hourglass inclusions: theory and application to the bishop

American Mineralogist, Volume 76, pages 530-547, 1991

Hourglass inclusions: Theory and application to the Bishop Rhyolitic Tuff

A. T. ANonnsoN, Jn.The Department of the Geophysical Sciences, The University of Chicago, 5734 S. Ellis Avenue, Chicago, Illinois 60637, U.S.A.

Ansrn-ncr

Hourglass inclusions are bodies of bubble-bearing glass in volcanic phenocrysts thatextend to the crystal rim through a niurow neck. Compared to enclosed inclusions, hour-glass inclusions are less devitrified, contain more gas, but contain less dissolved H2O, CO2,and Cl. Hourglass formation plausibly involves the unsuccessful capture of a gas bubble.Their evolution probably involves loss of some melt through the neck as a result ofdecompression in surrounding magma. The gas fraction attained within hourglass inclu-sions is governed by their size and shape as well as by both the amount and duration ofexternal decompression. A quantitative model of rhyolitic hourglass emptying is developedand applied to Bishop Tuff hourglass inclusions. Those in plinian pumice suggest rapidascant at l0 m/s consistent with theoretical eruption models. Hourglass inclusions fromthe Mono ash-flow lobe of the Bishop Tuff suggest (l) initial crystallization of quartz,formation of some enclosed and some hourglass inclusions at approximately 2400 bars;(2) magma decompression to approximately 1100 bars for at least a week (duration oferuption for the Bishop Tufl) while hourglass inclusions further evolved and bubbles ofgas attained a 50 lrm diameter; (3) magma ascent from I100 to approximately 700 barsat approximately I m/s, consistent with theory for ash-flow-producing (collapsing) erup-tion columns; (4) entrainment of some crystals that had decompressed to a pressure of400 bars for several weeks; (5) thermal quenching of hourglass evolution as magmaticfoam disrupted into fast-moving spray, erupted, and entrained cold air. Pressure atquenching is greater than predicted magma disruption pressures but possibly consistentwith preservation of long vesicles. Uncertainties are large but can be reduced by futurestudies of postdepositional cooling, hourglass volatile compositions, temperature, and vis-cosity to obtain estimates of eruptive and preeruptive magma movement and crystalli-zation rate.

DnrrxtrtoN, occuRRENcE, AND SIGNIFTCANCE tive pressure because the pressures at which it rigidifiedHourglass inclusions are characterized by a narrow neck and degassed are uncertain (Whitham and Sparks, 1986;

of glass connecting a larger body of glass in a crystal with Sparks and Brazier, 1982). Hourglass inclusions are in-its rim (Figs. I and 2). Reentrants differ from hourglass termediate: they decompress, but only partially, throughinclusions in that they have wide, open necks (Fig. 3). a retarding constriction. Because hourglass inclusions are

In addition to the Bishop Tufl hourglass inclusions gas saturated, pressure within an hourglass inclusion canoccur in the upper Bandelier plinian quartz phenocrysts be inferred from its volatile composition, or from its gas(Anderson, unpublished data), in the youngest Toba Tuf content if its initial bulk volatile content can be ascer-(Chesner, personal communication, 1990), and Paleozoic tained (e.g., assumed equal to that in enclosed inclusions).clay (Kozlowski, l98l). Thus, hourglass inclusions trace magmatic decompres-

Although various inclusions occur in various hosts, this slon.work is about hourglass inclusions and enclosed inclu- In the pages that follow, I first outline a quantitativesions of glass (including partially devitrified or crystal- model of melt loss through the necks of hourglass inclu-lizedglass)inphenocrystsofquartz. Consequently,inclusions as a result of external decompression. Second, Ision as used here signifies a wholly enclosed glass inclusion review the geology and petrology of the Bishop Tuff andin quartz. Hourglass means hourglass inclusion in quartz. describe and compare its enclosed and hourglass inclu-

The significance of hourglass inclusions lies in their sions. Third, I discuss, in the context of the Bishop Tuflrelation to the eruptive process. Volatiles in glass inclu- the problems of (l) diffusive boundary layers in melt, (2)sions can be used to constrain or reveal crystallization contraction resulting from the B-a inversion of quartz,pressures; these may be greater than the pressure of pre- and (3) preferential rupture of gas-rich inclusions. Fourth,eruptive magma storage. Pumice, on the other hand, is I use textures and compositions of enclosed and hourglassso decompressed that it is difficult to restore its preerup- inclusions to suggest an origin for the Bishop hourglass

0003-004x/9 1/0304-0530$02.00 530

ANDERSON: HOURGLASS INCLUSIONS 531

inclusions. Fifth, I apply the melt loss model to the Bish-op Tuffhourglasses to estimate (l) the pressure at whichrapid cooling stopped melt loss (plausibly near the pres-sure at which slow-moving magmatic foam disrupts intoaccelerated spray); (2) the duration of hourglass melt lossand decompression; and (3) some rates of ascent of theeruptrng magmas.

Qu,l,NrruuvE MoDEL oF HouRGLAss EMrTvING

I consider a fractional emptying process (Fig. a) where-by the hourglass cavity is assumed to lose melt but notgas. As melt is lost, the remaining melt and gas decom-press and equilibrate within the cavity. There results arelation between the pressure and volume fraction of gas

Fig. I . Mono ash-flow hourglass LV8 1- 184-20. Scale bar is250 pm long. The neck ofthe hourglass is at the bottom right.It points down out of the depth of focus and is approximately100 pm long and 7 pm in diameter. When this photo was taken,the glass in the neck had been largely dissolved in HBF., a smallportion of the glass in the hourglass near the neck was also dis-solved; weak lines near the neck mark the boundary of the glassand refractive index liquid filling the acid-etched neck. The bub-bles are subequally spaced and one bubble is more than twice aslarge as the others. Three of the five bubbles wet the wall of thequartz container. The three bubbles are asymmetrical such thatthe glass-bubble wall nearest the neck is less curved than theother. The asymmetry decreases in sequence away from the neck.Adjacent to the bubbles are narrow zones ofless devitrified glass(this glass has strain birefringence probably caused by hydrationfrom the high-pressure HrO-rich gas initially present in the gasbubbles during post depositional cooling). The long dimensionofthe hourglass is parallel to a. The glass has been analyzed byelectron microprobe and infrared (IR) spectroscopy at three spots:spot I between the first and second bubbles near the top end,spot 2 between the third and fourth bubbles, and spot 3 betweenbubbles four and five near the neck (see Table 2). Textural andcompositional features combine to indicate that this hourglasswas repressurized before eruptive quenching.(-

in the hourglass. The fractional process differs only slight-ly from that for closed system decompression. With lossof melt, the total mass fraction of volatile material in thesystem increases with decompression rather than remain-ing constant. Consequently, the volume and mass frac-tions of gas increase more per increment of decompres-sion in a fractionating hourglass than in a closed system.

In Appendix l,'I derive and solve a differential equa-tion that equates a decrease in the HrO content of theinclusion with the amount of HrO dissolved in the lostmelt. The expression is similar to many fractionationequations, but the variables cannot be easily separatedbecause there is a square root of pressure rule for thesolubility of HrO in the melt. The equation is a first order,linear differential equation and can be integrated usingthe standard procedure. The variables are (l) the initialpressure [or concentration of HrO dissolved in the melt(glass)l; (2) the volume fraction of gas present at the initialpressure; (3) the final volume fraction of gas in the hour-glass; and (4) the final pressure in the hourglass. The pro-cess is assumed to be isothermal, as a simplifying ap-proximation. In practice, it is possible to infer the initialpressure from measurements on enclosed inclusions, andto measure in the hourglass both the proportion of gasand the concentration of HrO dissolved in the melt. Con-sequently it is possible, in principle, to solve for the pro-portion ofgas present before decompression began.

I next consider the case where CO, as well as HrO ispresent. This sufficiently complicates the problem that a

' A copy of Appendix I may be ordered as Document AM-9 I -45 3 from the Business Ofrce, Mineralogical Society of Amer-ica, 1130 Seventeenth Street NW, Suite 330, Washington, DC20036, U.S.A. Please remit $5.00 in advance for the microfiche.

532 ANDERSON: HOURGLASS INCLUSIONS

t

Fig. 2. A typical Mono hourglass showing subequal bubbles surrounded by finely devitrified brown glass. Note the near rim (R)position of the hourglass and its round shape compared with the enclosed inclusion (E). Where the barely visible neck connectswith the rim of the quartz there is a depression or dimple (D) approximately 100 pm in diameter and 20 pm deep. The hourglassneck is roughly perpendicular to the faceted rim ofthe quartz phenocryst. The scale bar is 100 pm long.

numerical approach is needed. In addition, I take intoaccount gas nonideality and species-dependent solubilityrelations. Gas fraction and pressure calculated for threerelevant bulk compositions are in Figure 5. The impor-tant point is that the pressure within hourglasses can beinferred from the proportion ofgas, if the initial bulk HrO+ CO, composition is known (e.g., from enclosed inclu-sions).

DrvrrNsroNLESS HouRGLASS NUMBER, euENCHINGPRESSURE, AND ERUPTION DURATION

For a group of hourglasses with the same decompres-sion history it is possible, in principle, to constrain boththe duration and the external pressure ofdecompressionfrom their gas volume fractions and geometries.

Fig. 3. Reentrant in rim of quartz (Q) largely filled with glass(G). The scale bar is 50 pm long. Refractive index liquid fills thevoid (V).

Imagine a magmatic history as follows (and see Fig. 4):stage l, an hourglass forms in crystallizing magma at somepressure (Po); stage 2, the magma rises (decompresses)instantly to a new lower pressure (P,) and remains therefor some duration of time (/); stage 3, the magma is in-stantly erupted and quenched. Qualitatively, if there aresome hourglasses that would empty quickly because ofshort, wide-mouthed necks, then these will empty, duringstage 2, nearly to the limit imposed by the new externalpressure (P,), from which the magma was quenched (stage3). The gas fractions (g/V) in such hourglasses primarily

Fig. 4. Sketch illustrating the parts of an hourglass used inthe mathematical derivation of the relations between gas fraction(g), the internal pressure (P and P.), the external pressure P,, thevolume (/) of the hourglass, and the diameter (D) and length(Z) of its neck. The dimensionless hourglass number IHGN :

V/(D/L)l characterizes the sluggishness with which the volumefraction of gas will increase with time as melt escapes throughthe neck.

,N,AN [;r'o;l"t;;'Hzocoz

MASHll3'-[ft3lJJr8:'

aJ)o

(9

60

50

40


Ifan hourglass neck is narrow and long, then the absoluterate at which melt can extrude and gas volume increasewill be small, but if the inclusion volume is also small,then, after a certain interval of time, the proportion ofgas in the hourglass may be substantial. As defined, theemptying of an hourglass with a large hourglass numberis relatively sluggish: its proportion ofgas increases slow-ly compared to another hourglass with a smaller hour-glass number.

The quantitative relations developed in Appendix I(Eq. 2l) show that only two observable parameters [thevolume fraction of gas (G : C/ n and the hourglassnumber IHGN : V/(D4/L)] carry the principal informa-tion useful in evaluating the duration of time (t) and ex-ternal pressure (P,) common to a set of hourglasses. Someknowledge of temperature, melt composition, and initialvolatile content is required so that the viscosity and ini-tial pressure (Po) can be established. For two hourglassesthat formed during the same decompression history [(P6- P,) and ll, as outlined above there is enough infor-mation (two equations with two unknowns) to calculateboth P, and t. A useful graph (Fig. 6) shows the volumefraction of gas (G) vs. flGll with contours for variouscombinations of P, [strictly (P, - P,)] and l.

The curves on Figure 6 were calculated by stepwisedecreasing the pressure (P) within hourglasses and cal-culating, for successive pressure decrements, the corre-sponding increment of gas and the increment of time re-quired for loss of sufficient melt through the neck to makeroom for the gas increment. The rate of loss of melt de-creases with each pressure decrement because the meltviscosity increases as melt HrO decreases and because thepressure gradient decreases. The accumulated total gasfraction and time calculated from the running sums yieldthe curves on Figure 6. The computational procedure isfurther described in Appendix L

The sigmoid shape of contour lines of equal time du-ration (isochrons) on Figure 6 reflects two qualitativeboundary conditions: (l) for hourglass numbers larger thansome limiting value, the accumulated fraction of gas isnegligible; (2) for hourglass numbers smaller than somelower limit, the fraction of gas reaches the limiting valueimposed by the external pressure. Thus there are twoasymptotic limits to each isochron: (l) negligible gas frac-tion at very large hourglass numbers, and (2) equilibriumgas fractions at small hourglass numbers.

The transition between the asymptotic limits stretchesover approximately 4 orders of magnitude of the hour-glass number. The isochrons depend upon the initial con-centrations of HrO and CO, in the melt. Consequently,the isochrons on Figure 6 are peculiar to the Bishop Tuffand other magmas with similar HrO and CO, concentra-tions. Separate computations are required for other con-ditions. Copies of the program (in Basic A) may be ob-tained on disk from the author. The program listing maybe obtained from the author or from the journal (as partof Appendix l).

An inverse problem arises if the decompression is not

E

20

be 30

r0

0

0 t000 2000P bors

Fig. 5. Graph showing the relations between gas fraction andinternal pressure in evolving rhyolitic hourglasses for three ini-tial volatile compositions. The intercepts at 00/o gas along thehorizontal pressure axis give the respective gas saturation pres-sures. The curves for the plinian and Mono A conditions inter-sect at approximately 1700 bars, reflecting the important influ-ence of a high CO, content (Mono A) in causing an initially rapidfall in pressure as gas is produced. The volatile compositionscorrespond to those used in modeling the Bishop hourglassesillustrated in Figure 6.

reflect the decreased external pressure (P,). On the otherhand, if there are some very sluggish hourglasses (withvery narrow, Iong necks), then, upon eruptive quenching,these will retain an internal pressure (P) close to that ofthe initial pressure (Pr). Thus the gas fraction in the latterwill reflect primarily the duration 0) of the decompressedstage 2. The exact solution for both time and pressurefrom the properties of a group of hourglasses with a com-mon history depends on the quantitative details. Theseare presented in Appendix I and summarized below.

The rate at which melt will move out through a cylin-drical neck by laminar flow is given by the Poiseuilleequation (Eq. 19, Appendix l). This leads to the formu-lation of a dimensionless quantity, here termed the hour-glass number. It is the ratio of the volume of the hourglassto the fourth power of the diameter of the neck dividedby the neck length. The hourglass number is a geomet-rical attribute of an hourglass, which expresses the com-bined effects of its total volume and the dimensions ofits neck on the rate at which the proportion ofgas in thehourglass will increase as a consequence of external de-compression and consequent loss of melt through the neck.


instantaneous. Strictly, the emptying of any hourglass de-pends on the integral ofthe external pressure with respectto time. The above computations assume that the hour-glasses are instantaneously decompressed to some newpressure at which partial emptying occurs before quench-ing. The extent to which an array of observations followsa single isochron for the instantaneous case is a measureof decompression rate. The instantaneous isochrons areuseful as interpretive guides and should not be regardedas lines to which error-free data should conform.

The external pressure inferred for melt loss from a groupof hourglasses is roughly the pressure at which emptyingceased. The particular eruptive process responsible forquenching the hourglass emptying would need to be rapidcompared to the emptying rate of the hourglasses withthe smallest hourglass numbers. Such Bishop hourglasseswould attain observed gas fractions in minutes at crys-tallization temperature but would rigidify below 600 'C;

rapid cooling plausibly begins when magmatic foam dis-perses into spray (magma fragmentation of Wilson et al.,1980). In view ofthe essential role ofrapid cooling, it isappropriate that the pressure inferred for rigidification betermed the quenching pressure and be related to the pres-sure for magma disruption.

B,l,crcnouND GEol/ocy AND pETRoLocy oFTHE BISHOP TUFF

The Bishop Tuffformed 0.73 Ma when approximately600 km3 of rhyolitic magma erupted from the site of LongValley caldera on the eastern margin ofthe Sierra Nevadain east central California (Gilbert, 1938; Sheridan, 19651,Bailey et al.,1976; Hildreth, 1977,1979).It consists ofa basal, sorted, and stratified plinian ash-fall deposit anda group of poorly sorted ash-flow tuffsheets termed lobes.The Bishop Tuff may be divided into two gradationalparts on the basis of crystallization temperature and pres-ence of pyroxene phenocrysts: (l) an early-erupted, py-roxene-free part consisting ofthe plinian ash-fall depositsand overlying ash-flow lobes with relatively low pheno-cryst crystallization temperatures, and (2) a later-erupted,pyroxene-bearing part consisting of higher temperatureash-flows (Hildreth, 1977, 1979). Phenocryst composi-tions vary approximately monotonically with Fe-Ti oxideequilibration temperature and stratigraphic position (Hil-dreth, 1977 , 1979). This monotonic pattern together withthe uniformity of phenocryst compositions within indi-vidual samples (individual pumice clasts or closely relat-ed materials) reveals that little or no mixing occurredbefore and during eruption. Evidently, neither crystal set-tling, nor convection, nor even eruptive turbulence mixedthermally varied parts of the magma. The important im-plication is that either there were separate bodies of mag-ma or there was a single magma body that was stablystratified (nonconvecting before eruption and sequential-ly tapped during eruption) or the compositional zonationof the magma developed during the eruption.

Gas saturation in the Bishop magma is likely. Hildreth(1977, 1979) estimated that the Bishop plinian magma

0.8=-l.O

Hourg loss Number

Fig. 6. Graphs of hourglass number and gas fraction con-toured for various times and external pressures with parametersselected for the Bishop plinian magrna (A) and the Mono ash-flow magma (B) and (C) as in Figure 5. The horizontal scalesditrer: the scale for A is shown at top, B and C at bottorn. Eachgraph has three sets of curves (isochrons) corresponding to ex-ternal pressures of 400, 600, and 800 bars as shown. Only the400 bar isochrons have time value labels (e.g., 105 s) for clarity.As all equal-valued isochrons merge in the limit of low volo/ogas, the values for the 600 and 800 bar isochrons are readilyidentified from those for 400 bars. The values ticked offalongthe right side of the graphs give the pressure in kilobars corre-sponding to the equilibrium volo/o gas on the left (from Fig. 5).The size of the boxes provides a guide to the uncertainty in thehourglass numberand the gas fraction. Individual boxes are giv-en for some plinian hourglasses, as these vary depending oncomplexity of shape. The uncertainty in vol% gas is 100/0 to 20olorelative, thus the absolute uncertainty (box height) diminishesdownward toward the 00/o gas value. The vertical scale is ex-panded in B. Three hourglasses are not plotted (see Table 1).

was close to saturation with respect to pure HrO gas andthat the higher temperature magma was not. AlthoughHildreth's estimations have large unc€rtainties, his inter-pretation is not inconsistent with saturation of even the

Hourg loss Number

toz to3

8

1.0t.2t 6

l 4

n 5

0.620

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(9

bS

o

MONO ASH-FLOWH20=43wt 'L;C02= 669 OOt- 400 bors--- 600 bors' . " ' . . 800 bors

MONO ASH-FLOWH20=4Owt%;C02= l00ppm

A 7

0.80.9t.0

1.2

0,50.6

t o 5 c P L I N I A NH2O=5 .5w t % ;

\ - - 400borsl0os -- - 6o0 bors


Mono lobe magma with a gas rich in CO, as inferred byAnderson et al. (1989a). Anderson et al. (1989b) arguethat the pyroxene-free magma contained approximatelyl-2 wto/o of excess gas when inclusions formed in crys-tallizing quartz.

The rate of deposition of the Bishop Tuff appears tohave varied because the ash flows have multiple zones ofwelding, compaction, and devitrification (Sheridan, 19 67 ;Hildreth, 1977). However, the nature of the variations isargued. Snow and Yund (1988) have interpreted varia-tions in the exsolution in sanidine phenocrysts from athick ash flow to signify an eruptive-depositional inter-lude amounting to approximately I yr. Hildreth (1979)considered that the continuity of welding and negligibleerosion suggests a single continuous eruption. Althoughsome high-temperature material forms part of the earlyeruptive sequence south of the caldera, it is uncertainwhether the high-temperature Mono ash-flow lobe northof the caldera formed at a significantly later time.

S^q.Nrpr,rs

I have studied clasts of pumice from the plinian depositand the high temperature, late-erupted Mono ash-flowlobe. There is notable textural variability between clastsof pumice from the same stratigraphic level. This studyreports work on the following samples:

l. One 30-cm clast of long-vesicle, pyroxene-phyricpumice from the Mono ash flow: LV8l-18A. The clast isfrom nonwelded, vitric ash-flow tuffwithin a few metersof underlying Sierran granite at the Aeolian Buttes (B-77of Hildreth, 1977). The clast has a 2 cm thick buf rimaround a white core.

Approximately 100 m north and 20 m downhill fromthe sampling locality, the Mono ash flow is densely weld-ed and vitrophyric. Whether the difference in weldingreflects differences in depositional temperature, coolingrate, or overburden pressure is uncertain.

2. Pumice clasts (LV8l-32) from a proximal pumice-fall deposit at Sherwin summit on old U.S. highway 395(locality B-2 of Hildreth, 1977). Tragically, the clasts werecombined and treated as a single sample.

3. Two 3-cm clasts of pumice (B104-F, G) from a moredistal pumice-fall location from Hildreth's 8-104 sample(collected and donated by Hildreth).

S.q.]vrpr-n PREPARATTON

Crystals of quartz were extracted from clasts of pumiceby gentle crushing and by using heavy liquids or HrO tofloat off most of the glass. Glass was removed from thesurfaces of some quartz crystals by solution in HBF.. Thecrystals were immersed in 1.55 refractive index liquid forhours to days before handpicking to allow time for theliquid to penetrate cracks and vapor bubbles in crackedinclusions.

Pnrpu,ny cAS BUBBLES AND GAs SATURATToN

Primary gas bubbles in quartz would indicate that themagma from which the quartz and inclusions formed was

saturated with gas. A primary gas bubble is one that istoo large to have formed solely as a result of preferentialshrinkage of melt and too isolated to have formed fromnecking down (Roedder, 1979). In the Bishop quaftz,bubbles that comprise grcater than approximately 2 volo/oof uncracked, glassy inclusions are potentially primary.

Gas saturation means that gas is present. HrO satura-tion means that a gas is present that is virtually pure HrO.A magma can be gas saturated without being HrO satu-rated. The proportion of gas could be large or small.

This work calculates solubilities and gas saturationpressures for rhyolite by using Silver et al. (1990) for HrOand Blank et al. (1989) for COr.

ANr,vrrcl.r- METHoDS

HrO and CO, dissolved in one hourglass were deter-mined by infrared (IR) spectroscopy following Newmanet al. (1988). Some analyses were reported previously(Anderson et al., 1989a). Some hourglasses were analyzedby electron microprobe.

DnrnrurrNl.TroN oF HoURGLASS DTMENSToNS

The diameters of hourglass necks are critical for esti-mating durations of decompression because the time isinversely proportional to the fourth power of the diam-eter. Quartz samples were positioned in 1.55 index oiland the neck diameters were measured microscopically.Absolute uncertainties are approximately 0.5 to 2 p.m.Some necks narrow toward the crystal rim and some areoval in cross section. Generally, I recorded and used thesmallest neck diameter in the computations.

Neck lengths were measured similarly. A pythagoreancorrection was made if necessary.

Most hourglass volumes were estimated from two prin-cipal diameters measured in plan view. Some crystals wererepositioned so that the hourglass and its neck could beviewed in another perspective.

Srnucrunrs AND TExruREs oF BrsHop puMrcE.

QUARTZ, AND INCLUSIONS

Introduction

Certain features of the pumice, quartz, and inclusionshelp evaluate whether hourglasses form and empty dur-ing special episodes of magna evolution, quartz growth,gas bubble nucleation, pre- or syneruptive decompres-sion, or posteruptive cooling. I present evidence that somefeatures (vesicle size and inclusion shape) that might beassumed to be of posteruptive origin are at least partly ofpreeruptive origin.

Pumice

The size, shape, and abundance ofvesicles in Bishoppumice vary from clast to clast at the same stratigraphiclevel and within single clasts. Codeposited clasts had dif-ferent histories of vesiculation.

s36 ANDERSON: HOURGLASS INCLUSIONS

Fig.7. A conchoidally fractured surface (C) on a quartz phe-nocryst from the Mono ash flow. The conchoidally fracturedsurface is near the 200-pm scale bar and subperpendicular to theplane ofthe picture. Finely vesicular glass covers the entire frac-ture but is missing from most of the fractured surface parallel tothe plane of focus. The glass-coated fracture formed first in amelt-rich environment, and the uncoated fracture formed laterin a melt-poor (gas-rich) environment.

QuartzPhenocrysts of quartz are l-8 mm diameter subhedral

bipyramids. The crystal surfaces include flat faces, roundparts, and conchoidal fractures. All flat faces and someconchoidal surfaces (Fig. 7) are coated with vesicular glass.Fractures are both preemptive (glass coated) and post-eruptive (glass free). Many conchoidal surfaces are partlyfree of glass and intersect one or more cavities (Fig. 8),formerly inclusions of melt which burst. Such surfacesand burst inclusions plausibly formed in a gas-rich (pos-sibly posteruptive) environment. Most of the quartz massconsists of mostly faceted fragments comprising more thanapproximately half of the unfractured initial crystal. Aboutone in ten grains larger than 0.5 mm are euhedra. Com-pound grains of quartz containing two or more crystalsare virtually absent. The quartz fragments evidently re-flect natural and laboratory fragmentation of free-swim-ming individual crystals and no dislodgement of crystalsfrom intergrown 4ggregates and magma walls.

Glass coatings are thin and finely vesicular on mostplinian quartz and on all studied ash-flow quartz. Someplinian quartz has thick coatings of glass with thick-walledvesicles (Fig. 9). Because crystals with thick and thin glasscoatings occur in the same clast (e.g., Bl04-F), it seemslikely that variable outgassing occurred prior to pumiceclast lormation and extrusion.

Inclusions, hourglasses, and reentrants

There are significant variations in the devitrification,size, shape, abundance, and distribution of, and bubbleswithin, inclusions, hourglasses, and reentrants. Somevariations occur within individual crystals and likely re-

Fig. 8. A burst inclusion spread out over part of a fracturein a Mono quartz phenocryst. The incomplete coating of naturalfractures with glass indicates that some fracturing occurred in agas-rich environment probably after the ambient external meltlost the ability to flow. Scale bar is 50 pm.

flect preeruptive events. Others occur within and betweenpumice clasts and rock type and may reflect processesthat took place after deposition, as well as before extru-sion. The aim ofthis section is to describe and evaiuatecertain features that relate to the formation and evolutionof hourglasses before, during, and after eruption and de-position.

Fig. 9. A thick coating ofglass on a quartz phenocryst fromplinian clast B104-F. The glass coating lacks tiny vesicles suchas those seen in Figure 7, but has portions oflarge bubbles. Glassadhering to other crystals of quartz from the same clast of pum-ice is finely vesicular like that shown in Figure 7. The varioussizes ofbubble segments comprising attached glass on differentcrystals in the same clast of pumice suggests variable outgassingof melt prior to formation of pumice clasts. The scale bar is 200pm long.

-.1 'I


) l

Fig. 10. A plinian quartz phenocryst with large irregular in-clusions of glass. Numerous small inclusions occur throughoutthe quartz and most are smooth and equidimensional, but somenear the rim are elongate. The scale bar is 400 pm long.

Plinian inclusions, reentrants, and hourglasses are col-orless and not devitrified (Figs. l0-ll). Mono ash-flowinclusions from sample LV81-l8A are devitrified (Fig.l2), and the most finely devitrified (speckled) ones occurnear crystal rims (Fig. l3). The most coarsely devitrifiedMono inclusions are smaller than approximately 20 pm,but many tiny inclusions are poor in devitrification prod-ucts (Fig. l4). Mono reentrants are vitric (Fig. 3), as isthe glass that coats quartz crystals. Mono hourglasses rangefrom vitric (clear to brown and generally gas rich) to veryfinely devitrified (speckled and generally gas poor).

Devitrification is promoted by slow cooling and highHrO in melt or glass; devitrification of Mono inclusionsreflects slow cooling because their 4.00/o HrO comparedto 5.50/o in plinian inclusions (Anderson et al., 1989a;Skirius et al., 1990) would inhibit devitrification (for ex-ample degassed glass in reentrants and attached to crystal

Fig. I 1. A plinian hourglass with a large range of bubblesizes. The hourglass neck is poorly visible because it was largelydissolved with HBF4 and replaced with refractive index oil. Thedark edge ofthe photo is 400 pm long.

Fig. 12. An enclosed inclusion in Mono quartz showing de-vitrification speclles, sharp corners and edges, gas bubbles, anddaughter crystals attached to the bubbles. The scale bar is 100pm long.

surfaces is not devitrified). Some Mono hourglasses andreentrants are vitric because of low HrO content com-pared to inclusions (the reentrants cooled at the same rateas the inclusions). Extension of this reasoning suggeststhat fine devitrification of near-rim Mono inclusions re-flects low HrO melt of preeruptive origin. Increasedcoarsening of hourglass devitrifi cation (colorless to brownto speckled) with decreasing gas fraction is consistent withgreater melt HrO in gas-poor (less outgassed) hourglasses.

Most plinian inclusions are smooth and spherical, butsome that are smaller than 50 /rm are partly faceted. Pli-nian hourglasses and reentrants are also smooth. Monoinclusions from sample 18A are angular (faceted-Fig.

l2) to smooth (Fig. 15). Although some faceted inclusionsoccur near crystal rims, in crystals that contain both an-gular and smooth inclusions, the smooth inclusions arenearest the rim.

The faceted shapes of Mono inclusions are preeruptive

in origin because both round and faceted inclusions arefrom the same clast and are similady devitrified indicat-ing similar compositions as well as posteruptive cooling.


I

Fig. 13. Variably devitrified inclusions in a Mono quartz.The larger inclusion near the glass-coated rim of the quartz ismore finely devitrified. The photo is a mosaic because the twoinclusions are different focusing depth positions. A 100-pm scalebar.

Both kinds should, therefore, have annealed similarlyduring posteruptive cooling; their differences must bepreeruptive in origin. Beddoe-Stephens et al. (1983) sug-gested that faceting of inclusions reflects time-dependentannealing. Although preferential faceting of small plinianinclusions suggests more rapid annealing due to smallerdistances for solution and redeposition, the spatial ar-rangement of faceted and round inclusions in Mono quartzsuggests a dominant effect of time. Preeruptive evolutionof hourglasses might be associated with preeruptive an-nealing of Mono inclusions.

Bubbles are rare in plinian inclusions but almost ev-erpresent in inclusions from Mono ash-flow sample l8A.Most inclusion and hourglass bubbles are smooth andspherical, but some plinian hourglass bubbles are longwith sharp ends. Bubbles are smaller than approximately15 pm in inclusions and generally increase in size withinclusion size. Hourglasses have conspicuously largerbubbles up to approximately 100 pm. Single bubbles inMono inclusions increase in size up to approximately l5prm with increasing inclusion size; larger inclusions (ap-proximately 100-150 pm) that might contain larger sin-gle bubbles, instead contain multiple bubbles that com-monly are evenly spaced; many Mono inclusions largerthan approximately 150 pm have no bubble. All smallMono inclusions have a bubble. Most bubble-bearing in-clusions have only one bubble, but hourglasses common-ly have several. Reentrants generally lack bubbles. Mul-tiple bubbles in plinian hourglasses vary in size byapproximately a factor of five, but those in Mono inclu-sions and hourglasses are similar in size and are com-monly subequally spaced. Bubbles make up less than ap-proximately 4 vola/o of inclusion volume, except for Monoinclusions that are smaller than approximately 20 y"m.Bubbles make up 2-32 volo/o of most hourglasses (Figs.1,2, l l , and 16 and Table l ) .

When most bubbles formed, the melt was hot enoughto flow and form smooth spherical bubbles, but some

oo'

Fig. 14. Variably devitrified, bubble-bearing Mono inclu-sions. The smaller inclusions are most extensively devitrified.Scale bar is 100 pm long.

bubbles were quenched into long shapes that formed asmelt flowed outward through plinian hourglass necks. Thesmall bubble size, small gas fraction, and increase in bub-ble size with inclusion size indicates that inclusion bub-bles formed after inclusions were isolated (Roedder, 1979),but possibly belore eruption.

Some bubbles probably formed before eruption: twoanalyzed bubble-bearing plinian inclusions (B I 04-F-6 and-21) have greater CO, dissolved in the glass than bubble-

' a

.ri t.!--

Fig. 15. Round and faceted inclusions in a Mono quartz. Thelarger, rounder inclusion extends to a position closer to the glass-coated rim ofthe quartz. The scale bar is 200 pm long.

\

*


MONO ASH-FLOW LOBETlele 1. Textural data on hourglass inclusions

No. V D L HGN Gas Bubs Notes

F-1F-28F-28-2F-56F-57F-58F-60F-6232-50G10-62G10€0

0.61 . 90.391.31.O70.150.161 . 10.510.50.68

1 . 23.42.O0.680.781.971.470.840.64

15.92.80.380.421 . 1 40.14o.420.190.080.920.sri'0.49

Pinian hourglasses25 30 0.0046 8032 130 0.024 187.5 120 1.48 2

19 170 0.21 I20 50 0.03 2110 250 0.37 2720 50 0.005 't7

8.5 50 1.0 0.830 50 0.0031 3030 150 0.01 1320 50 0.02 80

Mono ash-flow lobe hourglasses7 5 0 2 . 5 57 100 't4.2 32

29 20 0.0057 6010 120 0.82 313 3 0 2 92 70 860

41 .5

1.5 68 1970 24.5 110 22.5 4

14 211 0.35 7.537 38 0.0322 1012 80 1 .1 8 .73 39 18.3 161.9 80 237 2.87.5 99 3.7 116 40 0.43 22

<1.0 ?60 2550 2.55 82 2.5 5.82 3 7 1 8 1 03.7 31 15.3 3.21 .9 37 103 5.51 12 590 2.6

many Ib

2 c2 h1 d9 d , g34 a , h1 a7 g

1 5 g , k

6 b , d5 a , b6 b , c , i , ? k2 b , d , e2 a , b3 c1 b , f

1 3 b , g1 b , g2 a , i1 b , g , h1 d , f1 c , b4 n , h1 a , g1 b , c , f1 b , c3 d1 b , c1 b , c4 b , a

1 12023263840455055o37074758283848597

1 1 01 1 11 1 6

Fig. 16. Line drawings ofhourglasses. Individual inclusionsare numbered, corresponding with Table l. Stippling indicatesbrown devitrification of gJass. Bubbles are unstippled.

free inclusions (Anderson et al., 1989a). If the bubblesformed from melts similar to those typified by the bub-ble-free inclusions, then the CO, would preferentially en-ter the bubble and deplete rather than enrich the glass inCOr. More CO, in bubble-bearing inclusions suggests for-mation at relatively high temperature and pressure: (l)cooling from a high entrapment temperature could causecrystallization of host quartz, preferential contraction ofmelt, and bubble formation; (2) a higher pressure of en-trapment (associated with a high temperature) allows moreCO, to dissolve in the melt.

The persistence of bubbles in the smallest Mono inclu-sions suggests that, contrary to the usual case (as for pli-nian bubbles) in which small inclusions are bubble-free(Roedder, 1979), there was, in the case of the Mono in-clusions, plenty of time to nucleate and grow bubbles.Likewise, the similar sizes of multiple bubbles suggestsurface energy (textural) equilibration typical of anneal-ing. The puzzlingabsence of bubbles in the largest Monoinclusions may reflect mechanical collapse of quartzaround the biggest (weakest) inclusions as melt cooledand contracted. This would only be likely at preeruptivepressures.

The large bubble size and gas content of hourglasses(as compared to inclusions) suggests decompression, lossof melt through their necks, and compensating bubblegrowth, as modeled above. Some gas volume in hour-glasses may be primary, and some volume probably isthe result of shrinkage during cooling.

The amount ofgas in Mono inclusions provides a guideto the amount of gas in hourglasses that may be of shrink-

Nofe: No. : inclusion number [nos. Fl to F-62 from 8104 (Hildreth,1977) pumice clast F; nos. 11-74from Mono ash-flow pumice block LV81-18A; no. 32-50 from plinian pumice LV8132; nos. G-10-30 and Gl0-62from 8-104 pumice clast Gl; V: volume of hourglass inclusion in units of10 6 cm3; D: diameter of hourglass neck in pm (10{ m); L : length ofneck in pm; HGN: dimensionless hourglass number : [Vl(AlLll x 10 ';

Gas : volume percent of gas in the hourglass; Bubs : number of separatebubbles ot gas in the hourglass; a: round shape; b: brown color; s:partly faceted shape; d : subround shape; e : two necks; f : bubblelocated near neck-gas lost from hourglass (?); g : neck terminates at afracture; h : irregular neck; i : off scale on Figure 6 (not plotted); j : gas-filled neck (not plotted); k : surface glassjree (not plotted).

age origin. For the Mono samples, the volo/o of gas variesinversely with inclusion diameter (relations are unsys-tematic for plinian bubbles). Inclusions (including somewith multiple bubbles) in ten Mono crystals roughly fitan inverse relation: G : 12 x Go x do/(d + dJl - Go,where Go is the extrapolated percent ofgas in an infini-tesimally small inclusion (d : 0), and do is the lineardimension (e.g., equivalent diameter) of the smallest in-clusion that is bubble free. For the Mono samples, thevalue of do is between 150 and 250 p.m and extrapolatedGo is around 4 volo/o regardless of inclusion shape. Inclu-sions that are comparable in size to most hourglasses(larger than approximately 100 pm equivalent diameter)have less than approximately 0.5 volo/o gas.

The numerous bubbles in plinian hourglasses and theirgreater range in size suggest continued nucleation causedby relatively rapid decompression. Low numbers of bub-bles in Mono hourglasses, by comparison, suggest littleor no bubble nucleation during decompression. If bubbles


nucleated during hourglass decompression, it is predictedthat hourglasses with small hourglass numbers would nu-cleate and grow more bubbles owing to more rapid de-compression. The evidence is equivocal on this point, butthe lack of bubbles in most reentrants suggests that fewbubbles nucleated during eruptive decompression. Al-though some postdepositional bubble modificatton seemsprobable, the small numbers and uniform sizes and spac-ings of Mono hourglass bubbles suggest nucleation beforeeruptive decompression.

Glass inclusions occur in most crystals of plinian andMono quartz and are sprinkled from core to rim. Zonesof inclusions are rare. Broad distribution of inclusionsindicates that inclusions of melt were trapped in quartzphenocrysts at many stages. Rare zones of inclusions sug-gest that episodes of preferential formation were few.

Although most reentrants are free of bubbles, some, incontrast with hourglasses, have a gas tube that extendsthrough the neck. Such reentrants could alternatively beconsidered to be gas-rich hourglasses. Because a gas tuberaises questions about how melt and gas escaped, I didnot consider such objects to be hourglasses.

Features of hourglasses are documented in Table I anddisplayed in Figures l, 2, ll, and 16. Mono ash-flowsample l8A yielded 20 hourglasses out of a populationof thousands of quartz crystals. In plinian samples, hour-glasses seem less common, but may be more difficult todiscern. Most hourglasses occur within approximately 300pm of the rim of the crystal (most necks are shorter than100 pm) and are slightly elongate in the direction per-pendicular to the rim. The long dimensions of a few hour-glasses are parallel to a [000] direction. Such long inclu-sions commonly lie near and parallel to a poorly developed(1010) face. Mono hourglasses are round with rare smallfacets, like large, near-rim enclosed inclusions. Hour-glasses with large necks are gradational with reentrants,which also are round and largely unfaceted.

Because of their near-rim position, it is likely that Monohourglasses formed later than most angular (faceted) en-closed inclusions. Mono hourglasses and near-rim, roundinclusions may have formed together in response to asystem-wide event.

That the necks of most hourglasses are growth-relatedis suggested by their orientation nearly perpendicular toa crystal face. A few terminate at conchoidal fractureswith an oblique angle. Two hourglasses have two, roughlycoplanar necks. The necks of the latter might have evolvedfrom cracks.

The necks of all but a few hourglasses studied terminateon quartz surfaces that are completely coated with glass.Even the conchoidal fractures that terminate hourglasses(LV8l-l8A-50, LV8l-l84-70, and Bl04-F-58) are com-pletely coated with glass. Hourglasses that vented into aregion that was hot enough and rich enough in melt sothat melt could wet newly formed fractures, probably lostmelt primarily before full vesiculation and extrusion. Rare,plinian hourglasses have a blob ofvesicular glass adher-ing to the surface of the crystal at the end of the neck.

Only hourglasses with glass-filled necks that terminate onglass-coated surfaces are plotted (Fig. 6) and interpreted.

Hourglass inclusion LVSl-l84-20 (Fie. l) is uniquelysignificant because ofthe large size, abundance, and pe-culiar shape of its bubbles. One of the five, almost equallyspaced bubbles is at least twice as big as the next largest.Three of the bubbles wet the quartz walls and are asym-metrical with their most strongly curved sides away fromthe neck. Within each bubble there is a single cluster ofradiating needle or blade-shaped birefringent crystals eachup to approximately 20 pm long. The longest crystals andthe biggest cluster of crystals are in the biggest bubble.Around each bubble there is a 20-40 pm wide region ofglass that has strain birefringence and is less devitrified(lighter tan in color). The hourglass has been analyzedbymicroprobe for major elements and spectroscopically forHrO and CO, near each end (Fig. l). The results are listedin Table 2 and discussed further below.

The textural features ofhourglass 20 are interpreted asfollows: the bubble shapes (more highly curved away fromthe neck) are taken as evidence of late flow of melt intothe hourglass. The largest bubble probably was the firstbubble to form; possibly it was present in the hourglasswhen decompression began. The equal spacing of thebubbles probably reflects the effect of difftrsion (mainlyof HrO) to increase the level of supersaturation with dis-tance from bubbles. HrO concentration and supersatu-ration and bubble nucleation rate would increase withdistance from preexisting growing bubbles. New bubbleswould preferentially nucleate near the point of maximumsupersaturation midway between preexisting bubbles. Thecrystals on the bubble walls probably formed by reactionbetween bubble gas and melt or glass on the wall.

CHnNrrclL coMposrrroN

Inclusions and hourglasses are high-silica rhyolite inboth plinian and Mono lobe quartz. Although nonvolatilemajor, minor, and trace elements are similar in plinianand Mono inclusions (Anderson et al., 1989a; Lu et al.,1990; Lu, unpublished data), Mono inclusions are richerin KrO and more variable in trace element composition.The work of Skirius (Skirius, 1989; Anderson et al., 1989a;Skirius et al., 1990; Skirius, unpublished data) revealsthat in terms of dissolved volatiles, there are two groupsof Mono inclusions: a high CO, group with CO, concen-trations between 480 and 600 ppm and a low CO, groupwith CO, between 300 and approximately 50 ppm. TheHrO concentrations are similar for both groups (3.7-4.5wto/o). Low CO, inclusions are most abundant and occurin five of five clasts; rare high CO, inclusions are knownin only two of the same five clasts. Angular and roundinclusions are present in both groups. Plinian inclusionshave more HrO but CO, similar to the low CO, Monoinclusions. H2O, COr, and Cl contents are lower in ana-lyzed Mono lobe hourglasses than in inclusions (Ander-son et al., 1989a; Skirius et al., 1990; Table l). HourglassLV8 I - I 8A-20 and two other Mono hourglasses have KrOtypical of plinian inclusions. Although the compositions

ANDERSON: HOURGLASS INCLUSIONS

TABLE 2, Chemical compositions of hourglass and other glass inclusions

541

Sample 20-1 20-2 20-3 1 1-1

sio,Alro3FeOCaONaroK"OSumHrOCO, (ppm)cl

77.312 .40.680.414.854.37

95.82 .1 '

21',0.00

77.212.40.600.504.814.53

96.02.6'

25-0.02

77.012.70.680.44.64.8

95.92.2

<500.02

/ 3 . C

13.30.760.43.56.1

93.64.6

3600.04

76.812.6o.720.53.55.8

96.74.5

2550.07

76.512.90.550.43.75.9

96.25.0

2800.08

78.011 .80.620.43.55.9

94.53.6

1450.06

77.613.30.60.33.94.6

92.5

0.08

76.213.2o.730.554.944.45

95.9nono0.05

77.212.90.60.43.75.9

94.3

Note: All numbered columns are individual glasses from Mono ash-flow pumice block LV81-18A. Column M : average Mono enclosed inclusion glass(Anderson et al., 1989a, Table 1, col.3); column P: average plinian enclosed inclusion glass (Anderson et al., 1989a, Table 1, col. 2); numbers 20-1'2O-2,20-3 are separate analyzed spots on inclusion LV81-18A-20 (see Fig. 1), spot 1 at far end, spot 3 near the neck, spot 2 intermediate. NumbersI and 1 5 were homogenized by heating before analysis. Numbers 20 and 1 are hourglass inclusions, the others, including the averages, refer to enclosedinclusions.

'Average of two determinations. Maior elements determined by electron microprobe using energy dispersive procedures and matrix @rrections asprogrammed for the Chicago microprobe by lan Steele, except for FeO and Cl which are based on crystal focusing spectrometers and aegerite andscapotite standards. Malor element oxides are normalized to 100% (except for minor rounding errors) based on the original microprobe sum that isgiven in the sum row. HrO and CO" determined by lR spectroscopy by C. Skirius at Chicago and Caltech using Nicolet 60SX instrumentation asdeveloped by Stolper and Newman and explained in Anderson et al. (1989a).

of plinian and Mono inclusions are more similar to eachother than are the respective bulk rocks, significant dif-ferences remain and indicate that the inclusions formedfrom distinct magmas. These facts reinforce the petro-graphic individuality documented by Hildreth (1977,1979) for separate parts of the Bishop Tuffand magma:separate quartz crystals formed in separate environmentsand did not mix, except perhaps at a late stage when somehourglasses formed.

Mnr,r INCLUsIoNs AND cRysrAL GRowrH

A concern is that melt inclusions will difer in com-position from the ambient melt as a result of boundarylayer processes (Watson et al., 1982). Except for one-component systems, a finite chemical potential gradientmust surround any actively growing crystal; if there wereno gradient, ingredients would not diftrse toward thecrystal and growth would stop. This is so whether chem-ical diffusion is rate limiting or not. The extent of enrich-ment (or depletion) is limited by the need to continuegrowth. Growth of qtartz, for example, requires that themelt next to the quartz has a lesser concentration of SiO,than that farther away. If the melt SiO, concentrationnext to quartz falls below the equilibrium value, growthof quartz may stop. Possibly quartz would continue togrow metastably from a melt with 70 wto/o SiO, (l0o/odepleted); such a melt might be in metastable equilibriumwith quartz, but would be supersaturated with respect tosanidine, etc. The range in AlrO. in inclusions and hour-glasses is approximately l5o/o (from ll.8 to 13.6 wt0/0,Table 2) including analytical error (4o/o) and variation dueto differentiation. Inverse correlations between compati-ble Mg, La, and incompatible U indicate that boundarylayer rejection oftrace elements from quartz is overshad-owed by the expected effects of crystallization differenti-ation of the polymineralic modal phenocryst assemblage(Lu et al., 1989, unpublished data). Although analytically

nondetectable boundary layer effects may influence nu-cleation (Bacon, 1989), boundary layer processes cannothave affected Bishop inclusion compositions except atlevels less than approximately l0o/o relative.

Gls nunnr-n voLUMES AND THE p-a rrrrvnnsroN

Quantitative interpretations of hourglasses depend ongas bubble volumes. At approximately 575'C (dependingon pressure), cooling quartz crystals undergo a sudden l0lovolumetric contraction due to the inversion from B to aquartz (Ghiorso et al., 1979). The volo/o of gas in an hour-glass or other inclusion might have been as much as lolomore (e.g., l.lolo rather than 0.lolo) before the 0-a inver-sion ofthe quartz host.

Clusns oF A LAcK oF pRTMARY GAS BUBBLES

Although the absence of large gas bubbles in large in-clusions is suggestive of gas-free magma, Donaldson andHenderson (1988) reveal that bubbles will migrate awayfrom growing q\artz, and Tait and Jaupart (1990) implythat bubble-bearing inclusions would preferentially rup-ture upon eruptive decompression. Donaldson and Hen-derson (1988) placed quartz crystals in superheated,gas-saturated melt and showed that gas bubbles erodereentrants into dissolving quartz phenocrysts. The ero-sive drilling of bubble and rnelt into the quartz occursbecause melt is swept around the surface of the bubbleand brought toward the dissolving quartz in response toa gradient in surface tension. The gradient in surface ten-sion arises because of the gradient in SiOn in the meltnext to dissolving quarlz. The transported melt acceler-ates the solution of the quartz because, coming from theside of the bubble farthest from quartz, it is more under-saturated with respect to quartz. If the quartz is crystal-lizing rather than dissolving, bubbles would migrate awayfrom, rather than toward, the growing quartz surface. Be-cause crystallization is required if a bubble is to become


trapped in quartz, bubbles must eventually tend to moveaway from the quartz. This is a plausible explanation forthe absence of primary bubbles of gas in inclusions inquaftz.

With isothermal decompression, inclusions larger thanapproximately Yt of the crystal are expected to rupture(Tait and Jaupart, 1990). Decompression is unlikely tobe isothermal, and a few degrees of cooling per kilobarsuftce to compensate for the elastic decompression effect.The survival of many inclusions up to 300 pm in sizesuggests that cooling during decompression has been suf-ficient to overcome the isothermal decompression effect.The survival of large inclusions with large bubbles is,however, problematical, because such inclusions wouldmaintain high internal pressures owing to the expansivityofthe gas. It is possible, therefore, that virtually all largebubble-bearing inclusions ruptured. Universal decrepi-tation of bubble-bearing large inclusions implies that allbubbles in surviving, large, uncracked inclusions formedas a result of posteruptive preferential contraction of melt.This is problematical for the two plinian inclusions men-tioned above that are rich in CO, and contain bubbles,and this is impossible for the hourglasses. The near ab-sence of large (possibly primary) gas bubbles in inclusionsis poorly explained by preferential rupture.

Trrn rNrrHr- cAs CoNTENT oFHOURGLASS INCLUSIONS

The observed gas and dissolved volatile contents of anhourglass can be used to infer whether the hourglass con-tained a significant amount of gas before decompression.As an example, consider the plinian-like, Mono lobehourglass LV8I-18A-20 (Tables I and 2). The bulk CO,in the gas + melt hourglass (approximately 3000 ppmassuming equilibrium between melt and gas at the esti-mated gas-saturation pressure of 360 bars) is much great-er than that of bubble-free COr-rich plinian inclusions(approximately 250 ppm COr, Skirius, unpublished data,1989). The excess CO2 points to the initial presence inthe hourglass of 2750 ppm of gaseous CO, (approximate-ly 2.5 volo/o of COr-rich gas at 1400 bars).

The amount ofgas estimated above is comparable withthe observed difference in volumes of the two largest bub-bles (approximately 5 volo/o of the entire hourglass). prob-ably, this hourglass contained a primary COr-rich gasbubble approximately 50 pm in diameter at approxi-mately 1400 bars.

OnrcrN oF HouRGLAss INcLUSToNsThe hourglasses either contained primary gas bubbles

or developed gas bubbles in the early stages of entrap-ment. The following reasoning shows that a bubble helpsan hourglass remain open. A 200-pm inclusion will ther-mally equilibrate with its surroundings in less than 0.01s, and a 2-mm quartz crystal will do likewise in less thanI s. Consequently, over the period (on the order of min-utes and greater) that seems likely for the formation andevolution ofhourglasses (see below), it can safely be as-

sumed that the temperature within the inclusion is buf-fered by that in the surrounding magma. If the surround-ing magma is gas saturated and decompressing, twocompeting processes will occur: (l) the quartz will tendto grow and enclose the inclusion because decompressioncauses H2O to exsolve thereby increasing the liquidustemperatwe of the ambient magma; (2) a bubble in anhourglass will expand with decompression and expel liq-uid through the neck thus tending to keep the neck open.Because the neck constricts the flow, the pressure withinthe inclusion will be greater than the ambient magmapressure outside the quartz. Consequently, the concentra-tion of HrO in the expelling melt will be greater than thatin the magma outside where quartz is crystallizing. (Lossof HrO from an hourglass by means of rapid diffusion ofH is limited by the small dissociation constant for HrOand by the inclusion's negligible redox capacity in com-parison with the available HrO [total oxidation of 0.5wto/o of FeO to FerO. would consume less than 0.07 w0/oof HrO].) For a given external decompressive supercool-ing necessary for continued crystallization of quartz, eachhourglass may approach a steady state condition wherebyfurther narrowing of the neck would result in a sufrcientlylarge pressure (and activity of HrO) within the hourglassthat the melt in the neck of the hourglass would not pre-cipitate qtrartz.In this way, the neck would not grow shut.Consequently, hourglasses have more gas than enclosedinclusions. According to this interpretation, two condi-tions must be met in order for hourglasses to form: (l)the magma parcel must be supercooled by efervescentdecompression, and (2) there must be a gas bubble in theforming hourglass. If this idea is upheld, we may inferfrom hourglasses that the magma containing them was(l) gas saturated, and (2) decompressing.

Hourglass formation by the above process underscoresthe obstacles to the entrapment of bubbles of gas in crys-tals of quartz growing in gas-saturated decompressingmagma. If a bubble-bearing reentrant or hourglass beginsto grow shut, pressure in the bubble causes melt relativelyrich in HrO to extrude through the neck and keep it open.If there is no bubble, the reentrant just grows shut andforms an inclusion. If there is no gas in the system, thereare no bubbles to be trapped and inclusions lack primarybubbles. If there is gas in the system, then there are twopossibilities: (1) the forming inclusion has no bubble andgrows shut, and, (2) the forming inclusion has a bubble,and because ofthis, it cannot grow shut. Instead, it formsan hourglass. In sum, physical factors lead to two pre-ferred outcomes: (l) an enclosed inclusion with no bubbleand (2) an hourglass with a bubble.

Assuprp"rroNs AND AppLrcATroNS To rHE BrsHopHOURGLASS INCLUSIONS

To apply the physical model outlined above and pre-sented in Appendix I to observational data, I make thefollowing necessary (l-4) and convenient (5-12) assump-trons:

ANDERSON: HOU RGLASS INCLUSIONS 543

l. The hourglass neck remained unchanged during meltloss.

2. There is a primary gas bubble, or there is a negli-gible delay in the nucleation ofthe first gas bubble.

3. Decompression was simultaneous for all hourglass-es in a single pumice clast.

4. Decompression was equal for all hourglasses in asingle pumice clast.

(As I discuss later, if sufficient data are available, it ispossible to test assumptions 3 and 4 and show that theyare not valid for all hourglasses in a single pumice clast.)

5. Decompression is isothermal.6. Enclosed melt inclusions and related hourglasses had

the same initial, bulk (gas + melt) volatile contents.7. Equilibrium is maintained between gas bubbles and

melt.8. Only melt (no gas) is lost from the hourglass.9. Any primary bubble was volumetrically negligible.10. Decompression was instantaneous.I l. Any yield strength of the melt is negligible com-

pared to the 1000 barlmm pressure gradients in the hour-glass necks.

12. The flow regime in the necks was laminar.All but four of the assumptions seem reasonable. Space

does not permit presentation of all of the justifications.Below, I discuss briefly the four assumptions that I findto be problematical.

Assumption 1. Except for possible stagnant periods (nopressure gradient in the neck) when diffusion might beimportant, the amount of melt that has been lost throughthe neck is the amount of melt that could deposit or erodequartz in the neck. I expect change in SiO, to be causedby and proportional to a drop in HrO content ofthe hour-glass melt (corresponding to the gas content-32 vo10/o forhourglass 20). Associating the maximum range in SiO,with the near maximum amount of gas for hourglass 20yields my estimate of 0.03/0,3 : 0.1 for the change inmass fraction of SiO, in melt per volume fraction of gasin the hourglass. Inclusions with narrow necks (largehourglass numbers) are most affected. Applying this rea-soning to inclusion 45, with one of the largest hourglassnumbers, yiolds the result that the diameter of the neckdecreased from 2.5 to 1.5 pm as a result of quartz de-posited from the escaping decompressed melt. The cor-responding effect on the hourglass number is approxi-mately a factor of eight. This is an overestimate becausethe early evolution of the hourglass is dominated by COr-rich gas that has little effect on liquidus relations andbecause temperature is assurned constant, but this valuemay rise with rapid release of latent heat of crystalliza-tion.

Assumption 4. External (decompressed) pressures pos-sibly differed for the various hourglasses. This possibilityis suggested by the variable vesicularity within clasts ofpumice and in glass adhering to phenocrysts. Shear ofmagma approaching the vent would be expected to bringtogether material from different initial depths (see Spera,I 984; Spera et al., I 986; Blake and Ivey, I 986). However,

this would only be important in the case where the hour-glasses did most of their emptying at pressures within thebody of magma below the eruptive conduits. The resultsand discussion below reveal that this is likely only forhourglasses with less than approximately 3 volo/o of gas.Wilson et al. (1980) point out the likelihood of recyclingof large clasts in the conduit near the depths of magmadisruption. Recycling would allow recombination ofmagma bits with varied decompression histories.

Assumption 8. It is at least conceivable that one ormore tiny bubbles of gas could be lost with the meltthrough the neck. This will not make a big differencebecause the lost gas, like lost melt, would be compensatedby new gas volume within the hourglass. In addition, therelatively low density of the gas limits the amount ofvolatile lost, but loss of gas could remove significant COr.Eventually analyses of hourglass volatiles (in glass andrestored gas bubbles) can be compared with those of en-closed inclusions. Ifthere has been significant loss ofgas,the bulk CO, contant of the hourglass will be low.

Assumption 9. The assumption that the amount of gaspresent before decompression was negligible is inconsis-tent with the proposed origin of the hourglasses. How-ever, for hourglasses with more than a few volo/o of gas,it probably is a satisfactory approximation. The primarybubble inferred for hourglass 20 is only 2.5 volo/o at 1400bars and would be less at greater pressures. We may ex-pect problems for hourglasses with small amounts of gas.This means that the quenching pressure is constrainedwith greater confidence than is the duration of decom-pression, since the duration depends mostly on hourglass-es that are poor in gas. For these hourglasses, both thepresence ofan initial bubble and the B-a inversion posesignificant problems.

Estimation of melt viscosity

In calculating the curves on Figure 6, I approximatedthe melt viscosity with an exponential function of tem-p€rature and HrO dissolved in the melt (Appendix I, Eq.22, approximated from Shaw, 1972). I assumed constanttemperatures equal to those of preeruptive intratelluriccrystallization (790 oC for Mono magma and 725 "C forplinian magma) documented by Hildreth (1979). Recal-ibrations of the Fe-Ti oxide geothermometer (see Storm-er, 1983; Andersen and Lindsley, 1988; Tacker, personalcommunication) shift temperatures upward by approxi-mately 35 "C. These changes, if adopted, would decreasethe times calculated for emptying the hourglasses by approximately a factor of 3.

Plinian ash-fall hourglass inclusions

By comparing observed fractions and dimensions(hourglass numbers) of hourglasses with appropriatecomputed isochrons, it is possible to estimate both the(minimum) duration of time and the quenching (or ex-ternal) pressure. Although subjective, this procedure yieldsa useful range ofconditions appropriate for various plau-sible initial conditions.

544 ANDERSON: HOURCLASS INCLUSIONS

Hourglasses in the plinian pumices are irregular andtheir hourglass numbers have large uncertainties. Nev-ertheless, a plot of gas fraction vs. hourglass number (Fig.6A) reveals the expected negative correlation for sevenout of nine hourglasses. Six of the seven are from thesame clast of pumice, Bl04-F. Hourglass 58, also fromBl04-F, is unusual in that it terminates on a conchoidalfracture and is carrot shaped. The spread of points onFigure 6 suggests a two-minute duration of decompres-sion. Time is so short that nonuniform cooling of pumiceblocks larger thart l0 cm in diameter might be expectedto cause detectable variation in evolution times. Aquenching pressure as small as approximately 400 barsis likely. The implied speed of ascent from 1800 to 400bars is approximately 40 m/s. If a constant speed of as-cent of 30 m/s (10 bars/s) is assumed, then the total pli-nian evolution time is increased to 3 min.

The Mono ash-flow lobe hourglass inclusions

Mono hourglasses (Fig. 68, 6C) range over 5 orders ofmagnitude from 300 to 2.5 x 107 and may be put intothree groups: (l) five hourglasses with very large hour-glass numbers and uniformly small gas fractions (nos. 40,45,75,84, and l16); (2) eight hourglasses forming thelower bound in terms of gas fraction [nos. I l, 38, 50, 55,65 (offscale at HGN : 300 and gas fraction : 0.1), 70,85, I l0l; and (3) the remaining seven hourglasses.

The Mono hourglasses cannot be explained by any sin-gle isochron (Fig. 6) representing instantaneous decom-pression. In view of their near-rim location, Mono hour-glasses are probably best interpreted as evolving frommelts like the low-CO, inclusions (Fig. 6C), since bothprobably formed late in decompressing magma. How-ever, comparison with Figure 68 (for the high CO, case)shows that this choice is not crucial. My interpretation isas follows. (l) The broad negative relation between gasfraction and hourglass number for the first two groupsindicates that the idea of emptying through the neck as aresult of decompression is valid for the Mono as well asplinian hourglasses. (2) Hourglass 65 (off scale on Fig.6B, 6C) has such a small hourglass number (300) that itwould evolve in less than 5 min at 790"C and 8 h at 635'C. [Hourglass 23 (also off scale on Fig. 68), although ofproblematical character, provides a similar result: l2 minat 790 'C.l Assuming similar cooling [reasonable forhourglasses in the large block (l8A) because its deposi-tional temperature was likely near or below 635 "C-seebelowl, an hourglass with hourglass number of 3000 wouldevolve only I volo/o gas while hourglass 65 evolved its l0volo/o gas. Hourglass 65 thus limits posteruptive gas evo-lution in most other Mono hourglasses to negligibleamounts. This limit and the glass coatings on quartz atthe ends of necks suggest that most hourglasses evolvedmainly before extrusion and in melt-rich (thus gas-poor,high-pressure, and hot) environments. (3) The low gasfractions in the group I hourglasses with large hourglassnumbers suggest a common decompression history inpreference to an accidental coincidence of similar pri-

mary gas fractions. Because isochrons that fit group Ihourglasses are too long for group 2 hourglasses, I con-sider these groups separately.

Group I hourglasses possibly reflect pressure equilibra-tion within a partially decompressed environment. I as-sume that 0.5 volo/o of gas was produced by shrinkage(suggested by analogy with shrinkage bubbles in associ-ated inclusions). The remaining 2.0 volo/o of gas corre-sponds to an internal pressure ofapproximately l.l kbar,assuming an initial high CO, melt composition appro-priate for the high CO, Mono lobe inclusions (Andersonet al., 1989a; Skirius et al., 1990; see Fig. 5). The l.l kbarvalue is in the range ofgas saturation pressures for lowCO, inclusions from the same clasts (Skirius et al., 1990)and less than most plinian inclusions. Thus, it is self-consistent to suggest that, during or after and as a con-sequence of eruption of plinian magma, the Mono mag-ma decompressed to l.l kbar from an initial pressure of2.4 kbar. Crystallization caused by the supersaturationattending effervescent decompression plausibly gave riseto a group of inclusions and hourglasses that formed atapproximately l.l kbar. Computations show that, ifhourglass 45 (Fig. 6C) evolved 2.0 volo/o gas as a result ofexternal decompression from 2.4 to l.l kbar, the timerequired is at least approximately 5 x lOs s (roughly aweek).

Group 2 hourglasses bounding the lower limit of thegas fraction fit roughly an intermediate isochron markedby a quenching pressure of approximately 0.7 kbar andapproximately lOa s (a few hours). The isochrons are morenegatively sloped than the data, however, suggesting anacceleration of decompression with time, as might be ex-pected for expanding magma rising into a uniform ornarrowing conduit. If these hourglasses started out with2o/o gas, like the low-gas hourglasses, then the time fortheir ascent and decompression would be only approxi-mately 1000 s (15 min). The amount of gas that the fivehourglasses with huge hourglass numbers would havegained during their last 15 min at 790 "C is negligible.The implied rate of ascent from l.l kbar to the quenchingpressure of 0.7 kbar is about I m/s.

The remaining Mono hourglasses (nos. 20,26,74, 82,83,97, and lll) have anomalously large gas fractions(Fie. 68). Of these hourglasses, 82, 97, and I I I are per-haps within the large uncertainties ofthe group 2 hour-glasses. Either the anomalous hourglasses had initiallylarge fractions ofgas or they decompressed to consider-ably lower pressures than the main group before beingcoextruded or both. The textural and compositional datafor hourglass 20 indicate preeruptive decompression toan external pressure of0.4 kbar or less. Because its hour-glass number is in the same range as the low-gas hour-glasses, but it evolved much more gas, it must have beenin a decompressed environment for a longer time (about2 weeks at least). Similar interpretations may be valid forthe other anomalous hourglasses.

It is noteworthy that the time (weeks) needed to par-tially empty hourglass 20 is similar to the time needed to


equilibrate the gas-poor hourglasses at I 100 bars. Bothof these are, however, minimal times. Because hourglass20 has a plinianJike KrO content, 1 srrggest that its esti-mated duration of decompression reflects an interval oftime separating eruption of the plinian magma from theMono magma. Although an eruption duration of twoweeks is significantly less than suggested by the work ofSnow and Yund (1988), Hildreth (1979, personal com-munication, 1990) considers that the lack of significanterosional breaks is best explained in terms of a continu-ous eruption of short duration. Further studies of hour-glasses from other parts of the Bishop Tuffare needed tocheck on the relations between hourglass evolution anderuption history.

Houncr,lssEs, ERUTTIoN DyNAMrcs, ANDQUENCHING HISTORY

I have argued above, on the basis ofobserved textures,that both the plinian and Mono hourglasses evolvedlargely before deposition and postdepositional cooling.This restricts postdepositional cooling to low tempera-tures (and high melt viscosities) or short times or both.Plinian pumice will be cooled below approximately 400.C by entrained air probably within l0 s of magma dis-ruption (Wilson et al., 1980; Woods, 1988). Models ofash-flow producing eruptions suggest that a Bishop-likerhyolitic magma with approximately 5 wto/o HrO would(l) cool by approximately 30 oC in less than l0 s due togas expansion between the depth of magma disruptionand the vent (Wilson et al., 1980); (2) entrain enough airin a collapsing eruption column to cause cooling of an-other 80 .C in approximately 20 s (Sparks et al., 1978;Woods, 1988); and (3) cool by less than approximately45 "C during approximately 200 s of ash-flow transport(Boyd, l96l; Sparks et al., 1978). Although the abovefigures depend on many unknown parameters such aseruption rate, vent size and shape, preeruption gas con-tent, etc. and can only be regarded as crude guides, it isevident that, compared with the times for evolution ofplinian as well as Mono hourglasses, the predepositionalcooling is likely to be fast. The amount of such cooling,however, need not be large for ash flows.

If predepositional cooling was small (<150 'C), thenpostdepositional evolution ofhourglasses can be signifi-cant. Near the sample site for Mono ash-flow sampleLV8l- l8A the ash flow is densely welded and vitrophyricindicating that some Mono ash-flow material reached thesampling locality while hot enough to weld (>625 "C-Smith, 1960). A temperature as high as 635 "C is consis-tent with the coolings enumerated above if the intratel-luric crystallization temperature was 790 'C (Hildreth,1977, 1979). The exact cooling environment of the Monosample is unknown, but the relations at the outcrop sug-gest that most samples would have cooled at elevationsless than approximately 5 m from cold ground. Accord-ing to conductive theory, the clast might have remainedwarmer than 600 oC for approximately I yr. Most hour-glasses would evolve a significant amount of gas at 635

"C in a year if they contained 4 wto/o of HrO and 100 ppmof CO, dissolved in the melt. Based on hourglass LV8 I -

l8A-65 (HGN : 300), this did not occur, possibly becausethe nonwelded Mono clast was deposited at or below ap-proximately 600 'C (significantly below that temperatureconsidered necessary for welding).

The magma ascent rate of approximately 40 m/s im-plied by plinian hourglasses is consistent with modeledrates of ascent of 2-100 m/s below the level of magmadisruption (Wilson et al., 1980). The magma ascent rateof 1 m/s implied by the eight Mono hourglasses with 3-l0 volo/o of gas is consistent with a maximum ascent rateof approximately I m/s for magmatic foam feeding a col-lapsing (ash-flow producing) fountain [the maximum vent(l bar) velocity of a collapsing fountain of rhyolitic mag-ma with 5 wto/o HrO is approximately 70 m/s (Woods,1988)1. The 700 bar quenching pressure of the Monohourglasses, although notably gtreater than predictedmagma disruption pressures (less than approximately 400bars), seems not surprising in view of long vesicles inMono pumice that suggest qualitatively htgh pressurequenching deep in a constricted conduit before vesiclescould expand and become equant. Possibly magma dis-ruption is aided by decompression transients associatedwith tensional cracking of the conduit.

A weeks-long eruption duration for the 600 km3 BishopTuffis consistent with theoretically predicted mass-erup-tion rates (Wilson et al., 1980; Woods, 1988) for bigrhyolitic eruptions. The implication that significant crys-tal gowth (entrapment of low-pressure melt inclusionsand evolution of gas-poor hourglasses with hourglassnumbers >106) occurred during the eruption may beproblematical. However, it is noteworthy that latent heatreleased by rapid crystallization in response to efferves-cent decompression would heat the magma and couldhelp account for the observed increase in temperature.

Some key assumptions in the above logic are that thegas bubbles suffered negligible delay in nucleating, thatthe gas bubbles had time to equilibrate and grow, andthat the preeruptive concentration of HrO in the hour-glass melt was roughly the same as that in enclosed in-clusions. These assumptions can be argued and tested. Inthe meantime, future work should make use of geologicaltests by studying hourglasses from separate clasts ofstratigraphically equivalent pumice at various distancesfrom the cold ground.

CoNcr,usroNs

Hourglass inclusions probably form in gas-saturated,decompressing magma as growing phenocrysts surroundreentrants of melt that contain a tiny bubble of gas. De-compression causes melt to be lost through a narrow neckthat is kept open because ofthe higher concentration ofHrO within the hourglass melt than in the surroundingdecompressed magma. As melt is lost, an equal volumeof gas forms within the hourglass. Consequently, theamount of gas in the hourglass increases. A quantitativemodel of the emptying process can be used to constrain


both the duration and extent ofdecompression from tex-tural data. In addition, it is possible to estimate the massand size of initial (high-pressure) gas bubbles in magmaby comparing the bulk volatile contents of hourglassesand coeval inclusions.

The concepts have been applied to hourglasses fromparts of the Bishop Tuff with the following results:

Plinian magma ascended rapidly (-40 m/s) as expect-ed.

Some Mono magma first decompressed from approx-imately 2.4 kbar to approximately l.l kbar over a periodof approximately a week. Final decompression to ap-proximately 700 bars took approximately l5 min, imply-ing a final ascent at I m/s. One (perhaps several) hour-glass was repressurized after being at 400 bars or less fora week or two, at least. The week-long duration may re-late to the interval of time between the eruption of theplinian pumice fall and the Mono ash-flow lobe. Thepressure of eruptive quenching (disruption of foam intospray?) was approximately 700 bars.

Inclusion LV8l-l8A-20 (derived from plinian-likemagma but extruded in the Mono ash-flow lobe) proba-bly had a primary gas bubble 50 pm in diameter at apressure of 1400 bars.

Hourglass inclusions preserve a record of eruptive phe-nomena on time scales ranging from minutes to weeks,at least. They can provide a temporal view of the fillingand evacuation of near-surface magma bodies that is oth-erwise accessible only from theory. Hourglasses shouldbe used together with enclosed inclusions to investigatedurations of eruptions and eruptive interludes, to inves-tigate rates of magma ascent, and to constrain the storagedepth of preeruptive magma. This may lead to a betterunderstanding of eruption mechanisms and preeruptivephenomena.

AcxhrowlnocMENTS

I especially thank Chrisrine Skirius and Fangqiong Lu, two graduatestudents at Chicago, for their helpful questions and discussions. In addi-tion, I am indebted to Skirius for obtaining and assessing the dau ofTable 2. I thank Wes Hildreth for some samples and Tim Druitt, FredNagle, and Stan Williams for other samples and for facts and ideas aboutfield and textural relations. Discussions with Wes Hildreth, Roy Bailey,Charlie Bacon, Bill Rose, and Gerhard Wtirner were helpful. John Wolffdrew my attention to the important work by Donaldson and Henderson.I am grateful to Ed Roedder, Bill Nash, and Wes Hildreth for reviewingthe manuscript. I owe a great debt to Sally Newman and Ed Stolper foradvice and help. Of course, I alone am responsible for any errors- Partsof this work were supported by NSF grants 85-20934 and 89-04070 andDOE contract 10763.

RnrnnrNcns crrEDAndersen, D.J., and Lindsley, D.H. (1988) Internally consistenr solution

models for Fe-Mg-Mn-Ti oxides: Fe-Ti oxides. American Mineralogist,73. 7 r4-726.

Anderson, A.T., Jr., Newman, S., Williams, S.N., Druitt, T.H., Skirius,C., and Stolper, E. (1989a) HrO, CO,, Cl and gas in plinian and ash-flow Bishop rhyolite. Geology, 17,221-225.

Anderson, A.T., Jr., Skirius, C.M., Lu, F., and Davis, A.M. (1989b) Pre-eruption gas content of Bishop plinian rhyolitic magma. GeologicalSociety of America Abstracts with Programs, 21, no. 6, A270.

Bacon, C.R. (1989) Crystallization of accessory phases in magmas by localsaturation adjacent to phenocryst. Geochimica et Cosmochimica Acta,53 ,1055 -1066 .

Bailey, R.A., Dalrymple, G.8., and Lanphere, M.A. (1976) Volcanism,structure, and geochronology of Long Valley caldera, Mono County,California. Joumal of Geophysical Research , 8l, 725-7 44.

Beddoe-Stephens, B., Aspden, J.A., and Shepherd, T.J. (1983) Glass in-clusions and melt compositions of the Toba tuffs, northern Sumatra.Contributions to Mineralogy and Petrology, 83, 278-287.

Blake, S., and Ivey, G.N. (1986) Density and viscosity gradients in zonedmagma chambers, and their innuence on withdrawal dynamics. Joumalof Volcanology and Geothermal Research, 30, 201-230.

Blank, J.G., Stolper, E.M., Sheng, J., and Epstein, S. (1989) The solubilityofCO, in rhyolitic melt at pressures to 1500 bars. Geological Societyof America Abstracts with Programs, 21, 4,157 .

Boyd, F.R. (1961) Welded tuffs and flows in the rhyolite plateau of Yel-lowstone Park, Wyoming. Geological Society of America Bulletin, 72,387-426.

Bumham, C.W. (1979) The importance of volatile constituents. In H.S.Yoder, Jr., Ed., The evolution ofthe igneous rocks- Fiftieth anniversaryperspectives, p. 439-482. Princeton University Press, Princeton, NewJersey-

Donaldson, C.H., and Henderson, C.M.B. (198E) A new interpretation ofround embayments in quartz crystals. Mineralogical Magazine, 52,27 -

33 .Flowers, G. C. (1979) Correction ofHolloway's (1977) adaptation ofthe

modified Redlich-Kwong equation of state for calculation of the fugac-ities of molecular species in supercritical ffuids of geological interest.Contributions to Mineralogy and Petrology, 69, 3 I 5-3 I 8.

Ghiorso, M.S., Carmichael, I.S.E., and Moret, L.K. (1979) Inverted high-temperature quartz; unit cell parameters and properties of the alpha-beta inversion. Contributions to Mineralogy and Petrology, 68,307-

Gilbert, C.M. (1938) Welded tuffin eastern California. Geological Societyof American Bulletin, 49, 1829-1862.

Hildrerh, E.W. (1977) The magma chamber of the Bishop Tuff: Gradientsin temperature, pressure and composition, 328 p. Ph.D. thesis, Uni-versity of California, Berkeley, Berkeley, Califomia.

- (1979) The Bishop Tuff Evidence for the origin ofcompositionalzonation in silicic magma chambers. Geological Society of AmericaSpecial Paper, l8O, 43-7 5.

Holloway, J.R. (1977) Fugacity and activity in molecular species in su-percritical fluids. In D. Fraser, Ed., Thermodynamics in geology, p.161-181. Reidel, Dordrecht, The Netherlands.

Kozlowski, A. (1981) Melt inclusions in pyroclastic quartz from the Car-boniferous deposits of the Holy Cross Mts., and the problem of mag-matic corrosion. Acta Geologica Polonica, 31,273-284.

Lu, F., Davis, A.M., Skirius, C.M., and Anderson, A.T., Jr. (19E9) Sig-nificance of uranium variations in rhyolitic melt inclusions frorn theBishop plinian and early ash-flow deposits. Geological Society ofAmerica Abstract with Programs, 21, no.6, 4271.

Lu, F., Anderson, A.T., Jr., and Davis, A-M. (1990) knplications of glassinclusions for the origins of high silica rhyolite and compositional zo-nation ofthe Bishop Tufl California. Eos, 71, 651.

Newman, S., Epstein, S., and Stolper, E. (1988) Water, carbon dioxide,and hydrogen isotopes in glasses from the ca. 1340 A.D. eruption ofthe Mono Craters, California: Constraints on degassing phenomena andinitial volatile content. Journal of Volcanology and Geothermal Re-search. 35. 75-96.

Roedder, E. (1979) Origin and significance of magmatic inclusions. Bul-letin Min6ralogique, 102, 4E7-5 I 0.

Shaw, H-R (1972) Viscosities of magmatic silicate liquids: An empiricalmethod of prediction. American Journal of Science, 272, 870-893.

Sheridan, M.F. (l 965) The mineralogy and petrology of the Bishop Tuff,165 p. Ph.D. thesis, Stanford University, Palo Alto, Califorma.

- (1967) Double cooling unit nature of the Bishop tuff in OwensRiver Gorge, Califomia (abs.). Geological Society of America, SpecialPaper, I 15, 351.

Silver, L.A., Ihinger, P.D., and Stolper, E. (1990) The influence ofbulkcomposition on the speciation ofwater in silicate glasses. Contributionsto Mineralogy and Petrology, 104,142-162.

Skirius, C.M. (1989) Pre-eruptive H,O and CO, in Plinian and early ashflow magma of the Bishop Tuff(abs.). IAVCEI Abstracts, New MexicoInstitute of Mines and Mineral Resources Bulletin. 131. 245.

Skirius, C.M., Peterson, J.W., and Anderson, A.T., Jr. (1990) Homoge-nizing rhyolitic glass inclusions from the Bishop Tuff. American Min-eralogist ,1381-1398.

Smith, R.L. (1960) Zones and zonal variations in welded ash-flows. U.S.Geological Survey Professional Paper, 345-f.

Snow, E., and Yund, R.A. (1988) Origin of cryptoperthites in the Bishoptuf and their bearing on its thermal history. Journal of GeophysicalResearch. 93. 8975-8984.

Sparks, R.S.J., and Brazier, S. (1982) New evidence for degassing pro-cesses during explosive eruptions. Nature, 295, 218-220.

Sparks, R.S.J., Wilson, L., and Huhne, G. (1978) Theoretical modelingofthe generation, movement and emplacement ofpyroclastic flows bycof umn collapse. Journal of Geophysical Research, 83, 17 27 -17 39.

Spera, R.J. (1984) Some numerical experiments on the withdrawal ofmagma from crustal reservoirs. Journal of Geophysical Research, 89,8222-8236.

Spera, R.J., Yuen, D.A., Greer, J.C., and Sewell, G. (1986) Dynamics ofwithdrawal from stratified rnagma chambers. Geology, 14, iZ3-726.

547

Stormer, J.C. (1983) The effects of recalculation on estimates oftemper-ature and oxygen fugacity from analyses of multi-cornponent iron-ti-tanium oxides. American Mineralogist, 68, 586-594.

Tait, S.R., and Jaupart, C. (1 990) Selective preservation ofmelt inclusionsin crystals. Eos, 71, 650.

Watson, E.8., Sneeringer, M.A., and Ross, A. (1982) Difrrsion of dis-solved carbonate in magmas: Experimental results and applications.Earth and Planelary Science Letters, 61, 346-358.

Whitham, A.G, and Sparks, R.S.J. (1986) Pumice. Bulletin of Volcanol-ogy,48,209-223.

Wilson, L., Sparks, R.S.J., and Walker, G.P.L. (1980) Explosive volcaniceruptions IY. The control of magma properties and conduit geometryon eruption column behavior. Geophysical Journal of the Royal As-tronomical Society, 63, I l7-148.

Woods, A.W. (1988) The fluid dynamics and thermodynamics of eruptioncolumns. Bulletin of Volcanology, 50, 169-193.

Mexr;scnrrr RECETvED Apnl 4, 1990Menuscnrr"r AccEprED JeNuenv I l, 1991

ANDERSON: HOURGLASS INCLUSIONS

hourglass inclusions: theory and application to the bishop

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