The influence of aeolian dust in non-allophanic Andosols on Yakushima Island

Abstract

The oxygen isotope (δ¹⁸O) composition of quartz and the d₍₀₆₀₎ values of clay minerals were determined from four pedons of non-allophanic Andosols derived mainly from the Holocene volcanic ash on Yakushima Island. These soils contained considerable amounts of aerosol-sized (1–10 µm) and coarse (>53µm) quartz. The δ¹⁸O values for the aerosol-sized quartz ranged from 14.7‰ to 17.4‰, which was comparable to or slightly lower than known values for loess-derived Red and Yellow soils on Tanegashima Island located approximately 20 km east of Yakushima Island. The abundance and δ¹⁸O values of the aerosol-sized quartz indicated that non-allophanic Andosols on Yakushima Island were strongly influenced by aeolian dust. However, the presence of coarse quartz implied that granite-derived materials were also incorporated into non-allophanic Andosols. X-ray diffraction patterns for most clay minerals showed two broad peaks around 0.154 and 0.150 nm, respectively. The d₍₀₆₀₎ values confirmed that 2:1–2:1:1 clay minerals consisted of dioctahedral and trioctahedral clay minerals. Since aeolian dust contains little or no coarse quartz and trioctahedral clay minerals, the abundance of coarse quartz and trioctahedral minerals confirmed that the occurrence of non-allophanic Andosols on Yakushima was influenced by biotite-granite, in addition to aeolian dust.

Keywords:

• aeolian dust
• clay minerals
• non-allophanic Andosols
• oxygen isotope ratio
• Yakushima Island.

Introduction

Most soils derived from volcanic ash and pumice exhibit distinctive properties such as high humus accumulation, strong phosphate fixation, low base status, and low bulk density that are not found in soils derived from other parent materials located under the same vegetation cover (Wada 1985). These volcanic ash soils are classified as Andosols according to the World Reference Base for Soil Resources (WRB) (IUSS-ISRIC-FAO 2007). The distinctive properties of Andosols are attributable to the formation of poorly ordered clay minerals (e.g., allophane and imogolite) and the accumulation of aluminum (Al)-humus and iron (Fe)-humus complexes (Shoji et al. 1993). The clay mineralogy of allophanic Andosols is dominated by poorly ordered clay minerals. In contrast, non-allophanic Andosols containing little or no poorly ordered clay minerals have a mineralogy dominated by layer phyllosilicates such as 2:1 and 2:1:1 clay minerals and their intergrades (Shoji et al. 1993).

Yakushima Island is located approximately 60 km south of Kyushu Island, in the northern part of the southwest islands of Japan (Fig. 1). Although the island was formed by granite intrusion into the Kumage Group of Paleogene sedimentary rocks (Saito et al. 2007), soils derived from the Kikai-Akahoya tephra (K-Ah) are widely distributed on the island (Machida and Arai 1978; Shimokawa and Jitousono 1984; Geshi 2009; Eguchi and Tamura 2012). In our previous paper, the morphological and chemical properties and the clay mineralogy of the soils formed from volcanic ejecta on Yakushima Island were described, revealing that non-allophanic Andosols were distributed on the mountainous area (Eguchi and Tamura 2012). Non-allophanic Andosols on the island have a clay mineralogy dominated by the 2:1–2:1:1 clay minerals such as vermiculite, smectite, hydroxyl-interlayered vermiculite, hydroxy-interlayered smectite, and Al-chlorite.

Figure 1. Location of study sites. TZH, Tanizaki-hana; YAP, Yakushima airport; MUR, Miyanoura-river rightside; YLH, Yakushima light house; ABR, Anbo-river right side; YSM, Yakusugi museum; EHH, Entrance of Hanayama-hodou; KSD, Kosugi-dani; EOH, Entrance of Ohkabu-hodou; YSL, Yakusugi-land; HYH, Hanayama-hodou; YGG, Yodogo-goya; NID, Nageishi-daira; MUD, Miyanoura-dake. Soils were collected at YSL, HYH, YGG and MUD. Sandstones were collected at YAP, YSM and NID. Mudstones were collected at TZH, MUR, ABR and YGG. Granites were collected at YLH, EHH, KSD, EOH, YGG, NID and MUD.

Several processes such as the alteration of mafic minerals, formation from amorphous material, the incorporation of hydrothermal alteration products during eruption, the solid-state transformation of volcanic glass, and aeolian dust deposition, have been hypothesized for the origin of the 2:1–2:1:1 clay minerals found in Andosols (Shoji et al. 1993). Nevertheless, the dominant origin of the 2:1–2:1:1 clay minerals found in Japanese soils formed in the late Quaternary volcanic ash is considered to be aeolian dust from the arid and semi-arid regions of inland China. This is based on the oxygen isotope ratio of the aerosol-sized (1–10 µm) quartz (Mizota 1982; Mizota and Matsuhisa 1985; Naruse and Inoue 1986; Mizota et al. 1990).

Quartz is a ubiquitous mineral that is resistant to weathering. The oxygen isotope ratio (δ¹⁸O) of quartz depends strongly on the formation temperature. The δ¹⁸O of quartz remains unchanged during weathering, transportation, and post-depositional diagenetic processes (Clayton et al. 1978). Therefore, δ¹⁸O is a good indicator of the origin of quartz (Jackson 1981). For example, loess, loess-derived soils, Andosols, Red Yellow soils, and aeolian-dust deposits in China, Korea, and Japan had δ¹⁸O values of 15–18‰, indicating they were derived from the same origin (Inoue and Naruse 1991). According to Inoue et al. (1993), the aerosol-sized quartz separated from Red and Yellow soils on the Nansei Syoto region, where Yakushima Island is located, had δ¹⁸O values of 15.6–18.5‰, indicating that aeolian dust deposition significantly influences soils in the region. In particular, the aerosol-sized quartz separated from loess-derived Red and Yellow soils on Tanegashima Island located near Yakushima Island had uniform δ¹⁸O values of 16.8–17.6‰ (Inoue et al. 1993). Therefore, the δ¹⁸O value of loess-derived Red and Yellow soils on Tanegashima would be a good indicator for non-allophanic Andosols on Yakushima Island.

On the other hand, Eguchi and Tamura (2012) suggested that granite was incorporated into non-allophanic Andosols as a minor parent material on Yakushima Island. Micas and plagioclase in granite serve as the origin for the 2:1–2:1:1 clay minerals (Tardy et al. 1973). Therefore, it is possible that the 2:1–2:1:1 clay minerals in non-allophanic Andosols on Yakushima Island originated from granite. Thus, the presence of the 2:1–2:1:1 clay minerals does not necessarily indicate the influence of aeolian dust on the island. That is, non-allophanic Andosols on Yakushima Island potentially have two parent materials added to the K-Ah: aeolian dust and granite. However, it is not known which of the two contributes more to soil development.

The objective of this study was to clarify the influence of aeolian dust as well as granite in non-allophanic Andosols on Yakushima Island to better discuss the origin of the 2:1–2:1:1 clay minerals in the soils. The authors elucidated the mineralogical composition of the soils using quartz-particle-size analysis, oxygen isotope analysis and X-ray diffraction analysis.

Materials and Methods

Background information and sample collection

Yakushima Island is located approximately 60 km south of the southern tip of Kyushu Island in southwestern Japan. The highest peak on the island is Miyanoura-dake (“dake” indicates peak; 1936 m above sea level). Because of its high mountainous relief, the island's climate ranges from subtropical on the western coast to cool temperate in the mountainous area (Eguchi 2006). Annual mean precipitation ranges from 2400 to 4900 mm along the coast, while it exceeds 10,000 mm in the mountains (Takahara and Matsumoto 2002; Kyushu Regional Forest Office 2010). The island's geology is mainly granite fringed by sedimentary rocks of the Kumage Group (Saito et al. 2007). The majority of the granite is biotite-granite containing quartz, plagioclase, potassium (K)-feldspar, and biotite as its major rock-forming minerals, and chlorite and dioctahedral micas as minor rock-forming minerals (Ministry of International Trade and Industry 1993). This is not a volcanic island; however, the K-Ah volcanic ash-derived soils are distributed widely throughout the island (Machida and Arai 1978; Geshi 2009; Eguchi and Tamura 2012). Soil samples described in our previous study (Eguchi and Tamura 2012) were used in the current study. Twenty-four soil samples were obtained from four non-allophanic Andosol pedons (Yakusugi-land, YSL; Hanayama-hodou, HYH; Yodogo-goya, YGG; Miyanoura-dake, MUD) and 14 samples of basement rock (seven granite, three sandstone, and four mudstone) located on Yakushima Island (Fig. 1). YSL, HYH, and YGG were located under a Cryptomeria japonica natural forest and MUD was located under Sasa (Psudosasa owatarii) grasslands. Granite gravels was observed in the profiles except for MUD. According to the WRB (IUSS-ISRIC-FAO 2007), YSL was classified as Vitric Andosol (Acroxic, Dystric); HYH and YGG were classified as Vitric Andosol (Dystric); and MUD was classified as Umbric Vitric Andosol (Acroxic, Dystric).

Quartz isolation and particle size distribution

Quartz was isolated by the following procedure (Sridhar et al. 1975). Soil samples were treated with a 6% hydrogen peroxide (H₂O₂) solution for several days and a 6 M hydrochloric acid (HCl) solution at 100°C for 1 h to remove organic matter, Fe oxides, and part of layer silicates. Then, the samples were separated into fractions of 1–10, 10–20, 20–53, 53–105, and >105 µm by repeated sedimentation and sieving. Rock samples were crushed using a stainless steel mortar and pestle, ground with an agate mortar and pestle, and treated with a 6 M HCl solution at 100°C for 1 h. All separated fraction samples and ground rock samples were first fused with sodium pyrosulfate (Na₂S₂O₇) to remove layer silicates and then washed with 3 M HCl and further digested with fluorosilicic acid (H₂SiF₆) to remove silicates other than quartz. The isolated quartz was washed with a saturated boric acid (H₃BO₃) solution to remove surface fluorates. The same treatment was used for pure silica sand mixed with feldspar powder. It was established that the oxygen isotopic composition of the silica sand did not change before and after treatment. A part of the granite samples was crushed with a tungsten carbide mortar and pestle, and the quartz was hand-picked. The hand-picked quartz had the same isotopic oxygen composition as the quartz isolated from the granite ground with an agate mortar and pestle, which confirmed that quartz contamination from the agate mortar and pestle was negligible.

Quartz oxygen isotope analysis

Oxygen isotope analyses of the isolated quartz were performed with a carbon dioxide (CO₂) laser-bromine pentafluoride (BrF₅) fluorination system connected to a stable-isotope mass spectrometer (SIRA12; Micromass, UK) at the Institute for the Study of the Earth's Interior, Okayama University. The analytical method used was similar to that employed by Sharp (1990), and the technical details are described by Kusakabe et al. (2004). ¹⁸O/¹⁶O was represented by the conventional δ notation used for the Vienna Standard Mean Ocean Water (Vienna-SMOW) as δ¹⁸O, and the measured values were normalized to the internal quartz standard NBS28 as δ¹⁸O = 9.6‰ (1σ = 0.10‰; N = 9). The 1σ external precision of the measurements was determined as 0.07‰ by HYH Bw3 (N = 8). Each analysis was conducted in duplicate or triplicate. The average values are shown in Table 1.

Table 1. Quartz content and oxygen isotopic compositions of aerosol-sized quartz

Horizon	Depth (cm)	Quartz content (g kg^−1)					Quartz contribution (%) 1–10 µm^†	δ^18OSMOW (‰)^‡ 1–10 µm
		1–10 µm	10–20 µm	20–53 µm	>53 µm	Total
YSL (Vitric Andosol)
Al	0–6	10	5	3	38	57	18	16.7
A2	6–17	13	5	4	103	126	11	16.6
AB	17–30	4	2	2	74	81	5	15.4
BA	30–42	15	5	3	100	123	12	16.7
Bwl	42–59	25	10	6	140	181	14	17.1
Bw2	59–76	22	12	7	140	181	12	17.2
Bw3	76–94+	25	8	8	142	182	14	16.9
HYH (Vitric Andosol)
A	0–8	18	12	5	150	184	10	17.1
AB	8–15	26	11	8	116	161	16	15.8
Bwl	15–30	32	9	5	145	190	17	17.0
Bw2	30–50	26	16	7	183	231	11	15.1
Bw3	50–70	31	11	7	112	161	19	17.0
BC	70–90+	32	15	9	164	219	15	16.8
YGG (Vitric Andosol)
OA	0–6	10	7	2	42	60	16	16.7
AB	6–14	18	11	7	123	158	11	16.3
Bwl	14–38	23	6	7	104	139	16	16.5
2Bw2	38–58	24	5	4	197	230	11	15.0
2BC	58–68+	3	2	15	172	192	2	14.7
MUD (Vitric Umblic Andosol)
Al	0–12	18	4	3	86	112	16	16.9
A2	12–24	11	5	4	81	102	11	16.9
A3	24–38	12	6	6	118	141	8	16.9
AB	38–50	18	5	5	114	142	13	16.8
Bwl	50–68	19	6	4	118	147	13	16.7
Bw2	68–85+	15	3	6	91	114	13	16.4
YSL, Yakusugi-land; HYH, Hanayama-hodou; YGG, Yodogo-goya; MUD, Miyanoura-dake; δ^18OSMOW, ^18O/^16O represented by conventional δ notation used for Vienna Standard Mean Ocean Water. ^†The contribution of aerosol-sized quartz (1–10 µm) to the total amount of isolated quartz.
^‡Oxygen isotopic compositions of coarse quartz fraction (>105 µm) from ABR Bw2. ABR 2C and YGG 2BC were also analyzed, giving 13.4, 13.2, and 13.1 ‰, respectively.

Determination of d₍₀₆₀₎ values

Soil samples were oxidized with a 6% H₂O₂ solution, dispersed by ultrasonic vibration, and modified to a pH of 3–4 or 9–10 using a dilute HCl or sodium hydroxide (NaOH) solution, respectively. First, the clay samples were treated with dithionite–citrate–bicarbonate (Mehra and Jackson 1960). X-ray diffraction (XRD) patterns over the 59 to 63° 2θ range were obtained using an X-ray diffractometer (JEOL, JDX-3530). The operating conditions were as follows: CuKα, Ni filter; 40 kV, 20 mA; Slit system, 1°–1°–0.2 mm.

Results and Discussion

Quartz content and particle size distribution

Table 1 shows the samples’ quartz content, quartz particle-size distribution, and the δ¹⁸O values of the aerosol-sized quartz (1–10 µm). The total quartz content ranged from 57.1 to 231.2 g kg⁻¹. Most samples showed a bimodal quartz particle-size distribution (Fig. 2). The peak of the aerosol-sized quartz (1–10 µm) implies the influence of aeolian dust. Coarse (>53 µm) quartz found in soils would be mainly derived from the granite basement because the K-Ah and aeolian dust in Japan contains little or no quartz in the sand fraction (Nagatomo et al. 1977; Inoue and Naruse 1987).

Figure 2. Particle size distribution of quartz separates from the soils. YSL, Yakusugi-land; HYH, Hanayama-hodou; YGG, Yodogo-goya; MUD, Miyanoura-dake.

Quartz oxygen isotope composition

The δ¹⁸O values of the aerosol-sized quartz (1–10 µm) isolated from the soils ranged from 14.7 to 17.2‰ (Table 1), which was comparable to or slightly lower than the values observed in loess-derived Red and Yellow soils on Tanegashima Island (16.8–17.6‰; Inoue et al. 1993). In contrast, the quartz isolated from granite had low and uniform (12.9–13.5‰) δ¹⁸O values (Table 2). A positive correlation existed between the contribution of the aerosol-sized quartz to the total amount of the isolated quartz and the δ¹⁸O values of the aerosol-sized quartz (r = 0.554; p < 0.01) (Fig. 3), indicating that the aerosol-sized quartz originated primarily from aeolian dust. The slightly lower δ¹⁸O values of the aerosol-sized quartz from the Yakushima Island soils as compared to those of the aerosol-sized quartz from loess-derived Red and Yellow soils on Tanegashima Island may be caused by the addition of quartz from the granite basement. According to Inoue and Naruse (1991), the δ¹⁸O value of volcanic quartz is 7 to 8‰. Since soils derived from K-Ah volcanic ash contain small amounts of silt-sized quartz (Nagatomo et al. 1977), this volcanic quartz may also contribute to the slightly lower δ¹⁸O values of the aerosol-sized quartz in Yakushima Island soils. The δ¹⁸O values of the quartz separated from mudstones and sandstones were comparable to or lower than those of the aerosol-sized quartz separated from the soils (Table 2). However, the incorporation of sedimentary rocks such as mudstone and sandstone into the mountainous area soils should be negligible because the island's central area contains granite. In fact, few sedimentary rock gravels (i.e., sandstone xenolith) were observed, and these occurred in the HYH BC horizon (Eguchi and Tamura 2012).

Figure 3. Relationship between quartz contributions and δ¹⁸O values of aerosol-sized quartz. YSL, Yakusugi-land; HYH, Hanayama-hodou; YGG, Yodogo-goya; MUD, Miyanoura-dake; δ¹⁸O_SMOW, ¹⁸O/¹⁶O represented by conventional δ notation used for Vienna Standard Mean Ocean Water.

Table 2. Oxygen isotopic compositions of quartz separates from the bedrock

Sample	δ^18OSMOW (‰)
Granite
YLH	13.0
EHH	13.2
KSD	12.5
EOH	13.0
YGG	13.0
NID	12.9
MUD	13.5
Mudstone
TZH	17.7
MUR	17.9
ABR	16.9
YGG	13.5
Sandstone
YAP	14.4
YSM	15.4
NID	13.3
YLH, Yakushima light house; EHH, Entrance of Hanayama-hodou; KSD, Kosugi-dani; EOH, Entrance of Ohkabu-hodou; YGG, Yodogo-goya; NID, Nageishi-daira; MUD, Miyanoura-dake; TZH, Tanizaki-hana; MUR, Miyanoura-river rightside; ABR, Anbo-river right side; YGG, Yodogo-goya; YAP, Yakushima airport; YSM, Yakusugi museum; δ^18OSMOW, ^18O/^16O represented by conventional δ notation used for Vienna Standard Mean Ocean Water.

X-ray diffraction patterns

Most random-mounted samples produced two broad peaks around 0.154 and 0.150 nm, respectively (Fig. 4). Although quartz exhibits a peak at 0.154 nm, the broad peak at 0.154 nm suggested the presence of trioctahedral 2:1–2:1:1 clay minerals because quartz produces a sharp peak. Since kaolin minerals exhibit a peak at 0.149 nm, a part of the broad peak at 0.150 nm would include the kaolin peak. Nevertheless, the broad peak at 0.150 nm suggests the presence of dioctahedral 2:1–2:1:1 clay minerals. Yakushima Island primarily consists of biotite-granite with a limited distribution of muscovite-granite (Saito et al. 2007). Biotite-granite on the island contains plenty of trioctahedral mica and a small amount of dioctahedral mica (Ministry of International Trade and Industry 1993). Furthermore, since mica in the aeolian dust deposited on the southwest islands of Japan and the surrounding ocean is muscovite (Inoue et al. 1993), the 2:1–2:1:1 clay minerals in the aeolian dust would mainly consist of dioctahedral minerals. Therefore, the trioctahedral minerals would originate primarily from granite. Since the clay sample isolated from the YGG 2BC horizon, which showed the lowest δ¹⁸O value, did not produce a peak around 0.150 nm, only a small amount or none of the dioctahedral minerals were contained in granite, at least in YGG. Under acidic conditions, the oxidation of Fe²⁺ in octahedral biotite sheets is balanced by the loss of octahedral Fe and magnesium (Mg), while some Al migrates from the tetrahedral sites to the octahedral sites (Douglas 1989). Some of the dioctahedral minerals can be formed from biotite through these processes or by weathering feldspar. Moreover, under acidic conditions, trioctahedral minerals such as biotite and trioctahedral vermiculite are less stable than dioctahedral minerals such as muscovite, dioctahedral vermiculite and smectite (Douglas 1989). Therefore, acidic conditions would promote the evolution of trioctahedral minerals to dioctahedral minerals, as the soil developed. In particular, the intense podzolization process induces a clear evolution of trioctahedral minerals to dioctahedral minerals from the parent material to the surface horizon (Mirabella and Egli 2003; Egli et al. 2008). The clay sample separated from the surface horizon of YGG had a higher proportion of the 0.150 nm peak to the 0.154 nm peak, as compared with the clay samples separated from AB and Bw1 horizons of YGG. These horizons showed uniform δ¹⁸O values; thus, the influence of the aeolian dust seems to be comparable. Therefore, it is possible that the proportion of the 0.150 nm peak compared to that of the 0.154 nm has increased owing to the decomposition of trioctahedral minerals and/or the transformation of trioctahedral minerals to dioctahedral minerals (Zanelli et al. 2006). XRD patterns did not show an apparent increase in the 0.150 nm peak compared to the 0.154 nm peak, except for the surface horizon of YGG. However, the decomposition of trioctahedral minerals and/or the transformation of trioctahedral minerals to dioctahedral minerals in horizons other than the surface horizon of YGG could not be ruled out because of their acidic nature (Eguchi and Tamura 2012).

Figure 4. (060) reflections of clay samples. YSL, Yakusugi-land; HYH, Hanayama-hodou; YGG, Yodogo-goya; MUD, Miyanoura-dake.

Implications of incorporating 2:1–2:1:1 clay minerals into non-allophanic Andosols

Mizota and Inoue (1988) demonstrated that heavy snowfall in regions of the Japan Sea could deposit fine-grained quartz and the 2:1–2:1:1 clay minerals in soils. Aerosol-sized quartz has higher δ¹⁸O values in the heavy snowfall areas of the Aomori Prefecture (maximum snow depth 3–5 m) in comparison with those in a site receiving lower snowfall (maximum snow depth <50 cm) in the same prefecture (Mizota et al. 1990). However, the positive correlation between rainfall and quartz (and mica) contents of soils was observed in snow-free areas such as Hawaii (Jackson et al. 1971). Climate records covering 1929–1937 and 1961–1965 for the village of Kosugidani (altitude 640 m, approximately 8 km northeast of the MUD) show a maximum snow depth of 1.85 m (Suzuki and Tsukahara 1987). Thus, the maximum snow depth could be greater than 2 m in the island's mountainous areas. Therefore, it is possible that a considerable amount of the aerosol-sized quartz was deposited as ice nuclei (Inoue 1981), and additional amounts were deposited by heavy rainfall from spring to autumn.

The rates of modern aeolian dust deposition around the Japanese archipelago are reported to be 3.6–7.1 mm per kiloannum (ka) during modern times and 13.5–22.9 mm ka^-1 during the last ice age (Inoue and Naruse 1987). The eruption age of the K-Ah is estimated to be 7.3 ka BP (Fukusawa 1995); hence, a considerable amount of the aeolian dust was deposited on the island before the eruption of the Kikai Caldera. Consequently, it is quite possible that aeolian dust-influenced soils were distributed on the island when the Kikai Caldera erupted. Jackson (1971) suggested that only a limited downward movement of the aeolian quartz occurred via mixing by faunal and floral activities in Hawaii. Therefore, the uniform δ¹⁸O values of the aerosol-sized quartz and high coarse quartz content through the profiles would indicate that the aeolian dust-influenced soils, mainly derived from granite, were incorporated into volcanic ejecta by secondary sedimentation. The incorporation of the aeolian-dust-influenced soils probably brought considerable amounts of the 2:1–2:1:1 clay minerals into non-allophanic Andosols.

Inoue (1981) indicated that the aeolian dusts deposited in soils under temperate and humid conditions might follow the sequence:

Biotite derived from granite could also follow the same sequence under acidic conditions (Barnhisel and Bertsch 1989). Since non-allophanic Andosols distributed on the island have a clay mineralogy dominated by vermiculite, smectite, hydroxy-interlayered vermiculite and/or smectite and Al-chlorite (Eguchi and Tamura 2012), it is probable that the 2:1–2:1:1 clay minerals incorporated into non-allophanic Andosol (originated from aeolian dust and granite) follow the sequence indicated by Inoue (1981).

Conclusion

The abundance of the aerosol-sized quartz particles and their δ¹⁸O values indicate that non-allophanic Andosols on Yakushima Island were strongly influenced by the aeolian dust. Thus, the 2:1-2:1:1 clay minerals that originated from the aeolian dust were obviously incorporated into non-allophanic Andosols on the island. Coarse quartz was also abundant in the soils, indicating that the granite-derived materials were also incorporated into the non-allophanic Andosols on the island. Moreover, all soils contained the trioctahedral 2:1–2:1:1 clay minerals probably derived from granite. Therefore, significant amounts of the 2:1–2:1:1 clay minerals derived from granite may also have been incorporated into the soils on the island.

Acknowledgments

Part of this research was supported by the Visiting Researcher's Program of the Institute for Study of the Earth's Interior, Okayama University. We wish to thank Prof. T. Higashi (University of Tsukuba) for his helpful criticism of the manuscript.