Darkfield Reflection Visible Microspectroscopy Equipped with a Color Mapping System of a Brown Altered Granite

Abstract

Visible darkfield reflectance spectroscopy equipped with a color mapping system has been developed and applied to a brown-colored Rokko granite sample. Sample reflectance spectra converted to Kubelka–Munk (KM) spectra show similar features to goethite and lepidocrocite. Raman microspectroscopy on the granite sample surface confirms the presence of these minerals. Here, L*a*b* color values (second Commission Internationale d'Eclairage [CIELab] 1976 color space) were determined from the sample reflection spectra. Grey, yellow, and brown zones of the granite show different L*, a*, and b* values. In the a*-b* diagram, a* and b* values in the grey and brown zones are on the lepidocrocite/ferrihydrite trends, but their values in the brown zone are larger than those in the grey zone. The yellow zone shows data points close to the goethite trend. Iron (hydr)oxide-rich areas can be visualized by means of large a* and b* values in the L*, a*, and b* maps. Although the present method has some problems and limitations, the visible darkfield reflectance spectroscopy can be a useful method for colored-material characterization.

Keywords

Visible microspectroscopy Darkfield Color mapping Iron hydroxides Granite

INTRODUCTION

Color is useful information in various fields. In Earth science, colors of natural materials are usually one of their most outstanding visual characteristics. In fact, Earth scientists describe their colors as the first property. Color is also one of the most useful properties for soil identification and appraisal.¹ In agricultural and food industries, color is an important component of quality. Consumers make purchasing decisions by color as a primary consideration because color is closely associated with freshness, ripeness, desirability, and food safety.^2,3

However, “color” is observed differently between individuals because color perception depends on the response of the eye to each wavelength. Therefore, measurements of visible reflectance spectra including 400–700 nm region and subsequent conversion to quantitative color values such as L*, a*, and b* are recommended by Commission Internationale d'Eclairage (CIELab) for describing colors of materials.⁴

Nagano and Nakashima⁵ used this spectrocolorimetry for analyzing color changes upon granite weathering and found that b* value (yellowishness) increased with increasing rock weathering. Since then, geo-engineers tried to use colors of various rocks for evaluating rock quality.⁶

The formation of yellow-brownish or reddish products upon weathering and alteration of rocks is a very common phenomenon occurring at the earth's surface (Fig. 1). These products are often iron oxyhydroxides in various chemical forms and have microscopic sizes (micrometers to nanometers). Therefore, a spectrocolorimeter under the optical microscope was needed for studying these microscopic alteration products. Nagano et al.⁷ developed a charge-coupled device (CCD) visible microspectrometer enabling measurements of visible reflectance spectra and color values in microscopic points in rocks, and they found the formation of iron hydroxides around biotite.

Fig. 1.

(a) An outcrop of granite rocks at Ashiya, Hyogo, Japan. A rock fragment was taken from a red-dotted zone. (b) A cut piece of the granite fragment: 18 × 18 mm. (c) A magnified figure of a blue-dotted rectangle in (b). The red long rectangle is the mapped area for visible microspectroscopy.

However, these alteration products are often distributed heterogeneously in rocks with brownish or reddish fronts (Fig. 1). Therefore, spectrocolorimetry in two-dimensional space is required for quantifying the distribution of colored materials in rocks. Although color digital cameras can obtain color images of materials, color values depend on manufacturers and models with a lack of universal color conversion algorisms.

We have developed in this study a visible darkfield reflectance microspectrometer equipped with an automated x,y stage and a batch conversion software of mapped spectra to L*, a*, and b* color values.

EXPERIMENTAL METHODS

Materials. In order to study microscopic color changes of rocks, a rock sample (granite) from an outcrop at Ashiya, Hyogo, Japan, was selected because the outcrop shows granite rock blocks (several tens of centimeters) with brownish colors spreading from the block surfaces (Fig. 1a). A fragment of a block containing borders of grey and brown zones (red-dotted rectangle in Fig. 1a) was taken from the outcrop and cut into an 18 × 18 mm slab (Fig. 1b). One of the slab surfaces was polished up to diamond paste (1 μm) level (Fig. 1b).

The granite belongs to Rokko granite (late Cretaceous) and is composed of quartz (33–43 volume %), pink K-feldspar (30–50%), plagioclase (12–28%), and biotite (0.5–7.6%).⁸

Visible and Raman Microspectroscopy. The analytical instrument used in this study is a home-built visible and Raman microspectrometer (Fig. 2). This microspectrometer is composed of an optical microscope (Olympus BX50), a dispersive spectrometer with three grating monochromators (Acton Research SpectraPro 300i SP-306), and a charge-coupled device (CCD) detector with 256×1024 elements (Andor DU420-OE; Fig. 2).

Fig. 2.

Visible and Raman microspectrometer equipped with darkfield optics and a color mapping system.

Visible spectra can be obtained in the wavelength region of 380–850 nm by using a 150 lines/mm grating. The spectral resolution is about 0.5 nm. In order to obtain a high signal-to-noise (S/N) ratio in the region, the near-infrared (NIR) cutoff filter set at the halogen light source of the optical microscope is removed.⁹ An Olympus LBD filter was added after the reflection light source (Fig. 2). For removing specular reflection components, a darkfield beam splitter was added to the reflection optics, and a darkfield type objective lens (5×) was used. The spatial resolution is about 20 μm by the use of 100 μm φ optical fiber connecting the microscope to the spectrometer.

Raman spectra were acquired in the 50–1950 cm⁻¹ range by using a 1200 lines/mm grating. The spectral resolution was larger than 2 cm⁻¹. A 532 nm double frequency neodymium-doped yttrium aluminum garnet (Nd:YAG) laser with a power of 100 mW was used in this study as an excitation source, and its power could be changed by neutral density filters. The scattered light from the sample passed through a notch filter to cut off the Rayleigh scattering. By using a 50× objective lens, the spatial resolution was larger than 2 μm. Raman spectra were measured in some points of the granite sample with the following conditions: 0.36 mW laser power, 50× objective lens, 30 s integration time, and accumulation numbers of 8.

Raman spectra of four standard powder samples (two-line ferrihydrite, goethite, lepidocrocite, and hematite) were also measured in aluminum pans with the following conditions: 0.22 mW laser power, 50× objective lens, 30 s integration time, and accumulation numbers of 5.

Analytical Methods. Visible reflectance spectra were measured on the sample surfaces (S) against the reflectance spectrum of white SiO₂ powder (B) placed in an aluminum pan with dark (D) subtraction [reflectance R = (S – D)/(B – D)]. For the spot measurement with high S/N ratio, 20 s of exposure time (three times) was employed, while for the mapping measurement, 1 s exposure was used for reducing the long duration of time. The mapping measurement area of the granite sample was 100 × 18 000 μm crossing a border of grey and brown zones (red elongated rectangle in Fig. 1b). The reflectance spectra were obtained every 20 μm with the 5× darkfield objective lens with the exposure time of 1 s.

For the better representation of absorption bands, Kubelka-Munk (KM) functions were applied to the sample reflectance spectra R, using the following KM transformation:

K M = \frac{{(1 - R)}^{2}}{2 R}

For the quantitative representation of colors of samples, the L*a*b* color space (second CIELab 1976 color space) was employed here.^7,9 The L* represents lightness (L* = 0: black and L* = 100: white), and a* and b* represent chromaticity (+a*: reddish, –a*: greenish, +b*: yellowish and – b*: bluish). In this study, these values are calculated assuming a CIE standard illuminant D₆₅, an observer of 10° field of view, and a wavelength range of 400–760 nm. Here, L*a*b* color values were determined from the sample reflectance spectra (100R) based on the CIE XYZ color system. The X, Y, Z tristimulus values are obtained by the following equations:⁴

X = k \int S (λ) R (λ) \bar{x} (λ) d λ

Y = k \int S (λ) R (λ) \bar{y} (λ) d λ

Z = k \int S (λ) R (λ) \bar{z} (λ) d λ

where S(λ) is a spectral distribution of illuminating light source, R(λ) is the sample reflectance spectrum, X̄(λ), ȳ(λ), and z̄ (λ) are the color-matching functions, and k is the normalization constant given by k = 100/[S(λ)ȳ (λ)dλ]. Then L*, a*, and b* values are calculated by the following equations:⁴

L * = 116 {(\frac{Y}{Y_{n}})}^{1 / 3} - 16

a * = 500 [{(\frac{X}{X_{n}})}^{1 / 3} - {(\frac{Y}{Y_{n}})}^{1 / 3}]

b * = 200 [{(\frac{Y}{Y_{n}})}^{1 / 3} - {(\frac{Z}{Z_{n}})}^{1 / 3}]

where X_n, Y_n, and Z_n are tristimulus values of the nominally white objective-color stimulus. These equations were with the constraints that X/X_n, Y/Y_n, and Z/Z_n > 0.01.

RESULTS

Visible Reflectance Spectra of Standard Fe (Hydr)oxides. Visible reflectance spectra of the standard Fe (hydr)oxide powders in aluminum pans under the visible microspectrometer are shown in Figs. 3a-3d. The reflectance spectrum for goethite shows a broad absorption band around 500 nm together with a small band around 420 nm and a broad band around 650 nm. The spectrum of ferrihydrite exhibits very low reflectivity at shorter wavelength region and a gradual increase in reflectance toward higher wavelength region. For lepidocrocite, the reflectance increases rapidly from around 550 nm. The increase in reflectance of hematite starts around 570 nm and continues up to around 720 nm.

Fig. 3.

Visible spectra of the standard Fe (hydr)oxide powders. The reflectance spectra of (a) goethite, (b) ferrihydrite, (c) lepidocrocite, and (d) hematite. The Kubelka–Munk (KM) spectra of (e) goethite, (f) ferrihydrite, (g) lepidocrocite, and (h) hematite converted from the reflectance spectra (a)–(d), respectively.

They are converted to Kubelka-Munk (KM) spectra by the Eq. 1 (Figs. 3e-3h). The absorption band for goethite is around 550–450 nm. This is consistent with the reported 480 nm band due to paired transition (double excitation) of Fe³⁺ electrons (2[⁶A₁ → ⁴T₁]).^10,11 This absorption band shifts to longer wavelength for lepidocrocite, ferrihydrite, and hematite, which correspond to 485, 500, and 530 nm bands due to the same Fe³⁺-Fe³⁺ electron pair transition of lepidocrocite, ferrihydrite, and hematite, respectively.^10,11

Goethite has additional absorption bands around 435 nm ([⁶A₁ → ⁴A₁, ⁴E]) and 650 nm ([⁶A₁ → ⁴T₂]) bands due to ligand field splitting of Fe³⁺ electrons^10,11 on the strong absorption tail to the ultraviolet (UV) region due to O^2–-Fe³⁺ charge transfer transition.¹¹

Visible Reflectance Spectra on the Rokko Granite Sample. Representative reflectance spectra obtained from the granite sample are shown in Figs. 4a–4c. They are also converted to KM spectra (Figs. 4d-4f). The KM spectrum (Fig. 4d) shows a weak absorption shoulder around 480 nm similar to that of goethite (Fig. 3e). Spectral features of Fig. 4f are somewhat similar to lepidocrocite (Fig. 3g) with a gradual decrease in absorption toward 580–600 nm. Figure 4e shows some-what similar features to goethite with a band around 480 nm. However, its UV tail does not rise up to the shorter wavelength region unlike the goethite spectrum (Fig. 3e). This flat UV tail can be reproduced by mixtures of goethite + lepidocrocite. Therefore, this type of spectrum (Fig. 4e) can be considered as mixtures of goethite and lepidocrocite.

Fig. 4.

(a)–(c) Visible reflectance spectra obtained from the granite sample. The KM spectra converted from (a)–(c), respectively: (d) goethite-like, (e) mixture of goethite + lepidocrocite, and (f) lepidocrocite -like spectral features.

Raman Spectra of Standard Fe (Hydr)oxides. Raman spectra of the standard Fe (hydr)oxides in aluminum pans are shown in Figs. 5a–5d (Table I). Hematite shows Raman bands at 225, 243, 293, 408, 499, 611, and 1313 cm⁻¹ (Fig. 5d). The bands at 225 and 499 cm⁻¹ are due to Fe-O symmetric stretching, and those at 243, 293, 408, and 611 cm⁻¹ to Fe-O symmetric bending.^12,13 The 1313 cm⁻¹ band is originated from 2-magnon scattering.¹²

TABLE I.

Raman bands for standard iron (hydr)oxides and their assignments. Raman bands for representative samples in feldspar matrix in Rokko granite are also indicated.^a

Mineral name (formula)	Standard Fe oxides Raman bands (cm⁻¹)	Rokko granite sample Raman bands (cm⁻¹)		Assignments	References
Ferrihydrite (Fe₁₀O₁₄(OH)₁₂)	700	709	Mineral A Ferrihydrite-like	Fe(O,OH)₆ octahedra	15
Goethite (α-FeOOH)	92	94	Mineral B Goethite-like
	243	248		Fe-O sym. str.	12,13
	299	303		Fe-O sym. bend	12,13
	392	398		Fe-O-Fe/Fe-O-OH sym. str.	12,13
	481			Fe-O asym. str.	12,13
	546	554		Fe-O asym. str.	12,13
	682	689		Fe-O sym. str.	12,13
	996
Lepidocrocite (γ-FeOOH)	249	250	Mineral C Lepidocrocite-like
	376	376
	524
	641	656
	1295	1302
Hematite (Fe₂O₃)	225			Fe-O sym. str.	12,13
	243			Fe-O sym. bend	12,13
	293			Fe-O sym. bend	12,13
	408			Fe-O sym. bend	12,13
	499			Fe-O sym. str.	12,13
	611			Fe-O sym. bend	12,13
	1313			2-magnon scattering	12

Abbreviations: asym. = asymmetric; sym. = symmetric; str. = stretching.

Fig. 5.

Raman spectra of standard (a) ferrihydrite, (b) goethite, (c) lepidocrocite, and (d) hematite powders and of (e) ferrihydrite-like, (f) goethite-like, and (g) lepidocrocite-like positions in the granite sample.

The spectrum of goethite has bands at 92, 243, 299, 392, 481, 546, 682, and 996 cm⁻¹ (Fig. 5b). The bands at 243 and 682 cm⁻¹ are assigned to Fe-O symmetric stretching.¹³ The 299 cm⁻¹ band is due to Fe-O symmetric bending.¹³ The strong band at 392 cm⁻¹ corresponds to Fe-O-Fe or Fe-O-OH symmetric stretching, and the bands at 481 and 546 cm⁻¹ to Fe-O asymmetric stretching.¹³ Assignments for 92 and 996 cm⁻¹ bands remain unknown.

Lepidocrocite shows bands at 249, 376, 524, 641, and 1295 cm⁻¹ (Fig. 5c). These bands agree with the reported ones,^12,14 but their assignments are unknown.

Ferrihydrite has a broad band around 700 cm⁻¹ (Fig. 5a) and can be assigned to Fe(O,OH)₆ octahedra.¹⁵

Raman Spectra on the Rokko Granite Sample. Some Fe (hydr)oxides were measured on the Rokko granite sample surface also by Raman microspectroscopy (Figs. 5e-5g). The spectrum in Fig. 5e has a broad band around 709 cm⁻¹ and additional bands at 156, 287, 479, and 512 cm⁻¹. The 709 cm⁻¹ band is characteristic of ferrihydrite (Fig. 5a, Table I), and the other bands are due to feldspar matrix.¹⁶ The spectrum in Fig. 5f shows bands at 94, 248, 303, 398 (strong), 554, and 689 cm⁻¹. These bands agree with those of goethite (Fig. 5b, Table I). The spectrum in Fig. 5g shows bands at 154, 250 (strong), 376, 479, 514, 544, 656, and 1302 (broad) cm⁻¹. The strong band at 250cm⁻¹ and the 376, 656, and 1302 cm⁻¹ bands are similar to those for lepidocrocite (Fig. 5c, Table I). Other bands at 154, 479, and 514 cm⁻¹ may be due to feldspar matrix.¹⁶ The assignment for the 544 cm⁻¹ band is unknown.

Line Color Profile of the Rokko Granite Sample. Single lines (Fig. 6a) were extracted from the mapped area (Fig. 1b red elongated rectangle), and their L*, a*, and b* values (obtained from Eqs. 2 –7) at every 20 μm step are plotted against the position (Figs. 6b and 6c). The left and right sides correspond to the grey and brown zones of the granite (Fig. 6a). The border zone between these two zones are named as the yellow zone, since their b* values are larger than a* values (Fig. 6c).

Fig. 6.

Line color profiles in the granite sample (Fig. 1c). (a) A picture around the measurement area crossing over the borders of grey, yellow, and brown zones. (b) The line profile of L* value (white). (c) The line profiles of a* (red) and b* (yellow) values.

Here, the L* value is relatively constant around 65 in the grey zone, while it fluctuates around lower values (50) in the brown zone (Fig. 6a). Also, a* values in the grey zone are around 5 with some larger regions (Fig. 6c). As well, b* values in the grey zone show similar trends around 10 (Fig. 6c). The a* and b* values show relatively sharp peaks in the brown zone with typical intervals of a few hundreds of micrometers (Fig. 6c). The higher a* (red) and b* (yellow) values generally correspond to lower L* values (dark).

The a* and b* values of the above line profile in the granite sample are plotted in an a*-b* diagram (Fig. 7). Four curves in this figure indicate colors of mixtures of the standard Fe (hydr)oxide powders with SiO₂ powder with varying proportions. Goethite shows the highest b*/a* ratios (around 2.8), and the b*/a* ratios decrease for ferrihydrite (around 1.3), lepidocrocite (around 1.2), and hematite (around 0.6; Fig. 7).

Fig. 7.

The a* (red) and b* (yellow) values of the line profile (Fig. 6c) plotted in the a*-b* diagram. The solid lines indicate the color trends of various contents of standard Fe (hydr)oxides (0–100 wt % in white SiO₂). The dotted lines indicate the least square fitted lines of the color trends: b*/a* ratios for goethite (around 2.8), ferrihydrite (around 1.3), lepidocrocite (around 1.2), and hematite (around 0.6).

Fig. 8.

The L*, a*, and b* value maps and a picture for the mapped area indicated in Fig. 6 (area A). The maximum and minimum values of L*, a*, and b* are represented by 256 light–dark levels of white, red, and yellow colors.

The a* and b* values in the grey (0–6490 μm), yellow (6510–8950 μm), and brown (8970–17 990 μm) zones are plotted in Fig. 7 as grey, yellow, and red symbols, respectively. Most of these colors of granite sample lie between the trends for goethite and lepidocrocite/ferrihydrite. The yellow zone shows data points close to the goethite trend. The brown zone data scatter around ferrihydrite and lepidocrocite trends extending to high a* and b* values. On the other hand, the grey zone data are also on the ferrihydrite/lepidocrocite trends, but their a* and b* values are smaller than the brown zone (Fig. 7).

Distributions of L*, a*, and b* values in the border of the yellow and brown zones (Fig. 6: line A) are plotted in Fig. 8 as grey, red, and yellow scales. The brighter portions correspond to larger values of L*, a*, and b*. Here, L* values in the brown zone are generally small (dark), while those in the yellow zones are larger (bright). The a* and b* values show opposite trends to that for L* values. Large chromaticness results in darker colors indicating high concentrations of iron (hydr)oxides in the area. This iron (hydr)oxide-rich area can thus be visualized by means of these L*, a*, and b* maps (Fig. 8).

DISCUSSION

The band position and band width are often used to characterize different phases in spectroscopy, and second derivatives can discriminate different iron hydroxides having broad absorption bands by diffuse reflectance spectrometry with an integrating sphere on powdered weathering products of rocks.^17,18 However, microscopic characterization of iron hydroxides in real rock textures cannot be made by the same method. Moreover, visible reflectance spectra under the present microscope have relatively low signal-to-noise ratios, which prevent meaningful second derivatives. Therefore, L*a*b* color space or an a*-b* diagram can provide an alternative method for discriminating iron hydroxides, especially for in situ measurements under microscopes.

Before discussing advantages and possibilities of the present visible darkfield reflectance spectroscopy, we will first consider problems and limitations of the method.

Limits of Visible Darkfield Reflectance Spectroscopy. The visible darkfield reflectance spectroscopy has the following limitations:

Absorption bands are generally broad in the visible region, and their positions are similar among mineral phases such as iron (hydr)oxides (Figs. 3 and 4).

Only one absorption band is generally present in the visible region (Figs. 3 and 4), and assignment of the multiple bands to certain phases is not possible.

In the diffuse reflection spectroscopy, the integrating sphere is used to eliminate specular reflection components. The darkfield illuminator and objective lens are used instead of an integrating sphere in this study. The sample is illuminated with high angles of incident lights, and the reflected lights are collected from smaller angles. Therefore, the darkfield system in this study collects mostly diffusely reflected lights. However, the smaller angles of collection might result in the smaller amounts of collected lights.

In polycrystalline aggregates such as the granite sample in this study, refraction and scattering at grain boundaries and cracks are so complex that we do not know if we can treat the reflection spectra by the diffuse reflection process for powders.

The light collection region can be affected by the transparency of the sample surface materials.

Advantages of Visible Darkfield Reflectance Spectroscopy. Although the present visible darkfield reflectance spectroscopy has the above problems and limitations, this method provides the following advantages.

Setup of the instrument is very simple. It is made of commercially available components such as an optical microscope, a spectrometer, and a detector.

Compared with microprobe analytical methods, such as Raman microspectroscopy, which are only surface sensitive, information from not only the surface but also deeper regions can be obtained depending on the transparency of the sample surface materials.

Although Raman spectra measurements are often difficult for fluorescent and colored materials, visible spectra can be always obtained.

Despite the broad visible absorption bands, the color values in L*a*b* space can be used to differentiate between different phases such as iron (hydr)oxides. In the a*-b* diagram, iron (hydr)oxides have characteristic b*/a* trends.

The L*, a*, and b* maps can detect regions of light/dark, red/green, and yellow/blue colored materials.

Therefore, the visible darkfield reflectance spectroscopy can be a useful method for various fields such as earth and planetary sciences, bionanomaterials, microscopic devices, nanotechnology, cosmetics, and painting.

CONCLUSION

Visible darkfield reflectance spectroscopy equipped with a color mapping system has been developed and applied to a brown-colored Rokko granite sample in this study. The following results are obtained:

Reflectance spectra obtained from the granite sample are converted to Kubelka-Munk (KM) spectra. They show similar features to goethite (a weak absorption shoulder around 480 nm) and lepidocrocite (with a gradual decrease in absorption toward 580–600 nm).

Raman microspectroscopy on the granite sample surface indicates the presence of Raman bands similar to those of goethite (94, 248, 303, 398 (strong), 554, and 689 cm⁻¹), lepidocrocite (250, 376, 656, and 1302 cm⁻¹), and ferrihydrite (709 cm⁻¹).

For the quantitative representation of colors of samples, the L*a*b* color values were determined from the sample reflection spectra. The L* represents lightness (L* = 0: black and L* = 100: white), and a* and b* represent chromaticity (+a*: reddish, –a*: greenish, +b*: yellowish, and –b*: bluish).

Here, L*a*b* values at every 20 μm steps on a single line profile were extracted from the mapped area including grey, yellow, and brown zones of the granite. The L* value is relatively constant around 65 in the grey zone, while it fluctuates around lower values (50) in the brown zone. The a* and b* values in the grey zone are around 5 and 10, respectively. On the other hand, a* and b* values in the brown zone show relatively sharp peaks with typical intervals of a few hundreds of micrometers. The border yellow zone has larger b* values than a* values.

The a* and b* values of the above line profile in the granite sample plotted in an a*-b* diagram are distributed between the trends for goethite and lepidocrocite/ferrihydrite. The grey and brown zone data are on the lepidocrocite/ferrihydrite trends, but their values in the brown zone are larger than those in the grey zone. The yellow zone shows data points close to the goethite trend.

Distributions of L*, a*, and b* values in the border of the yellow and brown zones are plotted as grey, red, and yellow scale maps. The L* values in the brown zone are generally small (dark), while those in the yellow zones are larger (bright). Iron (hydr)oxide-rich areas can be visualized by means of large a* and b* values in the L*, a*, and b* maps.

Although the present method has some problems and limitations, it provides the following advantages:

The instrument is simply made of commercially available components such as an optical microscope, a spectrometer, and a detector.

Although Raman spectra measurements are often difficult for fluorescent and colored materials, visible spectra can be always obtained.

Despite the broad visible absorption bands, the color values in L*a*b* space can be used to differentiate among different phases such as iron (hydr)oxides. In the a*–b* diagram, iron (hydr)oxides have characteristic b*/a* trends.

The L*, a*, and b* maps can detect regions of light/dark, red/green, and yellow/blue colored materials.

Footnotes

ACKNOWLEDGMENTS

The authors are grateful to Drs. Tadashi Yokoyama, Makoto Katsura, Yusuke Kirino, and other members of Department of Earth and Planetary Science, Osaka University for their useful advice and discussion. Mr. Kojima of Lucir Co., Mr. Yamai of Advansoft Co., Mr. Yatabe of Digital Data Management Co., and Mr. Matsuda of Andor Co. are thanked for their technical collaboration.

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