Contributions to Mineralogy and Petrology (2018) 173:7 https://doi.org/10.1007/s00410-017-1428-z

ORIGINAL PAPER

Phase-equilibrium geobarometers for silicic rocks based on rhyoliteMELTS. Part 4: Plagioclase, orthopyroxene, clinopyroxene, glass geobarometer, and application to Mt. Ruapehu, New Zealand Lydia J. Harmon1   · James Cowlyn2 · Guilherme A. R. Gualda1 · Mark S. Ghiorso3 Received: 9 January 2017 / Accepted: 27 November 2017 © Springer-Verlag GmbH Germany, part of Springer Nature 2017

Abstract A new phase equilibria geobarometer determines magmatic storage and crystallization conditions, including pressure, temperature, oxygen fugacity ( fo2 ), and the presence of a fluid phase for glass-bearing rocks containing the assemblage plagioclase + pyroxene(s). This newly developed geobarometer can better constrain crystallization conditions of shallow (< 500 MPa; <~ 20 km), glass-bearing andesites to dacites. The geobarometer utilizes rhyolite-MELTS to determine crystallization conditions in natural pumice and scoria samples. The validity of the geobarometer is tested by comparing it to results from experiments. Uncertainties are assessed using Monte Carlo simulations. We apply the geobarometer to the plag + opx + cpxbearing system of Mt. Ruapehu, in the southern Taupo Volcanic Zone, New Zealand. The samples from Mt. Ruapehu are tested from ~ 5 to ~ 400 MPa and from super-liquidus to 90% crystalline (~ 1200 to ~ 700 °C). Mt. Ruapehu serves as a methodological testing ground for the geobarometer, and results from our geobarometer agree with recent Mt. Ruapehu studies. Results show a distribution of crystallization pressures ranging from 50 to 150 MPa (~ 2.0 to 5.9 km) for different eruptions, with modes of 110 MPa (~ 4.3 km) and 130 MPa (~ 5.1 km). These are consistent with field interpretations of different eruptive styles based on juvenile clast textures and previous knowledge of the magma plumbing system. Mt. Ruapehu magmas are fluid saturated, with fo2 of ΔQFM ~ + 1 (NNO). Keywords  Geothermometry · Geobarometry · Rhyolite-MELTS · Andesite · Mt. Ruapehu · Thermodynamics

Introduction and motivation

Communicated by Timothy L. Grove. Electronic supplementary material  The online version of this article (https://doi.org/10.1007/s00410-017-1428-z) contains supplementary material, which is available to authorized users. * Lydia J. Harmon [email protected] 1



Earth and Environmental Sciences, Vanderbilt University, 2301 Vanderbilt Place, PMB 351805, Nashville, TN 37235‑1805, USA

2



University of Canterbury, 20 Kirkwood Ave, Upper Riccarton, Christchurch 8041, New Zealand

3

OFM Research - West, 7336 24th Ave NE, Seattle, WA 98115, USA



Understanding the storage conditions of magma bodies is essential when interpreting the history of magma evolution, crystallization, and eruption. Of the storage conditions, especially pressure can affect fundamental aspects of magma crystallization, including the crystallizing mineral assemblage, as mineral saturation is partially dependent on pressure (Powell and Holland 1999; Wark and Watson 2006; Blundy and Cashman 2008; Putirka 2008; Lange et al. 2009; Waters and Lange 2015). Understanding the pressure conditions yields insight into the crustal conditions in which the magmas evolve. The focus of this study is on constraining storage conditions of intermediate-composition volcanic systems (i.e., andesites to dacites), which are important in building the crust, as they are common in volcanic-arc settings (Grove and Kinzler 1986; Rudnick 1995; Reubi and Blundy 2009). Determining storage conditions for intermediate-composition magmas is especially important, since they can

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Vol.:(0123456789)

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erupt in a range of different sizes—small to super-eruption scale (Lipman et al. 1970; Mason et al. 2004; Bryan et al. 2010)—and styles—effusive to explosive (Dingwell 1996; Giordano et al. 2008). This diversity in eruptive styles and scales, therefore, makes intermediate systems particularly important to understand from volcanological and petrological standpoints. Several methods exist to estimate crystallization conditions of intermediate magmas, e.g., Al-in-hornblende (Johnson and Rutherford 1989; Thomas and Ernst 1990; Schmidt 1992; Lawford and Smith 1995), Fe–Ti oxide equilibria (Ghiorso and Sack 1991; Ghiorso and Evans 2008), abundance of trace elements in minerals, e.g., Ti in Zircon, Zr in titanite (Wark and Watson 2006; Ferry and Watson 2007), Ba/Sr in plagioclase (Blundy and Wood 1991), and ­H2O–CO2 equilibria of melt inclusions (Moore et al. 1998; Liu et al. 2005; Moore 2008). Putirka (2008) summarizes the many efforts in geothermobarometry, but points out the large uncertainties associated with previous geobarometry work. Our method aims to reduce these large uncertainties on pressure estimates, and to provide a new tool for estimating storage conditions for intermediate magmas. We focus on modeling magma storage pressure, but can also estimate temperature, fluid saturation, and oxygen fugacity ( fo2 ). Together, these parameters control the physical behavior of magmas, with pressure acting as a proxy for the depth of crystallization, temperature partially controlling mineral exsolution and stability, the fluid phase greatly affecting buoyancy and viscosity of magma bodies, and fo2 controlling the ratio of ferric to ferrous iron and thus influencing the stable crystallizing mineral assemblage, important in systems containing mafic minerals (Sack et al. 1980; Kilinc et al. 1983; Mysen et al. 1985; Johnson and Rutherford 1989; Lange and Carmichael 1990; Mysen 1990; Toplis and Carroll 1995; Moore et al. 1995; Baker and Rutherford 1996; Liebske et al. 2003; Ghiorso and Kress 2004). We expand on recent efforts to determine storage conditions by computationally modeling the thermodynamic conditions of a magma body using rhyolite-MELTS (Gualda et al. 2012; Bégué et al. 2014; Gualda and Ghiorso 2014; Pamukcu et al. 2015). The efforts of the previous phaseequilibrium geobarometers have focused on silicic systems bearing glass in equilibrium with quartz and feldspar(s). The present study follows and expands on the rhyolite-MELTS geobarometer to include intermediate-composition volcanic systems with the simple mineral assemblage of plagioclase and pyroxene(s). We demonstrate that in addition to pressure, rhyolite-MELTS can calculate the storage temperature, the presence of a fluid phase (modeled as H ­ 2O content in the melt), and fo2 of the system. This method finds applications in rocks that preserve volcanic glass that last equilibrated with assemblages consisting of plagioclase and either or both orthopyroxene and

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clinopyroxene [plag + pyroxene(s)]. The geobarometer utilizes the composition of observed glass as a proxy for the melt composition that was saturated and in equilibrium with the plag + pyroxene(s) mineral assemblage (for details, see Gualda and Ghiorso 2014). Crystal phases within these samples provide insight into the pre-eruptive (i.e., storage) crystallizing assemblage, while the rapidly quenched interstitial glass records, or very closely approximates, the pre-eruptive melt composition. Importantly, our calculations rely on the assumption that the melt was in equilibrium with the crystallizing assemblage—interestingly, calculations are likely to fail when equilibrium was not established, and they can serve as a test for the equilibrium assumption (see Bégué et al. 2014; Gualda and Ghiorso 2014; Pamukcu et al. 2015). We use whole clasts of pumice/scoria that represent a cohesive parcel of magma that did not fragment during eruption. The geobarometer works with glass shards or other noncohesive fragments, as long as the glass was in equilibrium with the plag + pyroxene(s) assemblage. We test the geobarometer against glass compositions from plag + opx + cpx + melt-bearing experiments retrieved from the literature, for which the crystallization conditions are known. We then apply the geobarometer to Mt. Ruapehu, New Zealand, characterized by rocks with glass, plagioclase, orthopyroxene, and clinopyroxene (plag + opx + cpx). Mt. Ruapehu is an active andesitic–dacitic volcano located at the southernmost tip of the Taupo Volcanic Zone (TVZ), one of the most active silicic volcanic zones in the world (Cole 1990; Wilson et al. 1995; Harrison and White 2004). The ~ 150 ­km3 composite cone was built in several discrete periods over the past ~ 250 ka (Hackett and Houghton 1989; Tanaka et al. 1997; Gamble et al. 2003), and it has been the focus of a number of petrological and geophysical studies (Hackett 1985; Graham and Hackett 1987; Hackett and Houghton 1989; Gamble et al. 1999, 2003; Nakagawa et al. 2002, 1999; Ingham et al. 2009; Kilgour et al. 2013, 2014; Cowlyn 2016). Mt. Ruapehu, therefore, serves as an ideal testing ground for the geobarometer.

The geobarometer The geobarometer uses rhyolite-MELTS to search for the conditions under which a melt of given composition can be in equilibrium with an assemblage of interest. Plag, opx, cpx, and fluid are the phases of interest for the purposes of this study. Since the glass composition is the target composition that equilibrated with the plag + pyroxene(s) mineral assemblage, we search for the conditions under which plag + pyroxene(s) simultaneously saturate and are in equilibrium with the melt composition at the liquidus. The same method for plag + opx + cpx assemblages can be used for systems with a plag + opx, plag + cpx, or opx + cpx assemblage,

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although they will have larger uncertainties (see Gualda and Ghiorso 2014). Using rhyolite-MELTS, we model the crystallizing magma from super-liquidus (0% crystalline) to near solidus (~ 90% crystalline) over a range of plausible crustal pressures, ­H2O contents, and fo2 values, to determine the conditions necessary to satisfy the set of conditions for which the plag + opx + cpx assemblage appears in simultaneous equilibrium with melt of the given composition. Although we model from 0% crystalline to 90% crystalline, we are interested in the conditions when the minerals first saturate, as the melt will have a composition different from the target composition at any temperature below the liquidus (i.e., due to further crystallization). For any given combination of H ­ 2O and fo2 conditions, we analyze the results in temperature–pressure space by inspecting the saturation (phase-in) curve for each individual phase (plag, opx, and cpx). As shown in Fig. 1, equilibrium requires that the three mineral phase-in saturation curves cross at a single point, which represents the specific pressure and temperature conditions at which these three minerals saturate and are in equilibrium with the input melt composition. There is only a single pressure–temperature condition at which equilibrium is possible, as the composition of the melt would be different from the given composition for temperatures below any of the phase-in curves. We refer to this single point, where all three phases simultaneously saturate

Fig. 1  Principle behind the geobarometer, adapted from Gualda and Ghiorso (2014). The three curves represent the pressure–temperature saturation conditions for the three mineral phases for a given melt composition. Rhyolite-MELTS can be used to calculate saturation curves like this for any given melt composition. The circle marks the “triple junction”, the point at which the three curves cross, which is the only point at which all three phases are in simultaneous equilibrium with the input melt composition. The triple junction represents the pressure–temperature storage conditions of the magma

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as the “triple junction”. For a more complete description of the concept, please refer to Gualda and Ghiorso (2014). Given the potential effect of H ­ 2O and fo2 on phase equilibria, we explore a range of H ­ 2O values, as well as a range of fo2 values. We model ­H2O as a proxy for the fluid phase in the system, as the presence or absence of a fluid phase is an important consideration for the geobarometer. In natural systems, fluid saturation would take place at lower H ­ 2O values due to the presence of ­CO2. In a modeled ­CO2-free system, fluid saturation can be accomplished by adding enough ­H2O to force saturation in a pure H ­ 2O fluid phase. In this sense, our focus is on the distance to fluid saturation, rather than on the absolute ­H2O values. Although we do not explicitly model the effect of C ­ O2, we vary the initial H ­ 2O content, which approximates the primary effect of ­CO2 in reducing the activity of ­H2O in the melt (Ghiorso and Gualda 2015a, b). For assemblages in which Fe-bearing minerals are abundant, such as the plag + opx + cpx assemblage, it is important to consider the effect of fo2 given that ferrous–ferric ratio controls, directly or indirectly, the stability of mafic minerals (Carmichael and Nicholls 1967; Lindsley et al. 1968; Mo et al. 1982). To model the storage conditions, the steps below were carried out for each glass composition using MELTS_Excel (Gualda et al. 2012; Gualda and Ghiorso 2015): 1. For each value of fo2 and H ­ 2O, we model plag, opx, and cpx stability from 400 to 25 MPa using a coarse 25 MPa pressure step. For each pressure step, the system is modeled from super-liquidus (0% crystalline, ~ 1200 °C) to near solidus (90% crystalline, > 700 °C) in 1 °C temperature steps. At each pressure step, rhyolite-MELTS determines the saturation temperature for each mineral phase, and it interrupts the temperature sequence once the total percentage of solids is above 90 wt%. The result of this sequence of calculations is a collection of saturation surfaces (Fig. 1). These calculations are performed with ­H2O and fo2 held constant. 2. We then consider the effect of water content on the system. For each composition, we consider water contents from water saturated to ~ 2 wt% below water saturation, in 1 wt% ­H2O steps. 3. We also test the sensitivity of the plag + opx + cpx system to fo2 , as the system has Fe-bearing minerals. For each ­H2O content, we model the system over a range of fo2 values, from 0 to + 2 to ΔQFM, in 0.5 ΔQFM steps (approximately − 1 to + 1 ΔNNO in 0.5 ΔNNO steps— see Lindsley 1991), with some samples modeled from 0 to + 4 ΔQFM in 1 ΔQFM steps (approximately − 1 to + 3 ΔNNO in 1 ΔNNO steps). For each fo2 value and ­H2O content, we perform the same sequence of pressure–temperature calculations described above.

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For a given glass composition, a total of 12 model runs are required to constrain the storage pressure of the plag + pyroxenes assemblage in equilibrium with the glass composition. After the initial survey described above, we refine the results by reducing the pressure steps from 25 to 5 MPa, and using a smaller pressure range of 100 MPa (e.g., 25–125 MPa in 5 MPa pressure steps), to more accurately determine the crystallization conditions. A smaller fo2 interval, in 0.5 ΔQFM steps instead of 1 ΔQFM steps, is usually necessary, given that results are particularly sensitive to fo2.

Pressure calculations and limitations To calculate each triple junction pressure, we plot the saturation temperature point of each individual plag, opx, cpx phase for each modeled pressure to create a saturation surface curve (Fig. 2). Each curve connects the phase-in saturation temperatures for an individual mineral phase. The model is successful when plag, opx, and cpx phases cross at a single temperature for a given pressure calculation, resulting in a triple junction of the three mineral phases. Because

Fig. 2  Example of an application of the geobarometer for Mt. Ruapehu sample X262AD. The saturation curves were calculated in pressure–temperature space, under water-saturated conditions and with fo2 equal to + 1 ΔQFM (~ NNO) (top panel). To find the triple junction (bottom panel), we calculate a residual temperature curve as the difference between the maximum saturation temperature and minimum saturation temperature for each pressure. We then fit a parabola to the minimum residual temperature, plus the two pressure calculations above and two pressure calculations below the minimum residual temperature to find the best estimate of crystallization pressure

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we use discretized pressure steps of 5 MPa, it is unlikely that we have sampled the exact plag + opx + cpx saturation pressure, so the saturation surfaces rarely cross exactly. Therefore, the triple junction pressure is calculated from the “residual temperature”, which is the difference in temperature between the first and last phases to saturate in the plag + opx + cpx system. The residual temperature decreases until it reaches the triple junction, before increasing as the saturation temperatures for plag, opx, and cpx diverge. To obtain the estimated storage pressure, we interpolate between pressure calculations to find the minimum residual temperature. We fit a parabola to five data points: the minimum in residual temperature, and two pressure steps above and below the minimum residual temperature (see Fig. 2). This interpolation procedure is described in more detail in Part 1 (Gualda and Ghiorso 2014). For the plag + opx + cpx systems investigated here, the geobarometer calculation is deemed successful if the residual temperature reaches ≤ 8 °C. If the residual temperature never goes below 8 °C, we conclude that there is no set of conditions under which the plag + opx + cpx can be in simultaneous equilibrium with a melt of the given composition. The 8 °C threshold is somewhat arbitrary, but our tests suggest that it is a conservative compromise between locating a viable triple junction and excluding spurious results. We use a larger residual temperature threshold in this study than in Parts 1–3 (Bégué et al. 2014; Gualda and Ghiorso 2014; Pamukcu et al. 2015), given that the fo2 steps are somewhat coarse, and the temperature threshold should be slightly higher than the 5 °C in the quartz + 2 feldspars geobarometer (Gualda and Ghiorso 2014). We also consider a threshold of 20 °C and show that the overall conclusions are not particularly affected by the specific choice of threshold value. For most of the rhyolite-MELTS calculations with Mt. Ruapehu samples, clinopyroxene undergoes a phase change at pressures slightly below the triple junction. In many of these cases, it is inaccurate to fit a parabola to the two data points at pressures below the minimum in residual temperature. There are two potential scenarios: 1. We calculate the estimated storage pressure based on the minimum residual temperature, two pressures above, and one pressure below the minimum residual temperature. 2. In cases where the phase change occurred right below the minimum residual temperature, a parabola cannot be fit. In this instance, the estimated pressure is simply the pressure corresponding to the minimum in residual temperature. Of the 13 Mt. Ruapehu compositions that produce a minimum residual temperature ≤ 8 °C, 5 samples require a pressure estimate based on the residual temperature.

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An example We demonstrate the methods of the geobarometer using one of the successfully modeled Mt. Ruapehu samples, X262AD (Cowlyn 2016), which shows the sensitivity of the results to pressure, temperature, H ­ 2O content, and fo2 . Figure 3 shows the results for the ­H2O and fo2 model conditions calculated for X262AD. It can be seen that the plag + pyroxenes phase assemblage is sensitive to the choice of fo2 and H ­ 2O content, with viable plag + pyroxenes triple junctions resulting only for a single combination of fo2 equal to ΔQFM + 1 (~ NNO) and fluid-saturated conditions. In Fig. 2, we show the more detailed rhyolite-MELTS calculation performed with 5 MPa steps at + 1 ΔQFM (~ NNO) and 10 wt% ­H2O (enough to be ­H2O-saturated at all

Fig. 3  Geobarometer results detailing the effects of fo2 and H ­ 2O wt% on triple junction viability for a single melt composition (sample X262AD). We ran a suite of rhyolite-MELTS calculations, varying fo2 and ­H2O wt% in each run, from water saturated to 2 wt% below saturation in 1 wt% steps (4.4, 3.4, and 2.4 H ­ 2O wt%) (shown on y-axis), and from ΔQFM to + 2 ΔQFM (approximately − 1 ΔNNO to + 1 ΔNNO) in 1 ΔQFM (~ 1 ΔNNO) steps (shown on x-axis). For each distinct fo2 and H ­ 2O condition, the model was run from 1200 to 700

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pressures investigated). From these results, we calculate the estimated crystallization pressure of 132 MPa.

Error analysis It is important to evaluate the uncertainties associated with the pressure calculations. Potential sources of error include (Gualda et al. 2012; Gualda and Ghiorso 2014): 1. Inherent uncertainties to the calibration of rhyoliteMELTS. 2. Uncertainties in the calculation of the best-fit parabola. 3. Uncertainties associated with the input glass compositions.

°C in 1 °C steps and from 400 to 25 MPa in 25 MPa steps, labeled on each individual graph. When the plag + opx + cpx saturation curves saturated within 8 °C, a triple junction was calculated. Of all the conditions, the only one to calculate a triple junction was modeled at + 1 ΔQFM (~ NNO) and was water saturated (top-center panel, outlined). The ­H2O and fo2 parameters indicate the storage conditions of the magma, since these are the only conditions which produce a triple junction

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As discussed by Gualda and Ghiorso (2014), there are uncertainties inherent to the calibration of rhyolite-MELTS, which are difficult to assess. We have reduced the errors associated with the parabolafitting calculations using a 5 MPa step, but the errors associated with the parabola-fitting can be up to 5 MPa when the triple junction parabola is calculated using < 5 pressure calculations due to clinopyroxene phase changes. The largest source of error is likely the error associated with the glass compositions, which can be attributed to a combination of analytical uncertainties and uncertainties due to glass alteration. We can avoid the most obvious alteration when we analyze the glass, but there is a significant amount of subtle variation that is more difficult to distinguish and avoid. The issue of subtle variation is discussed in more detail in Parts 2 and 3 of this series (Bégué et al. 2014; Pamukcu et al. 2015) and in Sect. “Equilibria and disequilibria” below. To quantify the uncertainty of the geobarometer, we conducted a numerical error analysis using a Monte Carlo simulation. Using the Mt. Ruapehu X262AD sample, we generated 150 random compositions based on the uncertainty of the original glass composition. The randomly generated compositions follow a normal distribution for each oxide, using the original X262AD composition as the mean and a standard deviation equal to the reported error of each oxide. The 150 compositions are given in the Appendix. Fig. 4  Histogram showing successful geobarometer runs from the Mt. Ruapehu (top) and LEPR 4799 (bottom) Monte Carlo simulations. The black bars represent a 20 °C cut-off residual temperature, while the gray bars represent an 8 °C cutoff residual temperature

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We ran the generated glass compositions through rhyolite-MELTS from 300 to 25 MPa at 5 MPa pressure steps, from 1300 to 750 °C in 1 °C temperature steps. For all compositions, fo2 equaled ΔQFM + 1 (~ NNO) and ­H2O was set to 10 wt% ­H2O to ensure fluid-saturated conditions at all steps, which are the conditions that produced a triple junction for the original X262AD composition. Of the generated compositions, 53/150 (35%) produce a viable triple junction with a residual temperature ≤ 8 °C. The mean pressure is 138 MPa, with a standard deviation of 18 MPa (Fig. 4), compared to the original geobarometer calculation of 132 MPa. We also explore results for a 20 °C residual cut-off, which result in 100/150 (67%) of the compositions producing a triple junction with a mean pressure of 139 MPa and standard deviation of 17 MPa. This analysis indicates that the pressure calculations are precise to ± ~ 20 MPa for both an 8 °C cut-off and a 20 °C cut-off—in this sense, the 8 °C cut-off we use in the study is somewhat conservative. To determine the impact of deviating from the original composition on the success of the geobarometer, we examine the Euclidean distance of each composition to the original composition (i.e., the sum of the squares of the differences between the randomly generated and original composition for all oxides). The pressure vs. Euclidean distance plots (Fig. 5) show that even with larger Euclidean distances, the spread of pressures remains relatively constant. The pressure

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Fig. 5  Pressure vs. Euclidean distance of oxides for Mt. Ruapehu Monte Carlo simulations. The black diamonds represent successful simulations with a 20 °C cut-off residual temperature, and gray diamonds represent successful simulations with an 8 °C cut-off tem-

perature. The points at the bottom of the graphs (plotted at 0 MPa) represent unsuccessful calculations, in which the residual temperature is never ≤ 20 °C

vs. CaO Euclidean distance plot (Fig. 5) shows that the pressures depend on the CaO content, since only a specific range of CaO contents produces a triple junction. None of the other oxides has a significant impact on the pressures despite larger errors (e.g., ­SiO2, Fig. 5). The sensitivity to CaO relates to its effect on pyroxene stability, especially clinopyroxene. In many of the geobarometer results, clinopyroxene undergoes that a phase change before the residual temperature is ≤ 8 °C.

For these three compositions, the pressures corresponding to the minimum residual temperatures are within 20 MPa of the experimental conditions. The plag + opx results for the experimental conditions yielded two double junctions with residual temperature ≤ 8 °C, and five double junctions with residual temperature ≤ 29 °C. For these, the calculated pressures are ≤ 10 MPa of the experimental pressure conditions, Table 2. It is noteworthy that none of the experimental compositions yielded triple junction pressures with a ≤ 8 °C residual temperature for the plag + opx + cpx triple junction and that the plag + opx double junction was more successful and yielded pressures ≤ 10 MPa when the residual temperature was ≤ 29 °C. Our results based on experimental compositions indicate that 8 °C is a conservative residual temperature for both plag + opx and plag + opx + cpx calculations and that the plag + opx + cpx triple junction residual temperature could be ~ 20–25 °C, although that increases the uncertainty in the pressure calculation. When applying the geobarometer to natural systems, there must be a balance between increasing residual temperature to yield a larger number of results and reducing the number of spurious results obtained—our approach with the natural data has been to be more conservative. It is interesting that the plag + opx pressures are in general more successful than the plag + opx + cpx pressures—the difficulty in successfully modeling clinopyroxene stability is likely due to the sensitivity of clinopyroxene to fo2. The rhyolite-MELTS quartz + 2feldspar geobarometer is particularly sensitive to the quality of the glass composition used (Bégué et al. 2014; Gualda and Ghiorso 2014; Pamukcu et al. 2015). We expect that the same will be the case with the plag + pyroxenes geobarometer. We devised a second Monte Carlo simulation to investigate if the lack of triple junctions in the experimental compositions might derive from inaccuracies in the measured glass compositions. We

Application to experiments We apply the geobarometer to experimental glass data, run under documented ­H2O and fo2 conditions. The experimental glass compositions were taken from the library of experimental phase relations (LEPR) database. We chose the experiments based on mineral assemblage (plag + opx + cpx-bearing), pressure (upper crustal pressures of < 1 GPa), and water content (documented ­H2O conditions in the samples). We modeled eight experimental glass compositions from the LEPR database that were taken from several different experiments, detailed in Table 1 (Vander Auwera and Longhi 1994; Kawamoto 1996; Grove et al. 1997; Moore et al. 1998; Prouteau and Scaillet 2003). When running the geobarometer, we use the H ­ 2O and fo2 conditions under which the experiments were conducted, temperatures of 1300–750 °C in 1 °C steps, and pressures initially from 500 to 50 MPa in 50 MPa steps, then using a ~ 200 MPa interval in 5 MPa steps, as detailed in Table 2. Although all of the experiments contained a plag + opx + cpx assemblage, the geobarometer did not calculate a triple junction for any of the compositions using the residual temperature residual temperature of ≤ 8 °C (Table 2). However, of the eight LEPR compositions tested, three (LEPR 3607, 4037, and 4799) had residual temperature ≤ 21 °C, Fig. 6.

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LEPR_Index_1426 LEPR_Index_1622 LEPR_Index_3603 LEPR_Index_3607 LEPR_Index_4037 LEPR_Index_4799 LEPR_Index_4801

71.65 63.50 68.20 61.80 60.70 62.39 63.73

0.24 0.35 1.03 0.61 2.34 0.80 0.77

15.26 18.90 13.70 16.50 13.20 15.69 15.15

Al2O3

Composition

Sample TiO2

Prouteau and Scaillet (2003) Kawamoto (1996) Moore and Carmichael (1998) Moore and Carmichael (1998) Vander Auwera and Longhi (1994) Grove et al. (1997) Grove et al. (1997) Grove et al. (1997)

LEPR_Index_1426 LEPR_Index_1622 LEPR_Index_3603 LEPR_Index_3607 LEPR_Index_4037 LEPR_Index_4799 LEPR_Index_4801 LEPR_Index_4806

0.00 3.00 0.00 0.00 0.00 0.00 0.00

Fe2O3 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2.08 0.00 3.16 3.77 7.25 3.93 2.68

FeO 0.00 0.00 0.00 0.00 0.00 0.00 0.00

MnO 1.00 2.96 1.20 1.70 2.98 1.32 1.32

MgO

Universite de Bretagne Occidentale University of Tokyo UC-Berkeley UC-Berkeley Lamont-Doherty Earth Observatory MIT MIT MIT

Laboratory

Cr2O3

PIN98s 8 PEM12-11 PEM12-19 TJ-34 1140mf #27 1140mf #29 1140mf #41

Experiment

0.00 0.00 0.00 0.00 0.00 0.00 0.00

NiO

IHPV PC IHPV IHPV 1-atm CSPV CSPV CSPV

Device 950 975 1000 975 1085 940 910 915

0.00 0.00 0.00 0.00 0.00 0.00 0.00

CoO

T (C) 400 500 44 100.8 0.1 100 100 150

2.99 5.30 3.20 4.91 5.77 3.42 3.01

CaO

4.50 4.44 4.20 3.50 2.79 4.75 4.95

Na2O

NNO + 3.2 NNO + 1.3 NNO + 2.8 NNO + 1.1 NNO NNO NNO NNO

P (MPa) fO2 cond

2.20 0.74 2.60 1.87 2.20 2.43 2.74

K 2O

0.00 0.00 0.00 0.00 0.00 0.00 0.00

P2O5

5.46 0.00 2.30 3.60 0.00 4.90 5.30

H2O

liq + plag + cpx + spn + opx cpx + opx + plag + spn liq + opx + plag + ox + cpx liq + opx + plag liq + plag + opx + cpx + ilm + spn liq + opx + cpx + plag + spn liq + opx + cpx + plag + spn liq + opx + cpx + plag + spn

Phases

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SiO2

Author (year)

Sample

Table 1  Details of experiment conditions and glass compositions for the LEPR glass compositions tested with the geobarometer

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Table 2  Geobarometer results for the LEPR glass compositions Sample

LEPR_Index_1426 LEPR_Index_1622 LEPR_Index_3603 LEPR_Index_3607 LEPR_Index_4037 LEPR_Index_4799 LEPR_Index_4801 LEPR_Index_4806

Geobarometry Results

Geobarometry Parameters

P (MPa)

T range (°C)

Residual T (°C)

Difference from experiment (MPa)

P range (MPa)

P step (MPa)

T range (ºC)

fo2 (ΔNNO)

300 – 195 105 10 120 125 165

822–884 1207–1215 906–975 972–992 1102–1123 932–948 913–951 754–875

62 – 69 20 21 16 38 121

−100 – 151 4 10 20 25 15

550–350 550–350 200–5 200–5 200–5 200–5 200–5 200–5

5 5 5 5 5 5 5 5

1250–750 1250–750 1250–750 1250–750 1250–750 1250–750 1250–750 1250–750

NNO + 3.2 NNO + 1.3 NNO + 2.8 NNO + 1.1 NNO NNO NNO NNO

Fig. 6  Geobarometer results for experiments from the literature compositions from LEPR 3607, 4799, and 4037 (Vander Auwera and Longhi 1994; Grove et  al. 1997; Moore and Carmichael 1998). Experimental pressure conditions for LEPR 3607 and 4799 were 100 MPa, while the pressure condition for LEPR 4037 was 5 MPa. The complete conditions of the experiments are in Table 1

chose LEPR composition 4799 (Grove et al. 1997) that did not produce a triple junction originally, but did have a residual temperature of 16 °C. The Monte Carlo simulation was designed to determine if a triple junction could be calculated

by considering the error associated with the glass composition. We used the same procedure as described in the “Error analysis” section to generate random compositions to use in a Monte Carlo simulation, see the Appendix for the compositions. We ran these compositions at fo2 equal to NNO and with 4.9 wt% H ­ 2O, as reported in the original experiment, see Table 1 (Grove et al. 1997). The Monte Carlo simulation based on the LEPR 4799 composition produced a triple junction for 21/150 (14%) of the generated compositions with a residual temperature of ≤ 8 °C. The mean is 109 MPa with a standard deviation of 11 MPa, compared to the experimentally measured pressure of 100 MPa. While the success rate is only 14%, the original composition yields a residual temperature of 16 °C and it does not produce a triple junction. For the extended 20 °C cut-off, we find that 60/150 (40%) compositions produce a triple junction with a mean pressure of 100 MPa and a standard deviation of 19 MPa. These results highlight just how sensitive the geobarometer is to the measured glass composition. If a triple junction is produced, the glass is likely in equilibrium with the plag + opx + cpx assemblage. It is noteworthy that all of the successful runs returned pressure estimates that were almost identical to the original experiments. The plag-opx results for the Monte Carlo simulation produce triple junctions for 106/150 (71%) for an 8 °C cut-off and 128/150 (85%) for a 20 °C cut-off. The mean pressures calculated are 73 MPa with a standard deviation of 26 and 74 MPa with a standard deviation of 24 MPa for the 8 and 20 °C cut-off, respectively. While there are many more double junctions calculated for the plag-opx calculation, the calculated pressures are systematically lower than those calculated based on the plag + opx + cpx triple junction. We also examined the Euclidean distance of each composition to the original composition for the plag + opx + cpx results of the LEPR Monte Carlo simulation. The results show that the pressures do not deviate significantly from

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Contributions to Mineralogy and Petrology (2018) 173:7

Fig. 7  Pressure vs. Euclidean distance of oxides for LEPR Monte Carlo simulations. The black diamonds represent successful simulations with a 20 °C cut-off residual temperature, and gray diamonds represent successful simulations with an 8 °C cut-off temperature.

The points at the bottom of the graphs (plotted at 0 MPa) represent unsuccessful calculations, in which the residual temperature is never ≤ 20 °C. Note that pressure is sensitive to CaO values, but is not very sensitive to S ­ iO2 or other oxides

the expected pressure of 100 MPa, Fig. 4, even when the Euclidean distances are larger, Fig. 7. Importantly, despite the original composition not producing a triple junction in the geobarometer, the Monte Carlo pressure estimates were close to the original experimental pressure of 100 MPa when a triple junction was produced. This suggests that the failure in obtaining a triple junction for the originally measured composition can be attributed to small inaccuracies in the measured glass compositions. This reinforces that the method is predicated on the quality of the glass compositions.

crustal zone of 500–900 MPa. By 160–115 ka (Wahianoa Formation), the magmatic system had become established at shallower depths, with pressures higher than 200 MPa, where a complex system of dikes and sills was emplaced (Price et al. 2012). The most recent eruptions (1945–1996) have significantly shallower storage conditions of ~ 50–230 MPa, based on analyzed volatile content of phenocryst-hosted melt inclusions (Kilgour et al. 2013). Kilgour et al. (2013) noted that the melt inclusions are more evolved and exotic to the transporting melt, indicating that the melt included crystals during transport. Unique ascent histories of different magma batches are apparent, and Kilgour et al. (2014, 2016) inferred that there are small magma volumes that develop, interact, and erupt over short timescales. The recent eruptions indicate that both pyroxene and plagioclase were stable, as there were inclusions of plagioclase in pyroxene, and vice versa (Kilgour et al. 2013). Melt inclusions contain relatively low water content (mostly 1–1.5 wt% ­H2O) and high ­CO2 content (25–1059 ppm), so it is plausible that magma was fluid-saturated at the inferred depths (250 MPa) of crystallization. Using mineral–liquid hygrometers, assuming 250 MPa, the temperature estimates ranged from 910 to 1080 °C, with most analyses falling within a range of 950–1050 °C. From geophysical data, the modern-day dike system is interpreted to extend to 6 km (~ 150 MPa), and there is a melt-bearing zone at 6–10 km depth (~ 150–255 MPa) (Ingham et al. 2009). For this study, we focus on pumice and scoria samples from several young (< 13.6 ka B.P. cal.) pyroclastic density current (PDC) deposits. The timing of these deposits coincides with a shift in Mt. Ruapehu’s eruptive style from large plinian and subplinian eruptions of the 27,097 ± 957 to ~ 10,000 cal. years BP Bullot Formation (Donoghue et al. 1995a, b; Pardo et al. 2011; Pardo Villaveces 2012)

Application to Mt. Ruapehu The ~ 150 ­km3 andesitic cone volcano is the southernmost volcanic center in the TVZ; it has been active for ~ 250 ka (Hackett and Houghton 1989; Gamble et al. 2003; Price et al. 2007, 2012), with the most recent eruption in 1995–1996 (Gamble et al. 1999; Nakagawa et al. 1999, 2002). Mt. Ruapehu has been the focus of multiple petrological and geophysical studies, as it is an active hazard region (Gamble et al. 2003; Kilgour et al. 2013). The previous studies have classified Mt. Ruapehu as having a complex array of magmatic reservoirs, which have evolved from deeper crustal origins to more shallow levels (Gamble et al. 1999; Price et al. 2012; Kilgour et al. 2013, 2014, 2016). The magmatic system is an open system at depth, which has been fed by mantle-derived MELTS with a combination of assimilation and fractional crystallization driving magma evolution through its history (Price et al. 2012). Using mineral-based geothermobarometry, e.g., clinopyroxene (Putirka et al. 2003) and Al-inhornblende (for the minor number of amphibole-bearing flows) geobarometry, Price et al. (2012) found that the Mt. Ruapehu magma system initially developed from a deep

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to smaller subplinian-to-vulcanian eruptions similar to Mt. Ruapehu’s modern activity (Donoghue et al. 1995b, 1997; Cowlyn 2016). These represent ideal deposits to investigate the changing storage conditions of Mt. Ruapehu’s young magma system. Here, we apply the geobarometer to better constrain the pre-eruptive storage conditions that led to Mt. Ruapehu’s PDC-forming eruptions, using 40 samples collected from 12 different PDC units during fieldwork in the Tukino Ski Area of eastern Mt. Ruapehu (Cowlyn 2016). Similar to the fall deposits, PDC deposit textures suggest that Mt. Ruapehu’s young (< 13.6 ka) PDCs were generated by a broad range of eruptive styles (Cowlyn 2016), spanning large plinian explosive eruptions through to smaller vulcanian and even spatter-forming events (Fig. 8). Cowlyn (2016) and Pardo et al. (2011, 2014) interpreted these to have occurred from at least two vents on the basis of both PDC and fall deposit distributions (Fig. 8). The PDC samples all contain glass plus plagioclase, clinopyroxene (augite), orthopyroxene, and titanomagnetite ± ilmenite, which makes the samples viable for application to the plag + opx + cpx geobarometer. Figure 8 summarizes the interpreted eruption sequence and eruption styles for

these units based on the detailed physical volcanological observations of Cowlyn (2016).

Fig. 8  Schematic eruption sequence inferred from Mt. Ruapehu’s PDC deposits. Column heights are drawn to approximate (interpreted) scale. a Between 13.6 and 11.6 ka, plinian eruptions from Ruapehu’s North Crater area sizeable PDCs in the Mangatoetoenui valley (Units 1–3). The plinian sequence ended with smaller eruptions from more degassed magma that produced small-volume PDC Units 11 and 12. b At ~ 11.6, the plinian Okupata–Pourahu eruption explosively excavated a new vent near South Crater to produce the Okupata tephra (Pardo et al. 2011) and pumiceous PDC Unit 4. At a

similar time, pre-existing (i.e., more open system) conduit in Northern Mt. Ruapehu produced a short-lived eruption of a frothy magma (PDC Unit 5) followed by (c) eruption of hot, more degassed magma through energetic fire-fountaining/spatter-forming eruptions that generated the PDC Unit 6 and Pinnacle Ridge Tuff deposits. d Mt. Ruapehu’s activity then shifted (< 11.6 ka) towards smaller (subplinian/vulcanian) eruptions from relatively degassed magmas sourced near the now semi-open southern vent, emplacing PDC Units 8–10. Adapted from Cowlyn (2016)

Analytical methods—glass analyses The glass compositions used in the rhyolite-MELTS calculations were obtained from averages of complete compositional analyses obtained using energy-dispersive spectrometry (EDS) on a scanning electron microscope (SEM) from thin sections of individual pumice/scoria clasts. The glass compositions were obtained at Vanderbilt University using an Oxford X-max 50-mm2 EDS attached to a Tescan Vega 3 LM Variable Pressure SEM. All glass analyses were obtained using 15 kV accelerating voltage at a working distance of 15 mm. Each individual analysis was performed using an area > 100 µm2. Specimen current was approximately 2 nA. Quality of the results was monitored by analyzing the reference standards glass mountain rhyolite (RGM1) fused in house from USGS reference powder and AGV andesite in the same analytical sessions, which are included in the Appendix. For each sample, we obtained 10–20 individual glass compositions, so as to minimize the effects of heterogeneities

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in the glass due to chemical alteration, physical imperfections, and presence of microlites. The analyses were obtained using the same methods and conditions as used by Pamukcu et al. (2015). After obtaining 10–20 glass analyses for each sample, the analyses considered most likely to represent pristine glass were checked for chemical consistency and then averaged, while outlying compositions were removed prior to averaging. We used a “ranked method” to determine the most suitable analyses for averaging. This method intentionally biases the average compositions towards higher ­SiO2 content to compensate for the effect of possible plagioclase microlites, which would artificially lower the ­SiO2 content of the glass. In these intermediate rocks, most of the crystal phases have lower ­SiO2 than the bulk rock composition; therefore, the most pristine interstitial glass analyses should be those with the highest ­SiO2 values. The ranked method, therefore, effectively identifies the most pristine glass even where microlites are too small to be visibly recognized. In the ranked method, the analysis with the highest ­SiO2 value is found, then additional analyses are added in order of decreasing S ­ iO2, assessed for chemical consistency (see below), and if they pass the consistency check, they are carried forward iteratively until at least five analyses are available for averaging. The checks for chemical consistency are applied before the analyses are used to produce the final average composition. To check for chemical consistency, we discarded chemical outliers using the median and median absolute deviation (MAD) values of the series of compositional analyses for each sample (Cowlyn 2016). The median composition (in wt%) of each oxide is calculated before the absolute deviation of each analysis from this value is recorded (i.e., the absolute difference between an oxide’s measured value and the median value for that oxide). The median average deviation (MAD) is then determined to be the median value of all of these absolute deviations. Assuming that the majority of the data is normally distributed, the relation ­MADE = 1.483 × MAD is then approximately equivalent to one standard deviation for the oxide data series (for further information, see http://www.academia.edu/5324493/Detecting_outliers_Do_not_use_standard_deviation_around_the_mean_ use_absolute_deviation_around_the_median). Since the calculations presented here rely on median values, not mean values, they are significantly less affected by outliers; use of ­MADE allows straightforward detection and removal of outliers, thereby largely preventing spurious analyses from affecting the data. Any glass analysis for which any of its oxide values exceeds the median ± 2.5 × ­MADE is deemed to be chemically inconsistent and discarded (i.e., this is broadly equivalent to removing any analysis that has one or more oxide values falling outside of the mean ± 2.5 σ for each

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respective oxide series). This method, therefore, selects only those analyses from the original data pool that have both the highest S ­ iO2 values (using the ranked method) and also demonstrate chemical consistency across the glass analyses. The glass composition input to the geobarometer is then determined by averaging the oxide values from these chemically consistent analyses. The assumptions are that (a) higher ­SiO2 values are good indicators of successful glass analyses and (b) heterogeneities due to sample alteration or accidental inclusion of microlites within analysis spots will be apparent in the oxide data. The Mt. Ruapehu compositions used for the geobarometry work are listed in Table 3. Based on petrographic thin section analysis, the Mt. Ruapehu PDC samples that returned pressures and temperatures (“Results from Mt. Ruapehu”) were mostly microlite-free (Samples 225-5B, 225AC, 225B1, 225C1, 225CE, 225D1, 225D3, 225DE, 129AC, 262-Y1, 13-262-4, 262AD), but a few samples contained small euhedral microlites (samples 161AC, 13-107, 259-1-2, parts of X109AC, parts of 225D3) that were generally easily observed in the SEM imagery. For the purposes of the work here, we consider microlites only the very smallest crystals (i.e., < 50 μm, and usually much smaller). Plagioclase, clinopyroxene, and orthopyroxene were present as phenocryst phases in most samples, and analyzed microlites in sample 161AC were also plagioclase, orthopyroxene, and clinopyroxene. Considering all samples (including those that did not return pressures and temperatures), the microlite-free samples generally correlate with PDC deposits from large plinian-style eruptions in which the glass is interpreted to have rapidly decompressed and quenched during eruption, whereas the microlite-rich samples correlate with PDC deposits from smaller vulcanian/ subplinian eruptions in which a slowly ascending and degassing magma column is interpreted to have promoted microlite growth immediately prior to eruption (Cowlyn 2016). The absence of microlites in many of the samples makes it difficult to prove that the melt was in equilibrium with plag + pyroxenes assemblage immediately prior to eruption, and this is a common problem with many rapidly quenched eruption products. Phenocrysts were typically subhedral to euhedral in shape, with many of the larger phenocrysts showing features that could argue both for and against equilibrium at different stages during magma storage, as would be expected during the longer residence times reflected by the larger crystals. The internal consistency of the rhyolite-MELTS geobarometer, in which a triple junction is only achievable if the measured glass composition is thermodynamically consistent with equilibrium crystallization of plag + opx + cpx, therefore, provides useful indirect support for equilibrium crystallization of the plag + opx + cpx assemblage with the observed melt composition, even if the phenocrysts were not in equilibrium during earlier stages of magma storage

225-5B 225A1 225AC 225B1 225 pink ash light separate glass 225C1 225CE 225D1 225D1 (highest excluded) 225D3 less vesicular glass (highest excluded) 225D3 less vesicular glass 225D3 less vesicular glass (highest excluded) 225D3 more vesicular bulk (3 analyses) 225D3 more vesicular glass 225DE 13-107 129A3 glass type 1 (banded Sample) 129A3 glass type 2 (banded sample) 129A5 (subsidiary clast type, magma type 2 in mingled eruption) X129AC 262-Y1 13-262-4 glass type 1 (LHS) 13-262-4 glass type 2 (RHS) (alternative method) 13-262-4 glass type 2 (RHS) 259-1-2 clast interior 259-1-2 glass chilled margin 259-1-2 matrix glass X262AD 274-1 13-301-1 (2 analyses) 109AC coarsely vesicular glass 109AC finely vesicular glass 109AC glass between microlites in microlite-rich areas (all 9 analyses) 109AC glass sites 8–9 (all 10 analyses) 108A1 bulk groundmass (all 5 analyses) 108A1 glass between microlites

Sample

70.09 69.60 69.51 69.73 69.42 69.32 70.32 69.49 69.54 68.04 68.04 68.04 67.85 69.74 70.10 69.68 72.09 69.68 72.62 72.06 70.45 66.31 66.57 66.57 69.89 70.37 72.05 70.99 70.20 60.84 70.50 64.30 63.63 62.70 61.18 64.08

SiO2 0.74 0.83 0.82 0.80 0.82 0.79 0.73 0.75 0.75 0.93 0.93 0.93 0.75 0.77 0.78 0.73 0.59 0.80 0.51 0.62 0.76 0.91 0.97 0.97 0.72 0.75 0.64 0.73 0.63 0.26 0.77 0.91 1.15 0.94 0.92 1.12

TiO2

Composition

Table 3  Mt. Ruapehu averaged EDS glass compositions used for the geobarometry

14.66 14.51 14.78 14.67 15.09 14.89 14.66 14.78 14.84 15.18 15.18 15.18 15.33 14.65 14.61 14.67 14.17 14.45 14.03 13.92 14.40 15.41 15.52 15.52 14.85 14.36 14.06 14.18 15.10 20.66 14.09 15.84 15.17 16.11 17.11 15.09

Al2O3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Fe2O3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Cr2O3 3.32 3.99 3.64 3.53 3.67 3.68 3.32 3.54 3.59 4.51 4.51 4.51 4.24 3.72 3.39 3.61 2.88 4.16 2.45 2.82 3.40 4.72 4.83 4.83 3.44 3.46 2.51 3.25 3.15 2.59 3.73 5.81 7.55 6.33 6.31 6.91

FeO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

MnO 0.84 0.77 0.94 0.92 0.96 1.03 0.78 0.95 0.92 0.84 0.84 0.84 1.15 0.89 0.84 0.99 0.58 0.78 0.55 0.60 0.83 1.43 1.49 1.49 0.86 0.94 0.73 0.73 0.74 0.83 0.85 1.98 1.56 2.50 2.49 1.74

MgO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

NiO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

CoO 2.69 2.90 2.98 3.03 2.86 2.93 2.60 3.08 3.08 3.64 3.64 3.64 3.88 2.84 2.72 2.96 2.15 2.93 2.06 2.26 2.71 3.69 3.71 3.71 3.45 2.69 2.22 2.52 3.01 4.78 2.75 4.95 4.97 5.49 6.41 4.82

CaO 4.25 3.86 3.99 3.89 4.00 4.10 4.12 4.00 3.90 3.85 3.85 3.85 4.00 3.70 4.09 4.00 3.64 3.64 3.78 3.71 4.07 3.63 4.01 4.01 3.46 3.50 3.67 3.93 3.94 4.13 3.66 3.49 3.48 3.63 3.53 3.50

Na2O 3.41 3.54 3.34 3.45 3.19 3.25 3.47 3.42 3.39 3.03 3.03 3.03 2.79 3.70 3.47 3.37 3.89 3.55 3.99 4.00 3.39 3.91 2.91 2.91 3.34 3.95 4.11 3.65 3.24 5.93 3.67 2.73 2.51 2.30 2.05 2.73

K2O

10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00

H 2O

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10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 2.72 4.13 2.74 2.78 2.82 2.37 1.93 2.66 2.09 3.23 2.02 2.99 3.60 3.59 3.68 3.33 3.63 3.56 3.56 3.43 3.50 3.76 3.92 3.55 4.76 1.70 4.56 4.97 4.39 5.26 6.51 5.06 6.37 3.25 6.24 3.99 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.56 0.47 1.88 1.70 1.60 2.17 2.77 1.68 2.38 0.96 1.36 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.76 2.86 6.25 7.40 6.87 6.85 6.24 6.77 5.88 4.91 4.45 4.71 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15.26 12.82 15.01 14.87 14.67 15.71 17.26 15.69 17.44 14.21 18.29 14.95

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Fe2O3 Al2O3

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(Pamukcu et al. 2015). Sample 161AC, containing microlites of plagioclase, orthopyroxene, and clinopyroxene, was nonetheless unequivocally in equilibrium with its melt at the time of eruption. Since it is possible to analyze large regions using the SEM-EDS (as opposed to single spots), candidate areas of glass avoiding vesicles and crystals were outlined and targeted for analysis. In the microlite-free samples, analysis regions typically 5–50 microns across were analyzed. In microlite-rich samples, much smaller regions (only a few microns across) between microlites were outlined and targeted. Potential sources of error, especially in the microliterich samples, include the intrinsic width of the electronic beam and the resulting excitation volume (which may then overlap adjacent microlites even when the defined analysis region does not), or the inclusion of unobserved microlites due to depth-averaging through the analyzed volume. However, by taking multiple analyses and then keeping only those with the highest ­SiO2 using the ranked approach, it was possible to confidently identify the ‘good’ glass analyses and discard analyses inadvertently affected by crystal phases and alteration. Again, the internal consistency of the rhyolite-MELTS geobarometer also provides indirect support that the glass compositions are good, as erroneous melt compositions would be unlikely to reproduce equilibrium crystallization and hence return a pressure estimate.

64.19 73.75 64.88 63.78 64.87 63.01 60.77 63.59 61.43 68.75 63.07 67.93

1.13 0.68 1.00 1.18 1.15 1.07 0.95 1.13 0.91 0.94 0.65 0.87

Equilibria and disequilibria

108AC glass between microlites (site 1) 108AC glass site 2 X108AD 108B1 glass between microlites X108BC glass between microlites 161A1 glass between microlites 161A1 glass bulk groundmass (all 5 analyses) X161AC glass between microlites X161AC matrix shards bulk (No limit) 12-225-19A 12-225-19A bulk (all 5 analyses) Ring plain M1 light separate

TiO2 SiO2

Sample

Table 3  (continued)

Composition

Cr2O3

FeO

MnO

MgO

NiO

CoO

CaO

Na2O

K2O

H 2O

Page 14 of 20

Application of the geobarometer is predicated on the assumption of equilibrium between melt and the assumed mineral assemblage. While all Mt. Ruapehu rocks studied contain plag, opx, cpx, and glass, this does not necessarily imply that they are in simultaneous equilibrium. The crystals could be inherited, the mush/melt could have undergone recharge, mixing, or could have migrated so that the melt is no longer in thermodynamic equilibrium with the crystals. While the textures of minerals can help to determine whether crystals are stable in a melt, there has been considerable attention paid to cases in which “cryptic” disequilibrium can exist (Kent et al. 2010; McLeod et al. 2012; Humphreys et al. 2016; Martel et al. 2017). However, as long as the melt equilibrated with the plag + opx + cpx assemblage during the last stage of magma storage, the geobarometer should produce a pressure estimate. This pressure estimate will be the last occurrence that the melt was in equilibrium with the plag + opx + cpx assemblage. If the melt has never been in equilibrium with the plag + opx + cpx assemblage, then no triple junction will be calculated. For Mt. Ruapehu, we can assume that the melt equilibrated with the plag + opx + cpx assemblage during its history, as this assemblage is consistent across all flows (Cowlyn 2016). The

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Table 4  Mt. Ruapehu geobarometry results and geobarometer parameters Sample

PDC unit

Magma-meter results

Magma-meter parameters

P (MPa) T (ºC) P range (MPa) P step (MPa) T range (ºC) fo2 (Δ QFM) 225-5B 225A1 225AC 225B1 225 pink ash light separate glass 225C1 225CE 225D1 225D1 (highest excluded) 225D3 less vesicular glass (highest excluded) 225D3 less vesicular glass 225D3 less vesicular glass (highest excluded) 225D3 more vesicular bulk (3 analyses) 225D3 more vesicular glass 225DE 13–107 129A3 glass type 1 (banded Sample) 129A3 glass type 2 (banded Sample) 129A5 (subsidiary clast type, magma type 2 in mingled eruption) X129AC 262-Y1 13-262-4 glass type 1 (LHS) 13-262-4 glass type 2 (RHS) (alternative method) 13-262-4 glass type 2 (RHS) 259-1-2 clast interior 259-1-2 glass chilled margin 259-1-2 matrix glass X262AD 274-1 13-301-1 (2 analyses) 109AC coarsely vesicular glass 109AC finely vesicular glass 109AC glass between microlites in microlite-rich areas (all 9 analyses) 109AC glass sites 8–9 (all 10 analyses) 108A1 bulk groundmass (all 5 analyses) 108A1 glass between microlites 108AC glass between microlites (site 1)

1 1 1 1 Ohinewairua middle pink ash 2 2 2 2 2

130 – 110 101 – 118 140 100 105 –

879 – 896 901 – – 868 905 901 –

175–100 175–100 175–100 125–5 400–25 125–5 175–100 125–5 125–5 400–25

5 5 5 5 25 5 5 5 5 25

1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700

1 1 1 1 1 1.5 1 1 1 1

2 2

– –

– –

175–100 175–100

5 5

1200–700 1200–700

1 1

2

–

–

125–5

5

1200–700

1

2 2 3 4

106 125 108 –

892 879 895 –

125–5 175–100 125–5 175–100

5 5 5 5

1200–700 1200–700 1200–700 1200–700

1 1 1.5 1

4

–

–

125–5

5

1200–700

1

4

–

–

175–100

5

1200–700

1

4 5 6 6

148 125 54 88

839 877 971 947

175–100 125–5 125–5 125–5

5 5 5 5

1200–700 1200–700 1200–700 1200–700

1 1 1 1.5

6 6 6 6 6 Pinnacle Ridge Tuff Te HeuHeu welded spatter 8A 8A 8A

88 99 103 – 132 – – 105 – –

948 910 886 – 863 – – 887 – –

125–5 125–5 125–5 125–5 175–100 200–75 200–75 100–5 400–25 400–25

5 5 5 5 5 5 5 5 25 25

1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700 1200–700

1.5 0.5 1.5 1 1 1 1 1 1 1

8A

–

–

100–5

5

1200–700

1

8B

–

–

100–5

5

1200–700

1

8B 8B

– –

– –

100–5 400–25

5 25

1200–700 1200–700

1 1

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Contributions to Mineralogy and Petrology (2018) 173:7

Table 4  (continued) Sample

PDC unit

Magma-meter results

Magma-meter parameters

P (MPa) T (ºC) P range (MPa) P step (MPa) T range (ºC) fo2 (Δ QFM) 108AC glass site 2 X108AD 108B1 glass between microlites X108BC glass between microlites 161A1 glass between microlites 161A1 glass bulk groundmass (all 5 analyses) X161AC glass between microlites X161AC matrix shards bulk (No limit) 12-225-19A 12-225-19A bulk (all 5 analyses) Ring plain M1 light separate

8B 8B 9B 9B 10 10

– – – – – –

– – – – – –

200–75 100–5 400–25 100–5 100–5 100–5

5 5 25 5 5 5

1200–700 1200–700 1200–700 1200–700 1200–700 1200–700

1 1 1 1 1 1

10 10

54 –

1001 –

200–75 100–5

5 5

1200–700 1200–700

1 1

11 11 M1

– – –

– – –

125–5 125–5 125–5

5 5 5

1200–700 1200–700 1200–700

1 1 1

Fig. 9  Frequency of calculated pressures from Mt. Ruapehu. The calculated pressures range from ~ 50 to ~ 150 MPa, with the majority of the calculations in the 100–150 MPa range. Our results suggest a lack of pressures in the 120 MPa bin; however, more data are needed to assess the potential significance of this gap

mineral compositions are not used for this method, as their compositions can change (e.g., zoning, sieving, etc.). The mineral phases can be used in the geobarometer as long as they had sufficient time to equilibrate with the melt. For the microlite-free clasts from Mt. Ruapehu’s PDC deposits, glass compositions should in general represent the pre-eruptive melt composition. For microlite-rich clasts, glass analyses were measured in small regions between the microlites, and thus represent the glass composition modified by microlite growth. This reflects the crystallization conditions at the time of microlite growth, and hence may reflect conduit conditions rather than the main storage zone. Many of the microlite-rich samples from PDC Units 8–10 did not return pressure estimates, and this likely reflects the difficulties in obtaining good glass compositions when targeting very small regions between microlites. Sample 161AC (PDC Unit 10), which contained microlites of plagioclase and orthopyroxene and clinopyroxene, was unequivocally in equilibrium with its melt. Sample 108BC

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also contained plagioclase and pyroxene microlites, and several other samples from PDC Units 8–10 had nearly identical microlite textures suggesting they too had convincing evidence for equilibrium with the melt. The fact that these samples, therefore, did not return pressure estimates provides convincing evidence of the sensitivity of the geobarometer, since it appears to have discarded the glass compositions that were taken from very small areas between the microlites, and hence were likely to be unreliable.

Results from Mt. Ruapehu For the 40 glass compositions, 13 yield a triple junction pressure based on a minimum residual temperature of ≤ 8 °C (see Table 4). Pressures obtained range from 50 to 150 MPa, which corresponds to magma storage depths of 2.0–5.9 km assuming a crustal density of 2600 kg/m3. A total of 11/13 of calculated triple junction pressures range from 100 to 150

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Contributions to Mineralogy and Petrology (2018) 173:7

Fig. 10  Mt. Ruapehu pressure–temperature results from this study. The temperature range of the samples is 840–1000 °C, and the pressure range is 50–150 MPa. The black data points in the gray box are from PDC 1 and PDC 2; all other data points are labeled with PDC eruption. One shallow sample from PDC 2, the PDC 6 sample, and the PDC 8A sample are from mingled pumice, so may not represent storage conditions. When correlated to the PDC units, storage conditions through time emerge. The older PDC units are generally cooler and deeper, and accompanied large plinian eruptions (Units 1–4), while the younger PDC units are hotter and shallower and produced smaller vulcanian/subplinian eruptions (Units 8, 10)

MPa (3.9–5.8 km; see Fig. 9), which implies that magma is stored at relatively shallow levels in the crust. The fo2 ranges between ΔQFM + 0.5 to + 1.5 (~ ΔNNO − 0.5 to + 0.5), with the majority of samples producing a triple junction at ΔQFM = 1 (ΔNNO ~ 0). We only find viable pressures in cases in which magma is fluid saturated. This pressure range corroborates the results found by Kilgour et al. (2013), with all of our pressure calculations falling within their range of 50–230 MPa. This range of pressure indicates that Mt. Ruapehu has a relatively shallow magma storage system. The temperatures estimated by Kilgour et al. (910–1050 °C; Kilgour et al. 2013) are slightly higher than our reported temperatures (840–1000 °C).

Implications for Mt. Ruapehu evolution We combine the results from the geobarometer with the volcanological evidence presented in Cowlyn (2016) to gain insight into the evolution of storage conditions for magmas that led to Mt. Ruapehu’s recent (< 13.6 ka) PDC-forming eruptions. The distribution of pressures and temperatures calculated using the geobarometer directly correlate with Mt. Ruapehu’s eruption ages, showing a trend from cooler, deeper storage to hotter, shallower storage through time. The changes in storage conditions also correlate with significant changes in eruption style, magma composition, and changing vent configurations as outlined in Cowlyn (2016) and summarized in Fig. 8.

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The oldest PDC units (Units 1–3; 13.6–11.6 ka) have some of the most evolved compositions studied (67.85–70.32 wt% ­SiO2), and were stored in relatively deep and cool chambers (Fig.  10). Eruption from these deep chambers produced some of Ruapehu’s largest known plinian eruptions. Plinian activity culminated with the Okupata–Pourahu eruption that emplaced PDC Unit 4 (~ 11.6 ka; Pardo et al. 2011), and the geobarometer calculates that this was again erupted from a relatively deep and cool chamber consistent with the earlier plinian events (Fig. 10). However, deposit observations suggest that the Okupata–Pourahu eruption excavated a new vent close to the currently-active South Crater Area (Fig. 8; Pardo et al. 2011; Cowlyn 2016), and this was followed by a marked shift to much smaller vulcanian/subplinian eruptions similar in style to Mt. Ruapehu’s modern-day activity (Donoghue et al. 1995b). The results from the geobarometer suggest that the opening of the new South Crater Area vent during the eruption of Unit 4 resulted in significant changes to Mt. Ruapehu’s magma system. This is reflected by the youngest and least evolved units studied here (Units 8 and 10–9 did not produce a pressure calculation; <11.6 ka; 60.77–73.75 (most <65) wt% ­SiO2), which ascended to much shallower storage zones beneath South Crater due to the now relatively unblocked ascent pathways (Fig. 10). Active degassing of these small, hot, and shallow magma bodies is interpreted by Cowlyn (2016) as a significant factor in the shift to smaller scale vulcanian/sub-plinian activity and cessation of plinian eruptions at Mt. Ruapehu. These examples highlight the utility of the geobarometer for not only determining the pre-eruptive storage conditions, but for also using the results to gain insight into the eruptive behavior at intermediate volcanoes like Mt. Ruapehu.

Conclusions and future work In this work, we present a new geobarometer for glass-bearing rocks containing the mineral assemblage plag + opx + cpx. The immediate outcome of this model is to determine the conditions, particularly pressure, temperature, fluid saturation, and fo2 , at which magma is stored and crystallizes prior to eruption. We test the geobarometer with experiments from the literature, and we show that: (1) when conditions are successfully calculated by the geobarometer, the results are consistent with experimental conditions. This suggests that, when successful, the geobarometer retrieves appropriate conditions. (2) When experiments do not yield viable conditions for the coexistence of plag + opx + cpx with melt of the given composition, this may indicate inaccuracies in the glass compositions. We use the geobarometer to constrain storage conditions of magmas from Mt. Ruapehu, New Zealand. Our results for Mt. Ruapehu suggest a

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correlation between pre-eruptive magma storage conditions and eruption style. The geobarometer can be run using a new version MELTS_Excel (Gualda and Ghiorso 2015), which will be made available on the rhyolite-MELTS website. Acknowledgements  Funding support provided by NSF grants EAR1151337 to Gualda and EAR-1321924 to Ghiorso, by University of Canterbury Doctoral Scholarship, the University of Canterbury Mason Trust Fund, a Project Tongariro Memorial Award and a Royal Society of New Zealand International Mobility Fund Grant (IMF14-02) to Cowlyn.

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