(1) Uncertainties Involved in the Variability of Subducted Materials

Appendix

(1) Uncertainties involved in the variability of subducted materials

To calculate the composition of slab-fluid, we have used the representative sediment and AOC sampled (drilled) at the site near the study area, with the most complete data set in terms of trace element compositions. There are considerable compositional variations of trace elements in the drilled sediment and AOC samples, which leads to a compositional variability of sediment-fluid and AOC-fluid, affecting subsequent compositions of slab-fluid and fluid-added source mantle. We have compiled the published trace element data sampled within PAC and PHS (Li, 1991; Hickey-Vargas, 1991; Elliot et al., 1997; Plank and Langmuir, 1998; Hauff et al., 2003; Plank et al., 2007), and estimated the compositional range of sediment and AOC. The compositional variability in the subducting materials and the range of experimentally determined mobility of element during dehydration (Fig.A1) cause the uncertainties associated with fluid processes, which are shown as vertical error bars in Figs.8, 9 and 11. It is noted that the compositional variety in slab-fluid is smaller compared to that in slab inventory due to strong modification during dehydration. This relatively small uncertainty in estimation of the slab-fluid composition assures the subsequent quantitative estimates for the fluid and melting processes as in Figs.9 and 11.

(2) Uncertainties involved in the inversion

By using a least square approximation of Bryan et al. (1969), we first test the mass balance among the starting and the target magma compositions, and the phenocryst compositions, to estimate the fractionation trends, which are shown in Fig.2. Based on these trends, we may put the plausible ranges of the primary magma composition, which are regarded as uncertainty associated with the estimation.

There is no evidence that signals a significant crustal contamination. The AFC modeling of these rocks based on Sr-Nd isotopes and major elements (Nakamura et al., 2008) also suggests that less than 5% contamination of the basement rhyolitic rock is possible. In addition to the uncertainty described in the previous paragraph, we subtract the 5% rhyolitic components (in terms of trace elements) to give the depleted bound for a 'safer' estimate. These bounds are used as the range of primary magma and are shown as vertical bars in Fig.10a.

To inversely estimate the melting condition, we calculate the chemical composition of melt from the fluid-added mantle, in which the uncertainties associated with slab-fluid,DMM and partition coefficients (Tables 4 and 5) are considered, resulting in uncertainty in the composition of the optimized melt. The combination of depleted compositions of slab-fluid and DMM (associated with depleted sediment and AOC, and the lowest mobility) and the maximum values of partition coefficient gives an upper limit for the trace element abundances in the calculated melt, while the combination of enriched compositions of slab-fluid and DMM (associated with enriched sediment and AOC, and the highest mobility) and the minimum values of partition coefficient gives the lower limit. Both are considered as uncertainties involved in optimization and are shown as vertical bars in Fig.10a.

Appendix figure caption

Fig.A1: Mobility used in this study and its uncertainty, based on the experimental results from the literature. The mobilities of elements during dehydration for sediment, altered oceanic crust and serpentinite are shown as the spidergram. The vertical bars represent the estimated uncertainty in the high-pressure dehydration experiments compiled from the literature (Tatsumi et al., 1986; Kogiso et al., 1997; Tatsumi and Kogiso, 1997; Aizawa et al.,1999).

Fig.A2: The DMM-normalized composition of calculated melt produced by partial melting of fluid-added mantle (red), which has been optimized to reproduce the primary magma (black) estimated from the most undifferentiated rock in each volcano. The vertical bars for calculated melt represent the estimated uncertainty originated through all the forward calculations concerning the dehydration and melting processes, while those for the primary magma are derived from the uncertainty in fractionated phases and their amounts with the analytical error. The elements simultaneously used for optimization are Nb, La to Ce and Zr to Lu. As discussed in the main text, various choices of Kdmineral/melt concerning mantle melting for a range in the water content (dry to 10 wt. %), pressure (1.3-3.0 GPa) and temperature (1080-1245 ºC) give roughly the same solution within ~10%, and the calculated melt compositions with the worst misfit is shown in this figure (cf. Fig.10a). The largest value of misfit is 4.84 as a total for four volcanoes in this modeling. In this case, the obtained parameters are as follows.

Alternatively, the best solution (Fig.10a) with the total misfit 3.75 is as below.