Geochemical differentiation processes for arc magma of the Sengan volcanic cluster, Northeastern Japan, constrained from principal component analysis

    Geochemical differentiation processes for arc magma of the Sengan volcanic cluster, Northeastern Japan, constrained from principal component analysis Kenta Ueki, Hikaru Iwamori PII: DOI: Reference:

S0024-4937(17)30271-2 doi:10.1016/j.lithos.2017.08.001 LITHOS 4384

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LITHOS

Received date: Accepted date:

14 April 2017 3 August 2017

Please cite this article as: Ueki, Kenta, Iwamori, Hikaru, Geochemical differentiation processes for arc magma of the Sengan volcanic cluster, Northeastern Japan, constrained from principal component analysis, LITHOS (2017), doi:10.1016/j.lithos.2017.08.001

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ACCEPTED MANUSCRIPT Geochemical differentiation processes for arc magma of the Sengan volcanic cluster, Northeastern Japan, constrained from principal component analysis

Kenta Uekia,* and Hikaru Iwamorib,c Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo, 113-0032, Japan

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Department of Solid Earth Geochemistry, Japan Agency for Marine-Earth Science and Technology, 2-15 Natsushima-

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cho, Yokosuka, 237-0061, Japan

Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo

152-8550, Japan

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*Corresponding author. Email: [email protected], Tel.: +81-3-5841-5785, Fax: +81-3-5802-3391

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ACCEPTED MANUSCRIPT Abstract In this study, with a view to understanding the structure of high-dimensional geochemical data and discussing the chemical processes at work in the evolution of arc magmas, we employed principal component analysis (PCA) to evaluate the compositional variations of volcanic rocks from the Sengan volcanic cluster of the Northeastern Japan Arc.

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We analyzed the trace element compositions of various arc volcanic rocks, sampled from 17 different volcanoes in a volcanic cluster. The PCA results demonstrated that the first three principal components accounted for 86% of the

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geochemical variation in the magma of the Sengan region. Based on the relationships between the principal components and the major elements, the mass-balance relationships with respect to the contributions of minerals, the composition of plagioclase phenocrysts, geothermal gradient, and seismic velocity structure in the crust, the first, the second, and the

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third principal components appear to represent magma mixing, crystallizations of olivine/pyroxene, and crystallizations of plagioclase, respectively. These represented 59%, 20%, and 6%, respectively, of the variance in the entire

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compositional range, indicating that magma mixing accounted for the largest variance in the geochemical variation of the arc magma. Our result indicated that crustal processes dominate the geochemical variation of magma in the Sengan

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volcanic cluster.

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ACCEPTED MANUSCRIPT 1 Introduction Chemical processes taking place during the differentiation of arc magmas are believed to play a predominant role in the compositional/chemical fractionation within subduction zones. In this study, we investigate the processes producing

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diverse magmas, from basaltic to rhyolitic, in a single volcanic cluster, by focusing on the compositional variations in 17 different volcanoes in the Sengan volcanic cluster on the volcanic front of the Northeastern Japan Arc. By employing

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multivariable analysis on trace element compositions, we investigate quantitatively the compositional variation, from basalt to rhyolite, and we discuss the chemical process active in the evolution of arc magmas. The bulk chemical composition of erupted volcanic rocks represents the series of chemical processes that had taken

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place during the generation and migration of the arc magma. The chemical reaction of the major elements is controlled by the nonlinear thermodynamic relationship (Ueki and Iwamori, 2013; 2014). Therefore, the major element

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composition of magma can be used as a proxy for estimating the pressure and temperature of magma processes, such as partial melting of mantle peridotite and the generation of primary magmas (e.g., Ueki and Iwamori, 2013; 2014), as well

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as crystallization in the crust (e.g., Gualda et al., 2012). However, the major element composition is easily overwritten

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because it represents low-dimensional data that exhibit a relatively restricted degree of freedom (maximum of 10 elements), with the constant sum constrained to 100%. Some independent processes may not be decomposed by

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analysis using only the major elements. On the other hand, trace elements can be used to detect reactions involving a specific phase or reaction regime (e.g., Depaolo, 1981; Sakuyama and Nesbitt, 1986; Pearce et al., 2005; Lee and Bachmann, 2014), as the solubilities of a specific trace element in various phases exhibit a wide range of variations

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(e.g., Blundy and Wood, 1994; Kessel et al., 2005). Therefore, trace elements have been used to understand the multiple geochemical processes recorded in chemical compositions, based on the specific element ratios or the spidergram of the selected sample. For example, geochemical study by Pearce et al. (2005) showed that the contributions of multiple components (i.e., various source mantle compositions and subduction components) in arc magmas could be evaluated by using multiple trace elements. Although geochemical processes in the subduction zone involve multiple elements and multiple processes, studies based on Harker diagrams (multiple samples on a two-dimensional plot) or spidergrams (multiple elements of a small number of samples) use only low-dimensional data to analyze high-dimensional trace element variations. Harker diagrams are particularly useful in identifying two-dimensional relationships between elements and variations in the concentrations, whereas spidergrams can be used to identify the relationships between the multiple elements of the selected samples. This means that valuable information contained in high-dimensional data, such as the distributions of data points and the relationships between multiple elements of multiple samples, is not utilized fully by these methods. The chemical reactions in the mantle wedge, subducting slab, lower crust, and upper crust are involved in the generation and chemical differentiation of arc magma (e.g., Annen et al., 2006). This means 3

ACCEPTED MANUSCRIPT that the chemical variations in arc magmas derive from multiple chemical processes. Therefore, multivariable analysis using multiple trace elements will be useful to understand quantitatively the overall structure of high-dimensional geochemical data and to investigate the processes that take place during the chemical evolution of arc magmas. Multivariable analysis is useful in investigating such high-dimensional geochemical data (Iwamori et al., 2017). Among

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various methods, including cluster analysis (e.g., Brandmeier and Wörner, 2016; Iwamori et al., 2017), independent component analysis (e.g., Iwamori and Albarède, 2008), and factor analysis (e.g., Melchiorre et al., 2017), principal

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component analysis (PCA) is a particularly valuable and intuitive method for understanding multidimensional data. This is because PCA facilitates dimensional reduction and examination of the overall structure of the data by transforming

Janousek et al., 2004; Ubide et al., 2012; 2014a; 2014b).

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the original set of variables into a new set of variables, called the principal components (e.g., Allègre et al., 1995;

In this study, we analyzed 14 trace elements of 262 samples. collected from 17 different volcanoes in the Sengan

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volcanic cluster in Northeastern Japan (Fig. 1). The geochemical variation of diverse compositions, i.e., basalt to rhyolite, from a relatively restricted eruption age and area was evaluated with PCA. The eigenvectors of the principal

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components and the relationships between the principal components and the major element composition, phenocryst

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mineral composition, and geophysical observation were used to interpret the principal components in petrological and geochemical terms. We found that only three principal components accounted for 86% of the compositional variation in

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the arc magma (Table 1) and corresponded to certain geological processes, i.e., magma mixing between mafic and felsic magmas, fractionation of olivine/pyroxene, and fractionation of plagioclase. 2 Geological setting

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The Pacific Plate is being subducted at a relative rate of 9.1 cm/year against the Eurasia Plate (NUVEL1A model; DeMets et al., 1994) beneath the Sengan region of Northeastern Japan Arc (Fig. 1). The depth of the slab surface is approximately 95 km beneath the Iwate volcano, which is the easternmost volcano in the region, and 105 km beneath the Akita-Yakeyama volcano, which is the westernmost volcano (Kawakatsu and Watada, 2007). Based on the seismic velocity structure and measurements of natural xenoliths, the upper crust beneath the Sengan region comprises granitoid, whereas the lower crust comprises hornblende gabbros (Nishimoto et al., 2005; 2008). Tomographic images show that the seismic low-velocity zone, which has been interpreted as a partially molten zone (Nakajima et al., 2005; Nishimoto et al., 2008) developed in the mantle wedge and the lower and upper crust beneath the region (Nakajima et al., 2001; Xia et al., 2007). The depth of the seismic Moho discontinuity has been estimated at ~35 km beneath the region (Zhao et al., 1992; Iwasaki et al., 2001). The Sengan region is a well-defined volcanic cluster (Kondo et al., 1998; Tamura et al., 2002) that is part of the volcanic front of the Northeastern Japan Arc. Fifty Quaternary volcanoes, including the active volcanoes of East Iwate, Akita-Komagatake, Hachimantai, and Akita-Yakeyama (Committee for Catalogue of Quaternary Volcanoes in Japan, 4

ACCEPTED MANUSCRIPT 1999), are closely spaced within a 25 km × 25 km area (Fig. 1). Previously reported geochronology of each volcano and representative phenocryst assemblages are given in Table I of the electronic supplement. The basement rocks of the Quaternary volcanoes are Tertiary sedimentary rocks, consisting of altered volcanic rocks and tuffs ('green tuff'), and sedimentary rocks such as siltstone and sandstone (Research Group for the Geological Map

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of Sengan Geothermal Area, 1985), which are overlain by the Tamagawa welded tuff, i.e., felsic pyroclastic flows

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(Suto, 1987). The Tamagawa welded tuff consists of pyroclastic flow deposits and covers an area of 2500 km2 (Fig. 1).

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The K-Ar ages of the Tamagawa welded tuff are 1.2–1.7 Ma for rhyolite and 0.9–1.2 Ma for dacite (Suto, 1982; 1987). Following the emplacement of the Tamagawa welded tuff, lavas from stratovolcanoes covered an area of approximately 800 km2 (Kawano and Aoki, 1959). Geochemical studies using Sr, Nd, and Pb isotopes, and trace elements (Shibata and

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Nakamura, 1997; Kimura and Yoshida, 2006), Li–B–Pb isotopes (Moriguti et al., 2005), Hf isotopes (Hanyu et al., 2006), boron concentrations (Sano et al., 2001), and halogen and volatile concentrations, and Pb isotopes in olivine-

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hosted melt inclusions (Rose-Koga et al., 2014) have shown that the primary basaltic magma from the Sengan region derived from the partial melting of the slab-derived fluid-fluxed mantle. The andesite magma of the Hachimantai and

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Akita-Yakeyama volcanoes in the Sengan region appears to have formed from mixing between mantle-derived basaltic

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magma and crustal felsic magma (Ohba, 1993; Ohba and Umeda, 1999; Ohba et al., 2007). A petrological and thermodynamic study by Kuritani et al. (2014) showed that the compositional variation in olivine basalt from the East

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Iwate volcano derived from the boundary layer fractionation of a magma chamber. A high-temperature (>350 °C) and young (~0.1 Ma U–Th–Pb age) granite pluton underlying the Tertiary and preTertiary sediments has been discovered in the Sengan region (Kanisawa et al., 1994; Doi et al., 1998; Sasaki et al.,

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2003; Tamanyu and Fujimoto, 2005; Ito et al., 2013). 3 Analytical method and whole rock composition 3.1 Analytical method

Erupted lavas from the Quaternary volcanoes were sampled over the entire Sengan region without any sampling bias. Samples were collected from lava flows, lava domes, and lava blocks. Rock chips were sliced using a diamond saw to avoid surface contamination, polished on a grinder, rinsed in an ultrasonic bath, crushed manually in a tungsten pestle, and ground in an agate ball mill. The rock powder was dried at 110 °C for more than 24 h before the preparation of fused glass beads. Whole-rock major- and trace-element concentrations were determined with a X-ray fluorescence spectrometer (XRF) at the Earthquake Research Institute of the University of Tokyo (Philips PW2400). Fused glass beads were prepared from a mixture of 1.8 g of rock powder and 3.6 g of lithium tetraborate flux, as well as 0.54 g of lithium nitrate in a platinum melting pot (1:2 sample dilution). The weighted powder was mixed on the touch-mixer. Fusing and agitation were carried out using a high-frequency bead sampler (Tokyo Kagaku Co. Ltd. NT-2100). Detailed analytical procedures and calibration procedures of XRF are given in Tanaka and Orihashi (1997) and Tani et al. 5

ACCEPTED MANUSCRIPT (2002). The accuracy and reproducibility of the apparatus used here are summarized in Tani et al. (2002). The reproducibility of the trace element composition of the standard rock GSJ JB-2 is less than 6% (relative standard deviation), except for the Pb (~10%) (Tani et al., 2002). The bulk composition data obtained by XRF analysis are presented in Table II of the electronic supplement, together with the reputation error of JB-2 during the analysis of this

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study. In addition, the recommended composition of the standard JB-2 (Imai et al., 1995) is given in Table II of the electronic supplement. The following analyses were conducted based on the normalized concentration being volatile-

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free and all the Fe as FeO.

The major element compositions of phenocryst minerals were determined with the JEOL JCMA-733MKII electron probe micro-analyzer (EPMA) at the Department of Earth and Planetary Science of the University of Tokyo, using the

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correction procedure of Bence and Albee (1968). The operating conditions were 15 kV accelerating voltage and 12 nA beam current, with 10 s counting time. The detailed analytical procedure for using an EPMA is presented in the study of

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Nakamura and Kushiro (1970). The modal abundance of phenocrysts was measured by point counting analysis. The representative EPMA results and the modal abundances obtained in the present study are given in Table III of the

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electronic supplement.

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3.2 Whole rock composition

Fig. 2 shows the major element concentrations of the whole rock, together with the previously reported data by Ueki

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and Iwamori (2016). Fig. I of the electronic supplement shows the trace element concentrations as a matrix of plots to visualize correlations among pairs of trace elements, together with the correlation coefficients among pairs of trace elements. The SiO2 concentration ranged from basalt to rhyolite compositions (50 to 71 wt.%). Both the calc-alkaline

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series and the tholeiitic series (Miyashiro, 1974) were observed. 4 Principal component analysis 4.1 Basic principle of principal component analysis We used principal component analysis (PCA) to understand the data structure of the original high-dimensional data. PCA is a simple and well-established method of multivariable analysis, where a set of orthogonal base vectors, called principal components, are defined from a set of observational data by rotating the original base vectors, so that the variance of data is maximized along the principal components. Detailed descriptions of the PCA calculation method and examples of its application to geochemical and petrological data are provided in Le Maitre (1982) and Albarède (1995). Previous geochemical studies have shown that PCA could be used to evaluate geochemical data, such as studying the compositional variation of volcanic rocks (e.g., Till and Colley, 1973; Butler, 1976; Allègre et al., 1995; Carn and Pyle, 2001; Maclennan et al., 2003; Janoušek et al., 2004; Lyubetskaya and Korenaga, 2007; Ubide et al., 2012; 2014a; 2014b; Brandmeier and Wörner, 2016; Kuritani et al., 2016) and surface regolith (Caritat and Grunsky, 2013), detecting the end-member composition and chemical reactions in mineral-solid solutions (Saxena, 1969; Saxena and Ekström, 6

ACCEPTED MANUSCRIPT 1970; Saxena and Walter, 1974), classification of tsunami deposits (Kuwatani et al., 2015), and detecting mantle isotope end-members and their mixing relations (Zindler et al., 1982; Allègre et al., 1987; Agranier et al., 2005; Debaille et al., 2006). These studies demonstrated that high-dimensional geochemical datasets, such as those from geochemical measurements of multiple elements on multiple samples could be reduced into a subspace spanned by

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several selected principal components that account for significant sample variance. By using the PCA, data sets with a large number of variables (concentrations of multiple elements) can be analyzed intuitively, based on the reduced

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dimension. Therefore, PCA is useful particularly for a dataset with a number of trace element concentrations. Eigenvalues and eigenvectors can be used to characterize each principal component because eigenvalues represent the contributions of the principal components in the variance of the original data, and eigenvectors represent the

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correlations between the original data and the principal components (e.g., Albarède, 1995; Pawlowsky-Glahn et al., 2015). By using PCA, we could reduce the dimensions of the original high-dimensional data to grasp the data structure

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and systematics.

However, we have to caution that the principal components do not always represent a geochemical 'process' or

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'component.' Although principal components are uncorrelated with each other, they are not always independent, as they

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are derived based on orthogonal coordinates, with the criterion of the largest variance of the original data. For multivariate Gaussian distributions, uncorrelated principal components are independent. However, that is not true for

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most distributions. This means that the principal component do not always represent geochemical processes, because natural geochemical processes do not always follow a multivariate Gaussian distribution or orthogonal coordinates (Iwamori and Albarède, 2008). Therefore, careful examination is necessary to connect principal components to

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geochemical processes. In this study, therefore, we focused on relationships between principal components derived from trace elements and other independent observations, such as major element concentrations, the phenocryst mineral composition, and geophysical observations, to demonstrate that principal components derived from trace elements represent certain geochemical processes. For PCA, we considered the projection of an original data matrix T

𝒙𝒊 = (𝑥1𝑖 , 𝑥2𝑖 , … , 𝑥𝑗𝑖 , … , 𝑥𝑝𝑖 )

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onto a new coordinate y using vector 𝝎𝒍 T

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𝑦𝑖𝑙 = (𝜔1𝑙 𝑥1𝑖 + ⋯ + 𝜔𝑗𝑙 𝑥𝑗𝑖 + ⋯ + 𝜔𝑝𝑙 𝑥𝑝𝑖 ) = 𝝎𝒍 𝒙𝒊

(2)

where 𝒙𝒊 represents the concentration of the j-th element of the i-th sample, where i = 1, …, n and j = 1 … p. The superscript “T” represents the transposed matrix. T

𝝎𝒍 = (𝜔1𝑙 , … , 𝜔𝑗𝑙 , … , 𝜔𝑝𝑙 ) , l = 1 … p, and 𝑦𝑖𝑙 represents the principal component score for the i-th sample with 𝝎𝒍 . Because concentrations of trace elements show a wide range of variation (Fig. I of the electronic supplement), 7

ACCEPTED MANUSCRIPT concentrations are standardized by using the average and variance of each element before the principal components are obtained. In this instance, we could obtain ω by solving the following eigenvalue equation in terms of the eigenvector ω and eigenvalue λ by eigen decomposition 𝑹𝝎 = 𝝀𝝎

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where R represents a correlation matrix of the original data matrix x.

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The eigenvector ω represents the loadings of the standardized data on the principal component. The eigenvalue λ

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represents the contributions of the principal components to the variance of the standardized data. The eigenvector ω that corresponds to the largest λ, which gives the greatest variance of the standardized compositional data, is called the first principal component. The eigenvector ω that corresponds to the second-largest λ, which gives the direction of the

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second-greatest variance perpendicular to the first direction, is called the second principal component, and so on. By taking the k principal components with the first k-th (k < p) largest eigenvalues, we could obtain the k-dimensional data,

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which are dimensionally reduced from the original p-dimensional dataset. We used the R language facilities (R Core Team, 2016) to evaluate the PCA calculation in this study.

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Some criteria have been proposed for dimensional reduction (e.g., Bishop, 2006). One criterion is to take the first k-th

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principal components, where the cumulative proportion of the eigenvalues exceeds >80% at the k-th component, another criterion is to take the principal components with eigenvalues higher than 1, and another criterion is to take the

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k-th principal components on a steep curve before a bend and a flat line on a Scree plot. 4.2 Principal component analysis results In this study, 14 trace elements (Sc, V, Cr, Co, Ni, Zn, Ga, Rb, Sr, Y, Zr, Nb, Ba, and Pb) of 262 rock samples from 17

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volcanoes were used for the PCA. Table 1 and Fig. II of the electronic supplement illustrate the eigenvalues of the principal components and their contributions to the total variance in our dataset. The eigenvalues are 2.88 for PC1, 1.69 for PC2, 0.92 for PC3, 0.749 for PC3, 0.569 for PC5, and so on. For the dimensional reduction, we adopted the criterion of cumulative proportion, because noticeable bends were not observed in the Scree plot (Fig. II of the electronic supplement). The first principal component (PC1) accounts for 59.3% of the sample variance, the second principal component (PC2) accounts for 20.4%, and the third principal component (PC3) accounts for 6.0%. Accordingly, 85.8% of the variance was accounted for by the first three out of the 14 principal components. This means that only three principal components described most of the observed variation of the 14 trace elements. Table 1 shows the eigenvectors (ω in Eq. (3)). In Table 1, the elements are ordered according to increasing atomic number from left to right. PC1 was dominated by anti-correlation between relatively compatible elements (Sc-Ga and Sr) and relatively incompatible elements (Rb, Y-Pb). Anti-correlations between Cr, Co, and Ni and Zn, Ga, Y, Sc, V, and Nb were observed for PC2. Positive loadings were shown by Sr, Rb, and Ga on PC3, whereas the other elements showed negative loadings. Regarding the amplitudes of the loadings, PC1 had the highest loadings on Rb, Zr and Ba; 8

ACCEPTED MANUSCRIPT PC2 had the highest loadings on Cr and Ni; and PC3 had the highest loadings on Zn and Y. The principal component scores for each sample (y in Eq. (2)), which denotes the coordinate of each sample in the new coordinate system after the projection by PCA, are given in Table II of the electronic supplement. The principal components (PC1–PC3) are interpreted in terms of geochemistry and petrology in the next section.

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5 Discussion 5.1 Geochemical interpretation of the principal components

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5.1.1 PC1

All trace elements used in this study exhibited clear positive or negative loadings on PC1 (Table 1). This means that all the trace elements were involved in PC1. Regarding the ionic radii (Shannon, 1976), the divalent cations (2+) exhibited

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positive loadings on PC1 at ionic radii smaller than 115 Å (Ga, Ni, Co, Zn, V, Cr, and Sr), whereas those with larger ionic radii exhibited negative loadings (Pb, Ba). The trivalent cations (3+) exhibited positive loadings with PC1 at ionic

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radii smaller than 80 Å (Sc, V, Cr, and Co). All 1+ (Rb), 4+ (Zr, Pb) and 5+ (Nb) ions exhibited negative loadings with PC1. Negative loadings were exhibited by HFSE (Y, Zr, Nb, Pb) with equivalent amplitudes (-0.33 to -0.24). The

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elements in the first transition series (Sc, V, Cr, Co, Ni, and Zn) exhibited positive loadings on PC1. Regarding LILES,

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Sr exhibited a positive loading and Ba and Rb exhibited negative loadings. The compositional variation represented by PC1 could be interpreted as fractionation of multiple minerals or overlapping of multiple crystal fractionation processes.

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However, the loadings of compatible elements against common phenocryst assemblages of intermediate to felsic rocks in the Sengan region (plagioclase, opx, cpx, and magnetite), i.e., Sc in cpx and opx, V in cpx and magnetite, Co in olivine and pyroxene, and Sr in plagioclase (e.g., Albarède, 2009; Philpotts and Ague, 2009) are equivalent

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(approximately +0.3). In addition, the magnitudes of the loadings of Nb, Rb, Zr, and Y were equivalent on PC1 (approximately −0.3). Even though Nb and Rb were highly incompatible with all the mineral phases observed in the Sengan region, Y and Zr could be partitioned into pyroxene, and Pb was compatible in plagioclase (e.g., Vannucci et al., 1998; Green et al., 2000; Aigner-Torres et al., 2007). In terms of eigenvectors, although PC1 is defined by the incompatible or compatible nature of the elements, PC1 could not account for the fractionation of multiple mineral species or the overlapping of multiple crystal fractionation processes. We tested this by plotting the PC1 score of each sample against the SiO2, MgO, Al2O3, CaO, and FeO* (total Fe as FeO) concentrations and the FeO*/MgO ratio (Fig. 3). The SiO2 concentration exhibited a linear negative correlation, whereas the MgO, FeO*, Al2O3, and CaO concentrations exhibited linear positive correlations with the PC1 score. This means all these major elements were involved in the process represented by PC1. Fig. 6 demonstrates the relationships between the Harker diagrams of the major elements (SiO2–Al2O3, –MgO, –FeO*, –CaO) and the PC1 scores, in addition to the Tamagawa welded tuff, experimental melt compositions of dehydration melting of the crustal rock (Shukuno et al., 2006) and olivine-, olivine-pyroxene-, and plagioclase-controlled trends. 9

ACCEPTED MANUSCRIPT The PC1 score is indicated by the color of the symbols. The PC1 score varied along with the compositional trend of the samples, from basaltic to felsic, toward the compositional range of the Tamagawa welded tuff in all the diagrams, rather than with the trends controlled by olivine, pyroxene, or plagioclase. This indicated that the vector representing PC1 was likely explained by the mixing of two components, although multiple elements were involved in the process, namely, a

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felsic (SiO2 enriched and MgO, FeO*, Al2O3, and CaO depleted) component enriched with Rb, Y, Zr, Nb, Ba, and Pb and a mafic (SiO2 depleted and MgO, FeO*, Al2O3, and CaO enriched) component enriched with Sc, V, Cr, Co, Ni, Zn,

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Ga, and Sr. 5.1.2 PC2

Strong negative loadings were exhibited by Cr, Co, and Ni on PC2, whereas the other elements exhibited positive or

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weak loadings (Table 1). Positive or weak loadings were exhibited by LILES and HFSE on PC2. The Cr, Co, and Ni fitted within the crystal lattice of olivine (e.g., Hirschmann et al., 1991; Li et al., 1995; Taran and Rossman, 2001). In

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addition, Cr, Co, and Ni could enter the crystal lattice of pyroxene (e.g., Deer, 1963; Wright and Navroisky, 1985; Taran and Rossman, 2001), which indicates that PC2 was related to processes involving olivine and pyroxene.

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Fig. 4 shows the plots of the PC2 score against the major element concentrations. The PC2 score exhibited a clear

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negative correlation with the MgO concentration and a clear positive correlation with the FeO*/MgO ratio. A weak positive correlation was observed between the PC2 score and the SiO2 concentration. The variance in the concentrations

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of Al2O3, FeO*, and CaO increased with the PC2 score. For example, the Al2O3 concentrations ranged from 15.8 to 18.6 wt.% at PC2<-2, but from 13.4 to 20.6 wt.% at PC2>0. This means that PC2 represented a process that fractionates MgO and increases the FeO*/MgO ratio, whereas other elements were not involved strongly. The involvement of metal

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oxides, such as magnetite, in the vector represented by PC2, is unfavorable because metal elements such as Zn, Ga, and Pb exhibited the opposite polarity with Cr, Co, and Ni or weak loadings in the eigenvector of PC2, and PC2 exhibited only a weak correlation with the SiO2 concentration. In terms of the relationship between the FeO*/MgO ratio and SiO2, PC2 corresponded to the tholeiite trend of Miyashiro (1974) (Fig. 4). Fig. 7 shows the relationships between the Harker diagrams of the major elements, their PC2 scores, and mineralcontrolled compositional trends. The Al2O3, MgO, FeO*, and CaO concentrations were plotted against the SiO2 concentration, along with the olivine-controlled trend and the olivine-pyroxene-controlled trend. The olivine-controlled trend was derived from the mass-balance calculation of the major elements, assuming the olivine addition at a fixed KDFe/Mg (Tatsumi et al., 1983). The olivine-pyroxene-controlled trend was derived from the addition of a 1:2 ratio of olivine + cpx. The PC2 score is indicated by the color of the symbols. The PC2 score varied with the olivine- and olivine-cpx-controlled trends in the SiO2–MgO, –FeO*, and –Al2O3 spaces. Both trends were semi-perpendicular to the vector indicated by PC1 in the diagrams (Fig. 6). The mass-balance trend indicated that with the addition of olivine or olivine-cpx, SiO2 and Al2O3 decreased and MgO and FeO* increased. Samples with lower SiO2 and Al2O3 10

ACCEPTED MANUSCRIPT concentrations and higher MgO and FeO* concentrations exhibited lower PC2 values in Fig. 7. On the other hand, in the SiO2–CaO space, the PC2 scores did not exhibit any clear relationship with the olivine-controlled trend or the olivine-cpx-controlled trend (Fig. 7). If PC2 represented the olivine contribution, the PC2 score could exhibit a systematic correlation with the olivine-controlled trend in the SiO2–CaO diagram. However, the PC2 score exhibited a

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weak relationship with the olivine-controlled trend in the SiO2–CaO diagram. Accordingly, our interpretation is that PC2 represented the contributions of both olivine and pyroxene.

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5.1.3 PC3

The eigenvalue of PC3 and its proportion in the total variance was small (6%) compared with those of PC1 and PC2, indicating that PC3 accounted for a minor portion in the chemical variation. In addition, PC3 was derived after the

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subtractions of PC1 and PC2 in the orthogonal coordinates. Therefore, in this study, PC3 is discussed more briefly than are PC1 and PC2. The Sr, Rb, Ga, and Pb concentrations were shown to have positive loadings, whereas the other

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elements displayed negative or weak loadings on PC3 (Table 1). In particular, Sr displayed a strong positive loading. The elements Sr, Ga and Pb are compatible with plagioclase (Aigner-Torres et al., 2007), whereas the other elements

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are incompatible. This indicated that PC3 represented a process particularly related to plagioclase.

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Fig. 5 shows the plots of the PC3 score against the major element concentrations. The Al2O3 and CaO concentrations exhibited positive correlations, and the FeO* concentration exhibited a negative correlation for samples with a PC3

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score of >0. The correlations between the major elements and PC3 were particularly well defined in the East Iwate, Kayou, and Akita-Komagatake samples. The SiO2 and MgO concentrations and the FeO*/MgO ratio did not exhibit any clear relationships with the PC3 score. The process represented by PC3 indicated variation with the Al2O3, CaO, and

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FeO* contents, but no apparent relationship with the SiO2 content and FeO*/MgO ratio. Fig. 8 shows the relationships between the Harker diagrams of the major elements, a plagioclase-controlled compositional trend, and the PC3 scores. The Al2O3, MgO, FeO*, and CaO concentrations were plotted against the SiO2 concentration, along with the plagioclase-controlled trend derived from the mass-balance calculation of the major elements, assuming the addition of plagioclase of a fixed composition. The PC3 score is indicated by the color of the symbols. The PC3 score varied with the plagioclase-controlled trend in all the Harker diagrams, which indicated that the vector in the trace element space represented by PC3 was parallel with the plagioclase-controlled trend in the major element compositional space. Based on the relationship between PC3 score and its relationship with the major elements, and eigenvector of PC3, PC3 was inferred to represent the process related to the crystallization of plagioclase. 5.2 Interpretation of the principal components 5.2.1 Petrological interpretation of PC1

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ACCEPTED MANUSCRIPT Fig. 9 shows the plots of PC1 against PC2 and PC3 to examine the relationships between the principal components. The Hachimantai and Akita-Yakeyama samples exhibited significant contributions from PC1, both in terms of range and amplitude. On the other hand, only weak contributions from PC2 were observed in those samples, meaning that the compositional variations of Hachimantai and Akita-Yakeyama were attributed mostly to PC1.

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Previous studies have observed petrological and geochemical disequilibrium features in the Hachimantai and AkitaYakeyama magmas. Ohba et al. (2007) conducted detailed petrological observations of the olivine-bearing high-

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magnesian andesite of the Hachimantai volcano. This olivine-bearing high-magnesian andesite corresponded to sample HM 15 in the present study. Ohba et al. (2007) showed that disequilibrium features of phenocryst minerals, such as dissolution texture and complex zoning of plagioclase, and reverse-zoned pyroxene were observed commonly in the

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Hachimantai volcano. In addition, linear relationships between the modal abundance of olivine and the bulk and groundmass compositions were observed. The modal abundance of olivine was correlated negatively with the modal

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abundances of other phenocrysts (plagioclase, pyroxene, and oxide mineral). Based on these observations, Ohba et al. (2007) concluded that these compositional and petrological variations of the olivine-bearing andesite of Hachimantai

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derived from magma mixing.

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Ohba (1993) observed abundant disequilibrium features in Akita-Yakeyama magmas, such as coexisting quartz and olivine in dacite, reverse zoning of pyroxene, and dusty plagioclase. Based on these petrological observations, trace

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element concentrations, and the Sr isotopic ratio, Ohba (1993) showed that magma mixing of crustal melt accounted for the chemical variation of the Akita-Yakeyama magma. In order to demonstrate the relationship between geochemical principal components and petrological disequilibrium

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features, representative line profiles of An% (mole percentage of the anorthite end-member component in plagioclase) of plagioclase phenocrysts are shown, together with PC1 and PC2 scores, in Fig. 10. Plagioclase was observed as a phenocryst mineral in all the samples in the present study. The Ca/Na partition between plagioclase and melt was highly sensitive to the H2O concentration of the melt and crystallization temperature (e.g., Housh and Luhr, 1991; Hamada and Fujii, 2007). Therefore, the composition of plagioclase could be a good indicator of the crystallization conditions. Complex and discontinuous zoning were observed commonly when the PC1 score was <0. The amplitude of the discontinuous zoning was as high as 35 An%. This magnitude of jump in An% is suggested to be the result of a largescale change in the growth conditions, such as magma mixing (Pearce and Kolisnik, 1990). The core and rim compositions were also variable when the PC1 score was <0. Plagioclase with s dusty core, honeycomb texture, skeletal texture, and irregular shape was often observed in the Hachimantai samples, shown in Fig. 10. On the other hand, plagioclase in most of the samples exhibited homogeneous core and normal or slightly reverse zoned rim when the PC1 score was >0 (Fig. 10). However, an exception was the highest MgO sample of Hachimantai (sample HM15), in which discontinuous zonings were observed even though its PC1 score was high. The plagioclase phenocrysts of Akita12

ACCEPTED MANUSCRIPT Komagatake, East Iwate, and Kayou samples shown in Fig. 10 exhibited a tabular shape, with a homogeneous core. The cores of these plagioclase phenocrysts were clear generally, and sometimes contained an inclusion-rich zone. In order to demonstrate quantitatively the compositional variation of plagioclase and the geochemical principal components, Fig. 11 shows the plots of the variation in core compositions of plagioclase phenocryst from each sample

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against the principal component scores from the whole rock. In order to illustrate the variation in the core composition of a single sample, which is interpreted as the general signature of the disequilibrium reaction induced by magma

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mixing (e.g., Sakuyama, 1979; Koyaguchi, 1986), we used the standard deviation for the core An% of each sample. The standard deviations in the core compositions of plagioclase for the selected samples are shown in Table II of the electronic supplement. The variation in the core composition of plagioclase phenocrysts for each sample showed a

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negative correlation with the PC1 score, with the upper and lower limits of the standard deviation of plagioclase increasing with a decreasing PC1 score. The relationship was clearer in the samples for which >20 samples were

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analyzed. The result indicated that the sample with a lower PC1 score derived through disequilibrium processes, such as a change in the melt composition during the crystallization of plagioclase, or the mixing of plagioclase of various

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origins. On the other hand, PC2 and PC3 were not related to such processes, as reflected by the heterogeneous

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plagioclase in a single sample showing no correlation with the PC2 and PC3 scores. 5.2.2 Interpretation of PC1: Magma mixing

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Based on the eigenvector, the relationships between the major elements and the PC1 score, and the correlation between the petrological disequilibrium feature, PC1 was inferred to represent binary magma mixing between incompatible trace element-enriched felsic magma, and compatible trace element-enriched mafic magma, rather than the crystal

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fractionation of multiple mineral phases. The linear correlations between the PC1 score and the concentrations of major elements were well-defined for samples with a SiO2 content of greater than ~57 wt.%, which trended toward the compositional range of Tamagawa welded tuff. This indicated that the Tamagawa welded tuff was a possible felsic endmember magma (Fig. 6). Regarding the FeO*/MgO ratio, we observed two different series, namely, one exhibiting various FeO*/MgO values with a weak PC1 contribution, and the other exhibiting a strong PC1 contribution with nearly constant FeO*/MgO values. The former corresponded to the tholeiite series, and the latter corresponded to the calcalkaline series of Miyashiro (1974). This means that PC1 represented a process producing the calc-alkaline compositional trend of Miyashiro (1974), with SiO2 and the incompatible elements being enriched with almost constant values of FeO*/MgO. We interpreted this as the calc-alkaline series being derived from binary magma mixing. The plagioclase in the olivine-bearing high-magnesian andesite of Hachimantai (sample HM15) exhibited complex and discontinuous zoning (Fig. 10), although its PC1 score was relatively high (2.25). Ohba et al. (2007) showed that the olivine-bearing high-magnesian andesite of Hachimantai was derived through magma mixing between basaltic-andesite magma and the andesite magma. This means that the compositional difference between the mafic end-member and 13

ACCEPTED MANUSCRIPT felsic end-member was relatively narrow. In addition, high-Mg# olivine (~Fo 90%) was observed in the olivine-bearing high-magnesian andesite (Table III of the electronic supplement; Ohba et al., 2007), and its Cr and Ni concentrations were higher than were those in other samples, meaning that the mantle signature was preserved strongly in the highmagnesian andesite. Therefore, PC1 did not represent the magma-mixing that produced olivine-bearing high-magnesian

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andesite of Hachimantai. In addition, some plagioclase exhibited a slightly reverse-zoned rim (e.g., sample IW17 and sample 60607 in Fig. 10), indicating that those samples with high PC1 values experienced some internal mixing. This

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means that PC1 represented a degree of contribution of crustal end-member magma, rather than the magma mixing process itself. 5.2.3 Petrological interpretations of PC2 and PC3

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Based on the geochemical analysis and the petrological context, PC2 was inferred as a process related to mafic minerals. The relationship between the modal abundance of olivine and the PC2 score (Fig. III of the electronic

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supplement) indicated that the maximum olivine abundance increased with a decreasing PC2 score, whereas the minimum value was always 0 (i.e., olivine was not observed as phenocryst), regardless of the PC2 score. This means

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that the range of modal abundance of olivine increased with a decreasing PC2 score (i.e., high Cr and Ni

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concentrations). Therefore, both the evolution of liquid composition by fractionation and the amount of phenocryst present in a sample (i.e., accumulation or incomplete separation of crystallized phenocrysts) were represented by PC2.

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Fig. 9 indicates that the compositional variation of the East Iwate samples was attributed to PC2 (contributions of both olivine and pyroxene) and PC3 (contribution of plagioclase) without a contribution from PC1 (contribution of felsic end-member magma). Based on the mass-balance calculation of the major elements using the least-squares fitting

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(Bryan et al., 1969), 7.3 wt.% of olivine fractionation was required to produce relatively low-MgO basalt (IW13: 51.9 SiO2 wt.%, 4.5 MgO wt.%) from the relatively undifferentiated basalt (IW17: 51.4 SiO2 wt.%, 7.1 MgO wt.%) of East Iwate. In terms of the PC2 score, IW17 corresponded to -2.79 and IW13 corresponded to 0.02, implying that this magnitude of the PC2 score (2.81) corresponded with the fractionation of 7.3 wt.% of olivine. Kuritani et al. (2014) carried out a petrological study of the olivine-plagioclase basalt of the East Iwate volcano. Olivine phenocrysts were homogeneous or normally zoned generally and some reverse zoning was present. The Mg# of olivine phenocrysts correlated positively with the An% of the coexisting plagioclase phenocrysts, indicating that they were cogenetic. Based on these observations and thermodynamic analysis, Kuritani et al. (2014) showed that the phenocrysts of the East Iwate olivine basalt were derived from low-temperature boundary-layer crystallization at the walls of a magma chamber (e.g., Kuritani, 1999), and the compositional variations of the olivine basalt were derived from the transportations of olivine and plagioclase, as well as the internal mixing between the relatively fractionated melt in the boundary layer and the relatively undifferentiated magma in the main body of a magma chamber. Accordingly, the compositional variation of the East Iwate olivine basalt is believed to be attributed to a process including 14

ACCEPTED MANUSCRIPT crystallizations of olivine and plagioclase, without the contribution of crustal melt. This result is consistent with our interpretation using PCA, with the compositional variation of East Iwate being attributed to PC2 (mafic contribution) and PC3 (plagioclase contribution), without any contribution from PC1. Kayou samples exhibited the least contribution from PC1 and a weak contribution from PC2. Fig. 9 indicates that the

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compositional variation of Kayou was attributed mostly to PC3. The Kayou lava is porphyritic, comprising abundant plagioclase up to >40 vol. % (Table III of the electronic supplement), indicating that the compositional variation of the

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Kayou samples, represented by PC3, was derived from the process involving those abundant plagioclase phenocrysts. 5.3 Geochemical processes in the arc crust

The PCA results showed that only three chemical processes were responsible for the compositional variation of magma

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in the Sengan region (Fig. II of the electronic supplement). PC1 was interpreted as binary magma mixing between mantle-derived melt and crustal melt, PC2 was interpreted as compositional evolution by crystallizations of olivine and

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pyroxene, and PC3 was interpreted as compositional evolution by the crystallization of plagioclase. These covered 59.3%, 20.4%, and 6.0%, respectively, of the variance, which indicated that the magma mixing accounted for the largest

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variance in the geochemical variation of magma in the Sengan region. The variations in the mantle process (e.g., source

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peridotite composition, melting degree, fluid addition, metasomatism, and across-arc variation) could be over-printed by the crustal signatures. A geochemical study by Kimura and Yoshida (2006) using trace elements and Nd–Sr–Pb isotopic

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compositions indicated that mantle-derived basalt were common geochemically in the frontal-arc of the Northeastern Japan Arc, and geochemical diversity could be attributed to mixing between various crustal melts. Our result, i.e., crustal processes dominated the geochemical variation of magma in the Sengan region, is consistent with the result of

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Kimura and Yoshida (2006). East Iwate and Kayou have the least contributions from PC1 among the volcanoes in the Sengan region (Fig. 9). Kimura and Yoshida (2006) pointed out that Kayou and East Iwate had stronger mantle signatures, which means that Kayou and East Iwate experienced the least crustal contamination among the frontal-arc lavas of the entire Northeastern Japan Arc. The PC2 and PC3 scores exhibited a wide range of variation when the PC1 score was >0 (Fig. 9), which corresponded with the volcanic rocks with <57 SiO2 wt.% on the SiO2 vs PC1 plot (Fig. 3). On the other hand, only a small range of variation was observed for PC2 and PC3 when the PC1 score was <0. In other words, PC2 and PC3 were responsible for the compositional variation from basalt to basaltic andesite, and PC1 was responsible for the compositional variation from andesite to rhyolite. These results indicated that PC1, i.e., magma mixing between a crustal melt and basaltic melt, contributed to the compositional variation of the felsic magma, and PC2 and PC3, i.e., crystallization processes in a magma chamber contributed to the compositional variation of the basalt and basaltic andesite. Kimura and Yoshida (2006) showed that intermediate and evolved lavas of the frontal-arc lavas were derived from mixing between basaltic magma and crustal melts, based on variations of isotopic ratios and trace element concentrations, and the geographical 15

ACCEPTED MANUSCRIPT distribution of the Sr isotopic ratio. Their results, derived by using multiple major and trace elements and isotope ratios, are consistent with the PCA result of our study. The variations in PC2 and PC3 decreased with an increasing PC1 score, which meant that their effects were overwritten by PC1. This convergence at high PC1 scores indicated that the felsic end-member had a narrow composition range,

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which possibly represented the cotectic composition of the crustal rock. The major element composition of Tamagawa welded tuff, a possible felsic end-member magma, coincided with the compositional range of partial melts of mafic-

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intermediate crustal rocks derived from the low-melting degree dehydration melting (Table 2). This indicated that the Tamagawa welded tuff was most likely a derivative of the partial melting of mafic or intermediate crustal rocks. Based on the loadings on PC1, it was inferred that the Sr concentration of the mafic end-member mantle-derived melt was

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higher than that of the felsic end-member crustal melt because Sr exhibited a positive loading on PC1. This could be explained by the geochemical nature of crustal melts. The major element composition of the Tamagawa welded tuff,

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i.e., possible felsic end-member magma, could be produced by the partial melting of crustal material (Table 2). Based on the trace element ratios and their trends, Kimura and Yoshida (2006) showed that partial melting of lower crustal

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amphibolite was the felsic end-member of the mixing in the frontal-arc of the Northeastern Japan Arc. Because

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plagioclase is a residual phase during dehydration melting of amphibolite (e.g., Beard and Lofgren, 1991), the Sr concentrations of partial melts of amphibolite were suppressed (Kimura et al., 2002; Kimura and Yoshida, 2006). On

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the other hand, a positive Sr spike was observed in the primary basaltic melt of the Northeastern Japan Arc because Sr was added via slab-derived fluid to the mantle wedge of the Northeastern Japan Arc (Kimura and Yoshida, 2006). In addition, some clustering was observed in the PC1–PC2–PC3 space (Fig. 9). The PC1 score exhibited a noticeable

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gap around PC1 = -2–0 (gray hatched area in Fig. 9), which corresponded with a SiO2 concentration of ~57 wt.% in Fig. 3. This corresponded with the Daly gap typically observed in arc magmas. This has been discussed as indicating different genetic processes for volcanic rocks with SiO2 concentrations above and below the Daly gap (e.g., Chayes, 1963). The gap and clustering in the PC space supports the interpretation that PC1, PC2, and PC3 represent different chemical processes under different physicochemical conditions in the arc crust. PC2 and PC3 were interpreted to represent processes related to crystallization of olivine/pyroxene and plagioclase, respectively. Crystallization experiments, using hydrous primitive basaltic magma from Northeastern Japan (Hamada and Fujii, 2008) and hydrous basaltic-andesite magma of East Iwate in the Sengan region (Takagi et al., 2005), showed that increasing both the pressure and H2O concentration lowered the liquidus temperature of plagioclase relative to olivine and pyroxene. If the fluid content were variable between PC2 and PC3, a signature related to the fluid mobile element would appear. However, principal components related to fluid mobile elements (e.g., Ba, Rb, and Pb) (Kogiso et al., 1997; Tatsumi and Kogiso, 1997; Schmidt and Poli, 2014) were not observed in our analysis. In addition, discussions based on H2O and CO2 concentrations in olivine-hosted melt inclusions from the Iwate volcano showed two 16

ACCEPTED MANUSCRIPT different degassing pressures (Rose-Koga et al., 2014). Based on the information on melt inclusions and seismic velocity structure (Nishida et al., 2008), Rose-Koga et al. (2014) deliberated that two different magma chambers were present at the upper crustal depth, and, at the lower crustal depth, beneath the Iwate volcano. Therefore, we inferred that the variation between olivine/pyroxene crystallization (PC2) and plagioclase crystallization (PC3) represented the

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variation in the depth of crystallization rather than the source H2O content. Takagi et al. (2005) showed that plagioclase crystallized as a liquidus phase regardless of the H2O content at 1 kbar from the hydrous basaltic-andesite magma of the

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East Iwate volcano. With increasing pressure, the liquidus temperature of plagioclase lowered, and olivine or pyroxene appeared as liquidus phases from the basaltic andesite at 2–5 kbar. We inferred that PC2 and PC3 could represent deep and shallow fractionation, respectively.

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5.4 Melting structure in the crust

Fig. 12 shows the spatial distribution of the PC1 scores. Samples with a high contribution of magma mixing (PC1 score

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<0) were distributed in the central part of the volcanic cluster associated with the voluminous Tamagawa welded tuff and Kakkonda granitic pluton (Fig. 1). In addition, Fig. 12 shows the crustal seismic velocity structure beneath the

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Sengan region at a depth of 15 km (Nakajima et al., 2001) and a geotherm at a depth of 2 km determined by borehole

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analysis (Tamanyu, 1994). The spatial distribution of PC1 exhibited a systematic correlation with the seismic lowvelocity zone in the middle to lower crustal depths. Furthermore, the spatial distribution of PC1 exhibited correlation

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with the high geothermal gradient region. Numerical modeling, based on topography and gravity anomalies, conducted by George et al. (2016) suggested magma intrusion at the middle to lower crustal depths beneath the central part of the Sengan volcanic cluster. The correlations between PC1, which was interpreted to represent magma mixing, and the

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crustal seismic low-velocity zone (i.e., a partially molten zone) (Nishimoto et al., 2008), high geothermal gradient, voluminous felsic tuff, and granite pluton indicated that the partially molten hot zone (Annen et al., 2006) developed extensively in the middle to upper crust beneath the central part of the volcanic cluster. 5.5 Geochemical data analysis and PCA Although PCA is a well-established and straightforward method, the results, particularly the second and later principal components, have to be treated carefully, as it assumes orthogonal coordination. As noted above, principal components are independent only when the data constitute a multivariate Gaussian distribution (Iwamori and Albarède, 2008). Therefore, careful examination is necessary to connect principal components to geochemical processes. In the present study, the PCA results using trace element concentrations were consistent with other independent data and observations, such as the major element concentration, phenocryst composition, and geophysical observations. This indicated that in our study, PCA properly extracted the geochemical processes from the trace element data. Fig. 9 suggests that PC1 (i.e., magma mixing), PC2 (i.e., mafic crystallization), and PC3 (i.e., plagioclase crystallization) exhibited orthogonal

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ACCEPTED MANUSCRIPT relations. Therefore, we inferred that PCA, which is based on orthogonal coordinates, could extract these geochemical processes of the arc magma. It is possible that non-Gaussian processes or minor processes were not detected with PCA. For example, as noted above, the mantle signature was not detected in the present study. In addition, Ohba et al. (2009) showed that some volcanic

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rock in the Sengan region contained garnet in olivine-hosted melt inclusions. However, principal components related to garnet were not observed in the present study. Variations in mantle-derived basalt or a garnet signature during

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fractionation or assimilation were not observed in the geochemical study using isotopes and trace elements, including REE (Kimura and Yoshida, 2006). Therefore, geochemical signatures of such processes would be minor, even if they were present. Introducing other multivariate analysis methods, such as independent component analysis (e.g., Iwamori

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and Albarède, 2008; Yasukawa et al., 2016) and cluster analysis (Iwamori et al., 2017), or increasing the number of elements involved in PCA, would enable us to discuss further geochemical processes. A comparison between analysis

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using the natural data and using the results of forward calculations, such as geochemical mass-balance modeling (e.g., Kimura et al. 2010) and thermodynamic calculations (Ghiorso and Sack, 1995; Ghiorso et al., 2002; Gualda et al.,

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2012; Ueki and Iwamori, 2013; 2014; Jennings and Holland, 2015) could be useful for further quantitative evaluation of

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the PCA results. 6 Summary

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In order to understand the data structure of high-dimensional geochemical data and investigate the geochemical process during the compositional evolution of arc magma, trace element compositions of volcanic rocks from 17 different volcanoes in the Sengan region of the Northeastern Japan Arc were subjected to principal component analysis. Three

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principal components accounted for 86% of the compositional variation in various arc magmas of the Sengan region. Based on analysis of the eigenvectors of principal components, major element composition, and petrological observations, the three principal components were inferred to represent magma mixing, crystallization of olivine/pyroxene, and crystallization of plagioclase. The PCA results demonstrated that differentiation in the arc crust was the primary process contributing to the compositional variation of arc magma, and intermediate-felsic magma (SiO2 > 57 wt.%) was derived from magma mixing. The results of this study demonstrated that multivariate analysis was applicable to high-dimensional geochemical datasets. Acknowledgments We thank Teruaki Ishii for permission to use the laboratory equipment for sample preparation, Hideto Yoshida for the EPMA analysis, Yuji Orihashi for the XRF analysis, and Jun-Ichi Kimura for the discussion. Our thanks are due to Tatsu Kuwatani and the Earthquake Research Institute’s cooperative research program (Geochemical data analysis using machine learning) for the discussions regarding PCA. We wish to thank Teresa Ubide and an anonymous

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ACCEPTED MANUSCRIPT reviewer for constructive reviews, and Andrew Kerr for the editorial handling of the manuscript. This work was supported by JSPS KAKENHI Grant Number 15H05833 for K.U.

Appendix A. Supplementary data

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Supplementary data to this article are available online.

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ACCEPTED MANUSCRIPT

PC1

PC2

PC3

PC4

PC5

PC6

PC7

PC8

PC9

PC10

PC11

PC12

PC13

PC14

Eigenvalue

2.882

1.691

0.917

0.749

0.569

0.561

0.474

0.416

0.380

0.316

0.234

0.203

0.197

0.123

Proportion in Total Variance

0.593

0.204

0.060

0.040

0.023

0.022

0.016

0.012

0.010

0.007

0.004

0.003

0.003

0.001

Cumulative Proportion

0.593

0.798

0.858

0.898

0.921

0.943

0.959

0.972

0.982

0.989

0.993

0.996

0.999

1.000

Sc

0.301

0.138

-0.199

-0.412

-0.107

0.105

-0.037

-0.450

-0.013

0.006

0.544

0.146

0.362

0.079

V

0.291

0.157

-0.170

-0.412

0.180

0.347

-0.371

0.117

0.170

0.261

-0.335

0.186

-0.379

0.020

Cr

0.114

-0.521

-0.215

0.147

-0.091

0.068

-0.113

-0.387

0.102

0.434

-0.224

-0.449

0.138

-0.059

Co

0.282

-0.224

-0.326

-0.057

0.150

0.196

-0.121

0.543

-0.265

-0.358

0.050

-0.294

0.313

-0.074

Ni

0.102

-0.520

-0.179

0.376

-0.069

0.037

-0.208

0.035

0.092

-0.106

0.255

0.591

-0.210

0.132

Zn

0.169

0.357

-0.501

0.380

-0.250

0.284

0.510

0.018

-0.037

0.113

-0.129

0.103

-0.039

-0.051

Ga

0.193

0.388

0.165

0.386

-0.447

-0.030

-0.613

0.079

0.110

-0.010

0.026

-0.129

0.155

-0.017

Rb

-0.330

-0.055

0.054

-0.059

-0.038

0.286

0.034

0.170

0.420

0.052

-0.260

0.265

0.624

0.248

Sr

0.263

0.143

0.300

0.423

0.701

0.279

0.035

-0.150

0.091

0.064

0.141

-0.043

0.114

0.040

Y

-0.239

0.211

-0.567

0.092

0.341

-0.365

-0.222

-0.219

0.313

-0.322

-0.093

-0.087

-0.002

0.066

Zr

-0.340

0.015

-0.080

0.010

0.068

0.188

-0.124

0.054

0.103

0.141

0.238

0.104

0.050

-0.848

Nb

-0.311

0.132

-0.197

0.093

0.184

-0.114

-0.235

0.107

-0.598

0.511

0.072

0.145

0.153

0.237

Ba

-0.331

0.023

-0.082

-0.006

-0.070

0.326

0.010

0.201

0.268

0.115

0.509

-0.410

-0.316

0.345

Pb

-0.315

-0.005

0.048

0.038

-0.080

0.543

-0.181

-0.420

-0.383

-0.432

-0.200

-0.020

-0.099

0.053

SC R

MA

D

TE

AC

CE P

NU

Eigenvector (Loading)

29

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Principal Component

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Table 1. Eigenvalues and eigenvectors of the principal components.

ACCEPTED MANUSCRIPT Table 2. Compositional ranges of partial melts produced by dehydration melts of crustal rocks and that of Tamagawa welded tuff. Experimental results are adopted from Beard and Lofgren (1991) and Shukuno et al. (2006). Bulk composition of Tamagawa welded tuff is adopted from Suto (1987). Compositions were normalized to total 100 % and all the Fe as FeO. Pressure and temperature ranges of the melting experiments are 1–6.9 kbar and 850–1050 ºC, respectively.

T

IP

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NU

MA D TE CE P AC

SiO2 TiO2 Al2O3 FeO* MnO MgO CaO Na2O K2O

Experiments Tamagawa tuff Maximum Minimum Maximum Minimum 79.22 60.76 76.27 62.48 1.69 0.12 0.87 0.21 17.35 11.61 17.12 12.47 9.58 1.70 7.94 1.60 0.37 0.02 0.17 0.02 3.08 0.24 3.29 0.14 6.65 1.74 5.69 1.30 5.30 2.41 4.60 2.33 2.56 0.15 4.70 0.51

30

ACCEPTED MANUSCRIPT Figure captions Fig. 1. (a) Simplified map around Northeastern Japan. The locations of quaternary volcanoes (Committee for Catalogue of Quaternary Volcanoes in Japan, 1999) are shown as triangles. J-EGG500 from the Japan Oceanographic Data Center

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of the Hydrographic and Oceanographic Department of the Japan Coast Guard (JODC) was used for the bathymetry data. (b) Simplified geographical and geological maps of the Sengan region, Northeastern Japan. The geological map is

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modified from that of the Research Group for the Geological Map of Sengan Geothermal Area (1985). Red triangles and abbreviations indicate volcanoes examined in this study. See Table I of the electronic supplement for the abbreviations of volcanoes. The estimated locations of eruption calderas of Tamagawa welded tuff (Suto, 1987) are

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shown by dashed lines. The location of the Kakkonda granite pluton (Kanisawa, 1994) is shown by a star. GTOPO30 from the USGS (United States Geological Survey, 2000) was used for the elevation data. Generic Mapping Tools

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(Wessel and Smith, 1991) were used to prepare Fig. 1.

Fig. 2. Al2O3, FeO* (total Fe as FeO), MgO, CaO, and Na2O+K2O concentrations plotted against the SiO2 concentration

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of the Quaternary volcanoes in the Sengan region. A SiO2–FeO*/MgO diagram (Miyashiro, 1974) is also given.

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Fig. 3. SiO2, MgO, FeO*, Al2O3, and CaO concentrations and the FeO*/MgO values plotted against the PC1 scores for each sample. Symbols are the same as in Fig. 2.

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Fig. 4. SiO2, MgO, FeO*, Al2O3, and CaO concentrations and the FeO*/MgO values plotted against the PC2 scores for each sample. Symbols are the same as in Fig. 2. Fig. 5. SiO2, MgO, FeO*, Al2O3, and CaO concentrations and the FeO*/MgO values plotted against the PC3 scores for

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each sample. Symbols are the same as in Fig. 2. Fig. 6. Harker diagrams with relationships between major elements, PC1 score, and the mineral-controlled trends. Al2O3, MgO, FeO*, CaO are shown against SiO2, together with the PC scores, which are indicated by colors. The olivine-controlled trend is shown by a blue line. The mass-balance olivine-controlled trend was calculated by assuming the olivine addition at a fixed KDFe/Mg (Tatsumi et al., 1983): 1 wt.% of equilibrium olivine was added to the bulk composition of the olivine–plagioclase basalt of the Iwate volcano (sample IW13, indicated by a blue star) in each calculation step until the magma composition equilibrated with Fo 90 olivine (the highest Fo content in the Sengan region). The compositional trend derived by addition of olivine + cpx is shown by a red line. The bulk composition of plagioclase–cpx–opx–olivine basaltic andesite from the Zarumori volcano (sample 3060211, indicated by a red star) was used as the starting composition of the calculation. The mass ratio of olivine:cpx was fixed at 1:2. The olivine composition was recalculated in each step by using the fixed KDFe/Mg. The cpx composition was fixed during the calculation, and the average core composition of phenocryst cpx in sample 3060211 was used. A green line shows the plagioclase-controlled trend derived by mass-balance calculation. During the mass-balance calculation, plagioclase was 31

ACCEPTED MANUSCRIPT added to the aphyric basaltic andesite of the Akita-Komagatake volcano (sample 60607, indicated by a green star) up to 50 wt.%. The anorthite content of the plagioclase was fixed to 90% for the calculation; this is the typical anorthite content that was observed in this study (see Fig. 11 and Table III of the electronic supplement). The major element compositions of the Tamagawa welded tuff (Suto, 1987) and the experimental melt compositions during dehydration

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melting of the crustal materials (Shukuno et al., 2006) are also shown.

Fig. 7. Harker diagrams with relationships between major elements, PC2 score, and the mineral-controlled trends. The

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PC2 score is shown by the colors on the Harker diagrams. Lines are the same as in Fig. 6.

Fig. 8. Harker diagrams with relationships between major elements, PC3 score, and the mineral-controlled trends. The PC3 score is shown by the colors on the Harker diagrams. Lines are the same as in Fig. 6.

the PC1 scores. Symbols are the same as in Fig. 2.

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Fig. 9. Relationships between the PC1, PC2, and PC3 scores. The PC2 and PC3 scores of samples are plotted against

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Fig. 10. Representative line profiles of An% of plagioclase and PC1 and PC2 scores of samples. The vertical axis of each profile indicates An%, and the horizontal axis represents a distance from a core of the phenocryst. Blue circles

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represent PC scores of samples, with the line profiles shown. Small gray circles represent the PC scores of all samples. Fig. 11. Variance in core compositions of phenocryst plagioclase (An%) of each sample plotted against the PC1–PC3

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scores. Black circles show samples with ≧ 30 grains of plagioclase that were analyzed in a single thin section, gray

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circles show samples with 20–30 grains, and open circles show samples with <20 grains to demonstrate the statistical reliability of the data in Fig. 11a. Histograms of An% of cores for representative samples are also shown. See the text for further discussion.

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Fig. 12. Map for PC1 scores, dVs velocity structure at a depth of 15 km (Nakajima et al., 2001), and a geotherm at a depth of 2 km (Tamanyu, 1994; 2000). The PC1 score of each sample is indicated by color. GTOPO30 from the USGS (United States Geological Survey, 2000) was used for the elevation data. The seismic velocity was drawn by using the Active Fault Database of Japan (June 23, 2009 version) (National Institute of Advanced Industrial Science and Technology, 2009). Generic Mapping Tools (Wessel and Smith, 1991) were used to prepare Fig. 12.

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ACCEPTED MANUSCRIPT Electronic supplement Table I. Representative phenocryst assemblages and previously reported geochronology of each volcano. Ages are adopted from the Committee for Catalogue of Quaternary Volcanoes in Japan (1999), unless noted. K-Ar age and historical records are shown.

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Table II. Bulk compositions and sampling location, variance in core compositions of plagioclase for selected samples,

analysis. Table III. Representative EPMA results and modal compositions.

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PC scores of samples, and recommended composition and repetition error of the standard sample JB-2 during the

Figure I. (a) Matrix of plots of trace element concentrations (ppm) of the quaternary volcanoes in the Sengan region to

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show correlations among pairs of trace elements. R language facilities (R Core Team, 2016) were used to evaluate Figure Ia. (b) Correlation coefficients among pairs of trace elements. Red colors indicate positive correlation, whereas

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blue colors indicate negative correlations.

Figure II. Scree plot of the eigenvalues of the principal components and the cumulative proportions. The horizontal

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axis indicates each principal component, and the vertical axis indicates the eigenvalue for which the sum is normalized

shown by the line and squares.

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to 1, and the cumulative proportion for a total variance. Eigenvalues are shown by bars and cumulative proportions are

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Figure III. Modal abundance of olivine (vol. %) plotted against PC2 score.

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Figure 11

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ACCEPTED MANUSCRIPT Highlights PCA was used to evaluate magma processes in the Sengan volcanic region, NE Japan.

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Three major principal components resolve magma mixing and crystal fractionation.

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Magma mixing accounts for 59% of the geochemical variance in Sengan region magma.

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