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1 Jour. Geol. Soc. Japan, Vol. 106, No. 5, p , May 2000 X CT Observation and analysis of internal structure of rock using X-ray CT * ** *** **** Tsukasa Nakano *, Yoshito Nakashima **, Ko-ichi Nakamura *** and Susumu Ikeda **** * Geological Information Center, Geological Survey of Japan, 1-1-3, Higashi, Tsukuba , Japan ** Geophysics Department, Geological Survey of Japan, 1-1-3, Higashi, Tsukuba , Japan *** Marine Geology Department, Geological Survey of Japan, 1-1-3, Higashi, Tsukuba , Japan **** Geological Institute, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo , Japan 23 August October November December May 2000

2 :2 X CT

3 :3 X CT Computerized Tomography X LAC CT LAC X X CT X LAC X CT FBP CBP CT X CT CT X X CT X CT

4 :4 Abstract X-ray computerized tomography (CT) is a technique to reconstruct a CT image showing the spatial distribution of X-ray linear absorption coefficients (LAC s) of the materials in a sample. This technique allows us to observe and to analyze the three-dimensional precise internal structure of rock non-destructively. The LAC is a physical property which depends on density, state and chemical composition of the material and X-ray energy used in the measurement. Chemical composition of a material greatly affects the LAC for the photon energy level of the medical X-ray CT scanners. Filtered back-projection (FBP) method and convolution back-projection (CBP) method are applied to the reconstruction of a CT image from the obtained X-ray projection data. A suitable choice of a reconstruction filter in the methods enables us to enhance the target texture in the image. An artifact called beam hardening occurs in the CT image obtained by the CT scanner with polychromatic X- ray. This artifact can be reduced by the use of a suitable pad for the sample and / or by the correction of the image using spectrum data of the X-ray source used in the measurement and bulk density and chemical composition of the sample material. To apply the X-ray CT to advanced observation and quantitative analysis of the internal structure of rock, it is necessary to understand the basic theory and the detailed techniques used in the X-ray CT.

5 :5 Ke y words : X-ray CT X-ray linear absorption coefficient (LAC) filtered back-projection (FBP) and convolution back-projection (CBP) methods reconstruction filter X-ray spectrum beam hardening internal structure of rock

6 :6 X CT Computerized Tomography X CT X X X X-ray Linear Absorption Coefficient LAC 1979 X CT CT LAC CT X CT CT X CT Hounsfield 1973 Ambrose 1973 X CT X CT 1 X X generation CT X X X X X 1 / 100 CT Misawa et al X CT X CT CT

7 :7 X CT 120 kv X X X CT S/N 10 cm X CT X CT artifact X X CT beam hardening CT CT X X Bonse and Busch 1996 Uesugi et al X CT X CT CT X X CT 2 3 X CT CT CT X X 0.1 1mm Shibata and Nagano 1996 Nakashima et al Kondo et al µm CT X CT X X X CT 0.1 % Hirano et al X CT 0.1 g / cm 3 X CT CT EPMA CT

8 :8 CT CT X CT X CT CT X CT X CT CT X S I 0 X I I = I 0 e µ S [1] Koch and MacGillavry 1962 [1] projection X p p = ln(i 0 / I) = µ S [2] µ X LAC cm -1 X [2] p X S p / S = µ = X CT LAC ρ g/cm 3 τ cm 2 /g X X-ray Mass Absorption Coefficient MAC MAC X τ = µ / ρ = w j Σ w j τ j (E) [3] j Σ w j = 1 j τ j (E) j E X j MAC

9 :9 Hubbell and Seltzer 1996 electron-pair creation MeV X τ j (E) Koch and MacGillavry 1962 τ j (E) = {σ R j (E) + σ P j (E) + σ C (E)} N Z j / A j [4] N Av ogadro Z j A j j σ R j (E) σ P j (E) σ C (E) photon interaction cross section per electron Rayleigh Compton Compton σ C (E) j X CT X 30 E 100 kev Z j 20 j Z j X E kev McCullough 1975 σ R j (E) = Z 2.00 j E 1.9 σ P j (E) = Z 3.8 j E 3.2 σ C (E) = e (E 30) [5] 4 X Compton X X Rayleigh [4] Z j / A j 1/2 Compton MeV X MAC X LAC CT X CT X LAC CT Si O g / cm 3 KAlSi 3 O g / cm 3 X CT CT Ikeda et al. 1999

10 :10 X MAC LAC [5] X absorption edge Koch and MacGillavry 1962 X X CT Hirano et al X CT X K kev X X X CT Radon X CT X CT CT X X Z CT Z X X CT Uesugi et al Z X Z X p [2] p = Σ µ k S k k [6]

11 :11 µ k S k k LAC X X k S k [6] p µ k X [6] LAC µ k CT ART Algebraic Reconstruction Technique Herman 1980 CT 1988 X CT CT ART Filtered Back-Projection method FBP Convolution Back-Projection method CBP 1983 CBP X CT FBP FBP CBP X CT X p(r) r Fourier r X 1 X r p(r) r z r cm z cm -1 G(z) = z W(z) [7] p(r) filtering G(z) reconstruction filter W(z) window function p(r) r W(z) 1 1 δ r = δ l l = 0, ± 1,...

12 : p(r) 0 W(z) W(z) = 1 z <z * 0 z z * [8] z * Nyquist X δ z * = 1/(2 δ ) [9] p(r) z * 0 CT δ CT 2 δ [8] Ramachandran 1983 X CT [7] sinc Hanning W(z) = sin( π 2 z z * )/( π 2 z z * ) [10] W(z) = cos(π z z * ) [11] [7] Shepp [10] Chesler [11] [8] p(r) r 2(b) 3 p(r) Chesler [8] [8] Gibbs

13 : CT CT 6 LAC LAC X p(r) LAC p(r) CT 6 CT δ Nyquist z * 5 Gibbs CT CT CT 6 CT CT CT CT CT X CT FBP back-projection CT CT X CT X CT CT

14 :14 X CT CT X CT Gibbs Shepp X CT [2] [6] X X X X CT CT X S X E [1] X i 0 (E) 7 (a) LAC µ(e) 7 (b) E I 0 = i 0 (E) de 0 I(S) = i 0 (E) e µ(e) S de 0 [12] [12] p(s) S 7 (c) X i 0 (E) E p(s) /S = f (S) f (S) S [13] S X LAC f (S) 7 (d) X X CT

15 :15 X CT X X CT X X CT CT beam hardening X CT CT 8 CT CT CT 8 (c) CT CT 1cm X CT CT [12] X LAC MeV X CT X X Bonse and Busch 1996 X Stonestrom et al CT CT CT CT X mm X CT CT

16 :16 9 X CT X CT X CT S p(s) 7 (c) S(p) Herman 1980 p p =S(p) p [13] LAC 1 Olson et al X CT X CT Meagher et al CT X CT CT OBS SIM CT OBS X S OBS X 7 (a) LAC 7 (b) X p(s) 7 (c) SIM OBS

17 :17 OBS X CT CT X CT X CT CT CT CT CT CT HU Hounsfield Unit 1979 [3] CT LAC 1g/cm 3 CT CT g / cm 3 X LAC X CT X CT LAC cm -1 CT 0 CT CT 1993 X CT CT X CT CT X CT CT-W2000 CT 7(a) X CT 5 Shepp

18 :18 9 VER-98-1 St. 6 PC Sec. 3B X CT 1010 mm 12 cm mm CT 1mm mm CT CT 10 7cm GSJ-R CT mm 10 (a) X CT CT OBS X 7 (a) X LAC 7 (b) G OBS 10 (b) SIM OBS SIM BHC 10 (c) 10 (d) CT OBS SIM BHC CT 11 CT Ikeda et al cm GSJ-R

19 : mm CT 0.5 mm 50 CT CT CT (a) 11 (b) CT CT CT CT 11 (c) 11 (b) 11 (d) 11 (e) cluster labeling Nakano and Fujii (f) 90 % 1997 CT CT EPMA X

20 :20 CT CT X CT X CT X CT X CT 1995 X CT Denison et al X CT X CT X SPring-8 X CT X CT X CT X CT

21 :21 SPring A X CT Ambrose J Computerized transverse axial scanning (Tomography), Part 2, clinical application Brit. Jour. Radiol Bonse U. and Busch F X-ray computed microtomography (µct) using syncrotron radiation (SR) Prog. Biophys. molec. Biol Denison C. Carlson W.D. and Ketcham R.A Three-dimensional quantitative textural analysis of metamorphic rocks using high-resolution computed X-ray tomography : part I. methods and techniques Jour. Metamorph. Geol Herman G.T Image reconstruction from projections Academic Press 316p. Hirano T. Eguchi S. and Usami K Study of quantitative elemental analysis of monochromatic X-ray CT using synchrotron radiation Jpn. Jour. Appl. Phys Hubbell J.H. and Seltzer S.M Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 kev to 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetric interest URL = http: // physics.nist.gov / PhysRefData / XrayMassCoef / cover.html. Hounsfield G.N Computerized transverse axial scanning (Tomography), Part 1, description of system Brit. Jour. Radiol Ikeda S. Nakano T. and Nakashima Y Three-dimensional study on the interconnection and shape of crystals in a graphic granite by X-ray CT and image analysis Mineal. Mag. in press P 9 222p.

22 :22 Irving A. J Pyroxene-rich ultramafic xenolith in the newer basalts of Victoria, Australia N. Jahrb. Mineral. Abh p CT 288p X CT X CT Koch B. and MacGillavry C.H X-ray absorption in International Tables for X-ray crystallography vol. III MacGillavry C.H. and Rieck G.D. eds. The Kynoch Press Kondo M. Tsuchiyama A. Hirai H. and Koishikawa A High resolution X-ray computed tomographic (CT) images of chondrites and a chondrule Antarct. Meteorite Res McCullough E.C Photon attenuation in computed tomography Med. Phys Meagher J.M. Mote C.D. and Skinner H.B CT image correction for beam hardening using simulated projection data IEEE Trans. Nucl. Sci CQ 238p. Misawa M. Ichikawa N. Akai M. Hori K. Tamura K. and Matsui G Development of fast X-ray CT system for transient two-phase flow measurement 6th Int. Conf. on Nuclear Engineering San Diego No CD-ROM. Miyazaki K Ostwald ripening of garnet in high P / T metamorphic rocks Contrib. Mineral. Petrol Nakano T. and Fujii N The multiphase grain control percolation : its implication for a partially molten rock Jour. Geophys. Res (7)

23 : X CT (1) CT Nakashima Y. Hirai H. Koishikawa A. and Ohtani T Three-dimensional imaging of arrays of fluid inclusion in fluorite by high-resolution X-ray CT N. Jahrb. Mineral. Mh X CT Olson E.A. Han K.S. and Pisano D.J CT projection polychromaticy correction for three attenuators IEEE Trans. Nucl. Sci I 163p. Shibata T. and Nagano T Applying very heigh resolution microfocus X-ray CT and 3-D reconstruction to the human auditory appratus Nature Medicine Stonestrom J.P. Alvarez R.E. and Macovski A A framework for spectral artifact corrections in X-ray CT IEEE Trans. Biomed. Eng Takagi H. Ishii K. and Kanagaw a K Pressure frings and pressure shadows indicative of progressive deformation Jour. Geol. Soc. Japan 102 IX X. Uesugi K. Tsuchiyama A. Nakano T. Suzuki Y. Yagi N. Umetani K. and Kohmura Y Development of micro-tomography imaging system for rock and mineral samples SPIE Conference on Developments in X-ray Tomography II Proc. SPIE FBP CBP X CT 1 X CT CT θ s X r r s CT (x, y) r s θ x y = cos θ, sin θ, sin θ r cos θ s [A1]

24 :24 X CT 1 X X FBP CBP CT X FBP CBP [6] p(r, θ ) = f (x, y) ds [A2] p(r, θ ) θ X r X f (x, y) θ r X s [A1] (x, y) LAC [A2] s f (x, y) 0 p(r, θ ) f (x, y) FBP f (x, y) Fourier F(t, u) F(t, u) = f (x, y) e 2 π i (t x + u y) dx dy [A3] i t u x y [A3] z θ P(z, θ ) [A1] [A2] P(z, θ ) F(z cos θ, z sin θ ) = f (x, y) e 2 π i z (x cos θ + y sin θ ) dx dy = f (x, y) e 2 π i z r dr ds = p(r, θ ) e 2 π i z r dr [A4] P(z, θ ) p(r, θ ) Fourier [A3] f (x, y) Fourier f (x, y) = F(t, u) e2 π i (t x + u y) dt du [A5] (t, u)

25 :25 t = z cos θ u = z sin θ < z < 0 θ π [A6] [A5] f (x, y) = π 0 F(z cos θ, z sin θ ) e2 π i z (x cos θ + y sin θ ) z dz dθ [A7] [A7] z G(z) [A7] [A1] [A4] G(z) z q(r, θ ) = P(z, θ ) G(z) e2 π i z r dz [A8] [A9] f (x, y) = π 0 q(x cos θ + y sin θ, θ ) dθ [A10] [A4] [A8] [A9] [A10] FBP p(r, θ ) (x, y) LAC f (x, y) [A9] q(r, θ ) θ X p(r, θ ) r z G(z) filtering [A4] [A8] [A9] [A10] X θ q(r, θ ) θ LAC back-projection [A9] P(z, θ ) G(z) Fourier P(z, θ ) Fourier p(r, θ ) G(z) Fourier g(r) convolution q(r, θ ) g(r) = G(z) e2 π i z r dz [A11] q(r, θ ) = p(r, θ ) g(r r ) dr [A12] FBP [A4] [A9] CBP [A11]

26 :26 CT CBP G(z) [A8] [A11] CBP FBP r θ CT

27 :27 1 X CT 180 X s X X X X r CT θ x y (x, y) (r, s) 2 X CT CT 20 cm (a) X CT CT-W mm CT 130 kv X X CT X (b) X CT HiXCT-3M X mm CT MV X X X CT MeV X CT LAC CT 1 Noorat Irving Takagi et al Kohistan mm Miyazaki 1991

28 :28 3 SPring-8 X CT Allende X CT Uesugi et al kev X 300 X 6 µm 6 6 µm 2 CT mm 3 (a) LAC 7.5 cm -1 CT (b) (c) (d) CT (d) X CT LAC X CT (d) 20 cm -1 LAC X 20 kev LAC g / cm 3 LAC cm -1 (b) 4 MAC X T MAC Rayleigh Compton R P C [4] [5] McCullough 1975 R +P+C= T MAC R +P +C=1 T MAC Hubbell and Seltzer FBP CBP W(z) [8] [10] [11] [7] G(z) z z * Nyquist [9]

29 :29 6 LAC 1 CT CT δ X 5 CT δ X CT X 1 7 X (a) X CT CT-W2000 X 120 kv ma X X 1mm 0.1 mm (b) GSJ-R X LAC Hubbel and Seltzer 1996 X MAC [3] LAC (c) 7 (a) X 7 (b) LAC X [12] (d) 7 (c) [13] LAC 8 X CT CT-W2000 CT (a) X CT CT OBS mm (b) OBS X 7 (a) OBS SIM (c) OBS SIM CT OBS Fobs SIM fsim OBS SIM CT

30 :30 CT 9 VER-98-1 St. 6 PC Sec. 3B X CT 1010 CT histogram equalization 1995 CT 12 cm 5mm CT 10 GSJ-R X CT (a) X CT CT OBS (b) OBS SIM (c) OBS Fobs SIM fsim Fbhc BHC (d) 10 (a) (b) (c) CT BHC CT OBS SIM mm 50 X CT GSJ-R Ikeda et al (a) CT CT mm (b) 11 (a) CT z=0 z=49 CT (c) 11 (a) CT df HU (d) 11 (c) 11 (b) (e) 11 (d) 11 (d) z=0 z=49 (f) 11 (e)

31 :31 11 (a) (c) HU CT 11 (b) (d)

32 r δ y x r = 0 s θ X I X I 0 X 1 65 %

33 (a) 2 3 (b) CT (HU) (g/cm3) %

34 (a) (b) (c) (d) 0 LAC (1/cm) %

35 O : Z = 8, A = Si : Z = 14, A = Fe : Z = 26, A = log(mac, cm2/g) R T C P log(mac, cm2/g) R P T C log(mac, cm2/g) C P R T (kev) 100 R P 30 (kev) 100 C (kev) 100 P R 30 (kev) 100 C (kev) 100 P 30 (kev) 100 C R 4 70 %

36 W(z) 1 Ramachandran sinc Shepp Hanning Chesler 0 G(z) z * z z * Ramachandran Chesler Shepp 0 z * z 5 70 %

37 Ramachandran 50 δ 150 δ 250 δ 350 δ 450 δ Shepp 50 δ 150 δ 250 δ 350 δ 450 δ Chesler 50 δ 150 δ 250 δ 350 δ 450 δ δ δ δ δ +4 δ 4 δ +4 δ 4 δ +4 δ 6 65 %

38 10000 (a) X i0 X i0 X = 120 kv / 0.5~0.6 ma = Al (1 mm) + Cu (0.1 mm) = X E (kev) 150 (b) X LAC µ (g/cm3) log( µ, 1/cm) 2 X LAC f (1/cm) 8X p B (c) X p = log(i0 / I) G K Q W 0 0 X S (cm) 10 (d) X LAC CT f = p / S B K G Q B: G: GSJ-R26347 K: Q: W: Ca3 P2 O8 K Al Si3 O8 Si O2 H2 O B G K Q 0.1 W 0 X E (kev) X S (cm) 10 W 7 80 %

39 Si O2, 2.65 g/cm3, * 3.13 cm2 Al, 2.66 g/cm3, * cm2 Al2 O3, 3.85 g/cm3, * cm2 Ca S O4 + 2 H2 O, 2.31 g/cm3, * cm2 Ca C O3, 2.72 g/cm3, * cm2 (b) SIM (a) OBS Fobs (HU) Fobs (HU) Fobs (HU) Fobs (HU) Fobs (HU) fsim (1/cm) fsim (1/cm) fsim (1/cm) fsim (1/cm) fsim (1/cm) (c) Fobs (HU) Fobs = * fsim Fobs fsim fsim (1/cm) Fobs (HU) Fobs = * fsim Fobs fsim fsim (1/cm) Fobs (HU) Fobs = * fsim Fobs fsim fsim (1/cm) Fobs (HU) Fobs = * fsim Fobs fsim fsim (1/cm) Fobs (HU) Fobs = * fsim Fobs fsim fsim (1/cm) %

40 VER-98-1, St.6, PC, Sec.3B : = 1010 (mm), lay-x = 196 / 393 ( mm), lay-y = 197 / 395 ( mm) lay-x CT (HU) lay-y (mm) 9 80 %

41 (a) OBS 219 * 219 pixels / * cm2 (b) SIM 438 * 438 pixels / * cm2 (c) BHC 219 * 219 pixels / * cm2 (d) Fobs (HU) CT Fobs = * fsim Fobs fsim fsim (1/cm) Fbhc Fobs (HU) fsim (1/cm) Fbhc %

42 (e) z = (a) (b) df = (f) (c) (d) %

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