Petrography of wet and dry basalts from the Sumisu Caldera Volcano, Izu- Bonin Arc, Japan

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1 Petrography of wet and dry basalts from the Sumisu Caldera Volcano, Izu- Bonin Arc, Japan Yoshihiko Tamura 1, Hiroshi Shukuno 1 and Richard S. Fiske 2 1 Research Program for Geochemical Evolution, Institute for Research on Earth Evolution, (IFREE) 2 Smithsonian Institution, Washington, D.C Introduction Fluxing of water released from the subducted slab into the overlying mantle wedge lowers the mantle solidus, triggering magma generation that results in the formation of arc-front volcanoes. Thus we expect arc basalts to be wet, and there are many examples containing a few percent of water to support this [e.g., Newman and Stolper, 2; Roggensack et al., 1996; 1997; Sisson and Layne, 1993; Sobolev and Chaussidon, 1996]. For example, Sisson and Layne [1993] have undertaken an ion and electron microprobe study of basalt and basaltic andesite glass inclusions in olivine phenocrysts from Quaternary eruptions of arc volcanoes and directly demonstrated that typical arc basalts and basaltic andesites can have high H 2 O contents, one of which exceeds 6 wt % H 2 O. Roggensack et al. [1997] showed that Cerro Negro s 1992 magma evidently retained a great abundance of volatiles (H 2 O and CO 2 ), as much as 6.1 wt % H 2 O and 139 ppm CO 2, and erupted explosively. On the other hand, substantial upwelling and pressure-release melting may also take place beneath arc-front volcanoes. Sisson and Bronto [1998] presented measurements of the volatile content of primitive magmas from Galunggung volcano in the Indonesian arc. There, inclusions of mafic glass in olivine phenocrysts of these basalts contain uniformly low H 2 O concentrations ( wt%), yet relatively high levels of CO 2 (up to 7 ppm) indicating that the low H 2 O concentrations are primary and not due to magma degassing. Such nearly H 2 O-free basaltic magmas, which are also found along the Cascade arc, were considered to be derived from the pressure-release melting due to upwelling in the sub-arc mantle [Sisson and Bronto, 1998]. Similarly, some basalt magmas on the front of the Izu-Bonin arc are either anhydrous or nearly so [Aramaki and Fujii, 1988; Fujii et al., 1988; Nakano and Yamamoto, 1991; Nakano et al., 1988]. Significantly, there is petrologic evidence that plagioclase phenocrysts accumulated in the upper parts of magma chambers beneath Izu-Oshima volcano. There, the plagioclase phenocryst content in lavas varies between and 2 % by volume and mafic phenocrysts are rare, yet all of the lavas have similar groundmass (melt) compositions. For plagioclase to float in a basaltic liquid, the H 2 O content must be less than.7% [Aramaki and Fujii, 1988; Fujii et al., 1988; Nakano et al., 1988; Nakano and Yamamoto, 1991], so the abundance of phenocrystic plagioclase and the paucity of mafic counterparts at Izu-Oshima suggest dry conditions at depth. Are arc basalts dry, wet or both? What are the relationships between flux melting and pressure release melting beneath arc volcanoes? The example we discuss is the Sumisu caldera volcano, Izu-Bonin arc. We present evidence that (1) there exist two kinds of basalts in the volcano, which have petrographic, mineralogic and geochemical differences. (2) These systematic and interrelated differences could have been resulted from different water contents in these magmas and differing degrees of melting in the source mantle, and thus dry and wet basalts can coexist in a single volcanic system. And (3) wet basalts have been derived from a more depleted source than dry basalts. 2. Analytical methods Major and trace element analysis by XRF followed the methodology of Tani et al. (2, this volume). Rare Earth Elements (REEs) were determined using a VG Elemental R PQ3 inductively coupled plasma mass spectrometer (ICP-MS) enhanced with a chicane lens system, following the procedures described in Chang et al. [23]. Whole-rock powder was digested with an acid mixture of HF/HClO 4 /HNO 3, finally dissolved in 2% HNO 3 and spiked with 11 In and 29 Bi for internalization of signal in ICP-MS measurements. Analytical precision of REE, as estimated from repeated analysis of well established reference rocks (JB-2 and BHVO-1), is better than 2% (1s). Microprobe analyses were carried out on the JAMSTEC JEOL JXA-89 Superprobe equipped with five wavelength-dispersive spectrometers (WDS). Olivine analyses were made with a counting time of 1 s, using an accelerating voltage of 2 kv, a beam current of 2 na and a probe diameter of µm to ensure reliable nickel values. Pyroxene and plagioclase analyses were made with a counting time of 2 s, using an accelerating voltage of 1 kv and a beam current of 1 na. 3. Two Types of Basalts There exist two types of basalt magmas at the Sumisu caldera volcano, which have different Zr contents and defined here as low-zr basalt and high-zr basalt of the Sumisu caldera volcano. Importantly, petrography such as phenocryst assemblages and phenocryst content, mineral chemistry, bulk-rock trace element contents and REE patterns are closely linked each other. Figure 1 shows the interpreted boundary between low-zr basalts and high Zr basalts. The low-zr basalts are represented by only 4 samples, and these include the samples having the least SiO 2 (D3R16) and the most MgO content (7R4). Low-Zr and less-evolved high-zr basalts have different phenocryst assemblages and phenocryst contents. Figure 1 shows the mode of phenocrysts, Y/Zr and U/Th ratios of low-zr basalts and representative high-zr basalts. All low-zr basalts contain olivine + clinopyroxene + plagioclase, and one of these contains more than 1 vol. % of clinopyroxene. Many high-zr basalts, on the other hand, contain only olivine + plagioclase. Augite appears only in the evolved lavas of the high-zr basalts. Evolved high-zr basalts contain clinopyroxene ± orthopyroxene up to 1 vol. %, but these are dramatically less in volume compared to the low-zr basalts. 1

2 4. Olivine Olivine phenocrysts are contained in both the low-zr basalts and high-zr basalts. Plots of NiO vs. Fo [1Mg/(Mg + Fe)] for real olivines from eight representative samples of Sumisu basalts are shown in Figure 2. There are interesting differences between olivines in low-zr, clinopyroxene-bearing basalts and those in high-zr, clinopyroxene-free basalts. (1) Fo contents in olivines in high-zr basalts mostly gather around Fo 7 to Fo 79, and range totally from Fo 7 to Fo 79 (Fig. 2a, b), but those in low Zr basalts range widely from Fo 71 to Fo 91 (Fig. 2a, c). (2) Some olivines from low-zr basalts overlap the distribution of olivines from high- Zr basalts. (3) Olivines in low-zr basalts have lower wt % NiO and/or higher Fo contents than those in high-zr basalts at given Fo contents and at given NiO content, especially around.-1. wt % NiO, respectively (Fig. 2). The effects of fractional crystallisation of olivines and chemical relationships between olivines and host basalts have been discussed in detail by using calculated equilibrium olivine compositions for Daisen basalts, SW Japan [Tamura et al., 2]. Here, we will consider the relationships between basalts and olivines based on fractionation models and the comparison between real and calculated equilibrium olivines. 4.1 Real vs calculated olivines A series of olivine and basalt compositions were calculated from an original basalt by olivine fractionation models of Tamura et al. [2], which used estimated K D (Fe/Mg) ol/liq values, which mostly ranged from.3 to.31, and D Ni ol/liq from Kinzler et al. [199]. Equilibrium olivines in low-zr basalts have higher Fo contents and lower wt % NiO than those in high-zr basalts at given NiO and Fo contents, respectively. For example, low-zr basalt D3-R16 and high-zr basalt D2-R4 are in equilibrium with olivines of Fo 8.2,.9 wt % NiO and Fo 8.3,.11 wt. % NiO, respectively. These calculated olivines are similar to the actual olivines and, generally, calculated olivines in equilibrium with low-zr basalts and high-zr basalts also show the similar contrast as in real olivines; the former are more magnesian at given NiO contents than the latter. The relationships between real olivines and calculated olivines are, however, different between low-zr and high-zr basalts. Figures 2b and 2c show plots of NiO vs Fo for real olivines, calculated equilibrium olivines and fractionation trends from four high-zr basalts (SI1, SI14, 7R7, and D2-R4) and four low-zr basalts (1394R4, 7R4, 7R and D3-R16), respectively. High- Zr basalts contain olivine phenocrysts whose compositions overlap those of the calculated equilibrium olivines, and continuously extend toward iron-rich compositions (Fig. 2b). On the other hand, low-zr basalts contain, (1) many olivines that are more ironrich and/or more Ni-rich than the calculated equilibrium olivines, and (2) a few olivines that are more magnesian (~Fo 9 ) and lower in NiO (~.1 wt %) than the expected calculated olivines. In other words, the distribution of observed olivine compositions from low-zr basalts cuts across the calculated olivine fractionation trends at a low angle (Fig. 2c). 4.2 Calculated primary olivines Sato [1977] pointed out that first olivines crystallizing from primary magmas should have NiO contents of ~ 4 wt %, because olivines of upper-mantle lherzolites have uniform NiO contents of ~ 4 wt %. Present understandings, however, show that peridotite olivines do not always have a regionally constant NiO content of.4 wt. %. Abyssal peridotite olivines, for example, fall in the range of wt % NiO [Dick, 1989]. It is, however, reasonable to assume that basalts of a single volcano, such as Sumisu, were derived from local mantle sources, which have similar and constant NiO contents. In Daisen volcano, SW Japan, for example, most magnesian olivines (Fo 89 ) contain ~.4 wt % NiO, and these were assumed to represent those crystallized from the primary basalts of Daisen volcano [Tamura et al., 2]. Thus we assume that olivines of the source mantle of Sumisu volcano have uniform NiO contents of ~.4 wt % and a series of olivine compositions were calculated from original low-zr and high-zr basalts by the method of Tamura et al. [2] until the calculated equilibrium olivines had NiO contents of ~ 4 wt %. We assume that the forsterite contents of these olivines equal that of olivines in primary magmas and source-mantle peridotites. Although these calculations ignore clinopyroxene fractionation, the effect of clinopyroxene fractionation in low-zr ol-cpx basalts increases the differences between primary low-zr and high-zr basalts. Thus the differences between primary magmas based on olivine fractionation models would represent minimum values of the actual differences between two mantle source peridotites. The primary olivine compositions calculated from low-zr olcpx basalts (2-R4, 2-R, 1391-R4 and D3-R16) range from Fo 88 7 to Fo On the other hand, those calculated from high-zr ol basalts (SI 1, SI 14, 7 R7 and D2-R4) range from Fo 86 to Fo 89. It is suggested that the source mantle of the low-zr basalts is more magnesian, and thus more depleted, than that of the high- Zr basalts.. Plagioclase Plagioclase is the dominant phenocryst phase in both high-zr and low-zr basalts and basaltic andesites, ranging in volume from 14 to 29%, except for one aphyric andesite (D2-R2). Figure 3 shows frequency histograms of An content [1*Ca/(Ca+Na)] in the low-zr basalts and high-zr basalts and basaltic andesites. Less evolved high-zr basalts and low Zr basalts have similar distribution patterns, which peak between An 8 to An 9. Most plagioclase rim compositions in these rocks override those of their core compositions (Fig. 3), indicating very weak zoning patterns in both basalt types. Plagioclases having >An9, however, only appear in low Zr basalts (especially in D3R16 and 7R4); those having > An 9 are rare in high-zr basalts compared to those in low Zr basalts. Evolved high-zr rocks (D1R9, 118R2, 7R1 and 7R2) have clear normal zonings of plagioclase phenocrysts (Fig. 3); cores have An content ranging An 8 to An 9, whereas rims have lower An contents ranging from An 7 to An Augite Augite phenocrysts appear at an earlier primitive stage in low- Zr basalts and at a more evolved stage in high-zr basalts. Figure 4a shows X Mg values of phenocryst cores of coexisting augites and olivines in low-zr and high-zr basalts. Generally, augites have higher maximum X Mg values than coexisting olivines, but the range of augite X Mg values is greater than that of olivines. Olivines and augites in Low-Zr basalts have much wider ranges in 2

3 composition than those in evolved high-zr basalts. 6.1 Olivine-Augite Geothermometry Figure 4b shows magmatic temperatures estimated by using the olivine-augite Mg-Fe-exchange thermometer of Loucks [1996]. To use this thermometer, we need a pair of compositions of olivine and augite and thus we estimated three temperatures from each rock using pairs of average, maximum, and minimum Mg values of olivine and augite cores. The high-zr basalt samples yielded consistent temperatures of C. In contrast, the three pairs of olivine and augite determinations from, low-zr basalts show varying, inconsistent temperatures in each rock sample. For example, the temperature estimated by using maximum Mg values of olivine and augite cores in 7R4 is ~ 13 C, but the temperature estimated by using average Mg values is below 11 C, 2 C lower than that of the maximums. Moreover, temperatures estimated by using minimum Mg values (~12 C) fall near the midpoint between the other two estimates. We therefore conclude that this geothermometer does not perform satisfactorily in the low-zr basalts. 6.2 Two-pyroxene thermometry The augite + hypersthene pairs are rare in the evolved high-zr basalts, limiting the use the two-pyroxene thermometer of Lindsley and Andersen [1983] (Fig. ). Pyroxenes in the evolved basalt 118R2 indicate magmatic temperatures of 11~12 C, whereas those in andesite 7R1 clearly indicate a lower temperature of ~ 11 C. Since olivines and augites in the same sample of 118R2 indicate a temperature of ~12 C, the two-pyroxene thermometry is consistent to that estimated by olivine-augite thermometer (Fig. 4). Based on the temperatures indicated by the olivine-augite and two-pyroxene thermometers, we conclude that the high-zr basalts and andesites had temperatures ranging from 12 C to 11 C, and that the andesites had slightly lower temperatures. 7. Were the low-zr basalts derived from a more depleted source than the high-zr basalts? The crystallisation and fractionation of olivine, or olivine plus clinopyroxene, will produce less magnesian magmas. Ni, however, is concentrated more in olivine than in clinopyroxene: most cpx phenocrysts in low-zr basalts contain <.1 wt. % NiO when they are analysed using an accelerating voltage of 2 kv and a beam current of 2 na. Thus the fractionation of olivine alone would result in a drastic decrease of NiO compared to the fractionation of an equal volume of olivine plus clinopyroxene. For example, low-zr basalt 7R is produced by crystal fractionation of 4% olivine, 7% augite and 1% plagioclase from the low-zr basalt 7R4. The calculated olivine in equilibrium with basalt 7R has a much higher NiO content than the olivine fractionation trend expected from 7R4. Thus, generally, the discrepancy between real olivines and calculated olivines for low-zr basalts could have resulted from the crystallisation and fractionation of augite phenocryst together with olivines. It is interesting, however, that the effect of clinopyroxene fractionation cannot be responsible for the differences between two types of basalt magmas in the Sumisu area, and, on the contrary, it tends to blur the differences between them. It should be emphasised that the original differences of olivine chemistry in the two primitive magmas may have been greater than that now observed in their differentiated products. We conclude that the sources of high- and low-zr basalts differed in fertility, and that the low-zr basalts were derived from a more magnesian, and thus more depleted source than the high-zr basalts. 8. Differences of water content in the source mantle beneath Sumisu caldera volcano Green [1982] showed that, under dry conditions in the - kb pressure range, plagioclase is the major liquidus or near-liquidus phase in tholeiitic basalt, which is joined by olivine and later by pyroxene. When % H 2 O is added to this tholeiitic basalt, however, the appearance of plagioclase is markedly depressed and pyroxene together with olivine are important near-liquidus phases in the basalt from 2 to c. 14 kb [Green, 1982]. Sisson and Grove [1993] show that at 2 kbar, with addition of H 2 O, the assemblage plagioclase + olivine + high-ca pyroxene appears at high melt fractions, apparently close to the liquidii of the high-alumina basalts. On the other hand, at low-to-moderate pressures, anhydrous high-alumina basalts crystallize plagioclase or olivine and plagioclase over extended temperature intervals before being joined by high-ca pyroxene [Grove et al., 1982; Baker and Eggler, 1983; Bartels et al., 1991]. Cotectic formation of augite is likely a consequence of elevated magmatic water content that promotes expansion of the clinopyroxene phase volume. These experimental results suggest that the phenocryst assemblage olivine + plagioclase crystallizes under dry conditions and the appearance of high-ca pyroxene together with olivine and plagioclase requires a few percent of water. Thus, low-zr basalts would have had higher water contents than high-zr basalts. K DFe/Mg ol/aug provides another indirect indicator of water content in magmas. The successful performance of the olivine-augite Mg-Fe-exchange geothermometer in the evolved high-zr basalts contrasts markedly with its poor performance in the low-zr basalts (Fig. 8). What causes the erratic performance of this thermometer? Loucks [1996] states that K DFe/Mg ol/aug shows no systematic correlation with temperature in systems having more than a few weight percent H 2 O in the melt, because in these cases, the phase assemblage olivine + augite + plagioclase + melt no longer behaves as an isobarically univariant assemblage. Thus the contrasting poor performance of the olivine-augite thermometer in the low-zr basalts may suggest that the low-zr basalt magmas contained more than a few weight percent of water. Acknowledgements. Samples used in this study were collected during JAMSTEC cruises in September October, 22 (NT2-1) and December, 22 (KR2-16). We are indebted to Captains F. Saito of R/V Natsushima and O. Yukawa of R/V Kairei, their crews, Commander H. Shibata, and the operation team of the research submersible Shinkai 2. References Aramaki, S. and T. Fujii, Petrological and geological model of the eruption of Izu-Oshima volcano, Bull. Volc. Soc. Japan 33, S297-S36 (in Japanese with English abstract and figure captions), Baker, D. R. and D. H. Eggler, Fractionation paths of Atka (Aleutians) high-alumina basalts: constraints from phase relations, J. Volc. 3

4 Geotherm. Res., 18, , Bartels, K. S., R. J. Kinzler and T. L. Grove, High-pressure phase relations of primitive high-alumina basalt from Medicine Lake volcano, northern California, Contributions to Mineralogy and Petrology 18, 23-27, Chang, Q, T. Shibata, K. Shinotsuka, M. Yoshikawa and Y. Tatsumi, Precise determination of trace elements in geological standard rocks using inductively coupled plasma mass spectrometry. Frontier Research on Earth Evolution (IFREE Report for 21-22) 1, , 23. Dick, H. J. B., Abyssal peridotites, very slow spreading ridges and ocean ridge magmatism. In Saunders, A. D. and Norry, M. J. (eds) Magmatism in the Ocean Basins. Geological Society, London, Special Publication 42, 71-1, Fujii, T., S. Aramaki, T. Kaneko, K. Ozawa, Y. Kawanabe and T. Fukuoka, Petrology of the lavas and ejecta of the November, 1986 eruption of Izu-Oshima volcano. Bulletin of the Volcanological Society of Japan 33, S224-S24 (in Japanese with English abstract and figure captions), Green, T. H., Anatexis of mafic crust and high pressure crystallization of andesite. In Andesites, Ed., Thorpe, R. S., New York: John Wiley, pp , Grove, T. L., Gerlach, D. C. and Sando, T. W., Origin of calc-alkaline series lavas at Medicine Lake volcano by fractionation, assimilation and mixing. Contributions to Mineralogy and Petrology 8, , Kinzler, R. J., T.L. Grove and S. I, Recca, An experimental study on the effect of temperature and melt composition on the partitioning of nickel between olivine and silicate melt. Geochimica et Cosmochimica Acta, 4, , 199. Lindsley, D. H. and D.J. Andersen, A two-pyroxene thermometer. Proceedings of 13th Lunar and Planetary Science conference. Journal of Geophysical Research 88, Supplement, , Loucks, R.R., A precise olivine-augite Mg-Fe-exchange geothermometer. Contributions to Mineralogy and Petrology 12, 14-1, Nakano, S., S. Togashi and T. Yamamoto, Bulk and mineral chemistry of products of the 1986 eruption of Izu-Oshima volcano. Bulletin of the Volcanological Society of Japan 33, S2-S264. (in Japanese with English abstract and figure captions), Nakano, S. and T. Yamamoto, Chemical variations of magmas at Izu- Oshima volcano, Japan: plagioclase-controlled and differentiated magmas. Bulletin of Volcanology 3, , Newman, S. and E.M. Stolper, H 2 O and CO 2 in magmas from the Mariana arc and back arc systems. Geochemistry, Geophysics and Geosystem 1, 1999GC27, 2. Roggensack, K., R.L. Hervig, S.B. McKnight and S.N. Williams, Explosive basaltic volcanism from Cerro Negro volcano: influence of volatiles on eruptive style. Science 277, , Roggensack, K., S.N. Williams, S.J. Schaefer and R.A.J. Parnell, Volatiles from the 1994 eruptions of Rabaul: understanding large caldera systems. Science 273, , Sato, H., Nickel content of basaltic magmas: identification of primary magmas and a measure of the degree of olivine fractionation. Lithos 1, , Sisson, T.W. and S. Bronto, Evidence for pressure-release melting beneath magmatic arcs from basalt at Galunggung, Indonesia. Nature 391, , Sisson, T. W. and T.L. Grove, Experimental investigations of the role of H 2 O in calc-alkaline differentiation and subduction zone magmatism. Contributions to Mineralogy and Petrology 113, , Sisson, T.W. and G.D. Layne, H2O in basaltic and basaltic andesite glass inclusions from four subduction-related volcanoes. Earth and Planetary Science Letters 117, , Sobolev, A. V. and M. Chaussidon, H 2 O concentrations in primary melts from suprasubduction zones and mid-oceanic ridges: implications for H 2 O storage and recycling in the mantle. Earth and Planetary Science Letters 137, 4-, Tamura, Y., M. Yuhara and T. Ishii, Primary arc basalts from Daisen volcano, Japan: equilibrium crystal fractionation versus disequilibrium fractionation during supercooling, J. Petrol., 41, , 2. 4

5 High-Zr vol % D2-R4 7R7 SI1 SI14 olivine D2-R2 7R1 7R2 cpx plagioclase groundmass Zr (ppm) D3-R16 SI14 7R4 D2-R4 SI1 7R7 2K1391R4 7R 2K118R Y/Zr U/Th Low-Zr vol % D3-R16 7R4 7R 2K1391R4 olivine cpx plagioclase groundmass Wt. % SiO 2 Y/Zr U/Th Figure 1. Zr vs SiO 2 for basaltic rocks of the Sumisu caldera volcano. Low-Zr and high-zr basalts have distinct phenocryst assemblages and percentages and Y/Zr and U/Th ratios. (a).2 olivines from high-zr basalts NiO (wt %) Fo (mol %) olivines from low-zr basalts (b).2 NiO (wt %).1 SI1 7R7 D2-R4 SI14 (c) NiO (wt %) R 1391R4 Fo (mol %) D3-R Fo (mol %) 2 7R4 Figure 2. Plots of NiO vs Fo [1Mg/(Mg + Fe)] for olivines. (a) Observed olivines from high-zr basalts (blue field) and those from low-zr basalts (red field). (b) Real olivines in high-zr basalts (squares) vs. calculated olivines (circles) and olivine fractionation trends (lines) determined from the bulk composition of high-zr basalt. The numbers on the lines indicate the percentage of added equilibrium olivines. (c) Real olivines in low-zr basalts (squares) vs. calculated olivines (circles) and olivine fractionation trends (lines) of low-zr basalt. Both real and calculated olivines in low-zr basalts are more magnesian or lower in NiO than those in high- Zr basalts at a given NiO content or a given Fo content, respectively.

6 low-zr basalts high-zr basalts high-zr basaltic andesite D1R9 118R2 7R1 7R SI 1 7R7 D2R4 SI D3R R4 7R4 7R Figure 3. histograms of An content [1*Ca/(Ca+Na)] of plagioclase in the low-zr basalts, high-zr basalts and basaltic andesites. Cores and rims are shown in green and yellow bars, respectively. augite (a) 9 olivine 9 1*Mg/(Mg + Fe) (b) Temperature ( C) low Zr basalts high Zr basalts 7R4 1391R4 7R7 D1R9 7R D3R16 118R3 118R2 low Zr basalts Temperature estimates: using average Mg values using maximum Mg values using minimum Mg values high Zr basalts 7R4 1391R4 7R7 D1R9 7R D3R16 118R3 118R2 Figure 4. (a) XMg [1*Mg/(Mg+Fe)] values of phenocryst cores of coexisting augites and olivines in low-zr and evolved high-zr basalts. Olivines and augites in Low-Zr basalts have much wider compositional ranges than those in evolved high-zr basalts. Average value divides each rectangle. (b) Magmatic temperatures estimated by using the olivine-augite Mg-Feexchange thermometer of Loucks [1996]. Three temperatures estimated from each rock using pairs of average, maximum, and minimum Mg values of olivine and augite cores. 6

7 Di 118R core rim 11 En Di 7R core rim 11 En Figure 4. Two-pyroxene thermometry for high-zr andesitic rocks of Sumisu caldera volcano, following the method of Lindsley and Andersen [1983]. 7