Rhyolites—Hard to Produce, but Easy to Recycle and Sequester: Integrating Microgeochemical Observations and Numerical Models

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Cenozoic Tectonics, Magmatism, and Stratigraphy of the Snake River 00969 1st pages / page 1 of 27 Plain–Yellowstone Region and Adjacent Areas themed issue

Rhyolites—Hard to produce, but easy to recycle and sequester: Integrating microgeochemical observations and numerical models

I.N. Bindeman1 and A.G. Simakin2 1Department of Geological Sciences, 1272 University of Oregon, Eugene, Oregon 97403, USA 2Institute of the Physics of the Earth, Bolshaya Gruzinskaya 10, Moscow, Russia

ABSTRACT genesis of rhyolites by recycling their some- the Snake River Plain and Yellowstone (west- times hydrothermally altered subsolidus ern USA) plume by McCurry et al. (2008) and Recent discoveries of isotopically diverse predecessors may be a common evolution- Whitaker et al. (2008). An alternative mecha- minerals, i.e., zircons, quartz, and feldspars, ary trend for many rhyolites worldwide, nism, partial melting of the lower basaltic crust in large-volume ignimbrites and smaller especially in hotspot and rift environments (Leeman et al., 1992; Dufek and Bergantz, lavas from the Snake River Plain (SRP; with high magma and heat fl uxes. Next, we 2005) has problems related to heat availability, Idaho, USA), Iceland, Kamchatka Peninsula, use thermomechanical fi nite element model- conduction, and the large amounts of basaltic and other environments suggest that this ing of rhyolite genesis and to explain (1) the magma required, often producing excessive phenomenon characterizes many silicic units formation of magma batches in stress fi elds amounts of associated cumulates (e.g., Beard studied by in situ methods. This observation by dike capture or defl ection as a function of and Lofgren, 1991; Petford and Gallagher, leads to the need for new models of silicic underpressurization and overpressurization, 2001; Ducea, 2001). Models involving fi lter magma petrogenesis that involve double or respectively; (2) the merging of neighbor- pressing, or reactivations of melts from cumu- triple recycling of zircon-saturated rocks. ing magma batches together via four related late piles and static or dynamic mushes, have Initial partial melts are produced in small mechanisms: melting through the screen advantages (e.g., conservation of latent heat and quantities in which zircons and other min- rock and melt zone expansion, brittle fail- space), but also signifi cant limitations on the erals undergo solution reprecipitation and ure of a separating screen of rocks, buoyant physical mechanisms of melt extraction and the inherit isotopic signatures of the immediate merging of magmas, and explosive merging slow rates of these processes (Wickham, 1987; environment of the host magma batch. Next, by an overpressurized interstitial fl uid phase Philpotts et al., 1996; Bachmann and Bergantz, isotopically diverse polythermal magma (heated meteoric water); and (3) mixing 2004; Huber et al., 2009; Streck and Grunder, batches with inherited crystals merge time scales and their effi cacies on extended 2008; Bindeman et al., 2008b). together into larger volume magma bodies, horizontal scales, as expressed by marker Many factors that militate against the produc- where they mix and then erupt. Concave-up method particle tracking. The en visioned tion of silicic magmas, including slow extrac- and polymodal crystal size distributions of advective thermomechanical mechanisms of tion, the room problem, and heat, are eliminated zircons and quartz observed in large-volume magma segregation in the upper crust may by a hypothesis of simple recycling of originally ignimbrites may be explained by two or three characterize periods of increased basaltic silicic or intermediate protoliths, which may episodes of solution and reprecipitation. output from the mantle, leading to increased have been formed by any or all of these slow and Hafnium isotope diversity in zircons demon- silicic melt production, but may also serve incremental processes. If rhyolites are thought strates variable mixing of crustal melts and as analogues for magma chambers made of to be produced by such recycling, estimates of mantle-derived silicic differentiates. The low dispersed magma batches. Although not the the total amount of silicic magma generated in δ18O values of magmas with δ18O-diverse focus of this work, dispersed magma batches a given magmatically active area, the amount of zircons indicate that magma generation hap- may be stable in the long term, but their basalt required, and the amount of heat required pens by remelting of variably hydrothermally coalescence creates ephemeral, short-lived become signifi cantly smaller. altered, and thus diverse in δ18O, protoliths eruptable magma bodies that erupt nearly A large-volume silicic eruption provides a from which the host magma batch, minute or completely. snapshot of an instant in the temporal evolu- voluminous, inherited low-δ18O values. This tion of a magma body; repeated eruptions over also indicates that the processes that generate INTRODUCTION millions of years give insights into petrogenesis zircon diversity happen at shallow depths of at depth (Lipman, 2007). However, the debate a few kilometers, where meteoric water can The origin of silicic magmas is a traditional over whether plutons and ignimbrites provide circulate at large water/rock ratios to imprint topic of igneous petrology that has fundamen- comparable records of magma genesis is ongo- low δ18O values on the protolith. We further tal signifi cance for the origin of the fi rst conti- ing, especially with reference to arc and col- review newly emerging isotopic evidence of nental crust (Hutton, 1794). It was recognized lisional environments, where batholiths may diverse zircons and their appearance at the early that fractional crystallization of basaltic be assembled over millions of years (Coleman end of the magmatic evolution of many long- magmas could only generate small, diffi cult to et al., 2004; Glazner et al., 2004; de Silva and lived large-volume silicic centers in the SRP extract, interstitial silicic liquids (Bowen, 1928; Gosnold, 2007) and magma bodies are kept and elsewhere, evidence indicating that the Tuttle and Bowen, 1958), recently advocated for near solidus.

Geosphere; October 2014; v. 10; no. 5; p. 1–27; doi:10.1130/GES00969.1; 19 ﬁ gures; 2 tables; 7 supplemental ﬁ les. Received 25 July 2013 ♦ Revision received 3 June 2014 ♦ Accepted 3 July 2014 ♦ Published online XX Month 2014

The study of the plume-related Snake River obscure their predecessors. At least six major m.y. Eruption of the ﬁ rst major tuff occurred Plain (SRP; Idaho, USA) silicic volcanism nested caldera clusters have developed over the after an ~2 m.y. hiatus from the last major erup- (Fig. 1) has an advantage over other areas of past ~15 m.y. (Fig. 1); current activity is cen- tion in the previous caldera center. The initial voluminous silicic volcanism because the North tered at Yellowstone. Each of the vol canic cen- Huckleberry Ridge Tuff of Yellow stone erupted American plate is moving at a speed of 2–3 ters is the site of several major caldera-forming at 2.1 Ma, after the 4.4 Ma Kilgore tuff, which cm/yr over the Yellowstone hot magmatic zone eruptions and overlapping calderas, although ﬁ nished activity at the Heise center to the south- (e.g., the hotspot and/or propagating rift; Pierce individual caldera boundaries are often obscured west, and the oldest Heise tuff, the 6.6 Ma Black- and Morgan, 2009), creating a conveyor-belt in the older 15–11 Ma centers. tail Creek tuff, erupted ~2 m.y. after the eruption record of silicic magma genesis as opposed to Recent work (Figs. 1 and 2) has demonstrated of the 8.3 Ma Pocatello tuff, the youngest tuff more stationary examples in convergent margins that Picabo, Heise, and Yellowstone, the three of the Picabo center (Fig. 1) (e.g., Christian- and subduction arcs, where volcanism occurs in most recent caldera clusters, share common sen et al., 2007; Morgan and McIntosh, 2005; a localized area and younger magmatic episodes features of magmatic evolution for the past 10.5 Drew et al., 2013). These relationships become

Syn and pre CRB silicic centers

Figure 1. Map of western North America showing essential magmatic and tectonic features discussed in the text (after Drew et al., 2013; Pierce and Morgan, 2009; Coble and Mahood 2012). The yellow dashed circle is the inferred infringement location of the Columbia River Basalt (CRB) plume head that resulted in basaltic volcanism such as the Steens and Columbia River Basalt Groups and scattered 16.7–15 Ma silicic magmatism (Coble and Mahood, 2012). Subsequent silicic volcanism, from ca. 13 Ma to present, along the Snake River Plain (SRP) was more organized and occurred in northeast-migrating caldera clusters resulting from the movement of the North American plate over the hotspot plume at a rate of 2 cm/yr (e.g., Pierce and Morgan, 2009); there were also contributions from rifting and coeval Basin and Range extension. There was a 1–2 m.y. gap before initiation of volcanic activity after the establishment of the new magma chambers with mantle input from the underlying mantle plume. Basaltiﬁ cation of the crust in the wake of the plume made crust infertile for further melting, resulting in a decrease of silicic volcanism; however, basaltic volcanism continued throughout the SRP after direct passage of the plume. 18 Occurrences of recycled rhyolites with low δ Omelt values and diverse zircons and other phenocrysts are found throughout the SRP and in some early post-CRB centers (underlined). The 0.704 (dotted black) and 0.706 87Sr/86Sr (dashed black) lines deﬁ ne the transition from accreted Mesozoic and Paleozoic terrain to the Precambrian ter- rains of North America (Fleck and Criss, 1985).

2 Geosphere, October 2014 00969 1st pages / page 3 of 27 Rhyolites—hard to produce but easy to recycle

YELLOWSTONE (2.1–0.07 Ma)

Quartz Plagioclase Clinopyroxene Zircon Obsidian Calculated melt δ18 O

Individual Zircon ranges (Fig. 3) A –3‰

HEISE (6.6–3.9 Ma)

B –1‰

PICABO (10.5–6.6 Ma) Idavada TAV 2.5 Mile HSpr TAF LRS SP SP2 Chokecherry

C Jim Sage W Pocatello –0.5‰

CPT V CPT III BRUNEAU-JARBIDGE CPT XIII CPT XI CPT XV (12.7–8.1Ma) CPT IX

CPT VII

– D CPT XII –

Figure 2. Temporal evolution of melt and mineral δ18O values in four caldera complexes. (A) Yellowstone. (B) Heise. (C) Picabo. (D) Bruneau-Jarbidge. The dashed line at 6‰ denotes the lowest possible normal δ18O rhyolite limit formed by crystal fractionation of normal δ18O, 5.7‰ ± 0.2‰ basalt. An overall decreasing trend in δ18O in the three youngest caldera clusters is explained by remelting of low δ18O hydrothermally altered materials after burial in calderas and rifts. Note the pervasive presence of low δ18O values in Bruneau- Jarbidge magmatism; our new data are plotted in D (larger symbols for minerals, see Table 1 for analyses). Other data (shown with individual unit abbreviations) are compiled from Bindeman and Valley (2001), Bindeman et al. (2008b), Watts et al. (2011, 2012), Drew et al. (2013), Wotzlaw et al. (2014), Boroughs et al. (2005), Bonnichsen et al. (2008) and Table 1; the ranges of the δ18O values of individual zircons (blue vertical bars) are from these studies and from Cathey et al. (2011) for Bruneau-Jarbidge (see Fig. 3). The origin of zircon and other phenocryst diversity is explained by segregation and mixing of isotopically diverse batches and is numerically modeled in this work.

Geosphere, October 2014 3 00969 1st pages / page 4 of 27 Bindeman and Simakin more obscure in the older and less-well-exposed units studied by in situ methods. We here sum- 2012; Boroughs et al., 2005; Ellis et al., 2010; central SRP centers (Fig. 1), including the Twin marize recent results of these investigations with Drew et al., 2013), and these rocks have gained Falls–Bruneau-Jarbidge centers, which also emphasis on the SRP. increasing attention as probes into upper crustal exhibited lingering silicic magmatism as young petrogenesis. Nearly all nested caldera clusters as 8–6 Ma (see Ellis et al., 2013, and references Zircon and Quartz δ18O Diversity and in the SRP have produced thousands of cubic therein), which were also likely infl uenced by Isotope Diversity in Other Minerals kilometers of rhyolites depleted in δ18O (the coeval rifting (Konstantinou et al., 2013), and volume of these magmas in the central SRP is are now buried by Quaternary SRP basalts. Early evidence of zircon and quartz δ18O 10,000–30,000 km3; Fig. 1; Bonnichsen et al., Ongoing investigation of the earliest ca. 15 Ma zoning and diversity in a few Yellowstone lavas 2008; Ellis et al., 2010, 2013), and individual vol canism before the Bruneau-Jarbidge center (Bindeman and Valley, 2001) has been observed units are as voluminous as 1800 km3 (Morgan (Colon et al., 2014), however, demonstrates in more than half of units studied in the Colum- and McIntosh, 2005). We advocate that the ori- a gap of ~1–2 m.y. between scattered post– bia River Basalt–SRP large igneous province gin of these magmas requires a two- to three- Columbia River Basalt volcanism and more (Figs. 1 and 3), and similar evidence is being step process: (1) hydrothermal alteration of the focused central SRP volcanism. The ~2 m.y. obtained for other areas (Fig. 4). This diversity protolith by low δ18O meteoric waters at large gap is suffi ciently long to generate the fi rst variably characterizes zircon δ18O, Hf isotopes, water/rock ratios; (2) remelting and convective voluminous silicic magma body at the begin- and sometimes older U-Pb ages from nearly mixing during which low and variable in δ18O ning of each caldera cluster cycle, compa- half of studied SRP tuffs and lavas erupted oxygen is homogenized in a newly formed rable to the Huckleberry Ridge Tuff batho- since ca. 15 Ma: Yellowstone (Bindeman et al., magma batch; and (3) formation of new crys- lith, ~5000–10,000 km3 in volume, assuming 2008b; Watts et al., 2012; Vazquez et al., 2009), tals representing batch-averaged δ18O compo- an erupted versus residual magma ratio of Heise (Watts et al., 2011), Picabo (Fig. 3; Drew sition, and repetition of 1 and 2. Washington 1:3. To produce these rhyolites, we therefore et al., 2013), Bruneau-Jarbidge and Twin Falls State University researchers favor the idea that favor slow incremental assembly of magma (Cathey et al., 2011), and the early post–Colum- step 1 signifi cantly predates step 2 (e.g., altera- by fractional crystallization of SRP basalt and bia River Basalt volcanism (Colon et al., 2014). tion preceding central SRP volcanism occurred melting of the lower crust in a hot zone (via The diversity of the refractory mineral zircon, during formation of the Eocene Idaho batho- sill emplacement; Annen and Sparks, 2002), the mineral with the slowest oxygen diffusion lith; Boroughs et al., 2005; Ellis et al., 2013), with insignifi cant contribution from the upper, rates, is not surprising, but diversity in δ18O while the University of Oregon group favors highly radiogenic crust, as is indicated by the quartz crystals is also present (Fig. 3). auto development of magmas from normal to modestly radiogenic values of rhyolites (Lee- In the SRP and in Iceland (Figs. 3 and4) there low δ18O values immediately before low δ18O man et al., 1992; McCurry and Rodgers, 2009), is common association of diverse zircon and eruptions via successive caldera collapse and or more rarely with an exclusively upper crustal quartz crystals with low δ18O magmas, indicat- rift burial (Bindeman et al., 2007; Watts et al., source (e.g., the Arbon Valley Tuff Member; ing their inheritance during remelting of buried 2011; Drew et al., 2013). Shallow crustal fi nger- Drew et al., 2013). Usual or slightly elevated and hydrothermally altered volcanic rocks printing by low δ18O meteoric water may also hotspot basaltic intrusion rates of 0.001–0.01 and their subvolcanic units (e.g., Carley et al., be accomplished via tectonically induced water- km3/yr (Pierce and Morgan, 2009) are suffi - 2011). However, there are also diverse zircons rock interaction during syngenetic rifting, core cient to explain the required volumes of silicic in several normal δ18O to moderately high δ18O complex formation, and alteration along normal magma to build the fi rst magma bodies that are rhyolites of the SRP, Iceland, and Kamchatka faults (Konstantinou et al., 2013; Drew et al., normal δ18O and have 60%–88% mantle con- Peninsula (Fig. 4). This suggests that nearly all 2013; Colon et al., 2014). Conditions for remelt- tribution to their radiogenic isotopes (Leeman studied low δ18O magmas worldwide, and some ing are optimized when the rocks are brought et al., 1992; McCurry and Rodgers, 2009; Nash nominally normal δ18O magmas, display δ18O down closer to the heat source during crustal et al., 2006). The rest of this paper deals with diverse zircons and sometimes other minerals. burial processes of caldera collapses, rifting, or the recycling of these fi rst magma bodies as a The isotopic fi ngerprinting of the upper crust both. Rifting and burial due to extension may chief mechanism of rhyolite petrogenesis. by low δ18O meteoric waters values thus serves have created additional hydrogeological condi- as a tracer of the processes of remelting and tions for hydrothermal fl uid circulation particu- GEOLOGICAL EVIDENCE FOR A recycling of hydrothermally altered rhyolites. larly in Iceland, where burial and alteration of RECYCLED ORIGIN FOR MOST If hydrothermal alteration happens at the sea- rocks were followed by remelting (Martin and SRP RHYOLITES AND MANY fl oor using 0‰ seawater, a spread from low to Sigmarsson, 2010; Bindeman et al., 2012; Figs. RHYOLITES WORLDWIDE high δ18O values will result (Grimes et al., 2013; 3 and 4). It seems highly unlikely that low δ18O Wanless et al., 2010; Bindeman et al., 2012), magmas are produced in any other way than The advent of microanalytical isotopic tech- potentially leading to high and low δ18O magma by remelting of hydrothermally altered low niques, i.e., single crystal laser fl uorination, batches. Finally, advocated processes may occur δ18O protoliths (for a review of old models, see isotopic dilution-thermal ionization mass spec- in nature even if the precursor rocks have not Taylor , 1974, 1986). trometry, single zircon analyses with high pre- been hydrothermally altered with respect to The remelting process happens in shallow cision, and ion microprobe analysis with worse δ18O, particularly in the lower and middle crust. depths available to meteoric water percolation, precision but superb spatial resolution, allows a thus requiring a shallow heat source to generate novel look at igneous petrogenesis. The rapid High δ18O, Normal δ18O, and Abundant thousands of cubic kilometers of magma in the and accelerating rate of discoveries of isotopi- Low δ18O Magmas in the SRP upper crust. It further reaffi rms, however, that cally diverse zircons, quartz, feldspars, and even if remelting occurs effectively in the shal- other minerals in large-volume ignimbrites and Throughout the past decade there has been low crust, magmatic recycling in the lower and smaller volume lavas worldwide suggests that rapid discovery of low δ18O magmas in the SRP middle crust should be even more prevalent, this phenomenon characterizes many silicic and worldwide (e.g., Bindeman et al., 2007, given higher temperatures and melt-segregation

4 Geosphere, October 2014 00969 1st pages / page 5 of 27 Rhyolites—hard to produce but easy to recycle

Age, Ma Age, Ma HRT 10.4 9.1 8.1 7.9 7.1 6.6 2.1 A B C 1.8 1.3 0.62 0.6–0.35 0.25 0.07 7 8 Picabo 10.4–6.6Ma Yellowstone 6.6–4.4Ma HRT cycle LCT MFT 6 7 A B LCT UBM CPM Qz 5 6

4 5

3 4

O(Zircon), ‰, SMOW ‰, O(Zircon), 2

18 δ

2 1

O(Zircon), ‰, SMOW ‰, O(Zircon), 1 18

0 A δ

0 Modern Mantle 0 –1

–2 –10 C –3 Age, Ma 6.6 4.8 4.4 –20 7 Hf(0) Heise 6.6–4.4Ma ε LostRiverSinks 6 Picabo Blacktail –30 Kilgore 5 post-Kilgore

4 –40 3 Archean Crust B

2 εHf

8 O(Zircon), ‰, SMOW ‰, O(Zircon),

–50 1 –14 –12 –10 –8 δ 3 1

18 δ 5 –1 D 6 –2

18 Figure 3. Individual zircon δ O and εHf diversity studied by in situ methods across the Snake River Plain (SRP) eruptive centers. (A) Picabo 18 18 18 zircon δ O. (B) Picabo εHf. (C) Yellowstone zircon δ O. (D) Heise zircon δ O. SMOW—standard mean ocean water. The range of normal δ18O zircons in equilibrium with mantle-derived magmas (5.3‰ ± 0.3‰; Valley, 2003) is shown by horizontal gray ﬁ elds. Pink horizontal 18 bars show equilibrium with melt zircon values (taken as Δ Omelt-zircn = 1.8‰) for each sample. Black vertical bars denote average ±2σ error on individual zircon δ18O analysis. Single crystal quartz analyses are by laser ﬂ uorination (Bindeman and Valley, 2001; error bars are 18 comparable to symbol size), and are only shown for units that demonstrate statistical diversity in δ OQuartz values. Most zircons and some 18 quartz are in disequilibrium with melt and are on both high and low sides of equilibrium δ O and εHf values; there are no zircons or quartz values lower than 0‰ to –3‰, although hydrothermal alteration by local meteoric waters is capable of generating –14‰ to –18‰ values.

The tremendous diversity of εHf data for Picabo and Heise (Blacktail Creek tuff) is shown in B and the inset in D; this range in values can result from pure melting of the low εHf Archean crust (orange ﬁ eld) or from silicic differentiation of basalts from the modern mantle. The U-Pb ages of these zircons are close to the eruption age with the exception of one Paleoproterozoic xenocryst shown by larger symbol in B. See text and Figure 5 for explanation. HRT, MFT and LCT are caldera forming tuffs of Yellowstone: Huckleberry Ridge, Mesa Falls and Lava Creek. UBM and CPM are post-LCT Upper Basin Member and Central Plateau Member rhyolitic lavas.

Geosphere, October 2014 5 00969 1st pages / page 6 of 27 Bindeman and Simakin

Isotopically diverse zircons from major ignimbrites around the world A SW Nevada B Iceland C Kamchatka 6 7 6 Qz: 5 Karymshina, 1.78Ma

Hekla, A.D. 1158

W W Laufafel, O

O 6 O Pleistocene M

M 4 S

M Pleistocene

S ,

, 5

‰ Pauzhetka, 0.45Ma

‰

, ‰

Askja, A.D. 1875 )

)

, n

) 3

o n

o 5

(

O 8

O 2

δ 18

δ 4 δ 4 1 ±2σ ±2σ cores ±2σ rims 3 0 3

D SW Colorado VF E Toba, Indonesia

Fish Canyon, Early, BFC125 Youngest Toba, Early, sample A102 Zircon in oxygen isotopic W equlibrium with melt O Qz: 8.13‰, Mt: 2.26‰

M Qz: 9.21‰, Mt: 3.22‰

Δ W

S T‚ (Qz-Mt)=760°C Δ Older zircon cores , O 7 T‚ (Qz-Mt)=752°C

‰

)

‰

)

(

18 Z δ cores σ ±2 ( σ rims O ±2

5 18 6 δ

cores rims

Figure 4. Zircon δ18O diversity in large- and small-volume ignimbrites from different tectonic settings around the world. SMOW—standard mean ocean water. Zircons from units in panels A–C were dated, and most returned U-Pb ages similar to Ar-Ar eruption ages, with the exception of zircons shown by larger symbols, which are statistically older by as much as 1 m.y. Core and rim analyses in A, D, and E are shown; B and C are for zircon core only. Pink horizontal bars show computed zircon δ18O values in equilibrium with host melt and major phenocrysts. Zircon diversity and corresponding Δ18O (melt-zircon) disequilibria range from equilibrium (Fish Canyon Tuff) and modest (Toba) to severe disequilibria (all other); in most cases, zircons are heavier than is required by equilibrium with host melt (pink bar). In the case of Hekla, Kamchatka, and Toba, cores are both heavier and lighter than equilibrium. Quoted precision shown as vertical bars on each graph refl ects uncertainty on standards run together with the unknowns and thus denote average ±2σ errors (95% confi dence) on individual zircon analyses. Mixing of both high- and low-δ18O magma batches are required to explain zircon diversity, see text and Figure 5 for explanation. Gray fi elds denote normal δ18O zircon values in equilibrium with mantle-derived silicic differentiate melt (5.3 ± 0.3‰; Valley, 2003). Data sources: (A) Bindeman et al. (2006), also note quartz δ18O diversity; (B) Bindeman et al. (2012) and Gurenko et al. (2013); (C), (D), and (E) new data from this study, Table 1, and the Supplemental Files. Data were collected in: (A) Wisconsin; (B) Nancy; (C) UCLA; (D) and (E) Alberta, on Cameca 1270-1280HR large radius ion microprobes. Note that Toba rims are in equilibrium with the melt. but cores spread a ~1‰ range, analytically resolvable due to superb precision by the University of Alberta Cameca 1280HR instru- ment (Richard Stern, analyst). Sample courtesy: BFC125–O. Bachmann, A102 (C. Chesner, see Bindeman, 2003, for crystal size distribution of quartz and zircon in this sample).

6 Geosphere, October 2014 00969 1st pages / page 7 of 27 Rhyolites—hard to produce but easy to recycle efﬁ ciency (Annen et al., 2006; Dufek and Ber- Multi-stage silicic magma recycling and sequestration to the upper crust gantz, 2005). Furthermore, this process must be

y relatively rapid, faster than mineral-diffusive UPPER CRUST: . Zircon T-t Destinies: and recrystallization time scales or currently m Sweet spot, partial eutectic a

e 1 the most precise geochronologic method, melting of silicic lithologies, r

< 2 4 t

batch assembly, mixing, eruption, <

ID-TIMS U-Pb dating (10 -10 yr; Wotzlaw r Zrc out δ18 , e

O p et al., 2014; see also the following and Binde- Y b solidus

zircons. Eutectic melting will e

T man, 2008). Both of these statements contradict A c cross diverse in δ18O and ε(Hf) areas, the currently prevailing view that silicic magma E time further rejuvenate U-Pb ages , are generated slowly (because it takes effort; T

see above), and in the lower crust (where it is A hotter), or via ﬁ lter-pressing extraction from the F mushy batholiths. Hydrothermal preconditioning of

intruded silicic rocks or batholith tops u

Insights from Zircon Hf Isotopes and δ18 a

generates diverse and low in O areas r

e solidus

Whole-Rock Sr-Nd-Hf-Pb Isotopes p

T In situ radiogenic isotope analyses provide time further insights. The Pb and Sr isotope diversity of individual feldspar crystals within single UPPER TO MIDDLE CRUST: .

y units (Watts et al., 2012) further ﬁ ngerprint the Silicic sills accumulation or . isotopic sources of Yellowstone lavas. Diverse batholith formation, m

future multiple recycling of 2

Sr and Pb isotopes in individual feldspars are a – well-known phenomenon worldwide (Davidson this batholith, further sequestration 1 of silicic magmas > et al., 2001), suggesting that many crystals are , D b a

R xenocrysts and antecrysts. Mixing generates average ε(Hf), r

A 18 c t The Hf isotopes within individual zircons rejuvenated U-Pb age, normal δ O a r Zrc out

p record crust/mantle melt proportions of each silicic rocks; Intrusion to the upper to , a b solidus

m magma batch from which the zircons crystal- middle crust W e T c lized (Figs. 3 and 5). In two extreme cases when O L time a silicic differentiate of the SRP crystallizes S ε high (mantle like) Hf zircon mixes with a pure ε LOWER TO MIDDLE CRUST: partial melt of silicic crust (ultralow Hf) zircons, the resulting fi nal magma may have extremely ε diverse Hf zircons (see Fig. 3B). While the segregate silicic melts with blended evidence for diverse Hf isotopes in zircons is ε(Hf) and δ18O values growing, preliminary data suggest that both homogeneity and heterogeneity of Hf isotopes in zircons is common in SRP magmas (Picabo: Figure 5. Model of multi-stage vertical delegated sequestration of silicic, zircon-saturated Drew et al., 2013; Yellowstone: Stelten et al., magmas leads to multiple recycling of zircons, blending together their oxygen and Hf iso- 2013). Nonetheless, sporadic ultralow-Hf zir- topic values and rejuvenating U-Pb ages. Slow initial segregation of small volume melts ε cons (Fig. 3; down to –47 Hf units; Drew et al., from mafi c protoliths and differentiates of basalts is contrasted by the rapid process of 2013) suggest addition of melts of Archean crust remelting of already segregated silicic materials containing diverse zircons. Different poten- during the late stages of magma segregation; in tial zircon temperature-time destinies are shown (e.g., A, B, C; see text). ε most cases ultralow Hf zircons have reset U-Pb ages, suggesting that remelts of the Archean crust appeared and then crystallized new zircons 18 before mixing with other magmas. Ranges of δ O and εHf Variations in Protolith canic intrusions (e.g., Taylor, 1974, 1986), and Ranges. Given the –14‰ to –19‰ δ18O intracaldera tuffs (McConnell et al., 1997; John Isotopically Diverse Crystalline Cargo: value of meteoric water, it is theoretically pos- et al., 2011) demonstrate higher and narrower Inheriting Isotopic Variations from sible to generate a volume of rock (or a vein) δ18O ranges (–2‰ to +7‰). Thus, the lack of Protolith with comparable δ18O values if the temperature observed –18‰ to –14‰ values in zircons and of exchange were >500 °C, meteoric water was quartz (Fig. 3) is partly a refl ection of incom- Gaining insights into the range of isotopic isotopically unshifted at these depths and tem- plete water-rock isotope exchange of their values and their spatial distribution within a perature, the water/rock ratio was high, and/or protolith, shifted waters, and a lower tempera- proto lith undergoing melting are important for the isotope exchange was 100%. Investigation ture of hydrothermal alteration. Another argu- our future modeling of the effi ciency of melting of hydrothermally altered intracaldera tuffs and ment is purely hydrologic; in order to expect and mixing and the mechanisms of incorpora- ore deposits around the world suggests that such a high water/rock ratio, high porosity and tion of these parameters into zircon and other conditions are rarely realized in nature. Isotopic permeability (open cracks) are required, and minerals (Fig. 4). ranges in and around shallow plutons, subvol- this is best achieved above the brittle-ductile

Geosphere, October 2014 7 00969 1st pages / page 8 of 27 Bindeman and Simakin transition (e.g., Norton et al., 1984). For silicic sands of zircons studied by in situ methods for in the lower layer. This process is not static and volcanic rocks these temperatures are likely to U-Pb age, only a few older xenocrysts survive. involves melting through the separating rocks be below ~400–450 °C (Simpson, 1985). Given This suggests that any partial melts of older by hot magma pulses (e.g., Simakin and Binde- Δ18 Orock-water fractionation (e.g., Cole and Charra- crust were heated above zircon saturation (e.g., man, 2012), mixing and diking between magma borthy, 2001), rocks are several permil higher in Fig. 5). In all of the subsequent melting history, batches, and segregation by buoyancy; these δ18O than equilibrium water at ~400 °C, further as shown in Figure 6, all processes lead to aver- processes are thermomechanically modeled in reducing the lowest possible δ18O rock value in aging out of isotopic differences, causing solu- the following. This set of processes is called hydrothermally altered rock. tion reprecipitation of zircons and other miner- bulk cannibalization (Bindeman, 2008; Watts Spatial δ18O distribution. Does the protolith als. Prolonged residence leads to oxygen isotope et al., 2011) and is similar to the reactive bulk typically contain a frequently spaced, centi- equilibrium between coexisting minerals, and assimilation model of Beard et al. (2005) and meter- to meter-scale network of isotopic varia- further homogenization of hydrothermally Bacon and Lowenstern (2005). tions such as ultralow δ18O veins in a normal induced heterogeneity. δ18 ε O matrix, or ultralow Hf Archean crustal An important insight into the partial remelt- Batch Assembly, Preeruptive Mixing of ε slivers in high Hf matrix? The isotopic varia- ing of hydrothermally altered rocks with and Melts, and Diverse Crystalline Cargo tions that we observe in zircons and other min- without zircons is provided by the Skaergaard Leading to Diverse Crystals erals will then have a highly localized (centime- intrusion in East Greenland (Taylor and For- ter to meter scale) origin. Partial melting of such ester, 1979; Norton and Taylor, 1979; Bindeman The advanced stages of segregation of areas will generate lenses of low-δ18O melt as is et al., 2008a). Following crystallization and 10–100 m magma batches lead to further aver- observed inside granodiorite blocks of the cli- hydrothermal alteration of the Skaergaard intru- aging out of isotope diversity of magma, but mactic Mt. Mazama eruption (e.g. Bacon et al., sion, the mafi c Basistoppen sill had intruded bring together isotopically-diverse crystal cargo 1989) or in remelted Icelandic crustal xenoliths 100 m above the hydrothermally altered sili- with diverse zircons. Because diffusion of oxy- (Gurenko et al., 2013). If such high-amplitude ceous Sandwich Horizon. The melting of Sand- gen and Hf is the slowest in zircons, the zircons variations span across wide regions undergoing wich Horizon at near eutectic compositions provide the best memory effect of the described melting (e.g., 8‰ δ18O variation over >40 km generated partial melt inside of the matrix of multistage segregation, while other minerals for the Kilgore tuff; Watts et al., 2011), this will rock of moderately diverse δ18O (Bindeman undergo greater reequilibration. Most impor- simplify not only the effi ciency of subsequent et al., 2008a; Wotzlaw et al., 2012). These low- tant, the majority of zircons are out of isotopic mixing, but may also help with mass and heat degree (<20%) silicic partial melts are diffi cult equilibrium with the fi nal melt they are erupted balance problems of extraction of small-vol- to extract; however, minerals in them become in (Figs. 3 and 4), which suggests that a preerup- ume, zircon-saturated melt batches with diverse isotopically equilibrated and zircons partially tive mixing episode was effi cient and isotopi- zircons. This extraction may be facilitated by reset their U-Pb ages and acquire oxygen and cally homogenized the melt. dikes and sills generated by external tectonic hafnium isotopes refl ecting each minute magma forces (e.g., Norton et al., 1984). Natural evi- batch. In the remelted Sandwich horizon of Textural Evidence of Recycling in Crystals dence, however, suggests that high-amplitude Skaergaard, isotope diversity of zircons occurs variations with limited isotopic magnitudes of on the 10–102 m scale (Bindeman et al., 2008a), Abundant bright cathodoluminescence rims several permil are also accompanied by larger a scale we use for modeling. The Skaergaard in quartz and zircon provide evidence of recy- scale (10–103 m) variations across greater iso- example is evidence that there are no extreme cling of as much as half of the crystal mass due topic magnitudes, but the detailed structure of δ18O values in the partial melts of variably to remelting processes, and the time between this variation still needs to be studied by isotope hydrothermally altered rocks, as iso topic dif- melting and mixing on the batholithic scale mapping. Mapping of bullseye alteration pat- ferences induced by heterogeneous isotopic is measured in centuries (Gualda et al., 2010; terns over plutons (e.g., Taylor, 1974, 1986), alteration (Taylor and Forester, 1979) are further Pamukcu and Gualda, 2010). The observation remote sensing of alteration products, and isoto- averaged out by melting process in line with the by Poldervaart (1956) that zircons in granites pic investigation of alteration in intracaldera tuffs reasoning above (Figs. 5 and 6B; stage III). The are have log-normal size distributions is sup- (McConnell et al., 1997; Livo et al., 2007; John Sandwich horizon recrystallized 20 k.y. later ported by investigations of zircons and other et al., 2011) provide concentric patterns of δ18O (Wotzlaw et al., 2012), without extraction of phenocryst phases in single pumice clasts from variation (10–103 m scale). Moreover, numeri- this partial melt, which only underwent limited major tuff units (Fig. 7; Bindeman, 2003). In cal modeling of meteoric fl uid fl ow through intercumulus fl uid fl ow (Tegner et al., 2009). Simakin and Bindeman (2008) we analytically porous media in one dimension (Bowman et al., If the Skaergaard intrusion had another sill computed that the abundant concave-down crys- 1994) and two dimensions (Norton and Taylor, intrusion soon after Basistoppen, and/or if the tal size distribution of zircons and quartz may be 1979) suggests predominance of continuous Basistoppen sill intruded closer to the Sandwich explained by only 1–3 remelting episodes that isotopic fronts with diffusive-hydraulic disper- horizon, it could have resulted in greater degree recycle the outermost 10%–30% of quartz or sion around fast pathways, isotopically shifted of partial melting approaching the extraction zircon radii (Fig. 7). Delayed nucleation leads waters, and overlapping, time-integrated fronts window of ~50% melt (Marsh, 1981; Wick- to concave-up distribution and often a lack of leading to laterally smoothed δ18O distribution ham, 1987; Dufek and Bachmann, 2010; stage the smallest zircon and quartz crystal sizes. on a scale of meters to kilometers (Hayba and V in Fig. 6B) and would have segregated silicic Ingebritsen, 1997). melt. Furthermore, if the sill intruded directly Time Scales as Recorded by Crystals under the Sandwich Horizon, partial melting Isotopic Reequilibration During Remelting: of this laterally confi ned eutectic area would Isotopic diversity in zircons occurs within Lessons from Skaergaard have been more effi cient, and large fraction error of U-Pb ion microprobe age dating (Watts Figures 3 and 4 demonstrate the large iso- partial melt extraction would have been thermo- et al., 2011; Drew et al., 2013) or even ID- topic diversity of zircons; however, among thou- mechanically driven by the viscous convection TIMS age dating with the precision of several

8 Geosphere, October 2014 00969 1st pages / page 9 of 27

Rhyolites—hard to produce but easy to recycle

R e t e n t i o n o f m i n u t e m e l t

s thousand years (Wotzlaw et al., 2014), but O

2 mineral-diffusive time scales suggest even shorter time scales of mixing. Because oxygen

water out

1.5 kbar 4

3wt% H s l a t s y r c diffusion in quartz is >10 times more rapid

f o e c

n a t i

r e h n

I than in zircons (Watson and Cherniak, 1997; , w o d n i w n o i t c a r t x E Plag out

Eutectic Range Cole and Chakraborty, 2001), the preservation Qz out % crystals of isotopically zoned crystals in many units

Zrc out 100 ppm suggests short times (e.g., hundreds of years) between segregation, mixing, and eruption. In (W/A) ratios 200 ppm many other units quartz is isotopically annealed ion of a range in hes. Later zircon zircon hes. Later “bulk” melting Qz+San+Plag

alteration of rocks alteration of rocks due to residence times >~100 yr (e.g., Binde- San in, liquidus s and disequilibrium 0 25 50 75 man and Valley, 2001; Bindeman et al., 2006). tial melting only zircon, tial melting only zircon,

artially reequilibrated. c lithology is also shown Furthermore, Cathey and Nash (2004) and

650

900 850 800 750 700

C) T ( T O values. Incomplete equi- ° Ellis and Wolff (2012) presented evidence for 18 C δ

cult to extract. At low degree At low degree cult to extract. compositionally (Fe-Mg) polymodal pyroxene crystals in the Cougar Point Tuffs (Table 1), which are largely unzoned and record very high (900–950 °C) temperatures. Fe-Mg interdiffusion in pyroxenes is even more rapid than 850 C) of silicic compositions and disappearance

° oxygen diffusion in quartz, and pyroxene crys-

c (green) assemblages using rhyolite-MELTS assemblages using rhyolite-MELTS c (green)

B u l k C a n n i b i z a t i o n a merging, mixing, heating l

Eruption tals are typically small; the occurrence of such , i g t l n e l m a r i t a

P crystals can help further constrain time scales of extraction from the hot, once recycled, low

batch δ18O crystal batches or mushes that underwent melting

assembly

t s l e m e t u n i m , s u d i l o

S very rapid preeruptive mixing.

760

i t c e l u

d Tasks for Numerical Modeling

melting –1‰

aters

+7‰

ed The microanalytical isotopic evidence men- e l t t i r

b 350 shift tioned here directs the numerical efforts. We aim O on a small scale shown by zigzag pattern (dotted black line). (B) Isotopic 18

δ to quantify our above observations on (1) efﬁ cacy

Temperature, °C, increasing with time Temperature, of melting and formation of magma batches, 200 alteration values higher than water, and shifts water to higher to higher and shifts water than water, values higher (2) efﬁ cacy of merging together of initially sep- C (see A and text for explanation). III: Heating the rocks above solidus results in the above solidus results explanation). III: Heating the rocks and text for A C (see ° rock

hydrothermal arated batches, (3) efﬁ cacy of mixing by con- O

18 vection and other processes involved in merging δ I II III IV V Water Rock the magma bodies with diverse crystal cargos, 10 and (4) the time scales of these processes, as well as the conditions when magma mixing is

–2

+2 +7

‰ ,

B O interrupted and magma bodies erupt.

–14 δ 1 8

METHODS

k c o r , ‰ , O

δ 8 1 5 0

–5 For this work we used proprietary written –10 –20 –15 and relatively simple two-dimensional fi nite element code to model of convection of incom- pressible fl uid at low Reynolds numbers (plug Albite Quartz Kaolinite Chlorite fl ow approximation), valid for small magma

—temperature. Note extended near-isothermal eutectic melting range (725–750 Note extended near-isothermal —temperature. sills with vertical dimensions of as much as T ~30 m. Additional calculations were performed

small W/R small on larger grids covering 100–1000 m to analyze

ned by the particular temperature-composition path of each magma batch (see Fig. 5). V: Subsequent creation of voluminous and Subsequent creation V: path of each magma batch (see Fig. 5). temperature-composition ned by the particular the mechanics of large-scale batch assembly,

Starting Rock from small magma batches through slow vis-

Temperature (°C) Temperature cous deformation of the frame rocks; numerical values at large water/rock ratio and temperatures <~400 ratio and temperatures values at large water/rock details are described in the following. We also rock O

brittle, W/R large performed several more roof melting + mixing 18 sanidine (San) and sometimes quartz (Qz) will be inherited as xenocrysts or antecrysts (Plag—plagioclase). Melting of mafi sanidine (San) and sometimes quartz (Qz) will be inherited as xenocrysts or diffi of partial silicic melts that are in low degrees range of eutectic melting resulting comparison with a narrow for will be p and zircons of partial melting (such as observed in Skaergaard; see text), interstitial minute melts will be retained paths are defi paths are (C) Results of melting experiments two silicic (beige and blue) one mafi eruptable magma body. (Gualda et al., 2010). At a likely melt extraction window above ~50% of par concentration. (Zrc) levels of zircon at different of minerals and zircons zircon compositions (similar to what is observed in Skaergaard; see text). IV: Continuing melting leads to growth of magma batc Continuing melting leads to growth to what is observed in Skaergaard; see text). IV: compositions (similar zircon appearance of low-degree partial melts in areas with eutectic compositions (see Fig. 5), resulting in diverse crystalline cargo with eutectic compositions (see Fig. 5), resulting partial melts in areas appearance of low-degree Figure 6. Modeling of hydrothermal alteration, remelting, melt extraction, and segregation. (A) Isotope effects of hydrothermal melt extraction, and segregation. alteration, remelting, 6. Modeling of hydrothermal Figure alteration at high water/rock by equilibrium isotope fractionation. Complete hydrothermal and minerals as expressed disequilibrium exchange will generate local diversity in librium and/or above the brittle-ductile transition will generate a range of diversity in rocks during progressive hydrothermal alteration and subsequent melting. I–II: Hydrothermal alteration and generat alteration and subsequent melting. I–II: Hydrothermal hydrothermal during progressive diversity in rocks δ experiments (started in Simakin and Bindeman, Silicic protoliths 2012; technical details provided therein). Pres-

Mafic sure was eliminated from the Navier-Stokes protoliths 50 150 250 350 450 550 650 750 A

5 0 equations with the penalty formulation (King

30 25 20 15 10 –5 2 O mineral-H 1000 ln 1000 O α

18 et al., 1990). Material transport is modeled by

Geosphere, October 2014 9 00969 1st pages / page 10 of 27 Bindeman and Simakin

Lagrange markers with 10× fi ner resolution in by mixing via convective melting; the roof col- Physics of Batch Assembly in each spatial dimension. The typical grid was lapses, leading to inheritance of partial melts and Stress and Density Fields 180 ×180. The code was tested with the ana- isotopically diverse crystalline cargo, in which δ18 ε lytical solution for the convection in the liquid O and Hf in zircons survive the longest (e.g., We consider simple numerical models with with sharp viscosity contrasts (Trybitsyn at al., Fig. 2). The melting processes of silicic, near two vertically separated and offset magma sills 2006). Further technical details and material eutectic, often glassy rocks are incredibly rapid (Figs. 9 and 10 and Supplemental Files 44, 55, and properties of magmas and country rocks are and energy effi cient (Fig. 8; Simakin and Binde- 66) and explore conditions of when and how these listed in Table 2. man, 2012), and serve as an energy sink, with sills can merge, and exchange and mix their crys- minimal heat dissipation to the environment. talline cargoes. In the following we employ scal- RESULTS OF NUMERICAL We thus consider several fi rst-order thermo- ing analyses, numerical experiments, and con- EXPERIMENTS mechanical mechanisms of growth and differ- sider relevant physical aspects of large magma entiation of larger volume magma bodies in the body assembly from batches in a stress fi eld. Formation of Larger Magma Bodies upper crust, assembled from these melts, and those that were produced in situ. These shal- Formation of Magma Sills and Batches Melting and generation of small magma low magma bodies should be at least as large Each magma batch forming in situ by melt- batches for hotspot and rift environments were and as hot as the volume and temperature of the ing, or those arriving from below into the zone numerically modeled in Simakin and Binde- observed erupted ignimbrites, i.e., 102–103 km3, of accumulation, can mechanically interact with man (2012) and continued in this work (Fig. 8; but likely more than twice that given that some neighboring batches if they are close enough see Supplemental Files 11, 22, 33). We model residual magma will remain in the crust. to each other, or with a large dominant magma multistage generation of eruptable high-silica reservoir. This interaction occurs through the rhyolitic magma bodies (Fig. 5). The fi rst is Expansion of the Melting Zone thermomechanical infl uence of the stress fi eld generation of silicic melts in the hot zone near With addition of heat and mass from below, around each magma sill that controls the genera- the Moho or lower crust (e.g., Annen et al., the upper crustal magma body may simply grow tion and direction of dike propagation (Fig. 9A). 2006) by differentiation of basalt and melting by expansion of the melting zone if magma While there are multiple studies of the interact- the lower mafi c crust; these dry and near-liqui- addition is faster than cooling. Continuous sup- ing vertical dikes (e.g., Takada, 1994a, 1994b), dus silicic melts rise up rapidly, carrying heat ply of new hot silicic differentiates of basalt to there are limited analytical or numerical simula- and undergoing further adiabatic decompres- the base leads to rapid upward expansion of tions of the mechanical interaction of a magma sion and overheating in pressure-temperature- the melt zone and sinking of separating screen reservoir and a rising dike. Field observations X compositional space. They are then intruded rocks. High versus low basaltic power outputs (e.g., Horsman et al., 2009) from some shallow into the upper crustal silicic lithologies defi ning (Lipman et al., 1972; Hildreth, 1981; Lipman, silicic intrusions of ~1 km in diameter document rheological or density traps, i.e., hydrothermally 2007; de Silva, 1989) determine particular that when small magma batches are emplaced altered portions of the silicic batholith or under temperature-time trends and the subsequent successively, magma bodies internally infl ate low δ18O silicic caldera fi ll (Figs. 5 and 6). For- lifetimes of each of these magma bodies, perti- then spread laterally, forming a series of silicic mation of these small, ephemeral magma bodies nent to the isotopic reequilibration of inherited sills emplaced on top of each other, creating proceeds rapidly, in which roof-rock melting of crystalline cargo (Figs. 5 and 6). voluminous silicic stocks. isotopically distinct protolith is accompanied Subsequent analysis of the interaction Merging by Melting Through between magma batches and a rising dike often Separating Screen Rocks employs consideration of the principle stress 1Supplemental File 1 is a generic melting by hot We envision that areas of melting and shapes (σ ) directions around a magma reservoir, rhyolite intruded into cold, solid rhyolite, both with 1 realistic phase diagrams (see Simakin and Binde- of magma bodies are initially complicated (e.g., defi ning approximate trajectories for diking man, EPSL, 2012). If you are viewing the PDF of Figs. 5 and 6) and may be originally determined via hydraulic fracturing of rocks (Jellinek and this paper or reading it offl ine, please visit http:// by country-rock composition, areas of higher dx.doi .org /10 .1130 /GES00969 .S1 or the full-text glass content (so less latent heat is needed), and 4 article on www .gsapubs .org to view Supplemental hydrated areas of hydrothermal preconditioning. Supplemental File 4 shows batch merging in File 1. gravitational and stress fi elds in viscoplastic crust, as 2Supplemental File 2 is a simulation of the bridge In addition, hydrothermal redistribution of silica described in Fig 9 and 10 of text of the paper. If you failure by “melting it through” without considering and alkalies will create local silica oversatura- are viewing the PDF of this paper or reading it offl ine, gravity or stress fi elds leading to subsequent mixing; tion conditions, favoring lower temperature please visit http:// dx .doi .org /10 .1130 /GES00969 .S4 The lower magma is a hot rhyolite with T=870°C, the eutectic melting in selected areas. Furthermore, or the full-text article on www .gsapubs .org to view upper is cold, near solidus rhyolite with T=730°C, Supplemental File 4. the green bridge is solid, higher melting T. If you are screens of higher melting temperature rocks 5Supplemental File 5 shows batch merging in viewing the PDF of this paper or reading it offl ine, may separate low-temperature eutectic rhyolite gravitational and stress fi elds in viscoplastic crust, as please visit http:// dx .doi .org /10 .1130 /GES00969 .S2 lithologies. Figure 8 and Supplemental File 2 described in Fig 9 and 10 of text of the paper. If you or the full-text article on www .gsapubs .org to view (see footnote 2) demonstrate such a scenario of are viewing the PDF of this paper or reading it offl ine, Supplemental File 2. amalgamation by two melt zones via the melting please visit http://dx .doi .org /10 .1130 /GES00969 .S5 3Supplemental File 3 is a melting run emphasiz- or the full-text article on www .gsapubs .org to view ing two refractory blocks in the roof rock, which through of separate screen rocks with different Supplemental File 5. have higher melting temperature (e.g. slivers of pre- silica contents. Stopping of these screen areas 6Supplemental File 6 shows batch merging in caldera ancient rocks). They release potential energy will lead to the release of gravitational energy, gravitational and stress fi elds in viscoplastic crust, as upon fall, promote mixing, and carry down frozen-in enhancing convective mixing. The thermo- described in Fig 9 and 10 of text of the paper. If you rhyolitic material. If you are viewing the PDF of this are viewing the PDF of this paper or reading it offl ine, paper or reading it offl ine, please visit http://dx .doi mechanics of convection play a more important please visit http://dx .doi .org /10 .1130 /GES00969 .S6 .org /10 .1130 /GES00969 .S3 or the full-text article on role than silica oversaturation (as also observed or the full-text article on www .gsapubs .org to view www .gsapubs .org to view Supplemental File 3. in Simakin and Bindeman, 2012). Supplemental File 6.

10 Geosphere, October 2014 00969 1st pages / page 11 of 27 Rhyolites—hard to produce but easy to recycle

1010 n -4 C io t 9 lu HRT-C o B s is h dissolutiond t w o 8 r growthg

, ln (n/LV), cm

6 HRT-A Kilgore Tuff 5

MFT 4 dissolution

LCT-A 3

new growth

2 HS14 2017B

Relative Abundance per cm Relative

1 HS10

0 5050 100100 150150 200200 250250 Zircon Long Axis, μm

Figure 7. Textural and crystal size distribution evidence for recycling of quartz and zircon. (A) Cathodoluminescence images of recycled zircons with variable δ18O values but similar ages from the Heise complex Kilgore tuff suggesting rapid preeruptive assembly of diverse magma batches. (B) Normalized (to the largest crystal) crystal size distribution (CSD) of zircon and quartz in Huckleberry Ridge Tuff C (HRT-C) of the Yellowstone Group requiring two solution-reprecipitation episodes, each recycling between 0.36 and 0.55 fractions of crystal mass, or 10%–20% of crystal radius (Simakin and Bindeman, 2008). Recycling was likely caused by changing temperature conditions during batch assembly, given the strong zircon and quartz diversity in this sample (Fig. 3; HRT-C).

DePaolo, 2003; Simakin and Ghassemi, 2010; (Fig. 9B) capable of growing into a separate, growing magma body in sites of active magma Karlstrom et al., 2012). This analysis leads to independent magma body with a continuing generation and high intrusion rate. At reduced the observation that for the overpressurized supply of magma. Pressure lower than litho- magma supply rates, crystallization and there- deep spherical magma reservoir (equally inelas- static may develop in a magma body with a low fore underpressurization of magma will pro- σ tic, viscoelastic, or viscous media), 1 directions supply fl ux during the solidifi cation of magma mote formation of separate magma batches, are such that the greatest compressive stress is due to the volume effect of crystallization and but underpressurization conditions may even σ radial to the magma body and 3 is tangential escape of exsolved fl uid phases, and due to exist at some high supply rates (Gregg et al., (Fig. 9). For the underpressurized magma res- extensional tectonics. Numerical simulations 2013). An additional factor promoting separate ervoir, principal stress directions are transposed of viscoelastic elliptic chambers (see Sima- magma batch formation may be preexisting σ and 1 becomes tangential. Our numerical kin and Ghassemi, 2010) demonstrated that at oblique faults that serve as structural traps for model shows (Fig. 9B) that an overpressurized magma pressures lower than lithostatic pres- rising magmas and relieve stress from over- magma body attracts a dike, causing it to propa- sures, expressed through the bottom-parallel pressured magma bodies (Fig. 9B; Simakin and σ gate radially and coalesce with the magma body, 1 stress directions, the rock envelope presses Ghassemi, 2010). This is particularly relevant thus causing the magma body to grow. into the chamber and undergoes radial exten- for Basin and Range faults and extension along When an underpressurized magma body sion. These arguments support accumulation of the SRP (Fig. 1), or any other silicic magma defl ects a dike, it may produce a separate sill newly arriving batches of magma into a single generation in rift zones.

Geosphere, October 2014 11 00969 1st pages / page 12 of 27 Bindeman and Simakin

TABLE 1. NEW LASER FLUORINATION ANALYSES OF QUARTZ, CLINOPYROXENE, AND PLAGIOCLASE OF COUGAR POINT TUFF UNITS IN THE BRUNEAU JARBIDGE ERUPTIVE CENTER AND THE KILGORE TUFF OF THE HEISE CENTER δ18O, ‰ SMOW Elevation Sample ID Qz Plag, or glass Cpx Magma* Latitude Longitude (ft) Description Bruneau Jarbidge Eruptive Center, Central SRP 2005-ID-14 CPT-III, 12.7 Ma 4.02 3.52 41°57.602′ 115°39.810′ 5355 Rowland, Pack trail 2005-ID-13 CPT-V, 12.07 Ma 4.53 1.68 3.8 41°57.602′ 115°39.810′ 5381 Rowland, Pack trail 2005-ID-3 CPT-VII, 12.8 Ma 0.71 0.21 41°55.995′ 115°25.402′ 5771 Deer Creek Rd 2005-ID-12 CPT-IX, 11.6Ma 2.52 0.62 2.02 41°57.610′ 115°39.786′ 5486 Rowland, Pack trail 2005-ID-5 CPT-IX, 11.6Ma 2.52, 2.64 2.08 41°55.227′ 115°25.716′ 5145 Deer Creek Rd 2005-ID-7 CPT-XI, 11.3 Ma 3.26 2.76 41°56.138′ 115°25.403′ 6347 Deer Creek Rd SB173† CPT-XII, 11.2 Ma – –0.91, –1.15 –1.92 –0.9 Deer Creek Rd 2005-ID-8 CPT-XIII, 10.79 Ma 3.67 3.22 3.27 41°56.517′ 115°25.363′ 6432 Deer Creek Rd 2005-ID-9 CPT-XIII, 10.79 Ma 3.62 3.16 41°56.576′ 115°25.336′ 6593 Deer Creek Rd 2005-ID-2 CPT-XVj, 10.5 Ma 3.61 3.08 2.58 42°02.7859′ 115°36.3833′ 5161 Murphy Hot Springs Twin Falls and Heise Centers INB-1 Shoshone Falls rhyolite, Twin Falls – 0.31 0.3 42°35.8333′ 114°24.11′ 3078 Twin Falls 2017B Kilgore Tuff, Heise, 4.4 Ma 3.62 2.75 (glass) 1.28 2.9 44°07.8′ 112°32.4′ NW of caldera Note: All data were analyzed in the University of Oregon Stable isotope lab; see Fig 2 for plotted data. *Samples were collected using descriptions from Bonnichsen (1981) and Cathey and Nash (2004). The effort was made to extract and analyze alteration-resistant minerals quartz and clinopyroxene to check and complement published bulk feldspar data (Boroughs et al., 2005; Bonnichsen et al., 2008). †sample kindly provided by S. Boroughs; * calcuated from phenocrysts

Merging of Vertically Stacked Magma Batches We also simplify our analysis also by neglect- fl ow as viscous material at slow deformation Sills that were closely spatially emplaced are ing complex and fast thermally activated pro- (Gerya, 2009; Kaus and Podladchikov, 2006). separated by bridges (or screens) of country cesses inside sills, such as convection, melting, Scaling analysis defi nes the Debora number, η rocks, or crystal mush if emplacement happens and crystallization, thus concentrating only on De = /Gt0, as a measure of viscoelastic behav- into a cooling and crystallizing batholith (Figs. the viscous (slow) deformation of the rocks. ior, in which η/G is the characteristic time of 10–13). If certain mechanical conditions of Viscoelastic materials (Maxwell viscoelastic- viscous relaxation of the deviatoric stresses, G interaction are met, these bridges can fail, caus- ity) behave elastically at fast deformation and is the shear modulus, and t0 is the time scale of ing sills to merge to form bigger magma bodies (e.g., Schofi eld et al., 2010, 2012a, 2012b). We consider two basic controls on the TABLE 2. SYMBOLS AND PHYSICAL PARAMETERS USED IN THIS PAPER mechanical interaction between sills: overpres- Δρ 3 density contrast between magma and rocks →s-→m, kg/m 100–1000 sure (Fig. 10), and the density contrast between 0.25 (convection), 30–200 m l length scale equals size of the element in numerical grid, m magma and country rocks (Figs. 11–13). In 0 (slow deformation) the modeling approach used here, when slow h viscosity, Pa·s 104–1018 h 8 13 motion of country rocks is simulated, dimen- 0 viscosity scale, Pa·s 10 –10 η η η 5 nondimensional viscosity / 0 1–10 sions of computational domain increase to tens η Δρ Ra Rayleigh number, Ra = 1 at t0 = 0 / gl0 40–120 of kilometers at the same grid size. In our simu- Δρ P0 pressure scale gl0 /Ra lations the viscosity contrast between deform- λP overpressure, MPa ing rocks and magma was set to 104.5, similar t time scale, Ra η /Δρgl 0 0 0 typical value 1 yr 5 τ to the maximum viscosity contrast 10 used by t/t0 Bittner and Schmeling (1995) for the modeling G shear modulus, GPa 5–50 σ of the Rayleigh-Taylor instability of the melting stress, MPa σ scaled stress σ/P front in the underplated silicic crust; this value 0 Sy yielding stress, MPa is less than the real ratio between hot coun- 0.1–150 Sy scaled Sy /P0 try rocks (1017–1018 Pa s) and silicic magma · ν Poisson’s ratio 5 6 ν 0.15–0.5 (10 –10 Pa·s). However, further increase in u undrained the viscosity ratio (above 104–105) has no effect B Skempton’s poroelastic coefficient 0.6–1. 0 α thermal (T—temperature) expansion coeffi cient of fl uid 9 10–4 (T = 800 °C) on the numerical solution for slow deforma- T,fl φ porosity 0.01–0.3 tion of rocks. It allows us to portray large-scale 0 C pressure conductivity, m2/s 5 10–3–1.3 10–5 slow features (this does not require accounting 2 –6 kT thermal conductivity, m /s 10

for the inertia term in the Navier-Stokes equa- pﬂ ﬂ uid pressure, MPa tion) instead of modeling the fast processes R circular shell radius

with the 10 cm scale resolution used for melt- h thickness: hsill = sill, hb = bridge between sills ing processes. Consideration of a far greater U diapir rise velocity, m/day viscosity ratio or equally high Rayleigh number V magma chamber volume W sill semiwidth (km) (Ra) requires a supercomputer approach (Longo 1/2 geometric factors, nondimensional parameters involving β <1; see text et al., 2012) for implementation of the inertia characteristic spatial dimensions. terms and integration of the small and large time δX marker horizontal displacement, m δ δ 0–30 m and spatial scales, but does not change our out- Xm X averaged over magma volume δ δ come for slowly deforming rocks. R pair of markers separation initial R0 = 2.5 cm

12 Geosphere, October 2014 00969 1st pages / page 13 of 27 Rhyolites—hard to produce but easy to recycle

700°C ABaround the magma sill arises at the very beginning of deformation, and changes slowly with the expansion of the sill, often leading to dike initiation. When the level of stress, a product of the second invariant of strain rate and viscosity, exceeds the yield stress of country rocks (Fig. 10), the screen rock between magma batches fails. Shear strain localization is facilitated by means of dynamic power law (DPL) rheology (proposed by Sleep, 2002, and developed by Simakin and Ghassemi, 2005, and Simakin, 2014, and references therein) to produce sharp, fracture-like shear zones (Fig. 10). The DPL model treats viscosity as a dynamic parameter accounting for the effect of the texture evolution and described by a system of ordinary differential equations on the material Lagrange parti- 850°C cles. As an asymptotic limit at a ﬁ xed strain rate (ė),the DPL model yields an ordinary power-law CDviscosity law [η = a(T)/ėm] where T is temperature, a is a some temperature-dependent parameter, and m is an exponent coefﬁ cient used in description of power laws (e.g., Becker, 2006). Calculations were performed in nondimensional form. Since density is uniform at the overpressure approximation (i.e., we consider magma overpressure over the lithostatic), the gravity term can be dropped by setting the Ray- leigh Number, Ra, to 0. Stresses and viscosity

are scaled with some pressure (P0) and time

scales of deformation (t0):

= η=η Sy Sy/P0 , /P0 /t0. (1)

In these calculations nondimensional viscosities η = 5 of the frame rocks are kept at r 10 and magma η = = m 1 with yield stresses at Sy 50–200. In the Figure 8. Simulation of the bridge failure by melting through leading to subsequent mix- following text we will use symbol Sy for the ing in the entire magma body. The simulation does not account for gravity or stress fi elds. scaled yielding stress. Then, for example, at P0 The lower magma is a hot rhyolite at 870 °C. The upper two layers are fully crystalline = 1 MPa, the physical value of Sy will be 50–200 rhyolites near solidus at 730 °C. The green bridge is a solid, silicic rock with excess quartz MPa. Time scales can be found by setting rock η η (45%);the lower and upper layers have 35% normative quartz. Box size is 30 m. (A) 0 days. viscosity t0 = r / r /P0. With the relatively low η 18 (B) 19 days. (C) 22 days. (D) 27 days. viscosity of the country rocks r = 3.0 10 Pa·s, close to the value estimated for the thermal aureole of the magma chamber underlying the the process. When De < 1, mechanical evolution slow deformation of the rocks around magma Long Valley Caldera (Newman et al., 2006), and of the viscoelastic solid can be approximated by sills below the brittle-ductile transition depth, pressure fi xed at P0 = 1 MPa we get a time scale 18.5–6-5 7.5 viscous fl ow. The viscous fl ow approximation of typically at 400–450 °C. for deformation t0 = 10 = 10 s, or ~1 yr. the deforming crust is likely the correct case, as In our experiments the normalized sill expan- τ is suggested by geodetic data on surface defor- Effects of Overpressure sion rate dV/V0/d was ~0.01 or 0.01/t0 = mation above an overpressurized magma cham- We investigated the effects of overpressure 0.01 yr–1 for the above parameters. By increas-

ber, data that include the volume of the rocks on a pair of vertically stacked sills (Fig. 10), ing P0 we proportionally increase the rock yield

in the thermal aureole (Newman et al., 2006). with the deeper sill undergoing gradual inﬁ ll strength Sy and the physical expansion rate of Newman et al. (2006) suggested that the thresh- at a constant volumetric rate. For this purpose the magma. In other words, these nondimen- old viscosity for liquid behavior of the thermal we use a vertical conduit of rectangular shape sional results can be interpreted equally with 15 aureole is 3 × 10 Pa·s (G = 5 GPa), and De ≤ (Fig. 10) and apply a parabolic vertical magma the choice of a high ﬁ lling rate and high Sy, or

0.26 for several months (global positioning sys- ascent velocity (with zero values at the walls) at a low ﬁ lling rate and small Sy, as these are lin-

tem and interferometric synthetic aperture radar the inlet. This sill inﬂ ates with time, inducing early interrelated. The linear scale, l0, remains

observations). The viscous approximation used viscous stress. At a given ﬁ lling rate, a quasi- arbitrary. Possible limits of l0 are constrained by in the following is therefore most likely valid for steady-state stress ﬁ eld in the country rocks the absolute intrusion rate (km3/yr). Results of

Geosphere, October 2014 13 00969 1st pages / page 14 of 27 Bindeman and Simakin

τ σ =Δ αη dV/d A b P= , (3) V0 σ where b is the stress component normal to the boundary (radial for circle inclusion) of the expanded sill, and α is some geometric factor <1, which depends on the particular geometry of the system; α can be determined analytically or numerically (Simakin and Ghassemi, 2010). For α 2 a circular cavity in the shell = 1 – (R1/R2) or 2 (R1/R2) = 0.5, which corresponds to equal volumes (areas in 2-D) of magma and rocks in the thermal aureole, α = 0.5. For an elliptic chamber and viscoelastic rocks the numerically estimated value of this coeffi cient is 0.32 (recalculated from Simakin and Ghassemi, 2010). By setting α τ B = 1/3, P0 = 1MPa, and dV/d /V0 = 0.01, we get an estimate of 333 MPa for the viscous stress in the bridge. These numerical experiments (Fig. 10) demonstrate how the process of thin bridge failure between closely spaced magma lenses proceeds in 2-D. In particular, they show that the bridge is initially faulted at one end at the very beginning of deformation and then rotates upward onto and into the upper sill as a handle or trapdoor, eventually giving way for lower magma to fl ow into the upper sill. The thicker bridge between magma lenses yields two fractures, leading to the extrusion of a part of the bridge in a piston- like fashion into the upper magma body (see Fig. Figure 9. Infl uence of overpressure and underpressure in both a spherical or sill-like 10); we call this mechanism an internal caldera single magma chamber will either cause dike attraction or defl ection. (A) Generalized pic- collapse. Our analysis also demonstrates that ture showing principle stress 1 (S1) around an underpressurized and pressurized circu- widely spaced magma batches can coexist for a lar magma chamber determining trajectories of dikes. (B, C) Numerical modeling of dike long time without interaction, and homogenize attraction and defl ection in a more complex stress fi eld involving a reverse Basin and Range their crystalline cargo and whole-rock chemical fault and free upper boundary (from Simakin and Ghassemi, 2010). B is an overpressurized and isotopic composition on time scales of cool- magma body, C is an underpressurized magma body. Chamber underpressure may lead ing. For example, Wilson and Charlier (2009) to dike defl ection, but also formation of an independent thin sill below the original magma demonstrated coeval, probably lateral, reser- body. If overpressure in the dike is stronger than in the chamber, the dike will be absorbed. voirs separated by ~20 km at the Taupo volcanic Here we assume that stress fi eld around a dike’s tip decays faster than stress fi eld around zone (New Zealand). The numerical results here chamber, with many orders of magnitude larger curvature. The dashed orange line depicts were obtained exclusively due to an overpres- saucer-type sill growth along the calculated σ1 direction. The continuous black line depicts sure response in the viscous media without con- the edge of a saucer-type sill resulting from analogue modeling (Galland, 2012). The dotted sidering density terms, which we consider next. line corresponds to the shape of the reconstructed sill in the Karoo Basin (South Africa; from Polteau et al., 2008). The black lines were scaled with conservation of proportions. Infl uence of Magma Buoyancy Blue line is a fault or frictionless contact surface. When sills are intruded into suffi ciently soft country rocks or into a crystal mush, the density difference between the magma and surrounding 2 dV/dt the numerical experiments with varying S and a ΔP=(1− (R /R ) )η , (2) media leads to slow deformations due to buoy- y 1 2 V constant fi lling rate (0.01) show that bridge fail- 0 ancy. In the set of stacked magma lenses (sills), ure occurs at Sy < 150 (150 MPa at P0 = 1 MPa). there are two possible mechanisms for buoyant

This confi rms that the order of magnitude scal- where R1 and R2 are internal and external (R1 < rise: (1) the large-scale diapiric rise of one or ing estimate of the viscous stress in the bridge R2) radii of the 2-D circular cavity fi lled with two magma bodies, thinning and disrupting the is correct, since 150 MPa is close to the typical liquid. The external radius in these approxi- screen rocks between, causing the merging of shear strength of the rocks (Barton, 2013). mations is defi ned as an elliptic envelope of these into a single magma body; and (2) devel- Overpressure defi nes the amplitude of the deformation, which coincides with the brittle- opment of Rayleigh-Taylor instabilities of the induced stress, and for the expanded two-dimen- ductile transition (Newman et al., 2006). In the plastic screen rocks separating the sills. Our sional (2-D) circular shell around a magma body case of two cavities next to each other, we can numerical experiments (Figs. 11–13) show that it was shown to be (e.g., Jellinek and DePaolo, expect the level of stress in the separating screen diapir-like motion always prevails in the set of 2003; Simakin and Ghassemi, 2010): rock to be: the stacked sills, as opposed to Rayleigh-Taylor

14 Geosphere, October 2014 00969 1st pages / page 15 of 27 Rhyolites—hard to produce but easy to recycle

A B

Figure 10. (A) Numerical modeling of merging magma bodies together at different nondimen-

sional country-rock yield strength (Sy, in MPa; see text) but identical magma and country- rock density. Viscosity of country rocks is 1018 Pa·s. The overpressure is created due to slow inﬁ lling of the lower reservoir by the feeder dike. (B) Flow structure in dike. See Supple- mental Files 4, 5, and 6 (see footnotes 4, 5, and 6) for temporal evolution movies. Note the various regimes of screen-rock failure. Three

models with Sy = 50 MPa differ in the shape of the connecting dike.

instability of the separating screen rock. Diapir- geometry for the various density contrasts and both sills has nondimensional radius 32. Because like motions are driven by horizontal density contrasts in viscosities and linear sizes, but on low-density material ﬁ lls only part of this large gradients. For diapiric batch rise, the maximum different time scales. The characteristic diapir circle, correspondence seems to be satisfactory.

fl ow rate during approximately one nondimen- velocity for a sill semi-width W can be com- Dimensional velocity of the diapiric fl ow (Ud) sional unit of time varies slowly, and the verti- pared with corresponding Stokes rise velocity strongly depends on the physical parameters. In η 13 cal position of the screen midpoint rises linearly Us of the sphere (3-D) or circle (2-D): a crystal mush environment with at r = 10 Δρ 3 above the ascending fl ow of the lower sill (Fig. Pa·s, l0 = 40 m, = 300 kg/m , and geometry = 2Δρ η 12B). For suffi ciently weak screen rocks, vis- Us kS R g/ r , (4) as in Figure 11, we obtain Ud = 6 m/day with cous stresses overstep the shear strength (yield maximal rise rate of as much as 4 m/min during stress in the frame of the viscoplastic rheology), where for a solid sphere kS = 2/9, for a solid plastic failure. Sills intruded into stiffer rocks η 18 resulting in sharp, fracture-like shear zones circle kS = 1/4, and for a gas 3-D bubble kS = 1/3; with r = 10 Pa·s, a value typical for a ther- splitting the screen rock and surrounding rocks, all values are for slow fl ow at small Re numbers. mal aureole of an intrusion, will undergo dia- thus facilitating further deformation. Our numerical experiment is not identical to any piric rise at a velocity of 2 cm/yr; i.e., a diapiric Numerical models of the buoyant rise can be of these geometrically idealized models. While component can only contribute little to the com- further rationalized with simple scaling analy- tentatively setting kS = 1/3, for the half-width of monly observed deformation rates of as much sis. With the nondimensional Navier Stokes the sill, W1/2, we rearrange the equation for Us in as several meters per year associated with sill equation, we use time scale t0, length scale l0 nondimensional form as: intrusion. The main factor of uplift in this case (size of the element grid), and viscosity scale is magma overpressure. l W l 2 η . Pressure (stress) scale is derived as P = Ra 0 ( 1/2 / 0) 0 0 Us = . (5) η 3 t (ηr /η ) 0/t0. With choice of the time scale equal to 0 0 Cooling and Deformation Rates η Δρ t0 = 0/ gl0 Rayleigh number (multiplier in Another important time scale involved is that

the scaled gravity term) becomes unity and P0 = Numerical nondimensional maximum ﬂ ow of the cooling and solidiﬁ cation of magma bod- Δρ gl0. If Ra is set larger than unity (for practi- velocity at the beginning of the experiment ies. Unlike salt diapirs, driven by a density insta- η η 5 = 0.18 cal considerations), then t0 = t0Ra. Thus gravity ( r/ 0 = 10 , Ra = 120, Us ) can be approx- bility without temperature contrast with country

ﬂ ow develops identically with the ﬁ xed initial imated with W1/2/l0 = 21.2 while circle inscribing rocks, magma sills cool and solidify; therefore,

Geosphere, October 2014 15 00969 1st pages / page 16 of 27 Bindeman and Simakin

A important on the cooling time scales (3–300 yr) inferred for the relatively small, 10–100-m-thick magma sills considered in this work. For Ra = 2 at β = 0.067 it yields small viscosities in the range of 1012–1015 Pa·s that are probably typical for crystal mushes (Lavalee et al., 2007) or for some nonwelded pyroclastic rocks and hyalo- clastites. For rock viscosity 1018 Pa·s, a value typical for rocks near the brittle-ductile transition and in thermal aureoles of intrusions (e.g., Newman et al., 2006), and to satisfy Equations 6 and 7 for Ra = 2 and Δρ = 300 kg/m3, the sill

sizes are W1/2 = 2165 m, and W1/2 = 3702 m, if the Ra = 10. Therefore, a signifi cant increase in size is required to compensate for an increase in viscosity, and so only less viscous bridges are capable of deformation due to buoyancy for B geologically realistic thicknesses and cooling time scales. Initial smooth deformations are accelerated and modifi ed after plastic failure of the surrounding rocks. For the geometry presented in Figure 10 we fi nd that the threshold nondimen-

sional yield strength, Sy providing for plastic failure of the bridge, rises linearly with Ra and

is 18 at Ra = 80. The dimensional value of Sy can be recalculated via natural scale for pressure as:

= Δρ Sy Sy l0g/Ra. (8)

With Δρ in the range 300–500 kg/m3 and l in Figure 11. Initial stage of the slow viscous deformations in the set of two stacked sills 0 the range 40–100 m, we estimate S as 10–120 (Ra = 80, initial log[η /η ] = 5, S /P = 16, R = 500 m, Δρ = 300 kg/m3; see text and Table 2 for y r o y 0 kPa. Such low values of S are compatible only abbreviations and symbols). Numbers on vertical and horizontal axes are nondimensional y with shear strength of the nonwelded pyroclas- linear coordinates in units of l0. Color coding strip denotes log(η /η ). Physical values of r o tics at the effective mean stress approaching parameters are on right (see Fig. 10). (A) Flow fi eld at the time, t = 0.232. (B) Viscosity distri- zero (σ = 10 kPa, S = 30–350 kPa, Cecconi bution at t = 1.19. Yielding stress is reduced to scaled value of 16 in the elliptic zones around n, eff y et al., 2010) or crystal mushes (S = 0.14 kPa sills partially seen as low viscosity areas; beyond these zones S is 200. y y for the solid fraction of isometric crystals, 50% and less; Hoover et al., 2001; or 0.3–4.3 kPa; Philpotts and Carroll, 1996). in order to be effective, the time of the screen- 10 increase in the sill half-width W1/2 requires Our analysis demonstrates that buoyancy rock instability and the ability to fail between a viscosity increase by a factor of 1000. The does not play a signifi cant role in the merging of 2 magma sills by diapiric fl ow (tb = hb/Us, where condition of the buoyant rise time scale over small (10–10 m) magma batches, unless they hb is screen or bridge thickness) should be less the conductive cooling time scale can be thus are already located in a weak mush. The brute than the characteristic conductive heat dissipa- expressed as this nondimensional quasi-Ray- force buoyancy approach in this case requires 2 tion time t1: t1 = hsill /kT, where hsill is half-thick- leigh number multiplied by the geometric fac- that magma batches are already of magma ness of the sill, and kT is thermal conductivity. A tor. The geometric factor allows comparison of reservoir size, >~15km, in order to cause dia- ratio of these two time scales gives: nondimensionalized parameters for different piric rise, but such sizes may cause caldera col- η geometric confi gurations. lapse (e.g., Ramberg, 1970; Geyer et al., 2006; = = hb tb hb /Us 2 de Silva et al., 2006; Gregg et al., 2012). Δρ 3 2 W1/2 g ΔρgW β 1/2 β 1 hsill t1 /tb = η 1, = . (7) and kT r 3 hbW1/2 Overpressure Versus Buoyancy—What 2 Δρ 3 Controls the Merging Processes and Stability = 1 hsill gR t1 /tb η . (6) β 3 hb R kT r The geometric factor ratio is proportional of Multibatch Magmatic Systems? to the product of the inverse aspect ratio Figures 10 through 12 demonstrate that over-

Note that the last multiplier in the above expres- (W1/2/hsill = 5) and the ratio of the sill half-width pressure due to magma production and supply sion is a quasi-Rayleigh number, which deﬁ nes to the bridge width (hsill/hb = 1). The resulting (which causes sill formation on the ﬁ rst place) the effectiveness of slow motion versus heat value of β here is 0.067. is primarily responsible for the merging of loss. Equation 6 demonstrates that in order for We can compute the required viscosities that magma sills. This is achieved through mechani- deformation to remain self-similar, a factor of are required for the gravity instability to be cal failure and dike focusing across separating

16 Geosphere, October 2014 00969 1st pages / page 17 of 27 Rhyolites—hard to produce but easy to recycle

ity radius, in agreement with theoretical and A numerical results (e.g., Jellinek and DePaolo, 2003; Simakin and Ghassemi, 2007). The stresses are thus reduced ~9 times when the distance between batches is increased from 1 to 4 times their radius. This has implications for the long-term stability of widely dispersed magma batches with distinct crystal cargoes. The magma batches may exist without merging, crystallizing new zircons with rejuvenated U-Pb ε δ18 ages and batch-averaged Hf and O (Fig. 4).

Overpressure in the Interstitial Fluid Phase Interstitial hydrothermal fl uid in country rocks may play an important role in low-pressure upper crustal conditions, in porous rocks, and especially in buried tuffs. Fluid pressure may rise rapidly in the thermal aureoles around magma lenses upon their emplacement or redistri bution, B leading to mechanical failure of the screen rocks in the fast elastic mode. Heating of the pore fl uid increases its pressure almost proportionally to the temperature (e.g., according to gas law) at a constant volume of pores, or faster if there is a phase change. Real rock expands and fl uid migrates in response to the internal pressurization, and the net effect is determined by the rock poroelastic properties and permeability. The direct proportionality of fl uid pressure with respect to temperature and its dependence on other parameters at the impermeable boundary of the heated porous half-space was provided by McTigue (1986). After simplifi cations,

2 φ α Δ 2GB o T, fl T p = , (9) fl 9(ν −ν) + u (1 c/kT )

Figure 12. Development of the magma fl ow structure between vertically stacked sills in G ν ν due to buoyancy inside of soft country rocks (crystal mush or pyroclastic rocks). (A) Large where is the shear modulus, and u are the viscosity contrast of 105 between magma and country rocks at nondimensional t = 0.312. drained and undrained Poisson’s ratio, respec- j c k (B) Small viscosity contrast of 300 at t = 0.378. Strongest deformation occurs in the bridge, tively, o is the porosity, and T are the pres- causing its failure and rapid fl ow of material from the lower to the upper sill. Numbers on sure and temperature conductivities, aT,fl is the Δ vertical and horizontal axes are nondimensional linear coordinates in units of l (see text). fl uid expansion coeffi cient, and T is the tem- 0 perature increment. Inserting typical parameter When l0 = 40 m, domains becomes 6.4 × 3.6 km. Reference vector represents nondimensional fl ow rate. For Ra = 80, Δρ = 300kg/m3, country-rock viscosity of 1013 Pa·s (see text), we get values from Detournay and Cheng (1993) and T 2.1 m/h rate per 1 nondimensional rate unit, corresponding to 146 m/h for non-dimensional calculating aT,fl for an ideal gas at = 800 °C, scale vector 68.8 shown in (A) and the above parameters. we get a fl uid pressure in the range of 16–470 MPa (e.g., typical for sandstone and marble). The fl uid pressure increase is the greatest for screen rocks connecting dikes, followed by the eruptions (Malfait et al., 2014; Caricchi et al., rocks with low permeability and high porosity, initiation of magma coalescence. Density differ- 2014), although the mechanisms for achiev- such as impermeable pumice, poorly consoli- ence between rock and magma may cause rapid ing the excess buoyancy postulated remain dated, clay-rich sediments, or hydrothermally coalescence of magma lenses only if they are unclear. Overpressure or external tectonic con- altered rocks. Intrusion of sills in such sedi- very close, longer lasting, and larger than the trols (Allan et al., 2012) were proposed as an ments at depths of <2 km results in fl uidization country rock screens, which have low viscosities explanation for the Taupo volcanic zone (New of the rocks (Reid, 2004; Buttinelli et al., 2011; and attributes of partially molten rocks, crystal Zealand) eruptions. Schofi eld et al., 2010), sometimes giving rise mushes, or nonwelded pyroclastic rocks. Buoy- The analysis here demonstrates that widely to clastic dikes (Svensen et al., 2006). Even at ant merging may be important at later stages of separated magma batches may exist without greater depths of 6–8 km, common for magma magma coalescence on a caldera scale, and may interaction. In 2-D, stresses around circular reservoirs, pressurization effects might reach be one of the causes of some caldera-forming cavities decay as 1/(R/Rc)2, where Rc is the cav- tens of megapascals; the details depend on the

Geosphere, October 2014 17 00969 1st pages / page 18 of 27 Bindeman and Simakin

A poroelastic properties and permeability of the country rocks. We stress that the rocks with large isolated pores, characteristic of vesiculated pyroclastic materials, are candidates for failure due to the strong pressurization and mechanical weakening at the thermal aureoles of sills, which we model. This makes realistic scenarios of sills merging due to buoyancy (see Figs. 11

and 12), as rocks with low viscosity and Sy can be interpreted as requiring ﬂ uid overpressure- degraded cataclastic materials.

Mixing Inside and Between Reservoirs

We next consider mixing effectiveness within merged batches. Many papers in the past 50 yr have documented abundant natural examples of effi cient magma mixing and mingling on short time scales of magma chamber refi ll, or on mineral dissolution time scales for a variety of compositions. Examples including mixed and unmixed ignimbrites are also abundant (for recent numerical treatment of this prob- B lem, see Huber et al., 2009, 2012; for a review of diffusion time scales, see Cooper and Kent, 2014). For example, buoyant overturn caused by bubbles demonstrates the effi ciency of this process on the order of hours or days (Ruprecht Melting Front et al., 2008), and work in the Taupo volcanic zone demonstrates effective rhyolite mixing on eruptive time scales (Wilson and Charlier, 2009; Allan et al., 2013).

Convective Mixing Within a Single Magma Batch In these sets of numerical experiments we studied the dynamics of the magma reservoir C Diverse in δ18O with fi ne spatial resolution, down to several centimeters, sufficient to resolve fine flow roofrocks, zircons structures in the compositional fi eld and thus evaluate goodness of mixing (Figs. 13 and 14; see Supplemental File 77). This effort continues from Simakin and Bindeman (2012), where coupled Navier-Stokes and heat transfer equations were solved with realistic phase diagrams and proper viscosity models. We observed in these and previous melting experiments that convective melting induces vigorous rates of compositional convection, significantly exceeding the intensity of thermal convection Figure 13. Mixing induced by compositional convection during roof melting. (A) Screen- in the solidifying magma chamber. This is shot of melting process showing descending plumes (illustrated by a numerical model from essentially due to the high effi ciency of in situ Simakin and Bindeman, 2012); colors depict composition (scale: roof rock–magma). See melting in generating density instabilities, as Supplemental File 7 (see footnote 7) for vorticities distribution movies. B and C are concep- compared with the far-fi eld control of chamber tual model for a convective random walk, which can explain bringing together separated cooling. Although somewhat counterintuitive, chemical markers, in this case isotopically diverse zircons from roof rock. (B) Localized, 7 18 Supplemental File 7 is a temporal evolution of closely spaced distribution of chemical markers (e.g., δ O, shown as veins and squiggly vorticity distribution, which is responsible for mix- 18 areas), with spacing of tens of meters. (C) Large-scale gradient distribution of δ O over ing. If you are viewing the PDF of this paper or hundreds of meters to several kilometers. Zircon crystallized from different δ18O areas (red reading it offl ine, please visit http:// dx .doi .org /10 and yellow) are brought together in one area by convection. .1130/GES00969 .S7 or the full-text article on www .gsapubs .org to view Supplemental File 7.

18 Geosphere, October 2014 00969 1st pages / page 19 of 27 Rhyolites—hard to produce but easy to recycle

δ m ment Xm is plotted as a function of time for the A averaged trajectories of 25 markers, originally located in the same square. During the fi rst 2 days, this parameter oscillates around 1 m, which corresponds to the lifetime of the individual plume (vortex), where particles move vertically with small periodic horizontal displace- δ ments. An abrupt rise of Xm corresponds to the moment of pulling apart the magma parcel. δ Later, the Xm increases, yielding oscillations with periods of 2.5–2 days and average rates of ~0.5 m/day. δ m Dependence Xm on time (t) after 10 days is B nearly linear with a rate of 0.5 m/day (Fig. 15B; R2 = 0.969). However, square root dependence on time is expected on the basis of physical 1D Markov chains model with diffusive stochastic jumps (Levin et al., 2008). If so, the diffusional relationship allows the defi nition of the marker diffusion coeffi cient:

δX = (Dt)1/2, D =δx2/δt, (11)

where δx is the size of the jump each δt time Figure 14. Distribution of horizontal displacements δX(x,y) of the 5 × 5 cm averaged markers units, and D is the effective diffusion coeffi cient. after days of convective melting in the rhyolitic magma chamber (see Fig. 12B). (A) After δ By using Xm (t) data for time >4 days we can 5 days. (B) After 17 days. Images are 25 × 50 m and color scale signifi es the magnitude of derive the square root of time approximation horizontal displacement in meters. Brown color corresponds to the surrounding unmelted with diffusion coeffi cient, D = 4 m2/day. These (static) rocks, static condition, δX(x,y) = 0; green stripes correspond to the maximum rela- are obviously very fast rates as compared to the tive horizontal displacement of markers. Although patterns appear as convective fl ow lines, chemical diffusion of SiO2 or ZrO2 in rhyolitic they here represent goodness of horizontal mixing. Large-scale fl ows are generated near the magma, 10–9 cm2/day (Baker, 1991; Harrison left steep edge of the chamber. Although the current model does not include a chemical dif- and Watson, 1983). fusional transport or crystal-melt separation, it is expected that effi ciency of diffusive com- Another way to treat mixing is to apply aver- positional mixing is a direct function of the total travel distance traveled by markers; their age separation between the markers approach prolonged exposure to larger volume of melt will be completely homogenize melt within (e.g., Ruprecht et al., 2008), as implemented each 5 × 5 cm volume. for magma chambers and mantle mixing problems. Average separation is defi ned as the average distance between initially neighboring it is thus the melting process that leads to con- tal motion and horizontal displacement can be pairs of material points in some domain Ω with vection and homogenization inside of magma approximately represented by random jumps NΩ points: bodies (Fig. 14; see Supplemental Files 1, 2, with steps proportional to a vortex diameter in and 3 [see footnotes 1, 2, and 3]). We observed size. An example of the distribution of the abso- δR(t) = (Simakin and Bindeman, 2012) that any roof lute difference between initial and fi nal horizon- heterogeneity in density or compositional char- tal coordinates, i.e., − 2 + − 2 ∑ (xi (t) xi+1(t)) (yi (t) yi+1(t)) NΩ. (12) acter (e.g., higher melting temperature blocks) Ω δ , ,τ = will release gravitational energy and induce X(x y ) − τ This parameter δR as a function of time was mixing upon downward movement through the ∑( xm (t=0) xm (t= ) ) nj1/4, (10) magma body. j1/4 calculated for 16,000 markers initially located Here we pay greater attention to the motion inside the 1 × 1m square shown in Figure 15A, and mixing in the horizontal direction respon- of the magma markers inside a model sill of and results of the numerical run are plotted in sible for the homogenization in sills with large 7 × 24 m is presented in Figure 13, recorded in 5 Figure 15C. Until ~4 days, separation almost aspect ratios (D/H), relevant for magma bod- and 17 days from the beginning of the numerical does not change; in the time interval 4–11 days ies parental to large-scale ignimbrite erup- experiment. Absolute displacements are aver- it undergoes exponential stretch, and demon- tions. Thermocompositional plumes chaotically aged over a subgrid with size equal to one-half strates square root dependence on time after- descending from the roof cause rotations of of the velocity elements (one-quarter by area). ward. Ruprecht et al. (2008) treated separation the multiphase fl uid, and are characterized by Trajectories of 6 markers initially placed as an exponential function of time, using a a spotty vorticity distribution. We observe that in the fi lled square are mapped after 8 days in Lyapunov parameter formulation with exponent due to relatively small scale stochastic fl ow, Figure 15A. Markers fi rst move coherently and defi ned as: liquid particles caught by successive vortexes then spread across the studied magma domain. rotate in different directions. Their horizon- In Figure 15B, absolute horizontal displace- λ(t) = lim −> ln(δR(t)/r (t = 0)) t. (13) ro 0 0

Geosphere, October 2014 19 00969 1st pages / page 20 of 27 Bindeman and Simakin

A Height, m Height,

Width, m

14 Figure 15. Redistribution of markers in the course B of convection. (A) Trajectory of markers initially 12 located inside blue box (1x1 m). Dotted yellow line depicts part of trajectory where markers move 10 y = 1.6t-1.1 together in the same plume (as in Fig 13A and 2 in “induction” period in C), before being pulled 8 R =0.969 apart by convection. (B) Horizontal distance δX 6 between two neighboring markers, averaged for X, m 1/2 δ y=(36.8t)- 6 25 markers, initially located in blue box in A, 4 R2=0.903 averaged as a function of time, t, plotted as ﬁ lled diamonds. Long-term divergence trends can be 2 approximated by the square root (solid red line) 0 or linear (dashed red line) functions with nearly 0 2 4 6 8 10 equal accuracy. (C) Average separation between initially neighboring pairs of points, calculated for time, days 1640 markers initially located inside the 1 × 1 m blue box in A. Note the change in functional depen- 0.8 Lyapunov exponent: dence on time; initially, markers travel with the 40 C 0.6 blue box for 4 days without separation (induc-

−

y 0.4 tion), then they undergo exponential separation.

d , 0.2 30 σ Inset shows computed Lyapunov exponent for 0.0 separation; after that, square root separation is a better approximation. See text for discussion 20 0 4 8 12 16 X, m time, days and implications. A–C represent particle separa- δ tion without side-wall effects. In the closed-box square root 10 experiment representing small magma chambers, mixing may reach an asymptotic limit for longer induction time scales due to side-wall effects deﬁ ned by the 0 magma pool width. It can be shown that during exponential perfect mixing δXm will approach a value of W/3, 0 4 8 12 16 where W is width of the pool. time, days

This temporal variation of the exponent We observe in our runs that exponential mixing ters with a simple increase in the size of magma parameter in our experiments is displayed in with the Lyapunov exponent is only a transient chamber results in a linear regression predic- the Figure 15C inset. The Lyapunov exponent phenomenon. tion of δX = 1 km in 2 yr. The diffusional model attains a maximum plateau with a level of 0.6 The random walk model with either square predicts 1 km dispersion in 684 yr. However, as day–1 that characterizes the intensity of convec- root time or linear dependence allows for exten- dispersion (mixing) occurs in parallel with melt- tive mixing in our case. Obviously λ decreases sion of the results obtained in the restricted space ing (Figs. 8, 13, and 14), horizontal parameters with time, since convective velocities are ﬁ nite domain toward the geologically more relevant are also affected by the overall rates of displace- while constant λ implies growth of average sep- larger dimensions and larger magma bodies. In ment of the convective body of the magma. Dur- aration with an exponentially increasing rate. particular, retaining the same dynamic parame- ing 2 yr of roof melting, the melting front will

20 Geosphere, October 2014 00969 1st pages / page 21 of 27 Rhyolites—hard to produce but easy to recycle displace the solid-melt boundary by 6–20 m, given modeled melting rates, um, of 4–12 m/yr; during 684 yr of melting, the magma body may migrate 300–1000 m, comparable with overall vertical chamber size, further contributing to homogenization. It is likely that this model of displacement due to repeated rotations in random directions in descending plumes provides a mini- mum proxy for chemical mixing and horizontal homogeniza tion in magma bodies. This is because it neglects the contribution of (1) the curved trajectories of the descending interact- ing plumes, and (2) occasional larger scale fl ows (magmatic avalanches), as seen in some runs (See Supplemental Files 1, 2, and 3 [see footnotes 1, 2, and 3]) and as widely specu- lated to occur in nature (e.g., layered intrusions; Wager and Brown, 1967). In the latter case, horizontal fl ows are occurring with signifi cant horizontal velocities of meters per hour, much faster than either the linear or ~t1/2 horizontal spreading rates mentioned here. However, compositional homogeniza tion on a centimeter scale is ensured by the slower and smaller scale motions. Effi ciency of mixing is also dependent Figure 16. Size distributions of parcels of melted roof rocks in the main convecting volume on the amplitude and spatial distribution of of magma sill (see Figs. 13A and 15) in numerical melting runs after 5.5 and 17 days in 15 × tracer heterogeneity (e.g., Figs. 14, 16, and 17), 80 m convecting magma body. The convective model does not consider chemical diffusion; whether large scale or small scale. The hand- in reality the small-scale heterogeneities will be annealed by diffusion. Size distribution of specimen iso topic homogeneity is achieved partially molten xenoliths in the analogous natural process is shown (data from Slabunov, when isotopically distinct individual minerals 1995). In the inset image of numerical mixing after 17 days, dark indicates pieces of the such as zircons with diverse ε and δ18O (Figs. Hf melted roof; size of the area is 1 × 1 m. L is the largest axis of the ellipsoidal inclusions, and 4 and 14) are brought together from areas that n/n is normalized on the maximum value of particles size distribution. were originally tens of meters apart. max In summary, our numerical results demonstrate that thorough compositional mixing is easy, and proceeds on time scales faster than are characterized by elliptic shapes in section and mixing. A three-layer melting experiment in cooling, but slower than mineral diffusive time and a unimodal distribution of the their short Figure 8 further illustrates how compositional scales. The process generates homogeneous axes with median values of 1.5–2 cm, a mean heterogeneities are effi ciently mixed when whole-rock composition with isotopically of ~5 cm, and a maximum of 18 cm. In our magma batches are merged together, in this case diverse crystalline cargo, including zircons. numerical runs we observe comparable size dis- by melting through the screen rock between. tributions of the partially molten roof material Comparison with Natural Data on Mixing scattered in the lower convecting rhyolite (see DISCUSSION There are attempts to study convective Fig. 16, inset). This means that our experiments homogenization in a magma reservoir in experi- correctly reproduce the initial stage of homog- Case for Short-Lived Batch Magma Bodies ments with real silicate melts. De Campos et al. enization, continuing with the fast diffusive in the Stress Field of the Upper Crust (2011) experimentally performed mixing of sili- dissolution of the smallest drops. Our results ceous and basaltic magmas in a high-T cell. The contradict earlier published conclusions of the Local high-resolution seismic tomography experimental setup with independently rotated small effi ciency of the convection in a magma (e.g., Fig. 18) provides information about the noncoaxial cylinders generated a chaotic (non- reservoir and its inability to achieve real mixing depths, sizes, and approximate shapes of pos- periodic) fl ow fi eld (Fig. 17). Mingling in the (Gutierrez and Parada, 2010). Both natural data sible magma bodies under Yellowstone and experiments at the large viscosity contrast of a (Vazques et al., 2009; Girard and Stix, 2010) elsewhere (Beachly et al., 2012). Miller and factor of ~1000 proceeds through formation of and numerical models (Huber et al., 2009; Bur- Smith (1999) and Husen et al. (2004) imaged the continuously twisted magma layers rather gisser and Bergantz, 2011) demonstrate high two separate regions of low Vp under the Sour than separated drops. The textures produced are effi ciency of mixing, extraction, and differentia- Creek (Yellowstone) resurgent domes at the similar to the commonly observed interlayer- tion in crystallizing rhyolites, and relative crys- same depth of 7 km (Fig. 18). The isotopically ing of dark and light bands of glasses in obsid- tal-melt separation promotes local scale mixing. diverse crystal cargoes in eruptive products best ians. Geologic observations (e.g., Slabunov, We thus consider that the large-scale merging argues that that the supposed magma chambers 1995) show us that partially melted xenoliths of magma batches that we modeled here creates in the SRP and elsewhere are short lived and of amphibole-bearing schist in an andesitic melt many possibilities for compositional convection ephemeral, like those shown in Figure 18, rather

Geosphere, October 2014 21 00969 1st pages / page 22 of 27 Bindeman and Simakin

A than a single convecting batholith. Provided C enough basalt and heat ﬂ ux is maintained, dispersed magma bodies can be stable in this form, crystallize, and be hydrothermally altered, or rapidly reactivated. Thermomechanical stability analysis of widely dispersed melt pockets is outside the scope of this paper, but instability can be triggered by a greater supply of basalt (thermal reactivation), or by changing stress B conditions (tectonic reactivation). Our modeling demonstrates that formation and mixing of large, eruptable magma volumes of 102–103 km3 may proceed rapidly by either amalgamation of these numerous bodies or continuous growth of one or several large ones, consuming the others.

Accounting for the Amount of Silicic Magma Produced

The estimates of the volcanic/plutonic ratio for the erupted rhyolites vary widely in any volcanic area, from ~10% erupted, 90% remaining (Smith, 1979), to 1:2 (Bonnichsen et al., 2008), or even 1:1, as we favor here due to effi cient near-eutectic melting and extraction. These estimates affect the corresponding amount of heat and basalt required to produce the observed Figure 17. Comparison of the numerical and experimental mixing of two liquids during amounts of silicic melt. Basalt differentiation or rotation. (A) Initial confi guration of a circular chamber with a solid, noncoaxial rotor and a partial melting of the mafi c crust (slow process; small circular liquid inclusion with identical viscosity. (B) Numerical structure after two full Fig. 6), or a combination of the two of these rotations. (C) Experimental texture of glycerin with dye after 10 alternate rotations (from processes, is a strong function of the melting De Campos et al., 2011). In both cases stretching and folding form multiple, thin layers effi ciency, i.e., how much heat is wasted for rather than separate blobs. heating of the country rock prior to and during

A B

δ18 O high

Depth, km

low

C fractal reservoir assembly

Figure 18. Seismic tomography data (Miller and Smith, 1999; Husen et al., 2004). (A) Yellowstone. (B) Isotopically diverse and dispersed batch magma bodies based on the results of this work.

22 Geosphere, October 2014 00969 1st pages / page 23 of 27 Rhyolites—hard to produce but easy to recycle partial melting (e.g., Annen et al., 2006; Dufek and Bergantz, 2005). Also, many such models do not take into account temperature-dependent thermal diffusivities and/or conductivities, multi-cyclic caldera which, if incorporated, would reduce the heat zoned ignimbrites contribution needed from basalts by a factor of Melt 3 ... N periodic rapid remelting ~2 (Whittington et al., 2009). Hot zone models batch assembly, mixing, eruption require signiﬁ cant amounts of maﬁ c cumulate to Melt3d HSR

Hydrothermal be produced at the end (Fig. 19), often in excess preconditioning Melt3 LSR of the observed thickness of the lower crust, BATCHES Brittle-DuctileBrittle-D transitiontransit requiring that these cumulates delaminated and sank into the mantle. Thus the room problem UpperUpper CrustCrust exists not only for silicic plutons in the crust,

PATHWAY

but also for parental cumulates and restites in PLUTONS RECYCLING

SEQUESTRATION the lower crust and upper mantle. In addition, Melt2d the material versus heat contribution of basalt is Melt2 one of the longest-discussed problems of igne- Lower Crust ous petrology (e.g., Hildreth and Moorbath, dynamicdy melt segregation 1988; Grunder, 1995; and many others). However, all of these mass, space, and heat Melt1Melt1 constraints are signifi cantly relaxed if silicic rocks are produced by remelting and recycling “Hot“Hot Zone”Zone” of already existing silicic magma bodies, which were formed by any of the above mechanisms. As we advocate here, such remelting is easy Basaltic Magma Flux and fast (fast process; Fig. 5), and leads to the Flowing, delaminating Cumulates sequestration of silicic melts into the upper crust. For example, in the Andes, the U-Pb zir- Figure 19. Rhyolite genesis by progressive recycling and crustal evo- con evidence suggests that nonerupted parts lution by upward sequestration of silicic material (Melt1.3d HSR; of older eruptions in the same magmatic sys- d stands for differentiated) leading to low-silica rhyolites (LSR) tem or sequence are commonly recycled (e.g., and high-silica rhyolites (HSR) in the upper crust. Each episode of Folkes et al., 2011), and a similar process must recycling involves melting, segregation, and differentiation of previ- also characterize the multicyclic San Juan vol- ously emplaced silicic material (fi ngerprinted by locally diverse iso- canic fi eld of Colorado, USA (Lipman, 2007), topic values), simplifying the room and heat problem. High magma although we note that these systems appear not supply rates yield effective sequestration and large volcanic/plutonic to be fi ngerprinted by low δ18O values, indicat- ratios, and create transient, short-lived, batch magma chambers in ing recycling of previously erupted and altered the upper crust (see Fig. 18). material (e.g., Folkes et al., 2013). Much recent work has been done on Taupo volcanic zone in New Zealand, also pointing to zircon recycling large screens of intracaldera roof rocks may thermal evolution. So, links between plutonic and short residence times of magma segregation sink to the bottom of a lower magma body, as and volcanic records should not be discarded (Charlier et al., 2008; Wilson and Charlier, 2009; well as result in mafi c magma recharge. Further- just because there is chronological discordance. Allan et al., 2013): oxygen isotopic evidence on more, plutons may undergo doming and upward recycling there is still to be investigated. motion on the order of 105–106 m.y. time scales, Predicting Yellowstone’s Future creating internal density redistribution (Ram- From Studying its Past What Remains in the Crust berg, 1970; Petford, 2003; Schubert et al., After Recycling? 2013). Here we emphasize an important con- The causes of the production and eruption of clusion: observations from plutonic examples magmas in the SRP (Fig. 1), have direct impli- The volcanic-tectonic processes that we signifi cantly postdate the stages of magmatic cations for the 620 ka Yellowstone caldera, and envision to characterize the evolution of an evolution documented by the volcanic evidence in particular on whether it represents the last of SRP-type environment leave behind basaltifi ed, (or processes inferred for the volcanic magma a series of eruptions in a caldera cluster (e.g., topographically reduced (Fig. 1), and bimodal chamber), and thus the observational records Watts et al., 2012) and a crustal block that has terrain in the wake of the plume. Internally, it may not be compatible (e.g., Glazner et al., been remelted and recycled from top to bottom, should lead to the complex intracrustal struc- 2004; Coleman et al., 2004) (e.g., the geophysi- and thus exhausted its eruptive potential, or if tures of dikes and sills, not common in typical cally imaged gabbro or gabbro-dioritic sill that generation and eruption of large volumes of clean granite plutonic examples such as those remains in the crust after passage of the Yellow- silicic magma is still possible. In other words, it of the Sierra Nevada (California). However, stone plume; Husen et al., 2004; DeNosaquo is important to estimate if the current (past 600 plutons represent signifi cantly prolonged histo- et al., 2009). Discordance between plutonic and k.y.) voluminous rhyolitic eruptions at Yellow- ries after cessation of volcanism (Paterson and volcanic records should be expected because stone represent the path of a dying cycle, and Vernon, 1995; Zak et al., 2007). In particular, plutonic rocks represent signifi cant posteruptive if a new Huckleberry Ridge Tuff–size magma

Geosphere, October 2014 23 00969 1st pages / page 24 of 27 Bindeman and Simakin

reservoir is currently being slowly established in easy process) then requires that these already tion and melt generation in the crust: Earth and Plan- etary Science Letters, v. 203, p. 937–955, doi: 10 .1016 southwest Montana with anticipated completion segregated areas are remelted more than once, /S0012 -821X (02)00929 -9 . in 1–2 m.y. If so, the next eruption is to be nor- each time accompanied by further fraction- Annen, C., Blundy, J.D., and Sparks, R.S.J., 2006, The gen- mal δ18O, assembled slowly and with diffi culty ation that increases crustal differentiation indi- esis of intermediate and silicic magmas in deep crustal hot zones: Journal of Petrology, v. 47, p. 505–539, doi: from the lower crust and differentiation of SRP ces (e.g., increasing Rb/Sr, Eu anomalies, and 10 .1093 /petrology /egi084 . basalt, with limited zircon diversity. SiO2, decreasing MgO). Each time, melting of Bachmann, O., and Bergantz, G.W., 2004, On the origin of The low δ18O magmas with diverse zircons siliceous lithologies proceeds rapidly; the 50% crystal-poor rhyolites: Extracted from batholithic crystal mushes: Journal of Petrology, v. 45, p. 1565–1582, (Figs. 2–4) that appeared at the end of each cal- melt extraction window (e.g., Fig. 5) is achieved doi: 10 .1093 /petrology /egh019 . dera cluster evolution (and throughout the cen- quickly as the heat of intruding hot silicic dif- Bacon, C.R., and Lowenstern, J.B., 2005, Late Pleistocene granodiorite source for recycled zircon and pheno- tral SRP) for at least the past 12 m.y., and likely ferentiates is very effi ciently consumed by the crysts in rhyodacite lava at Crater Lake, Oregon: Earth as early as 15 Ma (Colon et al., 2014) are identi- eutectic melting, without much heat loss on and Planetary Science Letters, v. 233, p. 277–293, doi: fi ed as derived by recycling of buried silicic (zir- rapid melting time scales. Basaltic magma may 10 .1016 /j .epsl .2005 .02 .012 . Bacon, C.R., Adami, L.H., and Lanphere, M.A., 1989, con saturated) hydrothermally altered volcanic also intrude the upper crust along the magma Direct evidence for the origin of low-δ18O silicic mag- and plutonic predecessors from the same crustal pathways (Fig. 19; e.g., Fowler and Spera, mas: Quenched samples of a magma chamber’s par- block. Relative similarities in the radiogenic 2010), delivering heat but offsetting the prog- tially fused granitoid walls, Crater Lake, Oregon: Earth and Planetary Science Letters, v. 96, p. 199–208, doi: isotope ratios and trace elemental abundances ress of sequestration. Rhyolitic bodies are then 10 .1016 /0012 -821X (89)90132 -5 . in early normal δ18O and subsequent low δ18O segregated in large volumes by upward seques- Baker, D.R., 1991, Interdiffusion of hydrous dacitic and rhyolitic melts and the effi cacy of rhyolite contami- rhyo lites (Hildreth et al., 1991; Hanan et al., tration, and our modeling demonstrates easy nation of dacitic enclaves: Contributions to Mineral- 2008; Christiansen and McCurry, 2008; Drew assembly, amalgamation, and effective mixing ogy and Petrology, v. 106, p. 462–473, doi:10 .1007 et al., 2013) suggest that the low δ18O rhyolites between disparate magma bodies. /BF00321988 . Barton, N., 2013, Shear strength criteria for rock, rock joints, are derived by recycling and remelting of the We point to the observation that bimodal rockfi ll and rock masses: Problems and some solutions: normal δ18O rhyolites after they became depleted basaltic-rhyolitic provinces predominantly Journal of Rock Mechanics and Geotechnical Engineer- in 18O by high-temperature alteration, which did occur within extensional and hotspot environ- ing, v. 5, p. 249–261, doi: 10 .1016 /j .jrmge .2013 .05 .008 . Beachly, M.W., Hooft, E.E., Toomey, D.R., and Waite, G.P., not disturb, or minimally affected elemental and ments with high basaltic power outputs, but 2012, Upper crustal structure of Newberry Volcano other isotopic abundances. Given that Yellow- also in continental arc areas with delamination from P-wave tomography and fi nite difference wave- stone has already erupted >600 km3 of recycled features. Rising basaltic magmas are trapped by form modeling: Journal of Geophysical Research, v. 117, B10311, doi: 10 .1029 /2012JB009458 . 18 low δ O rhyolites with diverse crystal cargo for density fi lters of silicic magma batches at dif- Beard, J.S., and Lofgren, G.E., 1991, Dehydration melting the past 620 k.y., we consider that it is on a dying ferent levels in the crust, leading to a Daly Gap and water saturated melting of basaltic and andesitic greenstones and amphibolites at 1–3 and 6–9 kbar: cycle, and that the crustal block under Yellow- (i.e., a lack of intermediate compositions; Selig- Journal of Petrology, v. 32, p. 365–401, doi:10 .1093 stone has been depleted in silicic melt, which man et al., 2014). The described process (Fig. /petrology /32 .2 .365 . was sequestered upward and recycled. 19) furthermore leads to crustal sequestration Beard, J.S., Ragland, P.C., and Crawford, M.L., 2005, Reac- tive bulk assimilation: A model for crust-mantle mix- of silicic material in the upper crust and mafi c ing in silicic magmas: Geology, v. 33, p. 681–684, doi: Big Picture View of Silicic Magma cumulates in the lower crust. We further specu- 10 .1130 /G21470 .1 . Petrogenetic Models and Crustal late that because high basaltic output conditions Becker, T.T., 2006, On the effect of temperature and strain- rate dependent viscosity on global mantle fl ow, net Evolution by Sequestration were predominant on the early Earth, the recy- rotation, and plate-driving forces: Geophysical Journal cling and sequestration processes were respon- International, v. 167, p. 943–957. Bindeman, I.N., 2003. Crystal sizes in evolving silicic The large-scale recycling model of rhyolite sible for the segregation of the upper silicic and magma chambers: Geology, v. 31, p. 367–370. petrogenesis in the upper crust that we propose lower mafi c crust, with signifi cant components Bindeman, I.N., and Valley, J.W., 2001, Low-δ18O rhyolites here (Fig. 19) serves as a previously under- of thermomechanical lower crustal convection from Yellowstone: Magmatic evolution based on analyses of zircons and individual phenocrysts: Journal of appreciated, important end-member to existing (e.g., Gerya, 2009). A dynamic view of silicic Petrology, v. 42, p. 1491–1517, doi: 10 .1093 /petrology models of formation of silicic magmas in the hot magma petrogenesis by sequestration is a must. /42 .8.1491 . zone in the lower crust during successive mafi c Bindeman, I.N., Schmitt, A.K., and Valley, J.W., 2006, U-Pb ACKNOWLEDGMENTS zircon geochronology of silicic tuffs from the Tim- sill intrusions (Hildreth and Moorbath, 1988; ber Mt/Oasis Valley caldera complex, Nevada: Rapid Huppert and Sparks, 1988; Annen and Sparks, Supported by National Science Foundation EAR- generation of large-volume magmas by shallow-level 2002; Dufek and Bergantz, 2005; Annen et al., CAREER-0844772 and EAR-1049351, and Russian remelting: Contributions to Mineralogy and Petrology, Foundation for Basic Research grant 07-05-00629. v. 152, p. 649–665, doi: 10 .1007 /s00410 -006 -0124 -1 . 2006), and the resulting assembly of large silicic Bindeman, I.N., Watts, K.E., Schmitt, A.K., Morgan, L.A., We thank Matthew Loewen, Dana Drew, Dylan magma bodies or batholiths in the middle and and Schanks, P., 2007, Voluminous low δ18O magmas in Colon, and Taras Gerya for comments, Chris Folkes, the late Miocene Heise volcanic fi eld, Idaho: Implica- upper crust (Schaltegger et al., 2009). Extrac- Graham Andrews, Ben Ellis, and two anonymous tions for the fate of Yellowstone hotspot calderas: Geol- tion of the partial silicic melt from lower crustal reviewers for their extensive comments, and Shan de ogy, v. 35, p. 1019–1022, doi: 10 .1130 /G24141A .1 . mafi c protoliths (slow and diffi cult process Silva for helpful editorial handling. Bindeman, I.N., Brooks, C.K., McBirney, A.R., and Taylor, H.P., 2008a, The low-δ18O late-stage ferrodiorite above and in Fig. 7) is facilitated by the slow REFERENCES CITED magmas in the Skaergaard Intrusion: Result of liquid coeval deformation (e.g., Spiegelman, 2003; immiscibility, thermal metamorphism, or meteoric Rabinowicz and Vigneresse, 2004; Simakin and Allan, A.S.R., Wilson, C.J.N., Millet, M.-A., and Wysoczan- water incorporation into magma?: Journal of Geology, ski, R.J., 2012, The invisible hand: Tectonic triggering v. 116, p. 571–586, doi: 10 .1086 /591992 . Talbot, 2001). 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