Journal of Volcanology and Geothermal Research, 11 (1981) 169--187 169 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

E R U P T I O N VOLUME, P E R I O D I C I T Y , A N D C A L D E R A A R E A : R E L A T I O N S H I P S A N D I N F E R E N C E S ON D E V E L O P M E N T OF C O M P O S I T I O N A L Z O N A T I O N IN SILICIC MAGMA CHAMBERS

FRANK J. SPERA and JOY A. CRISP

Department of Geological and Geophysical Sciences, Princeton University, Princeton, NJ 08544 (U.S.A.)

(Received March 10, 1981; revised and accepted April 30, 1981)

ABSTRACT

Spera, F.J. and Crisp, J.A., 1981. Eruption volume, periodicity, and caldera area: rela- tionships and inferences on development of compositional zonation in silicic magma chambers. J. Volcanol. Geotherm. Res., 11: 169--187.

In order to put constraints on the mechanisms of compositional zonation in magma chambers, data were collected on caldera areas, ash-flow volumes and repose times between zoned ash flows for a number of magmatic systems of different age, composi- tion, size and tectonic environment. First-order correlations between volume, repose time and stratification rate are apparent. Chemical zonation is developed to partially compensate for the internal production of entropy due to heat conduction through magma chamber thermal boundary layers. Repose times are proportional to eruption volumes and are consistent with convection-aided diffusion processes such as Soret diffu- sion or double-diffusive convection. Volume and area relations suggest that small-volume systems tend to be more conical than cylindrical in shape. An important factor control- ling magma chamber evolution appears to be the ratio of magma chamber surface area to magma chamber volume, other factors remaining the same. Small magma chambers ap- pear to stratify in shorter periods of time and at faster rates than large-volume systems.

INTRODUCTION

An i m p o r t a n t unsolved p rob lem in igneous pe t ro logy is the origin of com- posi t ional z o n a t i o n and compos i t iona l gaps in magma chambers o f inter- media te to acidic compos i t i on (McBirney, 1980; Shaw et al., 1976; Smith, 1979). A f requen t ly p roposed mechanism, crystal f rac t ionat ion , seems un- likely because o f geochemical inconsistencies (Hildreth, 1979; Smith and Bailey, 1966). Also, exper imenta l results on the rheo logy of high-silica magma indicate tha t rates o f crystal sett l ing are t oo slow to p roduce the ob- served compos i t iona l effects (Feigenson and Spera, 1981) in some magmat ic systems. Fol lowing the analysis o f Smith (1979) , we have compi led data on m a g m a e rup t ion vo lume (Vm), collapsed caldera area (Ac) and volcanic re- pose t ime (T) be tween compos i t iona l ly zoned erupt ions for a n u m b e r o f

0377-0273/81/0000--0000/$02.75 © 1981 Elsevier Scientific Publishing Company

170

intermediate to silicic magmatic systems ranging in age from Recent to Oligocene and spanning several volcano-tectonic settings. These include central-vent composite volcanoes (for example, Crater Lake), oceanic island volcanoes (Las Canadas, Tenerife), epicontinental ring structures (Yellowstone) and continental rift environments (Fantale, East African Rift). Vm-Ac data were collected for seventy-six well-characterized magmatic systems. For twenty of these systems, Vm-Ac-~ data were available or could be estimated with reasonable accuracy. It is noted that there is a natural bias in the data set in that small eruption volume systems seem to produce a more varied range of compositions, usually at more frequent intervals (Smith, 1979). However, study of the systematics of these data reveal signif- icant correlations which appear to be independent of tectonic environment and composition. Although we cannot rule out entirely the effects of com- position and structural type, these data, when taken as a whole, place some important constraints on mechanisms responsible for development of com- positional zonation in epizonal to mesozonal magma chambers.

One conclusion of this study is that the time scale (T) for development of compositional zonation is proportional to magma eruption volume. Large- volume systems (Vm ~ 103 km 3 ) evolve on time scales around l0 s to 106 years whereas small systems (Vm ~ 10 km 3 ) are associated with much shorter (102 to 104 years) time scales. This suggests that compositional zonation and compositional gaps (hereafter referred to as chemical structure) develop by mechanisms which operate on convective rather than diffusive time scales. A second, and less certain conclusion, is that small magma chambers {usually characterized by small eruption volumes) stratify or be- come chemically zoned at higher rates than systems with large volumes. This suggests that the surface area (AMc) to volume (VMc) ratio of a mag- ma chamber is an important evolutionary factor, perhaps related to the dis- sipation of magmatic heat (internal entropy production).

IRREVERSIBLE THERMODYNAMICS AND THE EVOLUTION OF SILICIC MAGMA CHAMBERS

There are obviously a multi tude of factors which govern the evolution of magma chambers. Although it is recognized that every volcanic terrain and probably every volcanic eruption is unique, it is equally clear that evolution of magma chambers is dominated by processes involving heat transfer. Examples of these processes include the injection of ho t basic magma in the bot tom of epi- to mesozonal chambers and the dissipation of magmatic heat by hydrothermal circulation systems which surround (and perhaps eventual- ly engulf) the magma reservoir. Crystallization of phases from the melt pro- vides an additional and significant amount of heat which eventually is dis- sipated. It is known that even a single-phase binary fluid can undergo spon- taneous development of chemical heterogeneity (chemical zonation) from an initially homogeneous state, given the right combination of fluid prop-

171

erties and thermal boundary conditions (Nicolis and Prigogine, 1977; Hurle and Jakeman, 1969, 1971; Schechter et al., 1972). In these studies, the fluid exhibits a spontaneous tendency to become self-organized; homogene- ity is wiped out and composit ional gradients can develop within the system. It is noted here that the chemical structure found in these experiments de- velops on a fast time scale by internal convection. This behavior can be unders tood in terms of a generalized form of the Moderation Theorem (Prigogine and De Fay, 1954; Prigogine, 1967) and is briefly discussed below.

Dissipation of magmatic heat leads to production of vast amounts of entropy within the magma chamber. This is primarily due to the conduct ion of heat through relatively thin thermal boundary layers along the walls of the magma chamber. The system at tempts to compensate or moderate the entropy product ion due to heat dissipation by undergoing a spontaneous chemical fractionation in a fashion consistent with the imposed thermal boundary conditions. The development of these composit ional gradients is consistent with the minimization of the rate of entropy production subject to constraints imposed by the thermal boundary conditions. Thermal entropy product ion is moderated by the development of chemical structure (chemical gradients and chemical gaps) (Verhoogen, 1980; Glansdorff and Prigogine, 1971). Because silicate melts are complex mul t icomponent non- ideal solutions, the magnitude and nature of established gradients will be complicated (Tichacek et al., 1956).

It is noted that the explanation given here of why compositional gradients develop in magma chambers is both heuristic and phenomenolog- ical. It is not sufficient to argue that gravitationally induced motions of a polythermal, but initially homogeneous melt will inevitably lead to develop- ment of a composit ional structure. Still unexplained are the mechanisms and rates involved, how specific features of the chemical structure develop and how this structure depends on the thermodynamic and transport prop- erties of magma. Some of these features will be explored in a later publica- tion (Spera and Crisp, in preparation). Here it is sufficient to note that the inevitability of a magma chamber to become zoned follows from three basic factors:

(1) Prodigious amounts of heat are transported across the boundary of a magma chamber. The heat content of a chamber may increase or decrease with time depending on the relative strengths of magmatic heat sources (basaltic magma underplating) and sinks (heat dissipated by hydrothermal- meteoric circulatory system).

(2) In a convecting fluid, kinetic energy is produced by the action of gravitational forces on density differences that arise due to thermal and composit ional heterogeneity within the fluid. A remarkable feature of mag- ma chamber convection is that, despite the large difference between thermal and mass diffusivities, the power released by the interaction of gravity and the thermal field is about equal to the power released by the action of the

172

gravitational field on small but inevitable compositional differences in the melt (Golitsyn, 1979; Spera, 1980b).

(3) The rate of diffusion of heat is much greater than the rate of diffu- sion of mass in silicate melts. That is, the lifetime of a concentration pertur- bation is much greater than that of an analogous thermal perturbation.

These considerations are discussed more completely in a later publication where it is shown that superimposed thermal and chemical boundary layers along the margins of a chamber will naturally lead to some major element (for example, SiO2) vertical gradients. In addition, Soret effects (Shaw et al., 1976; D. Walker, personal communication, 1980) may be important across rather thin thermal boundary layers which undoubtedly are present in systems with high thermal Rayleigh numbers. Because concentrat ion of trace elements has little effect on the density of melts, establishment of major oxide chemical gradients might be decoupled in rate and magnitude from analogous effects with minor and trace elements. Finally, the thickness and time scale for development of layered convection cells in silicic chambers as calculated by theoretical studies on related systems (Chen, 1974; Hart, 1971; Huppert and Linden, 1979; Tellepp and Harper, 1963; Spera and Crisp, in preparation) are consistent with observed field relations (McBirney and Noyes, 1979). The remainder of this report is concerned with a detailed analysis of observed systematic relationships between the sizes and periodicities of zoned ash-flow eruptions.

SYSTEMATIC RELATIONS

Magma eruption volume--caldera area correlation

Plotted in Fig. 1 are the magma eruption volume (Vm) and caldera area (Ac) data for seventy-six explosive volcanic eruptions, many of which are composit ionally zoned. In this report, attention is restricted to those erup- tions which were accompanied by caldera collapse. Ac ranges from 4500 km 2 to < 1 km 2 and V m from 3000 km 3 to < 1 km 3. For convenience, sym- bols have been defined in the table of nomenclature. Although Ac varies by a factor > 104 and Vm slightly < 104, log Ac correlates positively with log Vm- In fact, about 80% of the systems plot ted in Fig. 1 are consistent with magmatic drawdowns (A _= Vm/Ac) between 0.1 km and 3 km (a varia- tion of < 10 l"s). When the population of magmatic systems is limited to central-vent volcanic eruptions (composite volcanoes), about 80% of the sys- tems exhibit drawdowns between 0.07 and 1.5 km (a variation of 1013). The significance of smaller implied A values for central-vent eruptions is un- clear. However, if one assumes that small-volume magma reservoirs asso- ciated with central-vent volcanoes tend to be tapered with depth (for ex- ample, conical) rather than slablike (characteristic of large-volume chambers), then the discrepancy in inferred A values may be explained. That is, from

173

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Fig. 1. Plot of ca ldera area (Ac) versus ash-f low m a g m a e r u p t i o n volume. Lines are d rawn to ind ica te var ious d e p t h s of d r a w d o w n (A), assuming the m a g m a c h a m b e r s have a cyl indr ica l shape (~ = V m / A c ). Error bars r ep resen t bes t es t imates , n o t necessar i ly t rue error . If area and vo lume are given in t he l i t e ra tu re as exac t number s , t h e y are p lo t t ed as po in ts . Older - sys tems shou ld i n h e r e n t l y have more error t h a n younge r ones. Vo lumes for ocean is land ash flows, such as Kikai (po in t 32), are u n d e r e s t i m a t e s due to loss of ash in the ocean. In some cases, ash-f low vo lume is small because s u b t e r r a n e a n wi thd rawa l of m a g m a also c o n t r i b u t e d to ca ldera collapse.

N O M E N C L A T U R E

Yn2 Ac A VMc AMc A*

T

magma eruption volume (km 3) caldera area (km 2) magma drawdown, in cylindrical chamber, A --- Vm/Ac (km) magma chamber volume (km 3) magma chamber surface area (kin 2) magma drawdown in conical chamber, A* = 3a (km) volumetric production rate of zoned magma, Vm = AcA (kin3/10 s yr) rate o f magma chamber stratification (kin/10 s yr) repose time between composit ionally zoned eruptions (yr)

174

well-known formulae one finds:

A* = 3A (1)

where A _= Vm/Ac is the drawdown for a cylindrical magma chamber and /x* the drawdown for a conical one. This transformation has the effect of moving the central-vent eruptions to higher values of Vm at a fixed Ac value, thereby improving the linear correlation of log Vm and log Ac in Fig. 1. The reason (if any) for the apparent upper limit of A <~ 3 km in Fig. 1 is not known. Perhaps when the depth of the chemically stratified zone, which may be rich in volatiles, exceeds this limit an eruption is trig- gered. To some extent, this limit must be controlled by the thermal lifetime of the magmatic system. For example, a typical growth rate of the chem- ically stratified cap of a large-volume epicontinental magma chamber is about 0.3 km/10 s yr (see Fig. 3). Without a continuous supply of heat from below, growth of a stratified layer must eventually cease because the magma crystallizes. Parametric calculations by Spera (1980a) show tha t so- lidification times of magma chambers, defined as the time necessary for magma to cool from liquidus to solidus temperatures, vary as D 1.3 where D is the pluton diameter. A 20-km-diameter quartz monzonite pluton (Ac 315 km 2) emplaced at mesozonal depths has a solidification time around 106 years. In this period of time the thickness of the stratified layer would be about 3 km. Certainly there are other factors such as geothermal gradi- ent, country-rock temperature, hydrothermal fluid/magma volume ratio and magma viscosity which influence solidification times. Variations in these parameters may explain some of the scatter in Fig. 1.

Magma eruption volume--repose time correlation

In Table 2 we have collected information on the eruption volume--repose time characteristics for a number of magmatic systems of varying composi- tion and volcano-tectonic setting. This report will not discuss in detail in- dividual eruptions or volcanic terrains. However, sources of data for both Tables 1 and 2 are identified in Table 1. Precise data on the repose time between compositionally zoned eruptions (0 time data for many volcanic systems are not available. However, intensive studies of specific ash-flow ter- rains have been carried out for a number of volcanic provinces and it is these data that are summarized in Table 2.

The parameter r is defined as the time interval between compositionally zoned ash or pumice-flow eruptions which originate from the same or close- ly related (temporally and spatially) magma chamber-caldera system. For example, approximately 11.3 Myr ago, Timber Mountain I (see Table 1) caldera collapsed and a large compositionally zoned ash flow, the Rainier Mesa Tuff, was erupted. This catastrophic event was followed by a repose period of about 2 × l0 s years. About 11.1 Myr ago, a second collapse of the Timber Mountain caldera occurred and the Ammonia Tanks Member of the Timber Mountain Tuff was emplaced. Since both members of the

175

Timber Mountain Tuff exhibit compositional zonation (67--77% SiO2 ), we infer that in a time interval r = 2 X 10 s years, a volume of magma approx- imately equal to that of the Ammonia Tanks Tuff (Vm ~ 450 km 3 ) had be- come compositionally zoned. An obvious feature of the data given in Tables 1 and 2 is that Vm correlates positively with r. This has previously been noted (Smith, 1979) and is easy to understand intuitively; the longer the repose time, the larger the accumulated amount of zoned magma at the top of the chamber.

The parameter h, which is the rate of magma chamber stratification, is calculated by dividing the drawdown (A) by the repose time (r). That is:

;x =_ Vm/rAc (2)

Note that A, where A - Vm/Ac, is the magma drawdown implied for a cylindrical chamber. For chambers more funnel or dome shaped in cross- section, hypothetical drawdowns and stratification rates will differ from those determined here. For simplicity, we have assumed cylindrically-shaped chambers for all the systems listed in Table 2. This means that stratification rates listed in Table 2 are underestimates if, in fact, some chambers are more conical than cylindrical. This may be the case for central-vent systems.

;x-T and Vm-~ systematics

Fig. 2 is a plot of stratification rate (&) versus repose time (r). Stratifica- tion rates vary over 3 orders of magnitude whilst repose times vary by a factor of 104. There is clearly a negative correlation; magmatic systems characterized by small repose times apparently stratify at higher rates than systems with long repose times. For example, the apparent stratification rate leading up to the andesitic pumice-flow eruption of Mashu, a system with a short period (r ~ 3 X 103 years) and relatively small volume (Vm 50 km 3) system is about 25 km/10 s years, whereas the inferred stratifica- tion rate in the magma chamber which gave rise to the Tshirege Member of the Bandelier Tuff (Vm ~ 130 km 3, T ~ 3 X l0 s years) is about 10 -1 km/10 s yr. The dependence of T on /~ suggests that the stratification rate of a system should depend on the volume of the magma chamber (VMc). It has been argued (Smith and Shaw, 1973~ 1975; Smith, 1979) that not more than about one-tenth of the chamber volume is erupted during any one pyroclastic flow. If it is assumed that Vm ~ VMc, then given the posi- tive correlation between Vm and r, Vm should correlate negatively with stratification rate. Put in another way, small magma chambers apparently be- come stratified more quickly than large chambers. Fig. 3 is a plot of Vm versus ~. Although the correlation is less than perfect, it does seem that large chambers stratify at slower rates than small chambers. A plot of Vm versus Sz m is substantially of the same form as Fig. 3, and supports the idea that small chambers zone more quickly than large ones. It is not possible that

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, N

evad

a Y

ucc

a F

lat,

7

qu

artz

lat

ite

Tiv

a C

any

on

M

emb

er

00

48

Opa

la

15

5 ±

22

20

0--

25

0

? an

des

ite

Kam

chat

ka

18

49

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toro

3

58

± 1

0 5

80

-10

00

w

q

uar

tz l

atit

e C

olo

rad

o

La

Jara

Can

yo

n

29,

30,

58

Mem

ber

50

R

abau

l II

1

02

± 5

24

u

dac

ite

New

Gu

inea

21

51

S

an L

uis

13

4 -

+ 5

70

0-8

00

w

rh

yo

lite

, C

olo

rad

o

Nel

son

Mtn

. 32

, 58

q

uar

tz l

atit

e T

uff

52

S

anto

rin

i 8

3

60

-70

w

an

des

ite

Gre

ece

4 53

S

hik

ots

u I

1

13

± 2

5 6

8--

80

m

d

acit

e Ja

pan

2,

24,

54

54

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rra

la P

rim

aver

a 1

10

2

0

m

com

end

ite

Mex

ico

T

ala

Tu

ff

33

55

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ent

Can

yo

n

39

6

22

0-2

40

p

com

end

ite

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ada

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ckad

e W

ash,

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56

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ver

ton

1

86

± 5

2

5--

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0

u rh

yo

lite

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olo

rad

o

57

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mm

itv

ille

71

-+

2 1

50

--2

25

w

q

uar

tz l

atit

e C

olo

rad

o

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use

Can

yo

n

Cry

stal

Lak

e T

uff

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jito

Cre

ek,

Ra

Jad

ero

M

emb

ers

12

,31

,58

29,

30,

58

58

Tam

bo

ra

28 ±

2

10

0--

15

0

? an

des

ite

Su

mb

awa

51,

65

59

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ber

Mtn

. I

50

8 ±

5

12

00

w

rh

yo

lite

, N

evad

a R

anie

r M

esa

5, 6

q

uar

tz l

atit

e 60

T

imb

er M

tn.

II

30

4 ±

6

90

0

u rh

yo

lite

, N

evad

a A

mm

on

ia T

ank

s 5,

6

qu

artz

lat

ite

61

To

ba

20

00

-+

10

0

15

00

-20

00

? ?

rhy

oli

te

Su

mat

ra

To

ba

Tu

ff

64,

65

62

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led

o

11

9 ±

19

20

0-3

00

u

rhy

oli

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New

Mex

ico

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tow

i M

emb

er

7, 5

5 63

T

ow

ada

I 1

17

2

5--

45

u

dac

ite

Jap

an

1, 1

1, 2

8, 6

9 64

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oy

o

90 -

+ 5

8 w

rh

yo

lite

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pan

O

no

Tu

ff

35,

45

65

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ek

34

4 -

+ 25

4

17

÷

15

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yo

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A

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na

Rh

yo

lite

34

C

any

on

Tu

ff

66

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com

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gre

1

86

÷ 1

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0

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olo

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lon

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a 31

, 32

, 58

T

uff

67

Un

com

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gre

! 7

93

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16

10

00

p

rhy

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te

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lora

do

S

apin

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a 12

, 31

, 32

, 58

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an J

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su

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cite

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69

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les

43

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20

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30

0

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e M

emb

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5 q

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M

r. W

ith

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ton

1

03

7

12

50

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rhy

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New

Mex

ico

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ota

to C

any

on

13

71

Y

amak

awa

3.3

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w

and

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pan

35

72

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ello

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on

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46

48

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2

45

0

w

rhy

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om

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ge

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low

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28

0

w

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om

ing

M

esa

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ls T

uff

7,

8

74

Yel

low

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ne

III

24

35

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10

00

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rh

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g

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reek

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ff

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inja

u

21

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0

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lite

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um

atra

M

anin

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ff

73

76

No

var

up

ta

11 +

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16

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21

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m

and

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e A

lask

a 72

rh

yo

lite

an

des

ite

dac

ite

a T

his

nu

mb

er c

orr

esp

on

ds

to t

he

po

ints

plo

tted

in

Fig

. 1.

V

alu

es f

or

Bla

ck M

tn.

II,

Ku

tty

aro

an

d U

nco

mp

ahg

re

wer

e n

ot

plo

tted

, si

nce

they

ov

erla

p o

ther

da

ta.

b"w

" st

and

s fo

r th

e d

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e of

wel

din

g o

f th

e as

h-f

low

tuf

f.

If W

= w

, th

e v

olu

me

give

n in

th

e ta

ble

is

the

vo

lum

e o

f a

wel

ded

as

h fl

ow

(m

agm

a v

olu

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= 75

% a

sh-f

low

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lum

e).

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p

corr

esp

on

ds

to

a p

artl

y

wel

ded

as

h fl

ow

(m

agm

a v

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me

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2.5

% a

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lum

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W =

u

corr

esp

on

ds

to a

n u

nw

eld

ed

ash

flo

w

(mag

ma

vo

lum

e =

50%

ash

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w v

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me)

. If

W =

m,

the

vo

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e gi

ven

in t

his

tab

le i

s m

agm

a v

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c

Th

ese

refe

r to

nu

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th

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ticl

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2

Per

iod

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of

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der

a T

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r)

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ti

me,

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(y

r)

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dep

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(kin

)

£ (kin

/10

s

yr)

L

abel

a

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ter

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lack

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rail

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im C

any

on

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po

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h

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8

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rin

g

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any

on

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Can

yo

n

12

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-+ 0

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Mt.

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ji

17

07

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st L

ake

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u

70

00

yr

B.P

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asis

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ley

II

Tiv

a C

any

on

1

2.4

5

+ 0

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S

hik

ots

u

20

,00

0 y

r B

.P.

Sil

ver

ton

C

ryst

al

>2

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±

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ake

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+

0.5

T

imb

er M

t. I

R

anie

r 1

1.3

± 0

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Mes

a T

imb

er M

t. I

I A

mm

on

ia

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+

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ks

To

wad

a I

Un

com

pah

gre

/ S

ap±

nero

>

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+ 0

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an

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nk

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wn

M

am

mo

th

26

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Mtn

. U

nk

no

wn

W

asso

n

> 2

6.4

P

ark

<

26

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Usu

Z

enk

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<

0.0

1

Val

les

Ban

del

ier

1.1

Yel

low

sto

ne

II

Mes

a F

alls

1

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Yel

low

sto

ne

HI

Lav

a C

reek

0

.6

La

Gar

ita

Bla

ck M

tn.

I B

lack

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. II

S

leep

ing

Bu

tte

Cla

im C

ayo

n I

Ute

Cre

ek

An

des

ite

flo

ws

Cla

im C

any

on

II

Tar

um

ai S

om

ma

lav

a U

nc

om

pa

hg

re/S

an

Ju

an

Oas

is V

alle

y I

I

Tim

ber

Mt.

I

and

esit

e fl

ow

s U

nco

mp

ahg

re

Bac

hel

or

un

kn

ow

n

and

esit

e so

mm

a

To

led

o

Yel

low

sto

ne

I Y

ello

wst

on

e II

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± 0

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10

6

10

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. s

10

3--

10

4

0.6

4 ±

0.1

5

X 1

06

10

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1

50

0.8

±

0.5

×

106

4 ±

0.5

X

103

0.5

+ 0

.2 X

106

2

±1

X1

04

1.

0 ±

0.4

X 1

06

1.1

5 +

- 0.4

8 ×

10

6

0.2

+ 0

.I X

106

102--

103

0.3

± 0

.2 ×

10

6

0.6

+

0.3

×

106

0.2

+ 0

.i

X 1

06

22

.5

+ 2

.5 X

102

0.3

x

106

0.8

x

106

0.6

×

106

1.6

4--

2.2

1

0.5

7--

1.0

8

0.4

2--

0.5

4

0.3

2--

0.3

5

0.0

26

--0

.02

8

0.3

4--

0.4

6

0.9

1--

4.9

1

.06

0

.70

-1.6

1

0.4

9--

0.9

1

0.0

7--

0.2

8

1.75

--1.

79

1.45

--1.

51

0.11

--0.

19

0.77

--0.

80

? ? 0.05

6--0

.17

0.2

3--

0.3

5

0.5

5-

0.5

6

0.3

0--

0.3

1

0.1

49

--0

.73

7

18

.0--

34

1

4.2

--5

4

0.0

40

--0

.07

1

2.6

--2

80

2

27

--3

07

0

.07

0--

1.6

2

3.6

--3

0.3

0

.10

--0

.53

7

1.6

3--

9.1

0

.00

5--

0.0

47

0.1

07

--0

.26

7

0.4

83

--1

.51

11

--1

90

0

.15

4--

0.8

0

2.2

4--

8.5

0

.07

7--

0.1

17

0

.06

9--

0.0

7

0.0

50

--0

.05

2

CR

S T

TS

PC

F

uji

B

M

Mas

hu

T

C

Sh

iko

tsu

C

L

RM

AT

To

wa

da

S

M

MM

WP

Usu

B

M

F

LC

aSee

Fig

s. 2

an

d 3

.

181

10'

E

1 0 - -

1 - -

- 1 - - ~o I

ICR

RM LC TC

[]1 I IIA!I ] '] sMI

[--1MASHt? CL I T I

I T(3WADA I pC I I

- - ~ FoJ,E] I I I I

1~)1 1 ]0 10 2

/~ ( 'k in / I 0 5 yrs)

Fig. 2. Negat ive co r r e l a t i on b e t w e e n m a g m a e r u p t i o n vo lume ( V m ) a n d s t r a t i f i ca t ion ra te (;x). E p i c o n t i n e n t a l sys tems are label led as in Table 2. S t r a tovo lcanoes are label led by caldera names. Boxes ind ica te e r ror f r o m es t imates of volumes , areas, and t imes. Where a r rows are shown, the box e x t e n d s b e y o n d t he graph.

this time to offer a unique interpretation of the observed relationship between magma chamber size and the rate of development of stratification. Particularly lacking are fine-resolution repose time data for small-volume central-vent systems which are well documented both geologically and petro- chemically. However, if the negative correlation between Vm and r is in fact real, it places important constraints on mechanisms for development of compositional zonation.

In what follows, it is assumed that the relationship depicted in Fig. 3 is real (i.e., Vm correlates negatively with A). Two possible interpretations are offered to explain this relationship.

It may be that A fundamental ly depends on the time elapsed since initia- tion of ~rowth of the stratified layer at the top of the chamber. For in- stance, A may be determined by a first-order rate law such that:

/~(r) = z~0 exp (-r/O) (3)

where 0 is a relaxation time for the process that produces chemical zona- tion. In this case, the negative correlation of Vm and A is an artifact of the positive correlation between Vm and r. That is, larger systems with longer

182

thermal life times give smaller average values of ~ because the mechanisms which produce compositional zonation have been operating for longer time intervals. The relaxation time, ~, presumably depends on a number of parameters including viscosity, volatile content and bulk composition of the melt, size and shape of the magma chamber, distribution and strengths of heat sinks and sources.

Alternatively, the observation that small chambers stratify more quickly than large ones is consistent with the fact that other parameters remaining constant, small chambers lose heat more rapidly per unit area than large ones. This is due to the fact that heat flux across the boundary of a cooling chamber varies inversely at some fractional power with Ac (Spera, 19 77, 1980a,b). If it is assumed that /~ varies directly with the heat flux, a nega- tive correlation between Vm and ~ is predicted. This is consistent with the data plotted in Fig. 3.

10 2

10

E ..¢

15

ITOWADA

P( USU

I l I 10 2 10 3 10 4

~" Grs)

ISMBi TSI ,

10 5 10 6

RM

Fig. 3. Negative correlation between stratification rate (~) and repose time (r). Boxes and labels are the same as for Fig. 2.

SUMMARY AND CONCLUSIONS

The main aspects of this study may be summarized as follows: (1) The development of compositional gradients within the upper portion

of high-silica magma chambers can be viewed in a phenomenological sense

183

as an inevitable consequence related to the entropy produced by the dissipa- tion of magmatic heat. The theory of irreversible thermodynamics indicates that an initially homogeneous fluid can become compositionally zoned if a temperature gradient is imposed across the system.

(2) There are probably a number of mechanisms whereby compositional zonation of major, minor and trace elements develop in chambers. In calc- alkaline systems, crystallization of mafic phases along the margins of the chamber produces thin bouyant boundary-layer melts enriched in com- ponents such as SiO2, K20 and Na20 (McBirney, 1980). Chemical convec- tion currents will rapidly generate vertical compositional gradients due to the release of gravitational energy. Minor and trace elements, unlike temper- ature and major components, do not influence melt density. Minor com- ponents may become fractionated due to Sorer (thermal) diffusion across thin thermal boundary layers which undoubtedly exist due to the very large size of thermal Rayleigh numbers.

(3) For each magmatic system, variation of the repose time for composi- tionally zoned eruptions with erupted volume (Vm), area of associated col- lapsed caldera (Ac), and magmatic drawdown indicates a crude but system- atic variation. Large-volume epicontinental systems grow stratified structure at slower rates, but for longer periods of time than small-volume, typically central-vent type systems which erupt more frequently.

In summary, we note that more stringent constraints on the evolution of magma chambers of silicic to intermediate composition can be developed only by intensive geological, geochemical, isotopic and rheological studies of magmatic systems from all tectonic environments. We emphasize the need for precise time-composition data in order to better establish the rates of stratification in these chambers and we need further documentat ion of geo- chemical and thermal trends in individual zoned ignimbrites.

ACKNOWLEDGEMENTS

This research was supported by National Science Foundation grant EAR 81-04400. Critical Reviews by A. McBirney and B. Baker improved the form and content of this paper and are gratefully acknowledged. Technical assistance from L. Noodles and M. Bergman proved indispensable.

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