12. See Table I2 in (2).13. A systematic error of 4I km in the radii of all nine

Uranian rings would be required in order for theresonance radius to match the 8 ring radius. Theestimated uncertainty in the 8 ring semimajor axis isabout 5 km (2).

I4. The estimate of the satellite mass is based on astreamline formalism that does not take into ac-

count damping due to particle collisions. Conse-quently, the predicted satellite size is approximate.

IS. B. A. Smith, in Proceedigs of the Uranus andNeptune Workshop, NASA Conf. Publ. 2330, (1984), p.213.

I6. P. D. Nicholson, ibid., p. 589.I7. R. H. Brown et al., Nature (London) 300, 423 (1982).

Nature (London) 300, 423 (I982).

i8. We thank S. Tremaine for helpful discussions andfor suggesting that we search for Lindblad reso-nances and S. Levine for helping with the dataanalysis. Supported in part by grants NAGW-6s6and NSG-7526 from The National Aeronautics andSpace Administration.

20 November i985; accepted 26 December 1985

Model for the Intrusion of Batholiths Associated withthe Eruption of Large-Volume Ash-Flow Tuffs

JAMES A. WHITNEY AND JOHN C. STORMER, JR.

Pyroclastic eruption and the intrusion of batholiths associated with large-volume ash-flow tuffs may be driven by a decrease in reservoir pressure caused by the low density ofthe magma column due to vesiculation. Batholithic intrusion would then be accom-plished by the subsidence and settling of kilometer-sized crustal blocks through themagma chamber, resulting in eventual collapse to form large caldera structures at thesurface. Such a model does not require the formation of a large, laterally extensive,shallow magma chamber before the onset of large-volume ash-flow eruptions. Erup-tion could commence directly from a deeper reservoir, with only a small channelwaybeing opened to the surface before the onset of catastrophic ash-flow eruptions of thescale ofYellowstone or Long Valley. Such a model has wide-ranging implications, andexplains many ofthe problems inherent in the simple collapse model involving shallowmagna chambers as well as the process and timing ofbatholith intrusion in such cases.

IN THIS REPORT WVE OUTLINE A MODELfor the emplacement of batholiths andthe eruption mechanism for large-vol-

ume ash-flow tuffs. Because this model satis-fies many of the physical data now available,and since it has dramatic implications forvolcanic hazards and hydrothermal powerprojects, it should be considered as a possi-ble altemative to the shallow magma cham-ber collapse model currently being proposedfor all caldera-forming events.The emplacement ofbatholiths has always

been a problem in geology because of theneed to explain where the original rockswent. Since the magma comes from below,some process must cause crustal subsidenceto offset the upward movement of the mag-ma. Large-volume ash flows such as theBishop (1), Yellowstone (2), and San JuanMountains (3) tuffs represent 500 to 3000km3 of material, implying magma systems ofbatholithic proportions (a batholith is aminimum of 100 km2 in outcrop area; mostare not more than 5 km thick). Since manybatholiths are accompanied by cogeneticash-flow tuffs immediately before their finalemplacement, both share common originsand should be intimately related in intrusiveand extrusive history.A second problem is that a number of

recent ash-flow eruptions do not seem tohave left behind extensive and continuousshallow magma chambers, as would be sug-gested by the current model of caldera col-lapse into a preexisting shallow chamber (4).Therefore the question must be asked,where did the magma go?As silicic magma coalesces in the lower

crust, it will begin to rise diapirically whenthe body becomes large enough (5). Thistype of upward migration depends on thesurrounding material being plastic becauseof high temperatures and confining pres-sures. As the magma moves upward, it mustsoften the surrounding rocks by heatingbefore continued movement is possible (5).There is increasing geophysical evidence tosuggest that this process leads to a pondingofmagmas in the mid-crust, where the rocksbecome cooler and more brittle (4, 6). Geo-chemical evidence also suggests that themagma chemistry of batholiths representscrystal reequilibration at mid-crustal depths(7). The present model therefore starts witha large concentration ofmagma at depths of10 to 20 km.The density contrasts that lead to diapiric

upwelling still exist, and cause distension ofthe overlying crust and propagation of out-ward fractures (Fig. LA). The process isdriven by the pressure differential betweenthe upper part of the magma body and thesurrounding rocks. The lower crustal rocksbelow the body are plastic, having been

preheated. They push in on the lower mar-gin with a pressure corresponding to thelocal geobaric conditions. Since the magmais a fluid, although a rather viscous one,pressure is transmitted to the upper surfacewhere the magma pressure is equal to thelithostatic pressure at the base minus themagma column pressure. This pressure ishigher than the local lithostatic pressure atthe top by the term

P = 98.0655 Apdl (1)

where L is the thickness of the body inkilometers and Ap is the difference betweenthe magma density and that of the countryrock as a function of depth. If we assumethat the densities do not vary much over thethickness of the body, then Eq. 1 simplifiesto

P = 98.0655ApL (2)

The resulting pressure differential is about100 bars per 1 g/cm3 of density differentialfor every 1 km in thickness. This force willaid crack propagation in the tensional envi-ronment, especially if preexisting zones ofweakness are utilized, as is generally the casein the localization of plutons.Crack propagation therefore progresses

into the brittle environment, with fingers ofmagma expanding ring fractures toward thesurface (Fig. 1A). Such a process is nowoccurring under the Mammoth Lakes areain California (4, 8).

Eventually, the magma will reach the sur-face. If the magma channelway is bigenough, large volumes ofmagma may beginto be extruded as pyroclastic material, pro-vided there are sufficient volatiles to drivethe eruption. At this point, the fluid pres-sure in the magma chamber changes. If asignificant amount of material is moving upthe column, the pressure in the magmachamber will attempt to reach the pressureof the flowing magma column, which isgiven by the expression

JH

~~~~~~P=98.0655 pm,db (3)

where Pm is the density of the magma ingrams per cubic centimeter and H is the

3I JANUARY 1986

J. A. Whitney, Department of Geology, University ofGeorgia, Athens 30602.J. C. Stormer, Jr., Department ofGeology and Geophysics,Rice University, P.O. Box I892, Houston, TX 772si.

REPORTS 4.83

on Decem

ber 10, 2020

http://science.sciencemag.org/

Dow

nloaded from

depth to the magma chamber. The pressuredifferential between lithostatic pressure inthe overlying rocks and the fluid pressure inthe magma will be

H

AP = 98.0655j Apdh (4)

where Ap is the differential in density be-tween the magma and country rocks. If themagma body is 10 to 20 km deep, thispressure is 1 to 2 kbar for a density contrastof 1 g/cm3.The density of the magma column is not

constant, however. During active pyroclasticeruption, the upper portions are vesiculatedas gases are evolved to drive the eruptioncolumn. The density in the upper few kilom-eters may therefore be very low. Figure 2Ashows a possible density profile in a vesicu-lating magma colunn (9). The pressuredifferentials calculated for various models(Fig. 2B) are in the range 1 to 4 kbar. Inmost cases the full pressure differential willnot be realized since the viscosity is high andfriction is significant. However, in a systemunder full pyroclastic eruption, the flowrates would be high enough that the differ-ential may be approached. A more impor-tant limitation is that vesiculation in thisdynamic system will not reach equilibrium.

0

10

20

30

0

E0

le

However, as Fig. 2 shows, even the effectiveevolution of 1 percent water by weight issufficient to generate substantial depressuri-zation of a deep magma chamber.

If nothing else occurred, eruption wouldcease once this pressure differential was es-tablished. However, as a consequence of thereduced magma pressure, the previouslyfractured roof rocks are pulled into themagma chamber (Fig. 1B). Kilometer-sizedblocks may be engulfed, since regional jointsand zones of weakness are often on thisscale. Models by Marsh (5) suggest that thesettling rates ofsuch blocks exceed 10 m/sec.Such high settling rates of the blocks andtheir limited surface area means that theywill not significantly cool the surroundingmagma. The process will, however, causeupward movement of the magma body as itflows around the descending stoped blocks.Stoping may continue until the roof failsand a caldera forms (Fig. 1C).The collapsing of the overlying crust al-

lows eruption to continue with the extru-sion of large volumes of magma. The re-maining magma is now dispersed into small-er bodies around the stoped blocks of crustand a smaller, shallower magma chamber.These continue to cool, differentiate, and in-teract with crustal blocks, forming the com-plexly intruded lower portions of calderas.

iB _

D 7^rcla s k

\/ A rr...

v~

40 _-- _ __

Fig. 1. (A to D) Balanced cross section of intrusion and extrusion model. There is no verticalexaggeration. (A) Initial upward migration of fractures and development of ring fractures. (B)Beginning of eruption, vesiculation, and fracturing of roof rocks. (C) Caldera subsidence. (D)Resurgence and intrusion along ring fractures.

484

As the blocks settle, the residual magma issqueezed upward into shallower magmabodies. In addition, the topographic depres-sion of the caldera produces an isostaticreadjustment. The surrounding terrain sub-sides into the residual magma chamber, withthe magma being forced upward to causeresurgence of the caldera and establish iso-static equilibrium (Fig. ID).

Since the magma is more dispersed, it willcool and crystallize much more rapidly thana single, large chamber. The heat also drivesconvection of ground water and alteration,most of which will be localized aroundshallow apophyses rather than in a regionalpattern. The time it takes to establish a moreregional convection and alteration systemdepends on the thickness of the overlyingroof (10). The process may continue withsatellite eruptions of smaller volume fromremaining magma bodies, as in the case ofthe central San Juan Mountains, or withnew injections from depth on the same scale.The result is a crustal cross section con-

sisting of (i) smaller bodies ofmagma in thecatazone, intimately associated with plasti-cally deformed underlying material and largepieces of crustal material showing variousdegrees of reaction with the cooling magma;(ii) zones ofmetamorphic screens surround-ed by intrusive material; (iii) several periodsof intrusion corresponding to the mainbatholith emplacement, latter batholith em-placement, and small-scale intrusions of re-sidual melts; (iv) intensely injected and al-tered upper crustal or volcanic material; (v)blocks of the caldera floor composed ofprevious volcanic rocks and upper crustalmaterial and overlain by the cogenetic ash-flow tuffs; and (vi) later caldera-filling mate-rials surrounding zones of resurgence (Fig.ID).The emplacement model effectively dupli-

cates that described for portions of theAndes by Pitcher (11). The space probleminherent in the intrusion of a batholith issolved by the subsidence of large crustalblocks through the magma, driven by thedecreased reservoir pressure. This modelalso explains why the intrusion of batholithsoften follows ash-flow eruptions, with themain phases of intrusion extending up intothe ash-flow tuffs. The relation would bereversed if the shallow magma chamberwere first intruded and then ash-flow erup-tion occurred.

This model explains why mineral datafrom several large ash flows appear to recordhigh pressures of phenocryst equilibration(7). In the current model, the time betweenresidence in the mid-crustal magma chamberand eruption would be too brief to allowphenocryst reequilibration.The model successfully predicts that large

SCIENCE, VOL. 231

on Decem

ber 10, 2020

http://science.sciencemag.org/

Dow

nloaded from

PlIth.-Pmagma (kbar)2

Fig. 2. Density (A) and pressure (B) model for an erupting magma body with various initial watercontents (XH 0). The surface density in (A) is not zero, but on this scale is very close to the originbecause of the low density ofthe vapor phase. Varying density model for crust and melt does not changethe results significantly. Pressure differential in (B) is a maximum, as nucleation and vesiculation do notnecessarily reach equilibrium conditions. See (9) for solution model.

magma chambers underlying areas such as

the Long Valley area would be at depths of15 to 20 kmi, with only isolated smallapophyses extending to shallow depths (4,8). The model also predicts that regionalhydrothermal alteration driven by the deepmagma chamber would occur substantiallyafter the eruption process (10). This certain-ly seems to be the rule in most batholithicterrains. Furthermore, it predicts that theanomalously high heat flow which wouldfollow an eruption such as the Bishop or

Yellowstone tuffs would not be a regional,broad thermal anomaly, but would be con-

centrated above small, residual, shallowbodies. This pattern appears to be what hasbeen reported for such caldera areas (12).The overall resulting cross section (Fig.

1D) is substantially that reported for a num-

ber of batholiths where there is sufficientvertical relief to give a good crustal profile(11, 13). Therefore, the proposed model forintrusion and eruption being driven from a

deep magma chamber appears to be a validsubstitute for a shallow magma chambermodel where the intrusion of a laterallyextensive, shallow magma chamber precedeseruption of the ash-flow tuffs and associatedcaldera collapse.

If this model is substantially correct, thereare many implications for the earth sciences:

1) Major ash-flow eruptions in environ-ments such as Long Valley, Yellowstone, or

the San Juan Mountains during the Oligo-cene may not be preceded by the emplace-ment of a shallow, extensive magma cham-ber, but may start directly from a deeperchamber. Therefore, the warning eventsmay not be more significant than what isnow occurring at Mammoth Lakes.

2) The intrusion of upper crustal batho-liths in these areas may be initiated by thelowered reservoir pressure during ash-floweruptions and not precede it. This initialintrusion may be accomplished by the stop-ing of kilometer-sized blocks of crust, as

suggested for the Andes (11).3) The collapse of large calderas is the

surface manifestation ofthe stoping process,which would be the magmatic equivalent ofblock caving and the formation of a gloryhole in mining.

4) The resulting shallow magma cham-bers that drive hydrothermal circulation forhydrothermal power projects may be dis-continuous, dispersed, and much shorter incooling history than would be suggested bythe single shallow magma chamber model.

5) Regional circulation caused by theformation of an extensive batholith mayoccur significantly after the caldera-formingevent, as the regional magma chamber maybe deeper than supposed. Ifregional circula-tion is important in ore formation, theprocess may occur after volcanism stops.

Because these consequences are so far-reaching, future research should documentthe nature of the upper and lower marginsof batholiths, the chronology of initialbatholith injection and cogenetic ash-floweruptions, the distribution and extent ofshallow magma chambers under recent cal-deras, and the movement of magma in themid-crust under active areas. A nationaldrilling program, such as that outlined bythe National Academy of Sciences (14),would be most beneficial for such research.

REFERENCES AND NOTES

i. E. W. Hildreth, Geol. Soc. Am. Spec. Pap. I8o (i979),p. 43; D. P. Hil,J. Geophys. Res. 8I, 745 (1976); R. A.Bailey, G. B. Dalrymple, M. A. Lanphere, ibid., p.725.

2. G. P. Eaton, R. L. Christiansen, H. M. Iyer, A. M.Pitt, D. R. Makey, H. R. Blank, Jr., I. Fietz, M. E.Gettings, Scince I88, 787 (I975).

3. J. C. Ratte and T. A. Steven, U.S. Geol. Surn. Prof.Pap. 524-H (I967); T. A. Steven and P. W. Lipman,U.S. Geol. Surn. Prof. Pap. 958 (I976).

4. J. F. Hermance, Eos 63, II33 (1982); , W.Slocum, G. A. Neumann, ibid., p. 890; C. 0.Sanders, ibid., p. 890; J. H. Luetgart and W. D.Mooney, ibid., p. 890; C. R. Bacon, W. A. Duffield,K. Nakamura,J. Geophys. Res. 8s, 2425 (I980); A. H.Lachenbruch, J. H. Sass, R. J. Munroe, T. W.Moses, Jr., ibid. 8I, 769 (I976).

5. B. D. Marsh, Am. J. Sci. 282, 808 (1982).6. G. P. Eaton, Natl. Res. Counc. Geophys. Study Com-

mun. 96 (I980); M. R. Kane, D. R. Mabey, R. L.Brace,J. Geophys. Res. 8I, 754 (I976); E. J. Rinehart,A. R. Sanford, R. M. Ward, in Rio Grande Rift:Tectonics andMagmatism, R. E. Rieker, Ed. (Ameri-can Geophysical Union, Washington, DC 1979), P.237.

7. J. C. Stormer, Jr., and J. A. Whimey, Am. Mineral.70, 52 (i985); J. W. Geissman, M. J. Mathews, E. J.Essene, Eos S9, 1212 (I978).

8. D. P. Hill, J. Geophys. Res. 8i, 745 (I976) D. W.Steeples and H. M. Iyer, ibid., p. 849; F. Ryall andA. Ryall, Geophys. Res. Lett. 8, 557 (I98I).

9. Magma density model based on water solubilitydata summarized by H. W. Day and P. W. FennGeol. 90, 48S (1982)]. Solubility data were fitted toan empirical equation of the form XH20/PH20 =CeDP, where C and D are isothermal constants.Temperature was 800'C. Density data are from C.W. Burnham, J. R. Holoway, and N. F. Davis [Geol.Soc.Am. Spec. Pap. i32 (I969)]; S. P. Clark, Jr. [Geol.Soc. Am. Mem. 97 (I966)]; and R. A. Robie, B. S.Hemingway, and J. R. Fisher [U.S. Geol. Surn. Bull.I5S2 (1979)].

io. B. D. Marsh, Geol. Soc. Am. Abstr. Programs 13, 503(1981).

ii. W. Pitcher, J. Geol. Soc. London I3, 157 (I978).I2. H. H. Kieffer and M. Manley, Eos 45, 89i (1983).13. A. F. Buddington, Bull. Geol. Soc. Am. 7o, 67I

(i1sq); R. S. Fiske, C. A. Hopson, A. C. Waters,U.S. Geol. Surn. Prof. Pap. ^44 (I963).

I4. A National Drilling Program to Study the Roots ofActive Hydrothemnal Systems Related to Young Mag-maticIntruions (National Academy Press, Washing-ton, DC, I984); Mineral Resources: Research Objec-tives for Continental Scientific DriUing (NationalAcademy Press, Washington, DC, I984).

iS. Supported by NSF grants EAR-82-o4568, EAR-84-I6622, and EAR-84-I6560.S July I985; accepted 28 October I985

31 JANUARY I986

Density (g/cm3)

E

0

a

REPORTS 4.85

on Decem

ber 10, 2020

http://science.sciencemag.org/

Dow

nloaded from

TuffsModel for the Intrusion of Batholiths Associated with the Eruption of Large-Volume Ash-Flow

JAMES A. WHITNEY and JOHN C. STORMER JR.

DOI: 10.1126/science.231.4737.483 (4737), 483-485.231Science 

ARTICLE TOOLS http://science.sciencemag.org/content/231/4737/483

REFERENCES

http://science.sciencemag.org/content/231/4737/483#BIBLThis article cites 21 articles, 4 of which you can access for free

PERMISSIONS http://www.sciencemag.org/help/reprints-and-permissions

Terms of ServiceUse of this article is subject to the

is a registered trademark of AAAS.ScienceScience, 1200 New York Avenue NW, Washington, DC 20005. The title (print ISSN 0036-8075; online ISSN 1095-9203) is published by the American Association for the Advancement ofScience

1986 by the American Association for the Advancement of Science.

on Decem

ber 10, 2020

http://science.sciencemag.org/

Dow

nloaded from