp ypat aths hs ar aree no norm rmal al to fr frac actu ture ress di diff ffer erss fr from om th thee pr pres esta tack ck,, restric res trictedted-inci inciden dent-an t-angle gle,, P-P trace-gather amplitud amplitudes es of Figur Figuree 21, in which raypat raypaths hs normal to fractures result in larger amplitudes. No information is available that allows thee inc th incid iden ent-a t-ang ngle le ran range ge of the st stack acked ed da data ta to be co comp mpar ared ed wi with th th thee inc incid iden ent-a t-ang ngle le range of the 1500- to 2100-m offset trace-gather windows displayed in Figure 21 or to confirm whether plot gains were varied when making the two panels of each side-byside display, shown in Figures 21 and 23. Despite the differing reflection amplitude behaviors, this example of Al-Hawas et al. (2003) and those of Lynn (2004a, 2004b) and of Smith and McGarrity (2001) show that in some circumstances, P-wave data can detect fractures and define fracture orientation. Thus, if S-waves are not available for fracture analysis, efforts should be made to use Pwave data. When both P and S data are available, both modes should be used. Fast N50E

Fast N230E


149

Individual ual CMP P-wave trace gathers constructed constructed (a) perpen perpendicular dicular to and (b) parallel Figure 21. Individ to fractures. fractures. The residual moveout remaining on the gather gatherss (a) trendi trending ng normal to fractures shows that V P velocity is slower in that azimuth direction than it is (b) parallel to fractures. From Lynn, 2004a, Figure 10.

analyses in direct directions ions (a) normal to and (b) parallel to fractu fractures. res. Figure 22. P-P stacking velocity analyses V P velocity across a fracture interval decreases when measured in an azimuth normal to fractures. After Al-Hawas et al., 2003, Figure 4.

150


Figure 23. P-P stacked profiles in directions (a) normal to and (b) parallel to fracturing. From Al-Hawas et al., 2003, Figure 3.

Stress and fracture concepts Stress fields in the earth can be represented by three orthogonal stress vectors, s 1, s 2, and s 3, where s 1 is the direction of maximum stress, s 2 is the direction of intermediate stress, and s 3 is the direction of minimum stress. When stress-induced fractures are produced, the fracture pattern can be represented by failure planes A, B, and C, as shown in Figure 24. Failure plane B describes the orientation of extensional fractures, which align with maximum stress s 1. Failure planes A and C represent shear fractures that intersect the maximum horizontal stress vector at an angle F, where F is approximately 30 for most rocks. Twiss and Moores (1992) measured angle F between maximum stress vectors and shear fracture planes A and C for numerous rock types, temperature conditions, and pore-fluid mixtures. Their investigations, summarized in Figure 25, show that for approximately 130 tests, F could be described as a distribution function with a mean value of 28.7 and a standard deviation of 7.4 . In papers in which geophysicists investigate S-wave behavior and use fast-S polarization to define fracture orientation and stress direction, numerous investigators assume that fractures are aligned with maximum horizontal stress. That assumption might not be true when an interpreter is forced to use a limited amount of fracture-orientation information, as can be demonstrated by data collected across a west Texas producing oil field. The map in Figure 26 shows the location of 10 wells where formation microimager (FMI) data were acquired across a carbonate reservoir interval to understand the fracture system across the field. An example of the FMI image quality from these calibration wells is shown in Figure 27. The two fractures labeled on this image represent what the logging contractor used by the field operator defined as “high-confidence” fractures. 8

8

8


Figure 24. Relationships between stress fields and fracture fractu re planes. Extensional fractures B align with maximum stres stresss vector s 1. Shear fractures A and C intersect the maximum stress vector at an angle of approximately 30 for most rocks.

s 1 s 2

f

B C

A

s 3

151

s 3

8

s 2

s 1 s 1

s 1

s 1 = maxi maximum mum stress stress s 2 = interm intermedia ediate te stress s 3 = mini minimum mum stress stress

s 3

s 3

B

B = ex exten tensio sional nal fra fractu cture re

f

C

A = sh shea earr frac fractu ture re

A

C = sh shea earr fr frac actu ture re f ~ 30 30°°

Mean 28.7 S.D = ± 7.4

s10 n o i t a v r e s b o 5 f o r e b m u N 0

10

15

20

25

a f (°)

30

35

40

45

a f = angle between fracture plane and maximum compressive stress vector.

Measurements made for numerous rock types, temperature, and pore fluids.

Measurements ements of fracture shear angle for approximately approximately 130 combin combinations ations of rock Figure 25. Measur types, temperatures, and pore-fluid mixtures by Twiss and Moores (1992).

152


2 2 0

1 4 8 0

r 1 e b m u n e n i l s s o r 1 4 0 C

N

3 2 5 6

10 7

t 0 f t 1 1 0

8 9

1 0 0 1 2 8 0 0 1 2 4

1 3 6 0 1 3 2 0

r m b e e n u n n i i l n n I

Figure 26. Map showing wells where FMI data were acquired to analyze fracture systems.

3500

3505

) t f ( h t p e d d e r u s a e M

3510

0

90

Azimuth (°) 180

270

360

Fracture 1 Azimuth = 187° Dip = 88°

Fracture 2 Azimuth = 16° Dip = 84°

3515

high-confidence near-vertical near-vertical fractures observed in FMI data. Figure 27. Example of high-confidence


a)

b)

North

West

East

West

East

One well 28 fractures South

c)

North

North

West

East

Nine wells 134 fractures South

153

13 wells 244 fractures South

Figure 28. Azimuths of fractures as fracture analysis is expanded from (a) one well to (b) nine wells to (c) 13 wells. The azimuth of the dominant fracture population and thus of the maximum horizo hor izonta ntall str stress ess obviou obviously sly is infl influen uenced ced by the number number of fra fractur ctures es and the num number ber of wel wells ls used used for calibration.

Azimuths of FMI-based high-confidence Azimuths high-confidence fractures observed within the targeted reservoir interval interval across across the field are shown shown in Figure Figure 28. When data data are available available from only one one well (Figure 28a), the dominant fracture population is oriented slightly south of east. If no other fracture-sensitive data were available for calibration, the dominant stress direction also would be assumed to be the same direction, slightly south of east. However, when thee an th anal alys ysis is is ex expa pand nded ed to in incl clud udee da data ta fr from om ni nine ne we well llss (F (Fig igur uree 28 28b) b),, a la larg rgee fr frac actu ture re po popu pu-lation appears in the direction of north-northeast to south-southwest, and there is a new interp int erpreta retatio tion n of the dir directi ection on of the loc local al max maximum imum str stress ess dir directi ection on tren trendin ding g nor norththnortheast and south-southwest. When three more wells a short distance from the map boundaries shown in Figure 26 are included in the analysis, the original east-southeast orientation of the fractures diminishes significantly, and other fracture orientations grow in importance (Figure 28c). A stress analysis of this 13-well database is exhibited in Figure 29. With this expanded FMI database, the total fracture population now segregates into a definitive picture of extensional fractures oriented north-northeast (failure plane B) B) and shear fractures oriented approximately 30 east and west of the extensional fractures (failure planes A and C). Some version of the model exhibited in Figure 30 often appears in the literature to describe the relationship between fracture orientation and maximum stress azimuth. In this th is mo mode del, l, fr frac actur tures es ar aree or orien iented ted in th thee di dire recti ction on of ma maxi ximu mum m ho hori rizo zonta ntall str stres esss s 1, which wh ich is also also the the di direc rectio tion n of S1 (fa (fastst-S) S) polariza polarization tion,, and the S2 (slo (slow-S w-S)) mod modee is polari polarized zed normal to fracture planes, which is also the azimuth of minimal horizontal stress s 3. This model is proper in many situations, but its embedded assumptions must be considered on a case-by-case basis before implementation. First, the model assumes that all fractures are extensional fractures as defined in Figure 24. The data in Figure 29 show that there are often as many shear fractures as extensional fractures in a fractured-rock interval, and shear fractures are not aligned with s 1 stress direction. Second, the model implies that fracture-forming stresses have not rotated to new azimuths over geologic time after rock fracturing occurred. 8

154

Multicomponent Seismic Technology Incident S-wave

s

1

A

North B C

Polarization direction (f ∞ relative to s max)

s

3

East

West

s min

s

3

f ∞

C South B

A 13 wells 244 fractures

s max

s

1

AA, CC = shear fractures BB = extensional fractures

Figure 29. Horizontal-stress model inferred by the interpreted fractures. Although extensional fractures BB dominate the fracture population, many shear fractures (AA and CC) are present. For some fractured intervals analyzed with S-wave data, the fast-S mode at some locations across seismic image space might align with local shear fractures and thus not be aligned with maximum horizontal stress.

e s u r e u t c a F r a

o n i t o c e e r i r n d a ) o o x i t z a t o o s m r i z a a l l e p o a a l l e S 1 ( p a r

S p 2 o ol l a ar r i iz z a at t i io ( n o p a n ar r a al l l le re c l l t d i i r e c t t i io o s e o n o n m i n n )

fracture orient orientation ation Figure 30. Popular model relating fracture to th thee az azim imut uth h of ma maxi ximu mum m ho hori rizon zonta tall st stre ress ss.. Th This is mo model del assumes that all fract fractures ures are extensi extensional onal fractures (Figure 24) and that stress fields have not changed orientation entatio n after fracture format formation. ion.

Local stresses and fractures Current well-logging technology provides valuable information about fracture and stress orientations encountered by wellbores. Essential well logs are those that measure borehole ellipticity, define fast-S and slow-S polarization directions, or provide any indication where fractures intersect a wellbore. FMI log data and dipole sonic logs are particularly valuable valuable for those purposes. An example of stress and fracture orientations orientations interpreted from FMI data is displayed in Figure 31. Valuable insights into local variations of stress azimuths and fracture orientations are provided when FMI and sonic-dipole logs are available in a significant number of wells we lls acr acros osss a pr pros ospe pect ct ar area. ea. An ex examp ample le fr from om th thee no north rthern ern North North Se Seaa is sh show own n in Figure 32 to illustrate the variability in stress azimuths that might be present over rather short distanc distances. es. As shown in Figure 32, there are numerous faults across the area. Local orientations of maximum horizontal stress s 1 are shown as labeled arrows, with the labels identifying the


0

FMI log Azimuth (°)

155

360

13,850 Stress/fracture interpretation s 3

Shear fractures Breakouts Borehole ) t f ( h t p e D

s 1

s 1

Tensile fractures

s 3 s 1 = maximum horizontal stress s 3 = minimum horizontal stress

13,860

Interpretatio etation n of fract fracture ure and stres stresss orientations using FMI log data. A boreho borehole le elonFigure 31. Interpr gates in the direction of minimum horizontal stress s 3, and the elongation is detected by FMI sensor pads that contact the borehole wall. The azimuth of maximum horizontal stress s 1 differs from the s 3 by 90 . Thus, fractures appearing at the expected s 1 azimuth are assumed to be azimuth of s extensional extens ional fractures to confirm the interp interpretatio retation n of s s 1 azimuth. The positions of shear fractures are drawn on the borehole model to indicate where the fractures would appear if present. From Al-Hawas et al., 2003, Figure 8. 8

well where log data were acquired (Yale, 2003). There is good agreement between stress azimuths interpreted from dipole sonic logs and from logs indicating borehole ellipticity. Those data show that stress azimuths and thus S1 polarization directions can vary significantly over distances of only 2 or 3 km in some fault environments. A co comm mmon on da datata-pr proc oces essin sing g ass assum umpt ption ion us used ed wh when en cre creati ating ng S1 and S2 wa wave vefiel fields ds is tha thatt the S1 mode is polarized in the direction of regional maximum horizontal stress s 1. As shown in Figure 32, the regional azimuth of s 1 is north-northwest, but many of the local stress azimuths are shifted away from north-northwest by significant amounts. Thus, the simplifying assumption that S1 is polarized in the direction of regional stress should be used with caution.

156


N N 6Z W

6

E

S Regional stress (NNW) S-wave anisotropy ~3.5 %

C3 A1

A1Z

20

C2Z C2

15 4

From wellbore elongations From sonic-log S-wave

C1

7

34

B1

43

B2

9

Fault 0 0

3 mi 4 km

Effect ect of faulti faulting ng on the local orient orientation ation of maximum horizo horizontal ntal stress. Stress Figure 32. Eff orientations are shown by short arrows. After Yale, 2003, Figure 1. Courtesy of the Geological Society and David P. Yale. Used by permission.

Orthorhombic media The fr The frac actur tureded-ro rock ck phy physic sicss disc discus ussed sed to thi thiss point point ha hass bee been n lim limite ited d to med media ia tha thatt can be described in terms of two symmetry planes — an isotropy plane parallel to fractures and a symmetry plane normal to fractures. This HTI fracture model is appropriate when analyzing elastic wavefields propagating in a relatively thick, nonstratified layer of rock. If a fracture tu re in inter terva vall co cons nsist istss of thi thin, n, sta stack cked ed ro rock ck lay layer ers, s, th then en thr three ee sy symm mmetr etry y pl plan anes es ar aree emb embed edded ded in the rock, and the medium becomes orthorhombic (Figure 33). An HTI medium can be described in terms of five stiffness coefficients, but nine coefficients ficie nts are req requir uired ed to des describ cribee an ort orthor horhom hombic bic mate material rial.. An ort orthor horhom hombic bic med medium ium migh mi ghtt ha have ve on onee set of ali align gned ed fr frac actur tures, es, as ill illus ustra trated ted in Fig Figur uree 33 33,, or two set setss of or orth thog ogon onal al fractures. In the latter case, the second set of fractures would be aligned along symmetry plane 1 defined in the figure. If there are two sets of fractures but the fracture sets are not orthogonal to each other, then the medium is not orthorhombic but is a more complicated monoclinic rock. An example of an orthorhombic rock is the Marcellus Shale across the U. S. Appalachian Basin. An exposed section of Marcellus Shale is shown in Figure 34. The Marcellus has two embedded joint sets, labeled J1 and J2, which usually are observed to be orthogonal to each other, as they are in this exposure. The Marcellus Shale also is stratified in thin layers, completing the requirements for an orthorhombic rock. S-wave splitting is complex in orthorhombic media. An analysis by Wild and Crampin (1991) illustrates S1 orientation behavior behavior for a range of fracture densities and crack-aspect ratios in fractured, thin-bedded layering that has wide ranges of periodic thin-layer ani-


Symmetry plane No. 2

Symmetry plane No. 1

Symmetry plane No. 3 (horizontal)

157

Figure 33. An orthorhombic medium has three symmetry planes. The most common forms of orthor orthorhombic hombic rocks are fractu fractured red interv intervals als consisting consis ting of thin, stacked strata. strat a. The fracture system can be one set of aligned fractures, as shown in this illustration, or two sets of orthogonal fractures.

Exposuree of Marcel Marcellus lus Shale, Appalachian Basin, Basin, U.S.A U.S.A.. The unit is stratified into Figure 34. Exposur thin layers and has two orthogonal joint sets, J1 and J2, making the Marcellus Shale a classic orthorhombic orthor hombic seismic-propaga seismic-propagation tion medium. From Engelder et al., 2009, Figure 5a. AAPG#2009. Reprinted by permission of the AAPG whose permission is required for further use.

sotropy. One of the model results of Wild and Crampin (1991) is redrawn and modified in Figure 35. XX and YY define symmetry planes planes 1 and 2, illustr illustrated ated in Figure 33. The results found by Wild and Crampin (1991) predict that numerous singularities occur across S1 image space because of interference between S1 and S2 phase-velocity surfaces. At each singularity, singul arity, S1 polarization undergoes radical changes in direction. As a result, S1 polarization is not parallel to fracture planes except in limited portions of the image space. The wide variation in S1 orientation predicted by this theoretical model is a challenge to recognize in actual S-wave data. Mattocks (1998) determined S1 data orientation across the 9C 3D data-acquisition grid defined in Figure 45 of Chapte Chapterr 2 by analyzin analyzing g S-wav S-wavee first-ar first-arrival rival wavelets recorded by a downhole geophone in the receiver well at the center of that acquisition grid. Horizontal vibrators occupied each source station around the well to produce the S wavelets.

158


Figure 35. S1 polarization directions directions predicted for S-wave propagation propagation in an orthorhombic medium that has a fracture density of 0.01, a crack-aspect of 0.001, and periodic thin-layer anisotropy of appr ap prox oxim imat atel ely y 10 10%. %. XX an and d YY de defin finee sy symm mmet etry ry pl plan anes es 1 an and d 2 fr from om Fi Figu gure re 33 33.. Nu Nume mero rous us SS-wa wave ve point singularities occur, and S1 polarization undergoes significant reorientation at each singularity point. As a result, S 1 polarization parallels fracture orientation in only a limited part of the image space. S-wave polarization should not be distorted inside circle A. This plot is an equal-area pro jection onto a hemisphere, i.e., a polar map, not a flat map. New drawing patterned after Wild and Crampin, 1991. Courtesy of John Wiley & Sons, Inc. Used by permission.

The calculated S1 polarizations are shown here in Figure 36 with numerous possible interpreted singularity singularity points, several more singularities than proposed by Mattock Mattockss (1998 (1998). ). In addition, symmetry planes AA and BB have been added to the analysis to indicate the azimuths of regional maximum and minimum horizontal stress, respectively, stated in Mattocks (1998). This display in Figure 36 is a flat map, not a polar map as in Figure 35. However, the correspondence between this real-data behavior and the theoretical calculation of Wild and Crampin (1991) suggests that orthorhombic effects can be recognized in real S1 data if proper steps are taken in data acquisition and processing. S-wav Swavee sin singu gular larity ity be behav havior iorss sim simila ilarr to th thos osee exh exhibi ibited ted in Fi Figu gure re 36 ha have ve bee been n described by Hornby et al. (1994) in their analysis of elastic properties of shales. Examples


4000 ft

159

A

652,000

B

2000 ft

650,000

) t f ( g n i h t r o N

Receiver well

648,000

1000 ft

B 646,000

3000 ft A 753,000 S1 po pola lari riza zati tion on

756,000 Easting (ft) Poin intt sin singu gula lari rity ty

AA = sym symme metr try y pla plane ne

759,000 BB = iso isotr trop opy y pla plane ne

Figure 36. S1 polarizations determined across the 3D data-acquisition grid illustrated in Figure 45 of Chapter 2. Data analysis was restricted to downgoing S first-arrival wavelets recorded by a receiver at a depth of 1006 m in the central receiver well as horizontal-vibrator sources occupied surf su rfac acee so sour urce ce st stat atio ions ns ar aroun ound d th thee we well ll.. Nu Nume merou rouss abr abrup uptt ch chang anges es in S1 pola polariz rizati ation on occu occurr acr across oss the image space. Several of these anomalous behaviors are marked as possible S-wave singularity points. AA and BB are symmetry planes that indicate azimuths of regional maximum and minimum horizontal stress and are proposed as being related to planes XX and YY in Figure 35 above. The result is a fair representation of the theoretical prediction of S 1 polarization behavior in orthorhombic media made by Wild and Crampin (1991). Data have been modified from an example presented by Mattocks, 1998. Courtesy of Bruce Mattocks. Used by permission.

of slowness surfaces and wavefront geometries from their study are exhibited in Figure 37. Calculations are shown for two types of shales. The first example (Figure 37a and 37b) assumes that a shale medium can be described by the five cij elastic constants measured for a Cretaceous shale by Jones and Wang (1981). The second example (Figure 37c and 37d) uses elastic properties based on a distribution of clay platelet orientations observed on scanning-electron microscope images of a shale test sample. The short dashed lines drawn on wavefr wavefronts onts and slowness surfaces in Figure 37 define the directions of particle displacement for each labeled wave mode. When a slowness or

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velocit velo city y su surf rface ace is no nott no norm rmal al to pa part rticl iclee di disp splac laceme ement nt,, the ass assoc ociat iated ed wa wave ve mo mode de is cal called led a quasi-mode. When particle displacement is normal to slowness and velocity surfaces, the associated wave mode is called a pure mode. Two quasi-modes (qP and qS) and one pure mode (SH) are defined. Both the quasi-longitudinal mode (qP) and the quasi-transverse mode mo de (q (qS) S) be beco come me pu pure re mo mode dess on eac each h sy symm mmetr etry y ax axis. is. Sin Singu gular larity ity po poin ints ts wh wher eree S di disp splac laceement undergoes an abrupt change in orientation have been added to the displays as circled numbers in Figure 37 to emphasize similarities to the S displacements shown in Figures 35 and 36.

a)

b)

Symmetry axis 1 Slowness surfaces (ms/m)

600 400

4

Symmetry axis 1 4000

1

qP

qP

qS

2000 4

200

– 600

–400

–200

1

SH

SH

20 0

400

Velocity surfaces (m/s)

Symmetry axis 2

60 0

–4000

qS

–2000

2000

4000

Symmetry axis 2

–200 2

3 –400

3

–2000

2

–600

2 Po Point int singu singulari larity ty –4000

c)

d)

Symmetry axis 1


Slowness surfaces (ms/m)

600 4

qP

1 400

qP qS

200

–600

–400

Velocity surfaces (m/s)

–200

4

SH

2 00

40 0

–200

2000

1 SH

qS

600

Symmetry axis 2

–4000

–2000

2000

3


2 –2000

3

–400 –600

2 –4000

2 Po Point int sin singul gularit arity y

Slowness surfaces and (b) velocity surfaces surfaces for a shale described described by the five elastic Figure 37. (a) Slowness constants consta nts measured by Jones and Wang (1981). (c) Slowne Slowness ss surfaces and (d) velocity surfaces for a laboratory test shale in which clay platelet orientations were determined from scanning-electron microscope images. qP is a quasi-longitudinal (P) mode, qS is a quasi-transverse (S) mode, and SH is a pure horizontally polarized S mode. The short dashes drawn on the surfaces indicate particle-dis partic le-displaceme placement nt direct directions. ions. Singularity Singularity points (circled numbers) have been added to the original figures to illustrate similarities to Figures 35 and 36 above. Because the S displacement vectors on the slowness and velocity surfaces are difficult to see in the original figures, the ones redrawn here are exaggerated and might not precisely honor the orientations intended by Hornby et al. (1994). After Hornby et al., 1994, Figures 2 and 11.

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