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v13n1 Supplement — Putirka “Methods and Further Reading”

Methods and Further Reading by Keith Putirka 

Supplement to the February 2017 (v13n1) issue of Elements.

Disclaimer: this table was not reviewed by Elements nor were its contents verified.


Calculating Clinopyroxene and Amphibole Pressures

Clinopyroxene pressure and temperature estimates use Eqns. P1 and T2 of Putirka et al. (1996) for anhydrous systems (Hawaii) and the thermometers and barometers of Putirka et al. (2003) for hydrous systems (e.g., Cascades, Andes). For some Cascade systems (e.g., Lassen Peak) a new barometer appears to work slightly better, providing better matches for tests of equilibrium. In this new barometer, below, XiCpx are mole fractions of jadeite (Jd) and Diopside + Hedenbergite (DiHd) in clinopyroxene, and Xiliq terms are cation fractions of the indicated oxides (see Putirka 2008):

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This new barometer works best when paired with the thermometer expressed as Eqn. 33 in Putirka (2008).

Pressures are converted to depths using the density model of Hill and Zucca (1987), from which the following equation is derived: depth (km) = -2.77x10-5[P4] – 2.0x10-3[P3] - 4.88x10-2[P2] + 3.6[P] - 6.34x10-2, where P is in kbar.  At the Cascades, P-T estimates make use of Putirka et al. (2003), whose models are designed for hydrous and SiO2-rich systems; the density-depth models of Mavko and Thompson (1983) and DeBari and Greene (2011) are used to convert pressure estimates to depth (km): 2.4x104[P3] - 2.11x102[P2] + 3.66 [P] + 0.46, and where P is also in kbar. Cascade data are from GEOROC; Hawaiian data are as in Putirka (2008). Two-pyroxene P-T estimates and Mauna Kea data are as in Putirka (2008); Mauna Loa gabbroic samples are from Gafney (2002), also using the two-pyroxenes thermobarometers of Putirka (2008). For the Andes, pressure is converted to depth using Prezzi et al. (2009), from which we obtain: depth (km) = 4.88 + 3.30[P] - 0.0137[P - 18.01]2.

Amphibole temperature estimates are from Eqn. 5 in Putirka (2016a), in which only amphibole compositions are used as input (independent of pressure). For the Cascades, we find that only the amphibole barometer of Anderson and Smith (1995) yields pressures that match those obtained from Cpx barometry (nearly identical mean P estimates, of ca.1 kbar); these are illustrated, converted to depth as above.

Mantle potential temperatures are calculated as in Putirka (2016b; see electronic attachment in that paper) and assume that the picritic parental magmas at arcs contain 2 wt. % H2O.

Calculating Magma Density

We use the silicate liquid density model of Lange and Carmichael (1990) for anhydrous systems, with the hydrous correction of Ochs and Lange (1999). Water contents for primitive Cascade magmas are probably closer to 1 wt. % H2O (Wallace 2005) compared to 3 wt. % as used here. But most arc basalts have 1-6 wt. % H2O (Wallace 2005, Table 1), so a middle value is used. For water-saturated magmas, bulk density is taken as a weighted fraction of silicate liquid and fluid, where fluid densities are calculated as in Holland Powell (1991). For crystalline magmas, we again take a weighted proportion of liquid and crystals, assuming all crystals are olivine, at 3.3 g/cm3.

A crucial aspect of our density calculations is that we estimate magma densities at the pressure and temperature conditions at which the magmas are stored, rather than comparing all magmas at, say, 1 atmosphere pressure. This more realistic approach is crucial in that absent such an approach, the density vs. MgO comparison yields a density minimum (at about 8 wt. % MgO). This minimum (as obtained for MORB, see Stolper and Walker 1980) disappears for the Cascades and Hawaii when density is calculated at P-T conditions of storage based on Cpx thermobarometry. This approach also shifts the absolute values for calculated density.

The best approach for correcting liquid densities for thermal expansion or pressure-induced contraction would be to use P-T estimates from Cpx + liq thermobarometers. To calculate density for a much wider array of compositions, though, thermobarometers are used that do not rely on the composition of equilibrium crystals.   In Figure 3, T is first calculated using the P-independent (liquid composition only) Eqn. 14 of Putirka (2008) as an initial estimate; this T estimate is then used to estimate P (see below), and this P estimate is then used to refine our T estimate, using Eqn. 15 (P-dependent, but again using liquid compositions only) from Putirka (2008). These two thermometers (Eqns. 14 and 15 from Putirka 2008) assume that such liquids are saturated with olivine ± other phases at the liquidus. The model appears to slightly over-estimate temperatures for rhyolites (estimates range from 850-1000oC) but should be roughly representative of liquidus temperatures for andesitic to basaltic liquids. To estimate P, the only analytic barometers available for liquids are based on Si-activity (Putirka 2008), but application of these yields negative pressures for a great many compositions examined here. However, the highest T estimates for Cpx (e.g., Fig. 1, but also in other studies, e.g., Armienti et al. 2013) yield rather coherent P-T trends, with a near constant dP/dT; these Cpx saturation conditions are judged likely to provide a useful approximation regarding the depths at which magmas stall and partially crystallize. So P is thus estimated using a simple regression high-T Cpx + liquid P-T estimates: P(kbar) = 0.0811[T(oC)] - 85.787, applying a P-estimate of 2 kbar for all cases where the model yields a pressure less than this value. Yet another method, not applied here, would be to regress Cpx-derived P-T estimates against liquid composition, and then extrapolate such a model to obtain P and T for compositions where Cpx compositions are not available.

The variety of basalts produced by mantle partial melting

It is now well demonstrated by experiments that a wide range of basalt compositions are produced by partially melting peridotitic mantle. We emphasize that picrities will pond and partially crystallize in the lower crust and upper mantle, but mantle partial melts can range down to as little as 6-8% MgO, according to some experimental studies and so can pond at a wide range of depths in the crust – a range made wider still by adding water. See Takahashi and Kushiro (1983), O’Hara (1968), Stolper (1980), Takahashi’s (1986), Kinzler and Grove (1992), Walter (1998), Gaetani and Grove (1998), and Pickering-Witter and Johnston (2000), which illustrate the wide range of basalt compositions that can be produced, depending upon, T, P and bulk composition, including water.

Deep Seismic Activity

We highlight Aki and Koyanagi (1981) for their relevance to our Hawaiian example, but more recent studies also indicate magmatically induced seismic activity at depths extending at least into the lower crust, notably Shelly and Hill (2011) at Mammoth Mountain in California and Okubo and Wolfe (2008) at Mauna Loa. And in a fascinating study, Greenfield and White (2015) show seismic evidence not only of magmatic movement in the lower crust beneath Iceland, but the possible seismic signal as magma is transferred through a dike from a deeper sill to a more shallow one.

Mantle Xenoliths

There are many studies of mantle xenoliths, which are important for understanding mantle composition (e.g., McDonough 1990) and mantle processes (Ducea and Saleeby 1996), and are an important part of the magma transport story (e.g., Spera, 1984). Many studies concern xenoliths erupted in continental interiors, but Arai and Ishimaru (2008) provide a nice review of mantle xenoliths from arc localities. Ross et al (1954) may have been the first to recognize that ultramafic xenoliths in volcanic rocks may represent mantle material, and so by implication, at least some volcanic rocks are sourced in the upper mantle.

Sr/Y ratios and Garnet Stability

Chapman et al. (2015) propose that high magmatic Sr/Y ratios might reflect partial crystallization at great crustal depths. But the issue is not simple. Basaltic magmas require pressures that are quite high to place garnet on the liquids. For example, experiments by Baker and Eggler (1983) show that Aleutian high-Al basalts can precipitate garnet at the liquidus P>17 kbar (they state 19 kbar in their abstract, but their phase diagram places the boundary at about 17 kbar), where it replaces plagioclase. Plagioclase is the liquidus phase at all lower pressures. But their basalts are quite low in MgO (<10%), and high in Al. More mafic magmas, as might characterize the picritic lavas that precipitate high Fo olivine, are much more likely to have lower Al2O3 and precipitate garnet at even greater pressures. Maaloe (2004) obtains garnet (not on the liquidus) at P>22 kbar. And Eggins (1992) did not find garnet on the liquidus of his high MgO liquids at any pressure. The moderate MgO basalts (4-6% MgO) that Baker and Eggler (1983) examined, are much more likely to rise to middle or upper crust depths, and so will precipitate plagioclase, amphibole or olivine, depending upon water contents and pressure. Garnet fractionation, and hence high Sr/Y ratios, are much more likely to occur by partial melting of pre-existing crust, rather than by fractionation of primitive, mantle-derived basalts.

Lower Crust

The composition of the lower crust is usually considered to be mafic (Rudnick and Gao 2003) but has recently become a topic of debate. Hacker et al. (2015), for example, suggest that the lower crust is much more felsic than traditionally understood. The idea stems, in part, from an inference that lower-crust P-wave velocities of 7.0 km/s may represent andesitic, rather than basaltic, bulk compositions (Behn and Kelemen 2003). This appears to be contradicted in a review of experimental data by Huang et al. (2013); they show that only basaltic compositions are likely to have such high P-wave velocities. In any case, the Hacker et al. (2015) interpretation feeds into models of lower crust evolution. For example, Ducea and Saleeby (1996) emphasize the precipitation of dense, mafic cumulates as being important for the formation of granitic curst, and these cumulates are themselves denser the underlying mantle and eventually “delaminate”, i.e., sink into the mantle. This delamination leads to passive upwelling of asthenosphere, which then initiates a new round of mantle melting. In contrast, Kelemen and Behn (2016), while they also accept some degree of delamination, suggest that “relamination” is more important for explaining lower crust composition at arcs. In this model, andesitic composition materials (sediments, plutons from the arc) from subaerial parts of the arc are fed into the trench and forcefully subducted, but only partially, eventually rising upwards to re-laminate the base of the arc crust (see Hacker et al. 2015, their Figure. 15).

Magma Transport and Eruption Triggering

We refer to Tait et al. (1989) in the main text for convenience, as they nicely build on the earlier work of Blake (1984) and Blake (1981), and present other ideas of eruption triggering that are still relevant today. But Daly (1911) almost certainly deserves some credit for appreciating the importance of volatile saturation as a triggering mechanism. And subsequent studies by Snyder (2000) are also important, while Fowler and Spera (2008) provide a nice follow up to Tait et al. (1989), using more detailed and realistic phase equilibria, for four model basalt compositions—their Figure 2 shows that magma overpressures increase at about 850-900oC, or in other words, just after the onset of amphibole saturation for many systems. However, it is not clear that amphibole, or any other phase necessarily acts as a “phase equilibria trigger”, but rather the triggering mechanism is a function of total crystallization, as inferred by Tait et al. (1989). Also, while we again refer to Sparks et al. (1977), in part for the plethora of ideas contained therein regarding recharge and eruption processes, Eichelberger (1980) provides another early study that was key in demonstrating how mafic recharge magmas, upon crystallization and by reaching vapor saturation, may induce magma mixing, and by implication, trigger volcanic eruptions. Eichelberger (1995) also provides a very nice overview of possible eruption triggering mechanisms. Also, discussions of magma mobility and transport are utterly incomplete without references to Bruce Marsh’s (1981) ideas about crystallinity; it is his recognition that magmas with >50-55% crystals are immobile that have vitally influenced ideas of magma transport.

Finally, while melt production in the mantle is discounted as a useful “ultimate” cause of melting in the main text, recent work by Poland et al. (2012) at Kilauea, Hawaii suggests otherwise. They suggest that melt production rates in the mantle may indeed provide a useful ultimate or even proximal cause of eruptions there, as tracked by deep-seated CO2 degassing. An interesting issue here is whether CO2 degassing represents magmas ponded in subcrustal sills (and so not necessarily connected to mantle melt production), or freshly delivered from even greater mantle depths.

Crystal Residence Times

The result that crystal residence times are in the range 103-105 years is nicely illustrated in Cooper and Kent (2014) and other works cited in that paper. Cooper (2015) shows that these resident times (age dates) might be no longer than the ages of the volcanic centers from which the zircon are derived. The issue is perhaps no better illustrated than at the Lassen Volcanic center, where Klemetti and Clynne (2013) show that almost no zircons yield age dates that match eruption ages, but few to none actually precede the formation of the Lassen Volcanic center. This indicates that recharge events probably heat felsic systems beyond temperatures of zircon saturation.


A key thesis of the main text is that progress will be made by better understanding the links between storage depths, cooling rates, and recharge input rates, and by using observations of such to better understand the various causes of eruptions. Snyder (2000) provides a nice summary of cooling rates and the effects of mafic/felsic magma ratios with regard to cooling of one and heating of the other. He argues that heating of the felsic magma by mafic recharge is a key trigger for large explosive eruptions, since the heat added to a felsic system (from the recharge magma) significantly decreases the solubility of water in such magmas. Hawkesworth et al. (2000) also provide an excellent summary of tools that can be applied to understand the time scales of magma storage and crystallization, which can be directly applied with thermometers and barometers to better understand eruption triggering mechanisms.


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