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GEOPHYSICS, VOL. 72, NO. 2 �MARCH-APRIL 2007�; P. E69–E75, 9 FIGS., 5 TABLES.10.1190/1.2432263

referred orientation and elastic anisotropy of illite-rich shale

ans-Rudolf Wenk1, Ivan Lonardelli1, Hermann Franz2, Kurt Nihei3, and Seiji Nakagawa4

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ABSTRACT

Shales display significant seismic anisotropy that is attrib-uted in part to preferred orientation of constituent minerals.This orientation pattern has been difficult to quantify becauseof the poor crystallinity and small grain size of clay minerals.A new method is introduced that uses high-energy synchro-tron X-rays to obtain diffraction images in transmission ge-ometry and applies it to an illite-rich shale. The images areanalyzed with the crystallographic Rietveld method to obtainquantitative information about phase proportions, crystalstructure, grain size, and preferred orientation �texture� that isthe focus of the study. Textures for illite are extremely strong,with a maximum of 10 multiples of a random distribution for�001� pole figures. From the three-dimensional orientationdistribution of crystallites, and single-crystal elastic proper-ties, the intrinsic anisotropic elastic constants of the illite ag-gregate �excluding contribution from aligned micropores�can be calculated by appropriate medium averaging. The il-litic shale displays roughly transverse isotropy with C11 closeto C22 and more than twice as strong as C33. This method willlend itself to investigate complex polymineralic shales andquantify the contribution of preferred orientation to macro-scopic anisotropy.

INTRODUCTION

Shale anisotropy is a major consideration for seismic imaging andock properties estimation in hydrocarbon-bearing sedimentary ba-ins �e.g., Banik, 1984�. Additionally, anisotropy of kerogen-richhales may also provide information about their maturation state andas-oil migration paths �Meissner, 1978; Price, 1983; Vernik andur, 1992�. Anisotropy may also be indicative of overpressure asso-

iated with the temperature-driven transformation of smectite to il-ite that has been observed in Gulf Coast mudstones �Ho et al., 1999�.

Manuscript received by the Editor July 14, 2006; revised manuscript receiv1University of California, Department of Earth and Planetary Science, Ber2HASYLAB, DESY, Hamburg, Germany. E-mail: fhermann@hasylab.ed3Chevron Energy Technology Company, Seismic Analysis & Property Est4Lawrence Berkeley National Laboratory, Earth Sciences Division, Berke2007 Society of Exploration Geophysicists. All rights reserved.

E69

One of the factors contributing to seismic anisotropy of shales ishe preferred orientation of clay minerals �e.g., Jones and Wang,981; Vernik and Nur, 1992; Hornby et al., 1994; Sayers, 1994,005�. Preferred orientation or texture, as it is more commonlyalled in materials science, forms under slow compaction of plate-haped clay minerals that favor orientation of platelets parallel to theediment surface. The original pattern may be modified during di-genesis �Swan et al., 1989; Schoenberg et al., 1996�. Texture analy-is is well established in structural geology and has helped greatly tonterpret the deformation history of metamorphic rocks �e.g., Sand-r, 1950; Turner and Weiss, 1963�. More recently, it has been ap-lied to understand seismic anisotropy in the deep earth, such as thepper mantle �Montagner and Tanimoto, 1990�, the D” zone �Pan-ing and Romanowicz, 2004�, and the inner core �Song, 1997�, usingn situ texture measurements in diamond anvil cells up to pressuresorresponding to those encountered in the earth’s core �Wenk et al.,006�.

Despite these advancements in texture characterization of deeparth rocks, relatively little is known about the preferred orientationn shales. Because clay minerals are fine-grained and poorly crystal-ine, conventional techniques that provide experimental data foruantitative texture analysis, such as X-ray pole figure goniometrynd electron microscopy, are not applicable or very limited. An-ray transmission technique has been developed to measure polegures of sheet silicate basal planes and was successfully applied tolates as well as some shales �e.g., Kaarsberg, 1959; Oertel, 1983;intubin, 1994; Van der Pluijm et al., 1994, Ho et al., 1999, Mat-naar, 2002�. While pole figures of basal planes provide valuable in-ormation about the preferred orientation of clay minerals, knowl-dge of the 3D orientation distribution �OD� that specifies the fullrientation of crystallites �e.g., as a 3D probability distribution ofuler angles� is necessary to model the polycrystal elastic properties

n a rigorous and quantitative fashion. To date, no 3D crystal OD haseen measured for any of the clay minerals contained in shales.

Recently, synchrotron methods have become available for texturenalysis and show much promise for the investigation of poorlyrystalline and weakly scattering materials. Advantages are a very

ber 6, 2006; published online February 8, 2007.alifornia. E-mail: wenk@berkeley.edu; ivan.lonardelli@ing.unitn.it.

, San Ramon, California. E-mail: knih@chevron.com.ifornia. E-mail: snakagawa@lbl.gov.

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ntense and highly focused X-ray beam, short wavelength that per-its high sample penetration without major absorption, and two-di-ensional detectors �either CCD cameras or image plates� to record

iffraction images. The geometry of such an experiment is illustrat-d in Figure 1. Intensity variations along Debye rings immediatelyisplay qualitatively the orientation of lattice planes. Backstrom etl. �1996� first used synchrotron X-rays for quantitative texture anal-sis, and the method was further refined by Heidelbach et al. �1999�.ut this method only became established with the recent develop-ent of a Rietveld method to analyze a set of continuous spectra for

exture �Wenk et al., 2004; Ischia et al., 2005, Lonardelli et al.,005�. In this study, we investigate the intrinsic anisotropy of an illit-c shale by first determining the 3D OD with novel hard X-ray syn-hrotron diffraction methods and analyzing diffraction images forrystallography, phase proportions, and texture with the Rietveldethod MAUD �material analysis using diffraction, Lutterotti et al.,

997�. From the OD, we obtain polycrystal elastic properties by var-ous averaging schemes and can thus calculate direction-dependent- and S-wave propagation.

MATERIAL AND EXPERIMENT

The sample used in this work is a natural illite-rich shale �Cam-rian� from Silver Hill, Montana. �Table 1, and Hower and Mowatt,

able 1. Chemical composition of illite from Silver Hill,ontana (from Hower and Mowatt, 1966). Values are ineight percent oxides, loss on ignition (LOI) is mainly aeasure of volatiles „H2O + CO2…, but also includes some

ddition of oxygen resulting from oxidation of iron.

SiO2 49.30 FeO 0.55

Al2O3 24.25 CaO 0.43

K2O 7.83 P2O5 0.08

Fe2O3 7.32 MnO 0.03

MgO 2.56 LOI 8.02

Orientation sphere

Synchrotron beam

Pole

Sample

Detector

Debye ring

2

y

x

z

ω

θ

θ

η

igure 1. Diffraction geometry of a synchrotron experiment in trans-ission; the sample is rotated around the y-axis perpendicular to the

- and z-axes �� rotation� for improved pole figure coverage. For aowder with random orientation, the intensity along the Debye rings uniform; for a textured sample there are characteristic variations.

a

966, Clark et al., 1990�. A fragment of the sample, 3 X 2 X 1 mmn dimensions, was analyzed on beamline 41 at HASYLAB 6 of theerman Synchrotron facility �DESY� in Hamburg. A monochro-atic beam of wavelength of 0.1848 Å, 1 X 2 mm in size, was used.he sample was mounted on a metal rod parallel to the long dimen-ion �x� on a goniometer and rotated around this axis during the ex-eriment �Figure 2�. In the initial orientation, the bedding plane nor-al �z� is parallel to the horizontal incident X-ray, the long dimen-

ion �x� is vertical, and the intermediate dimension �y� horizontalFigure 2�. The sample was rotated from the starting position in five2.5° increments of angle � around vertical axis y �perpendicular tohe incident X-ray� from perpendicular �Figure 2a� to parallel to theoliation plane �Figure 2b�. This provides a pole figure coverage asndicated in Figure 3. Images were collected with a MAR345 image-late detector mounted at 129.75 cm from the sample. Counting

1mm. 1mm.

y y

z z

a) b)

igure 2. Illitic shale sample and coordinate system. �a� The samples positioned at � = 0° and the synchrotron beam is normal to the fo-iation plane. �b� The sample is positioned at � = 90° and the beams parallel to the foliation plane.

Beam

y1

2

3

4

5

igure 3. Pole figures coverage obtained by rotating the sample to= 0° �5�, 22.5° �4�, 45° �3�, 67.5° �2�, and 90° �1� around the �

xis.

td�iet

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Preferred orientation and elastic anisotropy E71

imes for individual images were 180 s. Afterata collection, images were corrected in FIT2DHammersley, 1998� for distortion and tilt, rely-ng on a LaB6 standard. Corrected images werexported from FIT2D in 16-bit tiff format for fur-her processing.

Three of the five images at different � anglesre shown in Figure 4. They immediately revealifferences with rotation �anisotropy�. In Figurea, with a view on the foliation plane, Debyeings are uniform with no significant intensityariations. In Figure 4c, with a view parallel tohe foliation, there are very strong intensity varia-ions. The image at � = 45° is intermediate �Fig-re 4b�. This sample shows strong preferred ori-ntation, most clearly expressed in intensity vari-tions along Debye rings �Figure 4c�. Notice thatighest intensities are in different directions forifferent reflections hkl. Particularly, the strongllite reflection 002 �arrow� has a maximum in theorizontal direction, indicating that basal latticelanes are oriented vertically. In other viewse.g., Figure 4a�, texture is less evident but wouldecome obvious by comparing relative diffrac-ion intensities with those of a powder withoutreferred orientation. For example, note thathere is no intensity for the strong �002� diffrac-ion peak because in this view on the beddinglane, no basal lattice planes are in reflection con-ition. While texture is visible on images, theuantitative texture interpretation relies on a rig-rous analysis of the diffraction data.

We are using the Rietveld code MAUD �Lut-erotti et al., 1997� to refine instrumental parame-ers, crystallographic parameters, sample charac-eristics and texture. This program was recently

odified to accept synchrotron diffraction dataLonardelli et al., 2005�. Tiff images with 16-bitynamic range obtained from Fit2D are entered,sing an image manager where it is possible to sethe correct parameters �sample/detector distance,anges for integration, center coordinates, number of spectra, etc.�.n this study, 72 spectra were obtained by integrating over azimuthalectors of 5°. Using five images, rotating the sample around � �y� in2.5° increments from 0° to 90° provides 5�72 = 360 spectra thatre used simultaneously for the Rietveld refinement. First, the in-trument parameters were refined using the LaB6 standard in order tobtain the correct center of the Debye rings. Next, backgrounds pa-ameters �four for each spectrum�, and after that, crystallographicarameters �lattice parameters and atomic positions� and anisotropicrystallites size were refined �Table 2�. We started with a muscovitetructure �Comodi and Zanazzi, 1995�, with space group C2/c, be-ause no structural data for illite are available �Meunier and Velde,004�. Finally, the texture was refined using a tomographic EWIMVlgorithm related to WIMV �Williams-Imhof-Matthies-Vinel, Mat-hies and Vinel, 1982�. For this study, we used 10° grid cells for theD.Figure 5 demonstrates a good agreement between experimental

ata �dots� and recalculated fit �solid line�. Notice that there are nu-erous overlapping peaks, particularly at low d-spacings. In the

Table 2. Crycoordinates)and the refin

a 5.195b 9.020c 20.068� 95.2�1

xT1 0.965T2 0.451M 0.249

K1 0.0O1 0.962O2 0.383O3 0.415O4 0.750O5 0.250OH 0.958

a)

Figure 4. Twoangles: �a� �plane; �b� 45°2b�. Arrows pflection.

stallographic parameters (lattice parameters and atomicfor the muscovite starting structure (Comodi and Zanazzi, 1995)ed illite structure. Standard deviations in parentheses.

Starting structure Rietveld refinement

Lattice parameters ���2� 5.220�3��3� 8.945�11��6� 20.048�5�� 95.39�8�

Atomic positionsy z x y z

3�5� 0.4301�2� 0.1350�5� 0.981�13� 0.468�8� 0.148�2�1�6� 0.2587�2� 0.1351�6� 0.497�8� 0.286�8� 0.146�3�1�5� 0.0830�3� 0.0005�4� 0.251�2� 0.062�6� −0.010�2�

0.0984�4� 0.25 0.0 0.108�10� 0.253�11� 0.4446�6� 0.0510�13� 0.875�19� 0.432�14� 0.046�6�2�13� 0.2508�7� 0.0536�13� 0.377�15� 0.245�14� 0.076�3�4�12� 0.0939�7� 0.1688�9� 0.341�12� 0.124�10� 0.164�3�0�13� 0.3100�7� 0.1576�10� 0.701�22� 0.317�10� 0.150�5�4�12� 0.3706�7� 0.1704�9� 0.274�22� 0.396�16� 0.157�4�0�12� 0.0623�6� 0.0519�9� 0.887�31� 0.168�10� 0.046�5�

(10-11) (10-11) (10-11)

(002) (002)(004) (004)

b) c)

-dimensional synchrotron diffraction images obtained at different tilting= 0° �corresponding to Figure 2a�, beam perpendicular to the foliationand �c� 90°, beam parallel to the foliation plane �corresponding to Figureoint to illite 002 and 004 diffraction peaks and the strong quartz 10–11 re-

(002)

(004)

(006)

1.0 2.0 3.0 4.0 5.0 6.0 7.0

QuartzIllite

2-theta (°)

Inte

nsiti

es (

au)

igure 5. Single diffraction spectrum showing the measured datadots� and calculated Rietveld fit �solid line�. Individual diffractioneaks for illite and quartz are marked below the spectrum. The inten-ity is in arbitrary units �au�.

mtst

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E72 Wenk et al.

ap plot of the diffraction spectra �Figure 6�, it is possible to identifywo phases present in the sample: illite with strong variation in inten-ity along each reflection, and quartz lines that show no appreciableexture and are more spotty �see, for example, the intense quartz

Multiplot Illite (ω = 0°)

2-theta (°)

1.0 2.0 3.0 4.0 5.0 6.0 7.0

360°

270°

180°

90°

0°

igure 6. Map plot of the 360 diffraction spectra used in the texturenalysis with intensities as gray shades. Arrows point to quartz dif-raction lines. Experimental data �bottom� and calculated data fromhe Rietveld fit �top�.

(002) (004) (110) (006) (200)

Inte

nsiti

es (

au)

1.0 2.0 3.0 4.0 5.0 6.0 7.02-theta (°)

10°

20°

30°

40°

50°

60°

70°

80°

90°

0°

igure 7. Some integrated experimental spectra of the � = 90° im-ge, selected from 0° �parallel to the foliation, bottom� to 90° �per-endicular to the foliation, top�. Compare with Figure 4c.

001x

y

010

igure 8. Pole figures �001�, �010�, and �100� for illite. Equal area pic pole density scale in multiples of random distribution �MRD�. Th

orresponds to that in Figure 2.

0–11 reflection indicated by arrows in Figure 6�. The quartz 10–11iffraction peak is superposed on the illite 006 reflection �Figure 5�.he strong alignment of the illite �001� planes is also evident in rela-

ive intensity differences in Figure 7, with spectra at different angleso the bedding plane.

RESULTS

Information about microstructure, atomic coordinates, and latticearameters can be extracted from the intensity, width, and the posi-ion in d-spacing of the diffraction peaks. Table 2 lists refined crys-allographic parameters for illite. The poor crystallinity of the sam-le and elastic microdistortions because of the presence of defectsnd heterogeneities do not permit a good refinement of the crystaltructure, but significant deviations from the muscovite startingtructure �Comodi and Zanazzi, 1995� are apparent. Lattice parame-ers are similar and atomic positions are well-constrained, with larg-st shifts from the ideal muscovite structure for oxygens and hydrox-ls. The size of the coherently diffracting domains evaluated fromhe line broadening of all hkl reflections show that crystallite dimen-ions are largest normal to �100� �44.5 nm� and �010� �49.1 nm�,nd smallest perpendicular to �001� �15.1 nm�. This is consistentith the sheet morphology of clay platelets and likely stacking faults

nd intercalation. The quantitative phase analysis gives a small vol-me fraction of quartz �3%�.

The MAUD-generated OD was exported and used in BEARTEXWenk et al., 1998� for further processing. From the OD, �100�,010�, and �001� pole figures were calculated for a visual texture rep-esentation �Figure 8�. Table 3 gives additional quantitative texturenformation such as texture index �Bunge, 1982�, minimum and

aximum of OD and of pole figures. The pole figures display thathe texture is close to axially symmetric around the direction perpen-icular to the foliation plane. The strong �001� maximum has a con-entration of 9.77 multiples of a random distribution �MRD� �Figurea�, indicating that almost 10 times as many �001� lattice planes aren this orientation as they would be in a randomly oriented powder.he minimum value of zero indicates that not a significant number ofrystallites are oriented with �001� perpendicular to the foliationlane. The width of the �001� texture peak �at half maximum� isbout 35°. �100� and �010� pole figures display small but distinct dif-erences and deviations from axial symmetry. There are two possi-le interpretations: Either this may be caused by a wavy alignment of001� platelets in the north-south plane �Figure 8a�, corresponding toipples and producing a lineation, or platelets have different �100�

and �010� dimensions, and align, for example,during flow. This would need to be investigatedwith a systematic study of oriented samples and isoutside the present scope. The fact that �100� and�010� pole figures are very similar indicates alikely fiber symmetry about the crystallographic�001� normal, at least in this sample.

DISCUSSION

As has been outlined by Hornby et al. �1994�,the elastic properties of shale depend on single

9.5

1 MRD

0.1

on. Logarith-inate system

100

rojectie coord

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Preferred orientation and elastic anisotropy E73

rystal properties, the orientation of clay particles, and the presencef fluid-filled pores and microcracks �O’Connell and Budiansky,976; Crampin, 1981; Schoenberg and Sayers, 1995�. From theeasured OD, we can evaluate the contribution of crystallite orien-

ation to elastic properties and their anisotropy ofhe aggregate. Unfortunately, elastic propertiesf clay minerals are poorly known �Katahara,996�. For this study, we have used the elastictiffness moduli of muscovite measured by Bril-ouin scattering �Vaughan and Guggenheim,986�, where muscovite is treated as monoclinicTable 4�.

Using the OD, we then calculate polycrystallastic properties by averaging over all orienta-ions, i.e., the orientation distribution. These elas-ic constants, listed in Table 4, describe the aniso-ropy resulting from the aligned crystallites of il-ite and do not include the possible contributionsrom aligned porosity. A total of 21 elastic con-tants are required to describe the elastic tensor oftriclinic material. Different averaging schemes

re used, such as Voigt �uniform strain� and Re-ss �uniform stress� �Bunge, 1985�, as well as aelf-consistent average �Kroener, 1961�. All ofhese schemes simplify the problem and do notake into account the grain shape and grain shapeistribution. A geometric mean �Matthies andumbert, 1993� has been shown to provide rea-

onable results for many materials. The elasticonstants of the illite aggregate, calculated withoigt, Reuss, and geometric mean models are

isted in Table 4. The aggregate stiffness coeffi-ients indicate an approximation to transversesotropy with C11 close to C22 and all off-diagonaloefficients I, J �3 close to zero, but in detailhey deviate. There are considerable differencesetween the different averaging models: Voigt isn upper bound, whereas Reuss is a lower bound,nd the geometric mean is intermediate. Voigtay be more applicable for elastic waves propa-

ating parallel to the foliation and Reuss for thoseerpendicular to it, based on grain-shape consid-rations �Bunge, 1985�. Using elastic propertiesf muscovite for illite introduces uncertainties instimating polycrystal properties, and actual val-es may be beyond Voigt and Reuss bounds.

A reduced expression to describe anisotropy inhales has been introduced by Thomsen �1986�.hese parameters assume transverse isotropy i.e., axial symmetrybout the foliation normal�,

� = �C11 − C33�/�2C33� �1�

� = �C66 − C55�/�2C55� �2�

� = ��C13 + C55�2 − �C33 − C55�2�/

�2C33�C33 − C55�� . �3�

Table 3. Quaof a randomhalf maximu

Texture inde�F2�

4.02

Table 4. Elaillite aggrega

M

C11

C12

C13

C14

C15

C16

C22

C23

C24

C25

C26

C33

C34

C35

C36

C44

C45

C46

C55

C56

C66

hese parameters are listed in Table 5, and a � − � plot for the vari-us illite averages is compared in Figure 9 with values for shales-rom the literature �Thomsen, 1986; Vernik and Nur, 1992; Wang,002�. The illite aggregate shows a strong anisotropy with high

ive texture information for OD and pole figures in multiplesution (MRD) and width of main texture peak (full width at

ODmax/min�

�001��max/min�

�010��max/min�

�100��max/min�

FWHM�001�

9.63/0.0 9.77/0.01 1.96/0.03 2.31/0.03 35°

ffnesses for monoclinic muscovite single crystal and triclinica).

vite Illite aggregate

cl.� �Voigt� �Reuss� �Geom. mean�

0 161.24 122.59 147.38

8 42.19 33.87 40.66

6 33.31 29.48 33.03

−0.019 0.099 −0.044

2 −6.899 −5.277 −6.786

−0.662 −1.018 −0.910

4 158.28 117.03 142.69

2 33.34 29.07 32.92

−0.188 −0.093 −0.155

1 −1.107 −0.784 −1.014

−0.582 −0.767 −0.749

6 72.07 62.47 66.32

−0.012 −0.011 −0.012

0 −1.957 −0.860 −1.394

0.116 −0.021 0.081

5 30.91 21.56 24.75

−0.102 −0.035

2 −3.045 −2.365 −3.006

5 31.47 21.85 25.22

−0.029 0.036 0.012

0 58.86 42.83 52.18

able 5. Anisotropy parameters and wave velocities (inm/s, assuming a density of 2.79 g/cm3).

Thomsenparameters

Muscovite Illite aggregate

�Voigt� �Reuss� �Geom. mean�

� 1.044 0.618 0.481 0.611

� 1.682 0.452 0.493 0.554

� 0.000 0.409 0.182 0.292

ntitatdistribm).

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0

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0

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0

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B

B

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M

M

M

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E74 Wenk et al.

homsen’s parameters � and �. It also illustrates a rather wide dis-ersion for the different averages, indicating the need for further re-earch to establish the most appropriate averaging scheme for shalesSayers, 2005�.

CONCLUSIONS

A new experimental method is described to obtain quantitativeexture information for clay minerals in shales. The synchrotron-ray diffraction measurements, combined with Rietveld image

nalysis provides information about the orientation distribution thats a primary ingredient for modeling aggregate elastic properties.his first application describes primarily the methodology and ap-lies it to a simple system: illite with a minor amount of quartz. In theuture, this method can be applied to other samples of shales with aore complex composition, and particularly to shales for which an-

sotropy of acoustic waves has been experimentally established.ith such information, one can then progress to comprehensiveodels to better understand the various factors influencing seismic

nisotropy in sedimentary rocks.

ACKNOWLEDGMENTS

Financial support from DOE-BES �DE-FG02-05ER15637� andSF �EAR 0337006� is gratefully acknowledged. We are apprecia-

ive for access to facilities at HASYLAB. Part of this research wasone while Wenk was on sabbatical leave at GFZ, Potsdam, and he ishankful for their hospitality. We are grateful for comments by refer-es that helped to improve the manuscript.

0.1

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Thomsen (1986)Vernik and Nur (1992)Wang (2002)Illite VoigtIllite geometric meanIllite Reuss

γ

ε

Shales and Illite

igure 9. Plot of Thomsen anisotropy parameters � versus � forhales studied by various authors �from Sayers, 2005�, and addingata for the illite sample investigated in this paper.

REFERENCES

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