Journal of Petrology Advance Access published online on May 28, 2007
Journal of Petrology, doi:10.1093/petrology/egm018
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Rates of Thermal and Chemical Evolution of Magmas in a Cooling Magma Chamber: a Chronological and Theoretical Study on Basaltic and Andesitic Lavas from Rishiri Volcano, Japan
1The Pheasant Memorial Laboratory for Geochemistry & Cosmochemistry, Institute for Study of the Earth's Interior, Okayama University, Misasa, Tottori 682-0193, Japan
2Institute for Geothermal Sciences, Graduate School of Science, Kyoto University, Beppu, Oita 874-0903, Japan
Received August 18, 2006; Revised typescript accepted March 27, 2007
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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Rates of magmatic processes in a cooling magma chamber were investigated for alkali basalt and trachytic andesite lavas erupted sequentially from Rishiri Volcano, northern Japan, by dating of these lavas using 238U–230Th radioactive disequilibrium and 14C dating methods, in combination with theoretical analyses. We obtained the eruption age of the basaltic lavas to be 29·3 ± 0·6 ka by 14C dating of charcoals. The eruption age of the andesitic lavas was estimated to be 20·2 ± 3·1 ka, utilizing a whole-rock isochron formed by U–Th fractionation as a result of degassing after lava emplacement. Because these two lavas represent a series of magmas produced by assimilation and fractional crystallization in the same magma chamber, the difference of the ages (i.e.
9 kyr) is a timescale of magmatic evolution. The thermal and chemical evolution of the Rishiri magma chamber was modeled using mass and energy balance constraints, as well as quantitative information obtained from petrological and geochemical observations on the lavas. Using the timescale of 9 kyr, the thickness of the magma chamber is estimated to have been about 1·7 km. The model calculations show that, in the early stage of the evolution, the magma cooled at a relatively high rate (>0·1°C/year), and the cooling rate decreased with time. Convective heat flux from the main magma body exceeded 2 W/m2 when the magma was basaltic, and the intensity diminished exponentially with magmatic evolution. Volume flux of crustal materials to the magma chamber and rate of convective melt exchange (compositional convection) between the main magma and mush melt also decreased with time, from 0·1 m/year to 10–3 m/year, and from 1 m/year to 10–2 m/year, respectively, as the magmas evolved from basaltic to andesitic compositions. Although the mechanism of the cooling (i.e. thermal convection and/or compositional convection) of the main magma could not be constrained uniquely by the model, it is suggested that compositional convection was not effective in cooling the main magma, and the magma chamber is considered to have been cooled by thermal convection, in addition to heat conduction. KEY WORDS: convection; magma chamber; heat and mass transport; timescale; U-series disequilibria
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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When a crystal-free hot magma is emplaced into the crust and forms a magma chamber, the magma is cooled by the surroundings and a mushy boundary layer develops along the chamber walls. Because various kinds of instabilities occur in the magma chamber as a consequence of heat transfer, magmatic differentiation is considered to proceed through combinations of dynamic processes, such as thermal convection in the molten portion of the magma body (the main magma), compositional convection involving the mushy boundary layer, gravitational settling or floating of crystals in the main magma, and mixing of the fractionated melt from the mush zones with the main magma (e.g. Jaupart & Tait, 1995
).
To understand quantitatively the dynamic processes that control magmatic differentiation, the underlying physics have been extensively investigated (e.g. Kerr & Tait, 1985; Turner et al., 1986; Campbell & Turner, 1987; Tait & Jaupart, 1989; Jellinek & Kerr, 1999). In addition to the physical approach, magma differentiation processes have also been studied extensively from a geological approach, mainly focusing on igneous intrusions (e.g. Hess, 1972; Shirley, 1987; McBirney, 1995; Simura & Ozawa, 2006). Although such studies have greatly advanced understanding of magmatic processes in cooling magma bodies, quantitative information that can be used to test the physical models has not fully been extracted. One of the most important parameters to characterize the dynamic processes is the timescale. However, exposed igneous intrusions reflect integrated processes that occurred over a long solidification time, and they do not provide temporal information about liquid-state magmas in evolving magma bodies. On the other hand, volcanic products can sample instantaneous states of magmas in cooling magma chambers, and they have the potential to provide information on the timescales of magmatic evolution. Unfortunately, however, repeated injections of new magmas are common in crustal magma reservoirs. In addition, there are few cases in which both a mafic magma and its derivative felsic magma have erupted. Therefore, there is still a shortage of timescale data that are useful to constrain physical models.
In this study, we investigate timescales of magmatic evolution for the Kutsugata and Tanetomi lavas, a basalt–andesite suite erupted sequentially from Rishiri Volcano, northern Japan. The pre-eruption magmatic history of the lavas has been investigated by detailed petrological and geochemical studies (Kuritani, 1998, 1999a, 1999b, 2001; Kuritani et al., 2005), and it has been shown that these lavas represent a sequence of magmas produced by assimilation and fractional crystallization in the same magma reservoir (Kuritani et al., 2005). No evidence of magma replenishment is found during magmatic evolution, except for the replenishment event that triggered the eruption of the Tanetomi lava (Kuritani, 2001). These lavas therefore provide an excellent opportunity to investigate the timescale of magmatic evolution in a cooling magma chamber without any other heat input. In addition, using previously obtained quantitative petrological and geochemical data for the lavas, it is possible to examine the rates of dynamic processes within the magma chamber by theoretical analysis.
The timescale of magmatic differentiation is estimated from the difference in the eruption ages of the Kutsugata and Tanetomi lavas. Because these lavas are considered to be younger than 42 ± 13 ka (Ishizuka, 1999), the eruption age of the Tanetomi lava can be estimated using 238U–230Th radioactive disequilibrium. The U-series isotopes have been used as powerful tools to investigate magmatic processes occurring on timescales from days to 105 years (e.g. Condomines et al., 2003, and references therein). In particular, the 238U–230Th isotope disequilibrium records U–Th fractionation on timescales of <350 ka, and it is suitable to date the Tanetomi lava. For the Kutsugata lava, 14C dating of charcoals formed at the time of the eruption has previously been carried out by Miura & Takaoka (1993), and an age >37 ka was obtained using the conventional radiometric technique. In this study we determine the 14C age of similar charcoals by accelerator mass spectrometry.
First, following brief geological and petrological descriptions of the lavas, magma chamber processes revealed by previous studies are summarized. Then, the eruption ages of the Kutsugata and Tanetomi lavas are determined, and the timescale of magmatic evolution from the parental basalt to the daughter andesite is estimated. Using the timescale data and constraints of mass and energy conservation, the thermal and geochemical evolution of the magmas in the Rishiri magma chamber is modeled, and the size of the magma chamber, convective heat flux from the main magma body, volume flux of crustal melt to the magma chamber, and rate of convective melt exchange in the magma chamber are estimated. Finally, mechanisms of the cooling of the magma chamber are evaluated.
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GEOLOGICAL SETTING |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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Rishiri is a volcanic island located west of Hokkaido, northern Japan (Fig. 1). Quaternary alkali basalt and calc-alkaline andesite form a large part of the volcano (Kobayashi, 1987
; Ishizuka, 1999). The geology of Rishiri Volcano was described in detail by Ishizuka (1999), and a simplified geological map is shown in Fig. 1. Ishizuka (1999) divided the volcanic activity into Early, Middle, and Late stages. The volcanic products of the Early stage are mainly andesitic lavas and pyroclastic-flow deposits, and dacitic lava domes. Those of the Middle stage are lava and pyroclastic-flow deposits of calc-alkaline andesite, forming the main stratovolcano. The Late stage is subdivided into two stages; L-1 and L-2. The volcanic products of the L-1 stage are lava flows of high Na/K alkali basalt (Kutsugata lava) and trachytic andesite (Tanetomi lava), whereas those of the L-2 stage are mainly lava flows of low Na/K alkali basalt with minor dacitic and rhyolitic pumice-fall deposits.
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The Kutsugata and Tanetomi lavas, investigated in this study, belong to the L-1 stage of Ishizuka (1999
), and were erupted sequentially from the western flank of the volcano (Fig. 1). The Kutsugata lava is widely exposed along the northwestern–southwestern coast of Rishiri Island and is also distributed on the sea floor, with a total volume of about 3.8 km3 (Ishizuka, 1999). The lava consists of numerous pahoehoe lava flow units, 0·2–5 m in thickness. On the basis of chemical and petrographic criteria, the Kutsugata lava has been divided into North and South lavas (Fig. 1); the North lava predates the South lava (Kuritani, 1998). The Tanetomi lava is distributed on the western flank of the volcano, with a volume of 0·15 km3 (Ishizuka, 1999). The Tanetomi lava consists of two main flow units, the Lower and Upper lavas (Fig. 1), and the Lower lava predates the Upper lava (Kuritani, 2001). The Lower lava has been further subdivided into the Lower lava 1 and Lower lava 2 (e.g. Kuritani, 2001; not shown in Fig. 1). The samples from the Rishiri Quarry (locality 6 in Fig. 1) that were used to estimate the eruption age of the Tanetomi lava belong to the Lower lava 2. |
ANALYTICAL METHODS |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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All the analyses, except for radiocarbon dating, were carried out at the Pheasant Memorial Laboratory (PML), Institute for Study of the Earth's Interior, Okayama University at Misasa (Nakamura et al., 2003
). In this study, we measured isotopic ratios and concentrations of U and Th for 15 samples from Rishiri Volcano. Whole-rock major element, trace element, and Pb isotopic compositions of some of these samples have already been reported by Kuritani et al. (2005) and Kuritani & Nakamura (2006). In this study, we obtained major element, trace element, and Pb isotopic data for additional samples. The analytical techniques were essentially the same as those described by Kuritani et al. (2005), and we followed Takei (2002) for major element analyses, Makishima & Nakamura (1997, 2006), Makishima et al. (1997, 1999), Yokoyama et al. (1999b) and Moriguti et al. (2004) for trace element analyses, and Kuritani & Nakamura (2002, 2003) for lead isotopic analyses. We have improved the techniques of Pb concentration analysis in rock samples by isotope dilution thermal ionization mass spectrometry (ID-TIMS) and we have revised the recommended value of the Pb concentration of our in-house rock standard, PML-JB3 (Kuritani et al., 2006). Therefore, we measured the Pb concentrations of the samples, including those reported by Kuritani et al. (2005), by the new method using NIST SRM 983.
Isotopic analyses of U and Th were performed using a thermal ionization mass spectrometer, Finnigan MAT262, equipped with seven Faraday cups, one normal secondary electron multiplier (SEM), and an SEM equipped with an energy filter system (RPQplus). The analytical techniques, including the procedures of sample digestion and chemical separation, were described by Yokoyama et al. (1999a, 1999b, 2001, 2003, 2006). Analytical reproducibility was evaluated by eight replicate analyses of the Rishiri sample (Ta-1), and we obtained 0·33% for 230Th/232Th, 0·54% for Th concentration, 0·13% for 234U/238U, and 0·64% for U concentration (all 2
error). All of the U and Th isotopic analyses were at least duplicated for each sample, and the analytical reproducibility is commonly better than those described above. Total procedural blanks were typically 10 pg for both Th and U, which are negligible for this study. Isotopic ratios in parentheses represent activity ratios throughout this paper. Decay constants of the U and Th nuclides used for calculations in this study were 
238U = 1·55125 x 10–10, 234U = 2·8263 x 10–6, 232Th = 4·9475 x 10–11, and 230Th = 9·158 x 10–6 (Le Roux & Glendenin, 1963; Jaffey et al., 1971; Cheng et al., 2000). Chemical pretreatment of charcoals and radiocarbon dating by accelerator mass spectrometry were performed at the Geo-Science Laboratory Co. Ltd., Japan.
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BACKGROUND |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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Petrology and geochemistry of the Kutsugata and Tanetomi lavas
Detailed petrographic, mineralogical, and geochemical descriptions of the Kutsugata and Tanetomi lavas have been given in our previous studies (Kuritani, 1998
, 1999a, 1999b, 2001; Kuritani et al., 2005; Kuritani & Nakamura, 2006). In this section, they are briefly summarized.
The phenocryst assemblage of the Kutsugata North lava is olivine and plagioclase, and that of the South lava is olivine, plagioclase and augite. The Kutsugata lava is porphyritic with a total phenocryst content of more than 30 vol.%. Phenocryst phases are commonly texturally and compositionally homogeneous, although rarely crystals have a central core with distinctive features. The main volume of phenocrysts, excluding the cores (<10% of phenocrysts), crystallized at a very shallow level during eruption (Kuritani, 1999a), whereas the cores are considered to have formed in the magma chamber (Kuritani, 1999b). In contrast to the Kutsugata lava, the Tanetomi lava is almost aphyric with a total phenocryst content of less than 3 vol.%. The phenocryst assemblage of the Tanetomi lava is hornblende, plagioclase and titanomagnetite. In the Lower lava 2, olivine and augite phenocrysts are also present, and they are considered to have been inherited from a replenishing injection of basaltic magma through magma mixing just before the eruption of the lava (Kuritani, 2001).
Whole-rock major and trace element contents and Pb isotopic compositions for representative samples listed in Fig. 1 are given in Table 1. Figure 2 shows variation diagrams for MgO, K2O, Pb and 206Pb/204Pb, plotted against SiO2 content. In the Kutsugata lava, the North-lava samples are lower in SiO2 than the South-lava samples. Similarly, the Tanetomi lava is clearly divided into the Lower and Upper lavas based on their chemical compositions; the SiO2 contents of the Lower-lava samples are lower than those of the Upper-lava samples. The products of both the Kutsugata and Tanetomi lavas form a series of smooth compositional trends, although distinct compositional gaps are present between the two lavas.
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Mechanisms of magmatic evolution inferred from previous studies
The Kutsugata and Tanetomi lavas have been the subject of a number of detailed petrological and geochemical studies (Kuritani, 1998
, 1999a, 1999b, 2001; Kuritani et al., 2005; Kuritani & Nakamura, 2006), which suggest that they represent a sequence of magmas that evolved in the same magma reservoir at depth, corresponding to 2 kbar pressure (Kuritani et al., 2005). The inferred mechanisms of magmatic differentiation for the Kutsugata and Tanetomi lavas are summarized in Fig. 3. Crustal melt, transported through fractures in the solidified margin of the magma chamber, was mixed well with the interstitial melt of the floor mush zone. Then, the mixed melt was further transported to mix with the main magma (Fig. 3), causing its geochemical evolution to be characterized by crustal assimilation and simultaneous boundary layer fractionation (ABLF; Kuritani et al., 2005). The geochemical variation from the Kutsugata lava to the Tanetomi lava (Fig. 2) can be explained by a low ratio of assimilated mass to crystallized mass.
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Magmatic temperatures were estimated to have decreased progressively with differentiation, from about 1100°C to 940°C (Kuritani et al., 2005
), and the estimated thermal evolution is shown in Fig. 4. Throughout the evolution of the magmas, the main part of the magma chamber was mostly free of crystals. This resulted not from gravitational separation of crystals from the main magma, but from suppression of crystallization in the main magma as a result of liquidus depression, caused by mixing of fractionated melt extracted from the mush zones (Kuritani, 1999b, 2001). During the magmatic differentiation from basaltic to andesitic compositions, no evidence of magma replenishment is found, except for that which triggered the eruption of the Tanetomi lava (Kuritani, 2001).
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), for the Kutsugata and Tanetomi lava samples [summarized by Kuritani et al. (2005 |
RESULTS OF U–TH ISOTOPIC ANALYSES AND 14C DATING |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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As summarized above, the Kutsugata and Tanetomi lavas represent a sequence of magmas produced by assimilation and fractional crystallization in the same magma reservoir beneath Rishiri Volcano. Therefore, the timescale of the magmatic evolution from the parental basalt to the daughter andesite can be estimated if we know the eruption ages of the Kutsugata and Tanetomi lavas. The eruption ages of the Kutsugata North lava and the Tanetomi Lower lava are estimated by 14C dating and 238U–230Th radioactive disequilibrium, respectively.
Samples for U and Th isotopic analysis
In this study, we analyzed the isotopic compositions and concentrations of U and Th in five samples from the Kutsugata lava and 10 samples from the Tanetomi lava. Yokoyama et al. (2003) showed that seawater can greatly alter the original (238U/232Th) ratio of rocks. For U and Th isotopic analyses, therefore, we did not use samples collected from the coastal area. Rocks of the Kutsugata lava are porous, and they are easily subject to weathering. For the North lava, we used two samples (Ta-25, Ta-31) collected from a quarry, in which fresh rocks are artificially exposed. On the other hand, fresh rocks of the South lava are, unfortunately, not exposed, although we carefully selected three samples (Kr-9, Kr-28, Kr-41). Unlike the Kutsugata lava, the rocks of the Tanetomi lava are dense and fresh, and they are all suitable for U–Th isotopic analysis. Isotopic and concentration data for U and Th for the studied samples are listed in Table 2.
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238U–230Th disequilibrium of whole-rock samples
The compositions of the samples measured in this study are plotted on a U–Th equiline diagram (Fig. 5). In the diagram, compositions of lavas from the Kamchatka arc (Turner et al., 1998
), which is adjacent to the Kurile arc (to which Rishiri Volcano belongs), are also shown for comparison. The Kamchatka samples lie on or to the right of the equiline. This 238U excess signature is common in arc lavas, and is attributed to the role of U addition by fluids from the subducting slab (e.g. Turner et al., 2003a). On the other hand, all the Rishiri samples plot on the left-hand side of the equiline. Considering that the depth to the Wadati–Benioff zone is 300 km at Rishiri Volcano, the 230Th excess signature may reflect the fact that the effect of U addition by fluids from the subducting slab was not so large as to counterbalance the effect of Th enrichment caused by melting in the presence of garnet or aluminous clinopyroxene (e.g. Beattie, 1993; Blundy & Wood, 2003). Detailed geochemical evaluation of the magma generation processes beneath Rishiri Volcano is beyond the scope of this paper, and will be discussed elsewhere.
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The compositions of the Kutsugata and Tanetomi lavas, except for those of the Tanetomi lava samples that underwent post-eruptive U–Th fractionation (crosses; discussed below), are indicated as circles and squares, respectively, in Fig. 6. The (230Th/232Th) and (238U/232Th) ratios of the lava samples show marked variations, and these ratios tend to increase systematically with increasing whole-rock SiO2 content, although the variations in the Tanetomi lava are insignificant. This variation is considered to reflect an ageing effect, as well as assimilation and fractional crystallization, and this will be explained in more detail in a later section.
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Dating of the Tanetomi lava
At the Rishiri Quarry (locality 6 in Fig. 1), the Tanetomi Lower lava consists of one flow unit with a thickness of about 20 m; clinker layers are present at the top and bottom of the unit (Kuritani & Nakamura, 2006
). Major element compositions are mostly homogeneous throughout the flow unit (58·8–59·4 wt % in SiO2; inset in the K2O–SiO2 diagram in Fig. 2). In this study, Th and U isotopic analyses were performed for one sample from the top clinker layer (Ta-28), one sample from the bottom clinker layer (Ta-17) and three samples from the main flow unit (Ta-1, Ta-2, Ta-11). In addition, rocks from the main flow unit were crushed to fine powders, and magnetite-rich powders were prepared by magnetic separation (sample ‘Tmt’). The data are listed in Table 2, and plotted on an equiline diagram (Fig. 7).
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The data show a good positive correlation between the (238U/232Th) and (230Th/232Th) ratios in the equiline diagram. One possible interpretation is that the linear array was produced by magma mixing; that is, mixing of magmas with low (238U/232Th) and those with high (238U/232Th) in the magma chamber and subsequent 230Th decay. Kuritani (2001
) suggested that the magmas of the Lower lava 2 experienced a mixing event with a replenishing basaltic magma. However, if the compositional variations were produced by magma mixing, variations of trace element concentrations should be coupled with the major element variations. Figure 8a shows the relationship between the Th and MgO contents of the five samples, Ta-1, 2, 11, 17 and 28. Although the variation is fairly limited (e.g. 2·34–2·41 wt % in MgO), a significant negative correlation is observed, and this linear array could be consistent with the magma mixing hypothesis. However, the variations of U and B contents and (230Th/232Th) are decoupled from the major element variations (Fig. 8b, c and d) and, therefore, magma mixing was not the principal process responsible for the positive correlation between (238U/232Th) and (230Th/232Th).
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Another possibility is that the variation of (238U/232Th) was produced by combined assimilation–fractional crystallization (AFC) in the magma chamber. Indeed, the overall chemical variation of the Kutsugata and Tanetomi lavas appears to have been produced principally by AFC (Kuritani et al., 2005
). However, it is difficult to achieve the significant depletion of U content and (230Th/232Th) ratio for the Ta-1 sample (Fig. 8b and c) by an AFC process. This is because, as in the case of magma mixing, trace element variations should be coupled with major element variations when compositional variations are produced by a series of AFC processes.
Instead of magmatic processes in the magma chamber, the depletion of U in the Ta-1 sample could be explained by processes during or after eruption. Kuritani & Nakamura (2006) showed that although the abundances of major elements and most trace elements are mostly homogeneous throughout the flow unit at the quarry, some trace elements, including Li, B, and Cs, are considerably depleted in samples collected from the main part of the flow unit, compared with those obtained from clinker layers. These systematics were inferred to have resulted from escape of these elements from the lava flow during post-eruptive degassing (Kuritani & Nakamura, 2006). Although the degree of the depletion of U is less significant compared with that of Li, B, and Cs, U may also have escaped from the main flow unit after eruption. In fact, it has been suggested that U is slightly volatile and can be transported by volcanic gases (Gauthier & Le Cloarec, 1998; Moune et al., 2006).
Sample Ta-1 (main flow unit), which shows the greatest fractionation of B, has the lowest U concentration, whereas samples Ta-17 and Ta-28 (clinker layer), in which no significant fractionation of B occurred, have high U contents (Fig. 8b and d). In contrast to sample Ta-1, samples Ta-2 and Ta-11 (main flow unit) might not have undergone significant fractionation of U, although B fractionation was extensive. These observations are considered to be related to the sampling localities. Sample Ta-1 was collected from the uppermost part of the main flow unit; on the other hand, the sampling locality of Ta-2 is a relatively internal part of the unit, and Ta-11 is from the lower part of the flow unit (see Kuritani & Nakamura, 2006, fig. 2b). Fractionation of U might have occurred more effectively from the upper part of the main flow unit. Sample Tmt has an intermediate U/Th ratio among the quarry samples (Fig. 7). This may result from the fact that the rock (before magnetic separation) was collected from the upper part of the flow unit (i.e. interstitial glass has low U/Th ratio after degassing), rather than from artificial U/Th fractionation by magnetic separation, considering that DU/DTh for magnetite is higher than unity (Blundy & Wood, 2003).
The Tanetomi magmas at the quarry had slight compositional variability just after eruption, as suggested from the major element variations (Figs 2 and 8). However, sample Ta-28 (highest MgO sample at the quarry) and sample Ta-17 (one of the lowest MgO samples at the quarry) have identical (238U/232Th) and (230Th/232Th) ratios within analytical uncertainty (Table 2 and Fig. 7). Because these two extreme samples were collected from the clinker layers and did not undergo any elemental fractionation during and after eruption (Kuritani & Nakamura, 2006), the conformity of the compositions of these samples suggests that, fortunately, the (238U/232Th) and (230Th/232Th) of the Tanetomi magma at the quarry were essentially homogeneous before post-eruptive degassing (note that the data of these clinker samples plot on the trend established by the Kutsugata and Tanetomi lava data (i.e. circles and squares in Fig. 6) (Figs. 6 and 7)). Therefore, we can regard the linear compositional array in Fig. 7 as an isochron formed by post-eruptive U–Th fractionation. The duration of the degassing event is considered to have been at most 2 years (Kuritani & Nakamura, 2006), and this is much less than the half-life of 230Th. Thus, the isochron gives a meaningful eruption age for the Tanetomi Lower lava of 20·2 ± 3·1 ka (2; calculated after Ludwig, 2003). The Tanetomi Lower lava is covered by scoria layers of the main L-2 stage products (Kuritani, 1995). Because the main activity of the L-2 stage is considered to have been finished by 8·2 ka (Miura, 1995), the Tanetomi Lower lava should be older than 8·2 ka. This is consistent with the estimated eruption age of 20·2 ka. The isochron intersects the equiline at (230Th/232Th) 0·98 (Fig. 7). This suggests that the (230Th/232Th) ratio of the quarry magmas at the time of eruption was 0·98.
Dating of the Kutsugata lava
Unlike the case of the quarry samples of the Tanetomi lava, the whole-rock variation in (238U/232Th) and (230Th/232Th) ratios of the Kutsugata lava (Fig. 6) cannot be regarded as an isochron, because the whole-rock variation could have been produced by assimilation and fractional crystallization on a timescale that cannot be negligible compared with the half-life of 230Th. The age of the Kutsugata lava can also be estimated from a U–Th model age (e.g. Widom et al., 1992; Bourdon et al., 1994). However, it is not clear that the source mantle was homogeneous in (230Th/232Th) beneath Rishiri Volcano, which is one of the required conditions for obtaining a meaningful model age. For these reasons, we used 14C dating, rather than U–Th radioactive disequilibrium, to estimate the age of the Kutsugata lava.
Charcoals for radiocarbon dating were collected from a sand layer just underlying the Kutsugata North lava at the northern coast of Rishiri Island (locality 11 in Fig. 1). The result of the 14C dating shows that the charcoals formed at 29 330 ± 600 years BP (2). Because the woods are considered to have been charred at the time of eruption of the lava, it is suggested that the eruption age of the Kutsugata North lava is 29 ka. The age obtained in this study is significantly younger than the >37 320 years BP age obtained for similar charcoals by Miura & Takaoka (1993). Unfortunately, we could not find a plausible reason for this discrepancy. However, Ishizuka (1999) determined ages of Middle-stage lavas (Fig. 1), before the activity of the Kutsugata North lava, to be 42 ± 13 ka by K–Ar dating. It is considered that there is a significant time interval between the activities of the Middle stage and the Kutsugata lava, because the Middle stage lavas are eroded, in contrast to the Kutsugata lava, which basically preserves its original lava morphology. This observation suggests that the younger eruption age of the Kutsugata lava (i.e. a longer time interval between the two eruptions) is more likely; therefore, we consider that the eruption age of 29 ka is more plausible than the >37 ka age of Miura & Takaoka (1993).
Miura & Takaoka (1993) also estimated the eruption age of the Nozuka lava (L-2 stage; Fig. 1) to be 28 230 ± 1020 yr BP by the radiocarbon dating method. If this is correct, the eruption ages of the Kutsugata lava (high Na/K basalt) and the Nozuka lava (low Na/K basalt) are similar. However, it is not likely that eruption of two very different kinds of voluminous basaltic magmas occurred almost contemporaneously in a single volcano. For the 14C dating, Miura & Takaoka (1993) did not use charcoals but (not charred) wood from a peat layer beneath the Nozuka lava. Therefore, we suggest that the 14C age of 28 ka does not indicate the time of the eruption, but provides an older limit of the eruption age. This interpretation is supported by the observation that the main activity of the L-2 stage is later than the eruption of the Tanetomi lava (20 ka).
Timescales of magmatic evolution
From the eruption age of the Kutsugata lava of 29·3 ± 0·6 ka and that of the Tanetomi lava of 20·2 ± 3·1 ka, it is concluded that it took 9·1 ± 3·7 kyr for the parental alkali basalt (SiO2 52 wt %) to evolve to the andesite (SiO2 60 wt %) by assimilation and fractional crystallization in the magma chamber beneath Rishiri Volcano. In Rishiri Volcano, no evidence of volcanic activity is found between the Kutsugata and Tanetomi lavas (Kobayashi, 1987; Ishizuka, 1999). In addition, detailed observation of zoning patterns in plagioclase phenocrysts in the Tanetomi lava suggests that a heating event (magma replenishment) of the magma chamber occurred only once—the injection of a mafic magma just before the eruption of the lava (Kuritani, 2001). Therefore, the magma chamber is considered to have been influenced only by assimilation of crustal materials.
Differentiation times of magmas in magma chambers have been reported by many workers utilizing U-series radioactive disequilibrium. Widom et al. (1992) estimated timescales of differentiation from a parental alkali basalt to trachyte to have been 90 kyr at São Miguel, Azores. Bourdon et al. (1994) showed that the time of evolution of phonolitic magmas from a parental basanite was about 100 kyr at Laacher See, Eifel. Turner et al. (2003b) estimated the timescale of basalt–andesite differentiation to have been 2 kyr at Sangeang Api, Indonesia. Johansen et al. (2005) showed a differentiation timescale from basanite to phonolite of 1550–1750 years at La Palma, Canary Islands.
Evolution of the Kutsugata and Tanetomi magmas
As described above, the (230Th/232Th) and (238U/232Th) ratios of the lava samples tend to increase systematically with increasing whole-rock SiO2 contents (Fig. 6). According to the mass balance model of Kuritani et al. (2005), the (238U/232Th) of the assimilant (partial melt of granodioritic crust) is estimated to have been about 1·8, which is higher than those of the lava samples (<1· 0). Although there may be a possibility that the compositions of the Kutsugata South lava samples are slightly modified by weathering, the systematic increase of (238U/232Th) of the lava samples is considered to reflect crustal assimilation with simultaneous fractional crystallization.
At the time of eruption, the Ta-31 magma had a higher (230Th/232Th) of about 1·0 compared with the present value (0·93), if the eruption age is 29·3 ka (Fig. 9). Similarly, the (230Th/232Th) of the Kr-74 magma (Tanetomi Lower lava) was 0·98 at eruption (Fig. 9). In the magma chamber, therefore, the (230Th/232Th) ratio of the magma changed with time through the effect of ageing and crustal assimilation, throughout the evolution in 9 kyr (a schematic trajectory is shown with a dashed line in Fig. 9). Then, the (230Th/232Th) ratio of each sample further decreased with time by decay of 230Th after eruption and the observed compositional variation is established. Unfortunately, we have no information on the (230Th/232Th) ratio of the assimilant, and we cannot model the geochemical evolution in further detail.
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RATES OF THERMAL AND CHEMICAL EVOLUTION OF MAGMAS IN THE RISHIRI MAGMA CHAMBER |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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In this section, the rates of the thermal and chemical evolution of the magmas in the magma chamber beneath Rishiri Volcano are estimated as a function of time using the timescale data obtained above, as well as mass and energy balance constraints. In the model, the thermal structure of a magma chamber is determined by conductive heat balance between the surrounding crust and the magma chamber, in which the main part of the magma chamber is cooled by thermal and compositional convection. The thermal evolution of the magma chamber is further constrained from the observed relationship between the estimated magmatic temperatures and bulk-rock chemical compositions (Fig. 4). Recently, quantitative evaluation of magma chamber processes has been made by a combined theoretical and geological approach (e.g. Jellinek & Kerr, 2001
; Turner et al., 2003b; Fowler et al., 2007). The feature of this study is that the quantitative petrological and geochemical information on the lavas is used as boundary conditions for the theoretical calculations.
Modeling of the thermal evolution of the magma chamber
Let us consider a layer of crystal-free magma emplaced into the crust (Fig. 10). Crustal magma chambers are likely to have sheet-like shapes, irrespective of their size (e.g. Marsh, 1989). Therefore, the model assumes a sill-like magma body, with a thickness of H (m), in which heat loss from the vertical walls of the reservoir is negligible (i.e. one-dimensional problem). The crust is assumed to be homogeneous in temperature before emplacement, and has a very large length scale relative to that of the magma body. The magma body is divided into three regions: the roof boundary layer, the main magma body, and the floor boundary layer. The roof and floor boundary layers are defined as the region with crystallinity greater than 
i1 and i2, respectively, in the magma body (Fig. 10). A mush zone consisting of crystals and interstitial melt is present within the boundary layers in which crystallinity changes from i1 to unity or from i2 to unity. Heat transfer through the boundary layers and the surrounding crust is assumed to occur principally by conduction.
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The heat conduction equation in the crust can be expressed as
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| (1) |
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| (2) |
(m2/s) is the thermal diffusivity, z (m) is the vertical axis, L (J/kg) is the latent heat of crystallization or melting, c (J/kg°C) is the specific heat, 
(kg/m3) is the density, is the crystallinity, and subscripts c and m denote the crust and the boundary layers, respectively. P1 (W/m3) and P2 (W/m3) are the heat source terms that account for heat exchange between the mush zone and the melt transported from the deeper mush zone, and that between the mush zone and the melt derived from the shallower mush zone, respectively, by compositional convection. In the Rishiri magma chamber, compositional convection is considered to have occurred in the floor mush zone. For the roof boundary layer, therefore, P1 and P2 have no significance and thus P1 = 0 and P2 = 0.
The model assumes that the main magma is homogeneous in temperature and composition. Although the Tanetomi lava shows a large range of chemical variation, from 59 wt % to 65 wt % in SiO2, the greater volume (90%) of the erupted magmas is homogeneous in composition (i.e. Lower lava; SiO2 59–60 wt %). Therefore, the model assumption of homogeneity of the main magma could be valid for the magmas to evolve, at least, to the Lower-lava compositions. In this case, the bulk temperature of the convecting main magma may evolve according to (e.g. Kerr et al., 1990)
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| (3) |
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| (4) |
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| (5) |
i1), and a (m) is the thickness of the roof boundary layer (Fig. 10). Given that the heat transport from the main magma to the underlying floor boundary layer by thermal convection is not significant (e.g. Jaupart & Brandeis, 1986), the growth of the floor boundary layer may be governed by the thermal balance between the heat conduction through the floor boundary layer, the latent heat of crystallization at the interface between the main magma and the floor boundary layer, and the specific heat needed to accommodate the increase in temperature as the boundary layer grows; that is,
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| (6) |
i2), and b (m) is the thickness of the floor boundary layer (Fig. 10).
The dimensional heat flux from a convecting liquid can be expressed as
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| (7) |
(°C–1) is the coefficient of thermal expansion, 
(m2/s) is the kinematic viscosity, and is an empirical constant (Nusselt–Rayleigh relationship; e.g. Turner, 1979; Kerr et al., 1990). The application of this equation to natural systems is, however, not easy, because it is difficult to estimate the temperature difference [Tl – Ti1 in equation (7)] during magmatic evolution. Worster et al. (1990, 1993) modeled the thermal evolution of cooling magma bodies in the diopside–anorthite system, utilizing parameters of the kinetic undercooling for that system. Unfortunately, however, such parameters are not available for natural magmatic systems. In this study, therefore, the temperature Ti1 is treated as a variable.
Compositional convection is assumed to occur through exchange of the melt in the main magma with the melt in the floor mush zone at which crystallinity is m (Fig. 10). The melt transported from the mush zone can cool the main magma, if thermal equilibrium is not attained during the transport in the mush zone (Tait & Jaupart, 1992). The dimensional heat flux associated with compositional convection is modeled in the Appendix, and is expressed as
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| (8) |
0) is a function of x, 
and three other parameters (f, fr, and R) in the mass balance model (ABLF model) of Kuritani et al. (2005) [equation (A17)], and these three parameters are constant (Table 3). The variable x is the ratio of the growth rate of the roof mush zone (da/dt) to that of the floor mush zone (db/dt). The parameter represents the degree of thermal equilibrium during transport of the melt from the floor mush zone to the main magma (Appendix), and this is an unknown variable. Thermal equilibrium is completely attained when = 1, and no heat exchange occurs when = 0.
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In addition to the heat flux induced by compositional convection into the main magma [equation (8)], heat source terms, P1 and P2, in equation (2) (only for the floor boundary layer) should be modeled. It is, unfortunately, difficult to obtain these terms, because we need additional quantitative information regarding the melt transport, such as structure and velocity of the melt transport system. For simplicity, the terms P1 and P2 are ignored in this study. In a later section of this paper, however, we will show that these terms might be negligible.
Constraints from mass balance considerations
To solve the governing equations presented above, two additional constraints are required, in addition to the initial conditions, because the two parameters (Ti1 and ), controlling the heat fluxes, Ft and Fc, are still unknown. In this study, the observed temperature–composition relationship shown in Fig. 4 is used as one constraint. To incorporate the constraint of this relationship into the model, it is necessary to link the composition of the main magma (i.e. K2O content) to some parameters used in the above energy balance model. The geochemical evolution of the Kutsugata and Tanetomi magmas, by crustal assimilation and simultaneous boundary layer fractionation, has already been modeled by Kuritani et al. (2005) (ABLF model), and this model is utilized for that purpose. To apply the ABLF model to the energy balance model described above, however, the original ABLF model needs to be slightly modified. In addition, Pb concentration data for the Kutsugata and Tanetomi lavas were redetermined by rigorous analytical techniques, and the values of some ABLF parameters of Kuritani et al. (2005) must therefore be revised. For these reasons, in the Appendix, a modified version of the ABLF model is described and the ABLF parameters are recalculated.
According to the modified ABLF model, the change in K2O content of the main magma with magmatic evolution can be expressed as
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| (9) |
(wt %) and 
(wt %) are K2O content of the main magma and assimilated crustal melt, respectively. 
and 
are the ABLF model parameters (Appendix), and they consist of x and some other model parameters, fr, f, 
and R (Table 3). F is the ratio of the mass of the main magma to the initial mass of magma, and may be approximated as
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| (10) |
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| (11) |
is
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| (12) |
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| (13) |
and are constant and are already known (Appendix; Table 3). In addition, can be expressed as a function of Tl using equation (11). Therefore, equation (13) can be written as the following form:
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| (14) |
h/H) and x ( da/db) in equation (14) can be related to the parameters used in the governing equations (1)–(6)
, and equation (14) can be easily incorporated in the above energy equations.
Model calculations
In the preceding sections, we present the governing equations for the thermal evolution of the magma chamber [equations (1)–(6)], and also show one additional constraint [equation (14)] to close the governing equations. However, we still have one degree of freedom except for initial conditions, because there are two unknown variables (Ti1 and ) while we have only one constraint. Therefore, in this study, model calculations will be performed under some arbitrary conditions for the parameters Ti1 and . In this section, first, some simplifications of the model are described. Then, the conditions of the model calculations are presented, and the numerical method and the values of the physical parameters are provided. Finally, we show one example of the result of the model calculations.
Simplification of the model
Throughout the evolution of the Kutsugata and Tanetomi magmas, the main magma was basically free of crystals, and therefore, l is zero. This was caused not by gravitational settling of crystals formed in the main magma body, but by suppression of crystallization in the main magma as a result of liquidus depression resulting from mixing with the fractionated melt from the mush zones (Kuritani, 1999b, 2001). In the calculation, i1 = i2 is assumed (Ti1 = Ti2). A volume of erupted magma may be less than 1% of the volume of a magma chamber (e.g. Tait et al., 1989). Therefore, the volume contraction of the magma chamber as a result of eruption of the Kutsugata magmas is ignored. It is further assumed that volume expansion of the magma chamber caused by influx of crustal melt is ignored, because the ratio of assimilated mass to crystallized mass was low (< 4%).
Conditions of the model calculations
As noted above, we cannot determine uniquely the variations of the two variables (Ti1 and ) during the magmatic evolution, and we need to fix one more condition to close the governing equations. In this study, as a mechanism of cooling of the main magma, the following three cases are considered: cooling of the main magma solely by thermal convection (case 1); cooling of the main magma by both thermal convection and compositional convection (case 2); cooling of the main magma solely by compositional convection (case 3). The thermal evolution of the main magma may also be modeled solely by conductive cooling; that is, we use a single heat conduction equation, instead of equations (2)–(6), for the magma chamber. In this case, however, it is expected that the temperature of the main magma was constant at about 1100°C in the early stage of the magmatic evolution, contrary to the observed relationship shown in Fig. 4. In addition, when compositional convection was active, thermal and chemical mixing processes are considered to have inevitably occurred in the main magma (Jellinek & Kerr, 2001; Kuritani, 2004). These considerations contradict the purely conductive cooling model.
Numerical methods
For case 1, a contribution of compositional convection to cooling of the main magma is absent ( = 1). The only unknown parameter, Ti1, is obtained by simultaneously solving equations (3), (5), (6), (7) and (14) in each step of the Runge–Kutta scheme (described below). For case 2, we simulate the thermal and chemical evolution of the magma chamber for the arbitrary condition = 0·5. The interface temperature, Ti1, is similarly obtained from the simultaneous equations. For case 3, the parameter can be obtained uniquely from the relationship between dF and dTl [equation (14)], using equations (A16) and (A17). In addition, we need not solve equation (3), because we have information about dTl/dF [equation (14)] and dF is directly related to the growth of the boundary layers by the relationship
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| (15) |
i = 0·01, whereas Ft is fixed to zero.
The ordinary differential equations are solved numerically by the fourth-order Runge–Kutta scheme. The diffusion equations are solved by the Crank–Nicolson implicit method, and those for the mush zones are solved with the front-fixing method through Landau transformation. The values for the physical parameters adopted are: c = m = l = 8 x 10–7 m2/s, Lc = Lm = 4·0 x 105 J/kg, cc = cm = cl = 1·3 x 103 J/kg°C, c = m = l = 2·5 x 103 kg/m3, and = 5·0 x 10–5°C–1 (Table 3). In equation (7), = 0·056 is used (Denton & Wood, 1979), and dynamic viscosity of magmas, µl (kg/m s), is simply expressed as a function of temperature, µl = 70 – 0·6 x (Tl – 1000), obtained from the model of Shaw (1972). The solidus of the crust is assumed to be 700°C, but heat transport as a result of movement of crustal melt is ignored. The liquidus volume change of the crust, ds/dT, is approximated to be –3·33 x 10–3°C–1. A solidus temperature of the magma (Ts) of 800°C is assumed (Lambert & Wyllie, 1972). An initial magma temperature of 1100°C is used (corresponding to the Ta-31 magma), and we assume that the crust was initially homogeneous in temperature at 300°C.
Model calculation and estimation of chamber thickness
Figure 11 shows examples of the calculated thermal evolution of the main magma, with a chamber thickness of 1 km, for the three model cases. The calculation of case 3 is terminated at about 800 years (indicated with arrow), because the parameter , which is initially about 0·35, decreases progressively with time, and reaches zero at 800 years. This result indicates that cooling solely by compositional convection is not enough to explain the temperature–composition relationship of the lavas, and contribution of cooling by thermal convection, in addition to compositional convection, is required after 800 years.
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Although the thermal evolution in case 3 is terminated at
800 years, the three trends are basically similar. Importantly, the timescales required for the main magma to evolve from the Ta-31 composition to the Kr-74 composition are mostly similar, for cases 1 and 2. This is not so surprising, because the total heat flux out of the main magma is mostly fixed if the thickness of the magma chamber ( timescale of the evolution) and the relationship between dTl and dF are fixed. In this model, the length scale is proportional to the square root of the time scale (Fig. 12). Therefore, given that the evolution time was 9·1 ± 3·7 kyr as estimated above, the thickness of the magma chamber (H) can be estimated to have been 1·7 + 0·3/–0·4 km (Fig. 12), irrespective of the mechanism of the thermal evolution. As the volume of the Kutsugata North lava is 2.8 km3(Ishizuka, 1999) and this may be <1% of the volume of the magma chamber (Tait et al., 1989), it is inferred that the magma chamber had a volume of more than 280 km3. If this is correct, the horizontal area of the chamber was >150 km2. This is consistent with the inferred sill-like shape of the magma chamber.
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Rates of magma chamber processes beneath Rishiri Volcano
We can estimate the thermal and chemical evolution of the magmas in the Rishiri magma chamber as a function of time, if the model calculations are performed for the chamber thickness estimated above (i.e.
1·7 km). Figure 13a and b shows the thermal and chemical evolution of the magmas, respectively. We show only the evolution of case 1 (thermal convection case), because the evolution trends of the three cases are mostly similar (Fig. 11). In the diagrams, the magmas corresponding to the sample Ta-31 (Kutsugata North lava) and Kr-74 (Tanetomi lower lava), as well as the sample Km-6 (one of the most differentiated samples in the Kutsugata South lava; Kuritani et al., 2005), are indicated. In the Rishiri magma chamber, the cooling rate was mostly in the range 0·01–1°C/year during the evolution of the Kutsugata magmas, and it was always less than 0·01°C/year when the magmas evolved to the Tanetomi lava compositions. As is shown in Fig. 13b, the rate of chemical evolution has also decreased progressively with time. Unfortunately, the eruption age of the Kutsugata South lava could not be obtained by age dating. However, the model calculation shows that the activity of the Kutsugata South lava must have finished by at most 1000 years after the eruption of the North lava magma (Fig. 13b).
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Figure 14 shows how the roof and floor boundary layers increase in thickness with time, at a given chamber thickness of 1·7 km, for the three model cases. The roof and floor boundary layers grow symmetrically for case 3. On the other hand, when thermal convection is active (cases 1 and 2), the growth of the roof boundary is suppressed as a result of convective heat flux through the roof boundary layer.
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Figure 15a shows the variation of the heat flux from the main magma for case 1. Throughout the evolution of the Kutsugata lava, the heat flux was always more than 2 W/m2. Given that the horizontal area of the magma body was >
150 km2 as inferred above, the power output was >300 MW. The flux decreased progressively with magmatic evolution, and it was less than 0·3 W/m2 during the evolution of the Tanetomi magmas. The volume flux of crustal melt to the magma chamber through the floor, Q a (m/s), can be obtained from the relationship (Appendix)
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| (16) |
0·002 m/year when the magma evolved to the compositions of the Tanetomi Lower lava. Figure 15c also shows the variations of the volume flux of interstitial melt from the floor mush zone to the main magma, Qr (m/s), by compositional convection, calculated using the relationship (Appendix)
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| (17) |
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Mechanism of cooling of the Rishiri magma chamber
Using the model calculations with the constraint of the relationship between dTl and dF, we have successfully obtained the rate of thermal and chemical evolution of the magmas in the Rishiri magma chamber (Fig. 13a and b). Unfortunately, however, the above model calculations could not constrain uniquely the mechanism of cooling of the magma chamber (i.e. cases 1–3). In this section, therefore, a role for compositional convection in the cooling of the magmas is roughly considered, by evaluating the parameter
.
It is assumed that, in compositional convection, the interstitial melt was transported to the main magma through stable vertical circular pipes, with a diameter d (m) and a number density n (m–2), within the floor mush zone (e.g. Tait & Jaupart, 1992). Let us consider a part of the pipe with a length L (m) (L << b) with the ambient temperature of Ta (°C) (Fig. 16). The temperature of the melt at z = z1 is T1 (°C), and that of the melt at z = z2 is T2 (°C) (Ta > T2 > T1). Now, we evaluate the distance of melt transport, L, in which the melt at temperature T1 is heated to T2 by the surrounding hot mush zone at a temperature Ta.
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The heat flow required to increase the temperature of the melt from T1 to T2 is
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| (18) |
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| (19) |
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| (20) |
m·cm·m·d–1 (where Nu is theNusselt number), we obtain the following equation:
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| (21) |
), it has been observed that the vertical cylindrical pipes are distributed in the lower part of the body with the density of 0·1–0·01 m–2 (R. Simura, personal communication). Therefore, it is assumed that the number density of the pipes was >0·01 m–2 in the Rishiri magma chamber. Using these conditions, the following relationship is obtained:
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| (22) |
)
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| (23) |
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| (24) |
0·6 m. Considering that the thickness of the boundary layer is >200 m for most stages of the evolution (Fig. 14), the parameter may have been close to unity (case 1 above), and it is expected that compositional convection could not have effectively cooled the main magma in the Rishiri magma chamber. The inference that compositional convection does not carry a significant heat flux is consistent with experimental results by Kaneko & Koyaguchi (2000). Therefore, the cooling of the main magma is considered to have been caused principally by thermal convection in the Rishiri magma chamber. |
CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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To understand quantitatively the magmatic processes occurring in a cooling magma body, the rates of thermal and chemical evolution of magmas have been investigated for the Kutsugata and Tanetomi lavas from Rishiri Volcano. Thus, we reach the following conclusions.
- The eruption age of the Kutsugata North lava was constrained to be 29·3 ± 0·6 ka by radiocarbon dating of charcoals. The eruption age of the Tanetomi Lower lava (trachytic andesite) was determined from a whole-rock isochron, produced by selective fractionation of U during degassing from the solidifying lava after eruption; an age of 20·2 ± 3·1 ka was obtained. This may be the first example of determination of eruption ages using this method; this dating method might be useful for other young volcanic systems.
- From the difference of the estimated ages between the Kutsugata and Tanetomi lavas, we obtained the timescale of 9·1 ± 3·7 kyr for the parental alkali basalt magma (SiO2 52 wt %) to have evolved to the daughter andesite magma (SiO2 60 wt %). The estimated timescale may be consistent with a relatively large eruption volume of 3·8 km3 for the Kutsugata lava.
- Rates of thermal and chemical evolution of the magmas were obtained using constraints of mass and energy balance, coupled with constraints from petrological and geochemical observation on the lavas. By utilizing a timescale of 9·1 ± 3·7 kyr, the thickness of the magma chamber is estimated to be 1·7 + 0·3/–0·4 km.
- The convective heat flux from the main magma, the volume flux of assimilant from the partially fused crust to the molten main magma, and the rate of convective melt exchange between the main magma and the floor mush zone were estimated as a function of time. In the future, these estimations may be used to test physical models.
- The heat transfer associated with compositional convection was evaluated using the estimated rate of convective melt exchange, and it is shown that the fractionated interstitial melt is considered to have been thermally equilibrated with the surroundings during transport to the main magma. Therefore, the main magma of the Rishiri magma chamber was not effectively cooled by compositional convection, but was cooled principally by thermal convection.
- On the basis of chronological and physical constraints, in combination with the detailed petrological and geochemical studies (Kuritani, 1998, 1999a, 1999b, 2001; Kuritani et al., 2005), we successfully obtained quantitative information on magmatic evolution in a cooling magma chamber beneath Rishiri Volcano. We show that, for quantitative understanding of magmatic differentiation, volcanic rocks provide important constraints that cannot be obtained by investigations on igneous intrusions.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONGEOLOGICAL SETTINGANALYTICAL METHODSBACKGROUNDRESULTS OF U-TH ISOTOPIC...RATES OF THERMAL AND...CONCLUSIONSAPPENDIXREFERENCES |
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A modified assimilation and boundary layer fractionation (ABLF) model
To relate the chemical composition of the main magma (i.e. K2O content) to the parameters used in the energy balance model [equations (1)–(6)
], the ABLF model of Kuritani et al. (2005) is used. However, to apply the ABLF model to the energy balance model, the original ABLF model needs to be slightly modified. In this Appendix, a modified version of the ABLF model is described, and the revised values of the ABLF parameters are determined. Then, the heat flux as a result of compositional convection is modeled.
Modified ABLF model
A box model of the ABLF process is shown in Fig. A1. The original ABLF model of Kuritani et al. (2005) was based on the boundary layer fractionation model of Langmuir (1989) and the open magmatic system models of Neumann et al. (1954) and DePaolo (1981). In the modified ABLF model, growth of the roof boundary layer is newly incorporated. Liquid is separated from the crystal-free main magma, with a mass of dMc, to become the floor mush zone. Similarly, liquid is separated from the main magma, with a mass of dMu, to become the roof boundary layer. Assimilated crustal material with mass dMa is added to the floor mush zone, and then the mush zone is crystallized to fraction 1 – f. Fractionated interstitial melt, with a fraction of fr relative to the total mass of the mush zone (dMc + dMa), returns to the main magma (dMr). [Note that, in the study by Kuritani et al. (2005), the definition of the parameter fr was not consistent with their equation (1), and the definition should have been ‘the fraction of interstitial melt, relative to the mass Mc, returning to the main magma’.] The mush zone remaining in place then solidifies as the floor boundary layer (dMb).
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The mass of interstitial melt returning to the main magma can be related to the mass of magma separated from the main magma and the mass of assimilant transported from the crust by
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| (A1) |
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| (A2) |
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| (A3) |
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| (A4) |
and 
are the concentrations of the element in the main magma and the interstitial melt returning to the main magma, respectively. If we assume fractional crystallization in the mush zone, can be written as
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| (A5) |
is the concentration of the element in the assimilant and Di is the bulk distribution coefficient of the element.
Here, the ratio of the mass of the main magma (Ml) to the initial mass of the magma (M0) is defined as F. This parameter can be related to the governing equations (1)–(6) by the relationship
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| (A6) |
, the change of the elemental concentration in the main magma with F can be expressed as
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| (A7) |
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| (A8) |
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| (A9) |
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| (A10) |
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| (A11) |
is the initial concentration of the element in the magma.
The ABLF calculation requires the following input parameters; the compositions of the initial magma (), those of the assimilant (), distribution coefficient of element i between melt and bulk fractionating phases (Di), the melt fraction of the mush zone (f) and the fraction of the interstitial melt returning to the main magma (fr). In this study, concentrations of K2O and Pb, and Pb isotopic compositions are used, following Kuritani et al. (2005). The compositions of the initial magma () are taken to be those of the sample Ta-31 (Table 1). The bulk distribution coefficients, Pb isotopic composition of the assimilant, and a value of f (= 0·7) are the same as those used in Kuritani et al. (2005).
The model parameters, fr and x, do not affect the estimation of the R value. The parameter fr represents the efficiency of the melt transport from the floor mush zone to the main magma. For example, when fr = 0, no melt transport occurs and no chemical evolution takes place in the main magma. On the other hand, when fr = 0·7, all the interstitial melt is removed from the floor mush zone and no interstitial melt is left in solidified rocks (adcumulate), because we adopt f = 0·7. In relatively large igneous intrusions, adcumulate is common in lower part of the bodies (e.g. Tait & Jaupart, 1996), and we adopt fr = 0·7 in this study.
Assuming that = 3·5 wt %, the two unknown parameters, 
and the R-value, are optimized, so that the residuals between the observed data and the modeled trend (as a function of F) are minimized in K2O–Pb–206Pb/204Pb compositional space (Kuritani et al., 2005). Thus, we obtain = 12·9 ppm and R = 0·0385. The estimated value of R = 0·0385 is slightly higher than R = 0·0224 obtained by Kuritani et al. (2005). This discrepancy simply reflects that the Pb concentration data of Kuritani et al. (2005) were 3–5% lower than those measured newly in this study.
Heat flux as a result of compositional convection
The heat flux associated with compositional convection is treated as an unknown variable in the energy conservation model. In this section, we model the convective heat flux so that it is expressed as a function of a parameter that is easily conceivable. In compositional convection, the interstitial melt in the floor mush zone, at a temperature Tr (°C), is transported to mix with the main magma (Fig. A1). During the transport, the melt may be heated from the surroundings. Therefore, the temperature of the melt mixed with the main magma, Tq (°C) (Fig. A1), can be higher than Tr. Here, the degree of thermal equilibration, , is defined as
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| (A12) |
= 1), Tq = Tl. If no heat exchange occurs during the transport ( = 0), Tq = Tr. Given that dMb and dMu are removed from the main magma by conductive cooling (corresponding to the growth of the boundary layers), energy balance in the main magma, cooled solely by compositional convection, may be expressed as
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| (A13) |
m), at which temperature is Tm (°C), is simply modeled as
|
| (A14) |
m = 1 – f), we obtain
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| (A15) |
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| (A16) |
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| (A17) |
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| (A18) |
|
| (A19) |
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| (A20) |
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ACKNOWLEDGEMENTS |
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We are grateful to Kazuhito Ozawa for useful discussions throughout this study. We thank Ryoji Tanaka and all other members of the Pheasant Memorial Laboratory, Institute for Study of the Earth's Interior (ISEI), Okayama University, and the members of Institute for Geothermal Sciences, Kyoto University, for useful discussions. Fruitful comments and editorial handling by Wendy Bohrson and critical improvement of the manuscript by Ross Kerr, Axel Schmitt, and one anonymous reviewer are greatly appreciated. We also acknowledge Naoko Matsumoto for helping T.K. to collect excellent charcoals at Rishiri Volcano. This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology of the Japanese Government to T.K., and also by the program for the ‘Center of Excellence for the 21st Century in Japan’ to ISEI, Okayama University.
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FOOTNOTES |
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Present address: Department of Geology, University of Maryland, College Park, MD 20742, USA 
*Corresponding author. Present address: Department of Earth and Planetary Materials Science, Graduate School of Science, Tohoku University, Sendai, Miyagi 980-8578, Japan. E-mail: kuritani{at}mail.tains.tohoku.ac.jp
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