Liquid fractionation. Part I: Basic principles and experimental simulations

Journal o f Volcanology and Geothermal Research, 24 (1985) 1--24 Elsevier Science Publishers B.V., Amsterdam - - P r i n t e d in The Netherlands

1

L I Q U I D F R A C T I O N A T I O N . P A R T I: B A S I C P R I N C I P L E S A N D EXPERIMENTAL SIMULATIONS

ALEXANDER R. McBIRNEY', BRIAN H. BAKER' and ROBERT H. NILSON 2 Center for Volcanology, University o f Oregon, Eugene, 97403 OR, U.S.A. 2Systems Science and Software, Box 1620, La Jolla, CA 92038, U.S.A. (Received May 16, 1984)

ABSTRACT McBirney, A.R., Baker, B.H. and Nilson, R.H., 1985. Liquid fractionation. Part I: basic principles and experimental simulations. In: B.H. Baker and A.R. McBirney (Editors), Processes in Magma Chambers. J. Volcanol. Geotherm. Res., 24: 1--24. A possible explanation for the closely associated magmas of contrasting compositions erupted from many mature volcanic centers can be found in the large differences of density produced by relatively small compositional variations in liquids that evolve by crystallization or melting at the walls of shallow magma chambers. A mechanism of liquid fractionation in which differentiated liquids segragate gravitationally to form compositionally graded columns of magma may surmount the long-standing problem of explaining large volumes of highly evolved liquids that reach advanced degrees of differentiation in times that are too short to be consistent with conventional models of crystal fractionation based on crystal settling. In those types of magmas that decrease in density as they differentiate, a fractionated liquid next to a wall may form a b u o y a n t compositional boundary layer that flows up the wall and accumulates as a separate zone in the upper levels of the reservoir. Magmas that increase in density as they differentiate will have the opposite behavior; they descend along the wall and pond on the floor. Both types of systems can be modeled using simple aqueous solutions and techniques similar to those developed by Chen and Turner (1980). The insights gained through experiments of this kind suggest a number of processes that may be responsible for common types of volcanic behavior and patterns of differentiation in shallow plutons.

INTRODUCTION For many years, one of the most perplexing problems of igneous petrology h a s b e e n t h e c l o s e a s s o c i a t i o n o f m a g m a s o f c o n t r a s t i n g c o m p o s i t i o n s e r u p t e d f r o m the same or closely related vents or in single o u t p o u r i n g s of c o m p o s i t i o n a l l y g r a d e d l i q u i d s . T h e d e g r e e s o f d i f f e r e n t i a t i o n are t o o g r e a t , t h e v o l u m e s t o o large, a n d t h e t i m e i n t e r v a l s t o o b r i e f f o r t h e diff e r e n t i a t e d m a g m a s t o b e p r o d u c e d b y f r a c t i o n a l c r y s t a l l i z a t i o n as it is n o r m a l l y e n v i s a g e d . E n o r m o u s b o d i e s o f m a f i c m a g m a w o u l d h a v e t o diff e r e n t i a t e at rapid rates a n d with great efficiency to p r o d u c e the observed compositions and volumes of differentiates by conventional mechanisms.

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© 1985 Elsevier Science Publishers B.V.

Moreover, the bimodality of many igneous suites requires that they differentiate in a way that enables the undifferentiated magma to erupt together with the products of its own crystallization. Attempts to deal with this problem date back more than a century. Shortly after Bunsen (1851) proposed that mixing o f rhyolitic and basaltic magmas could produce a wide range of intermediate liquids, Sartorius yon Wattershausen (1853) pointed out that magmas with such large differences in densities could scarcely coexist at the same level in magmatic intrusions and were more likely to form compositionally stratified columns with rhyolite over basalt. A few years later, Durocher (1857) considered the chemical aspects of these relations and suggested that an initially homogeneous magma could become vertically zoned under the influence of gravity while still in the liquid state. This concept was widely accepted on the continent of Europe, where Loewinson-Lessing (e.g. 1911, 1954) was its most notable advocate. Daly (1914) seems to have been the first to suggest a specific mechanism by which stratification could be produced when he deduced that compositional zonation could result from assimilation of crustal rocks in basaltic magma. Holmes (1931) elaborated on this idea by showing how crustal fusion may lead to a stratified column of magma with a felsic anatectic melt over a convecting basic magma. Shaw (1974) proposed a more sophisticated model in which absorption of water, along with other components from the walls of shallow intrusions could lower the density of liquid next to the wall and cause it to rise and accumulate under the roof of the chamber. More recently it has been proposed that the same effect may be achieved if crystallization or melting at the wall produces a liquid differing in density from its parent (McBirney, 1980). Geological evidence that some such process operates in magmas is not hard to find. Compositional zoning is a c o m m o n feature of large pyroclastic eruptions (Smith, 1979; Hildreth, 1981) and, to a lesser degree, of individual lava flows (e.g. Wilcox, 1954) and sills (Hamilton, 1965). Some of these inhomogeneities seem to develop in periods of thousand years, others in a few decades, but the tendency for the volumes, silica contents, and explosivity of felsic magmas discharged from large mature volcanoes and calderas to be direct functions of the interval of repose preceding the eruption is well established (Thorarinsson, 1954; Spera and Crisp, 1981; Simkin et al., 1981). PRINCIPLES OF LIQUID FRACTIONATION Recent studies of crystallizing fluids (e.g. Chen and Turner, 1980; McBirney, 1980; Sparks and Huppert, 1984) have shown how these types of differentiation and compositional zoning could result from crystallization or melting at the walls of a shallow sub-volcanic reservoir. We refer to such a process as "liquid fractionation", in order to emphasize that it is primarily

a segregation of compositionally distinct magmas that are still largely, if not wholely, in the liquid state. The unique feature of the process is its power to segregate highly differentiated liquids w i t h o u t gravitational settling of large proportions of crystals. The principle underlying liquid fractionation rests on two basic relations affecting fluids at a moving liquid--solid interface. First, the densities of fluids are a function of both temperature and composition, and during a process of crystallization or melting these factors may differ in sign as well as magnitude. Second, the gradients of these two properties, temperature and composition, tend to have very different forms, owing to the fact that the diffusivity of heat is much greater than that of chemical components. Both types of variations are possible in magmas (Fig. 1). Magmas that crystallize proportionately large amounts of phases rich in heavy components, such as iron, may be reduced in density, even though the falling temperature and thermal contraction tend to have the opposite effect. Such a magma is said to have a positive "fractionation d e n s i t y " (Sparks and Hubbert, 1984). Liquids with negative fractionation densities are residually enriched in heavy components and become denser. Basic tholeiitic liquids are progressively enriched in iron over much of their range of solidification, and this compositional effect strongly reinforces that of thermal contraction. Beyond a certain m a x i m u m level of iron enrichment, however, this trend is reversed and subsequent liquids become lighter. Some alkaline magmas probably vary in a similar way. The behavior of tholeiitic and alkaline volcanoes will depend to a large degree on the stage of evolution of the magmas and on whether their fractionation density is positive or negative. As several workers have pointed out (Walker, 1975; Sparks et al., 1980; Stolper and Walker, 1980), magmas that become denser with differentiation have less chance of reaching the surface if they must rise through lighter, less differentiated liquids. For this reason, intermediate volcanic members of these series are relatively scarce compared to less dense rocks. Once over the "density h u m p " , however, the rate of enrichment of iron becomes less than that of silica, alkalies, alumina, and water, and the trends are reversed; subsequent liquids become less dense than their parents. Where tholeiitic volcanoes erupt infrequently, as they do, for example, in parts of the Galapagos Archipelago and Iceland, they are more likely to differentiate beyond this "density trap" and discharge highly evolved felsic magmas. Where activity is more frequent and differentiation more restricted, as it is, for example, in Hawaii, magmas rarely reach a stage at which they surmount this physical barrier and produce large volumes of explosive siliceous differentiates. Calc-alkaline magmas, on the other hand, become less dense throughout their entire course of differentiation. The magnitude of this change can be seen in a simple example. The density of an andesitic liquid at a typical temperature of 1100°C is about 2.45 g cm -1, while that of rhyolite at 900°C

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is close to 2.20 g c m -1. H e n c e , the average p r o p o r t i o n a l v o l u m e t r i c c h a n g e per degree o f c o o l i n g as the liquid changes f r o m one c o m p o s i t i o n to the o t h e r is 1/2.20 -- 1/2.45 =

--5.1 × 10 -4 deg -1

(1/2.20) (900--1100) This is in contrast to typical values of 2 or 3 X 10 -S deg-' for thermal contraction (Murase and McBirney, 1973). EFFECTS OF HORIZONTAL THERMAL AND COMPOSITIONAL GRADIENTS The t y p e s o f b e h a v i o r t h a t m a y result f r o m these relations can be visualized b y c o n s i d e r i n g h o w differing rates o f t h e r m a l and chemical diffusion w o u l d be reflected in t h e f o r m s o f t h e r m a l and c h e m i c a l b o u n d a r y layers n e x t t o a steep wall (Fig. 2). T h e r m a l diffusion, n o r m a l l y a b o u t 3 to 5 X 10 -3 c m 2 s -1, is relatively rapid c o m p a r e d to chemical d i f f u s i o n (usually b e t w e e n 10 -s and 10 -1° c m 2 s-l). As a result, t h e t h e r m a l b o u n d a r y layer t e n d s to be m u c h wider t h a n t h e c o m p o s i t i o n a l b o u n d a r y layer. If the t w o effects act in the same d i r e c t i o n , as t h e y d o in m o s t tholeiitic and alkaline m a g m a s , t h e y r e i n f o r c e one a n o t h e r , b u t if t h e y are o p p o s e d , as t h e y are in calc-alkaline m a g m a s , the d e n s i t y d i s t r i b u t i o n will p r o d u c e a thin b u o y a n t z o n e i m m e d i a t e l y a d j a c e n t t o the crystals and a wide denser o n e e x t e n d i n g f a r t h e r into the interior. In this latter case, the interior o f an i n t r u s i o n m a y c o n v e c t in the n o r m a l fashion, while a b u o y a n t layer a d j a c e n t to the surface o f c r y s t a l l i z a t i o n rises t o w a r d the u p p e r levels o f the reservoir. C o n v e c t i o n due t o h o r i z o n t a l gradients of d e n s i t y is n o t limited by a critical Rayleigh n u m b e r ; flow o c c u r s even with the w e a k e s t o f d e n s i t y gradients. B u t t h e n a t u r e o f c o n v e c t i v e flow in d i f f e r e n t parts o f the b o u n d a ry layer m a y take a variety o f forms. It m a y be either laminar or t u r b u l e n t , d e p e n d i n g o n the physical p r o p e r t i e s o f the b o u n d a r y layers, and in the case o f c o u n t e r f l o w , where a thin b u o y a n t layer close to the wall rises while a b r o a d e r t h e r m a l l y driven c u r r e n t descends, it is possible t h a t one of these t w o m o v i n g layers m a y be s t r o n g e n o u g h t o carry away the other. Q u a n t i t a t i v e aspects o f these various c o n d i t i o n s are e x a m i n e d in Part II o f this series (Nilson et al., 1 9 8 5 ) . A m a j o r u n c e r t a i n t y in a n y o f these analyses is the n a t u r e o f the " w a l l " . Fig. 1. a. Variations of density with temperature for some common igneous compositions. The dashed line is drawn through the liquidus temperatures of the various rocks of calc-alkaline composition to illustrate how much greater is the effect of changing composition than the effect of falling temperature at constant composition. (Data from Murase and McBirney, 1973.) b. Variations of density with differentiation of the major types of igneous series. The calc-alkaline series is based on average rocks of the Cascade Range. The tholeiitic series is for rocks of the Galapagos Islands, and the alkaline one for the phonolitic series of Tahiti.

i n o u r c o n c e p t u a l m o d e l s , t h e w a l l is u s u a l l y v i s u a l i z e d as a w e l l - d e f i n e d b o u n d a r y b e t w e e n a m o v i n g f l u i d a n d a r i g i d s o l i d , b u t in r e a l i t y , it m a y b e an interface between moving and static liquids of differing viscosities and c r y s t a l c o n t e n t s . O u r p r e s e n t k n o w l e d g e is i n a d e q u a t e t o t a k e i n t o a c c o u n t all t h e c o m p l e x r e l a t i o n s d u e t o t h e e f f e c t s o f t e m p e r a t u r e , c r y s t a l c o n tent, and composition on the rheological behavior of the boundary layer.

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Fig, 2. Boundary layers next to the steep walt of acrystallizing magma may have one of two possible relations, depending on whether the chemical variations reinforce or oppose the effects of thermal contraction. The lower part of the diagram illustrates the case of a tholeiitic magma that becomes denser as it evolves. The dense boundary layer descends and ponds on the floor to form a stable bottom zone. In the case of a calc-alkatine magma, however, the compositional boundary layer close to the wall becomes lighter and rises to accumulate as a separate upper zone even though the thermal effect on density causes the magma to descend in the region farther from the wall. The diagram on the left illustrates the profiles of temperature (T), concentration of heavy components (C), density (p) and velocity (V). MODELING THOLEIITIC MAGMAS In order to gain insights into the ways these principles may affect the behavior of magmas, we have contrived a series of simple models using

aqueous solutions that can be observed closely as they crystallize and differentiate under laboratory conditions. While analog experiments of this kind are purely heuristic, they can be highly instructive in illustrating processes of potential importance in natural magmatic systems. Matters of scaling and other quantitative aspects of the processes are deferred to Part II of this series (Nilson et al., 1985). The behavior of most types of igneous systems can be modeled by simple aqueous solutions, such as that for Na2CO3, illustrated in Fig. 3. The density of the solution varies directly with the concentration of the solute and, to a lesser degree, inversely with temperature. Na2CO3 and ice have a simple binary eutectic relation. Calc-alkaline magmas are represented by solutions richer in Na2CO3 than the eutectic, because crystallization of Na2CO3 leaves the solution more dilute and hence lighter; a tholeiitic system can be modeled by a more dilute solution that first crystallizes ice and becomes denser as it is residually enriched in the dissolved component.

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The best known geologic example of a strongly differentiated tholeiitic magma is the Skaergaard Intrusion of East Greenland. So much data, both structural and compositional, is available for this body that it is an ideal example to model. The tank used in our experiments was constructed to resemble an east--west cross-section through the intrusion (Fig. 4); it measures 10 by 55 cm by 45 cm high and has three cooling tanks, one across the top and one at each vertical wall. Filler blocks were placed at the base of the tank to give it a shape that tapers downward. Since these blocks separate the liquid at lower levels from the direct cooling effect of the walls, they serve to model the contrast between the strong cooling by hydro-

Fig. 4. P h o t o g r a p h o f t a n k used to m o d e l a tholeiitic b o d y with t h e f o r m of the SkaeJ-gaard I n t r u s i o n . T h e t o p a n d sides are c o o l e d by c i r c u l a t i n g a refrigerated c o o t a n t t h r o u g h brass tanks.

thermal circulation through permeable basalts in the upper walls of the intrusion and the lower rate of heat transfer through the relatively impermeable metamorphic rocks in the lower walls (Norton and Taylor, 1979). Flow and segregation of liquids of differing compositions and temperatures can be observed by projecting a strong parallel beam of light through the tank, so that differences of refractive indices form images on a translucent sheet attached to the front face of the tank. The felsic gneiss intruded by the magma was represented by a layer of pure ice frozen along the top and upper walls of the tank. At the beginning of the experiment, the solution flowing into the tank through an orifice in the b o t t o m was at room temperature and began to melt its "wall rocks". When this happened, the solution in contact with the walls mixed with the resulting melt-water and, owing to its lower density, formed a b u o y a n t layer t h a t rose to collect under the roof, As long as the main body of liquid was warm enough to melt its walls, this process continued, and the result was an upper zone that convected independently and eventually crystallized as a nearly closed system. When the main body of liquid reached a temperature at which it ceased to melt its walls and began to crystallize ice, the density relations of the

Fig. 5. A descending boundary layer produced by crystallizing ice on the upper walls of the tank illustrated in Fig. 4. The compositional part of this boundary layer ponded and stratified at the bottom of the chamber, while the thermal part circulated back through the interior of the main zone. b o u n d a r y l a y e r w e r e reversed. I n s t e a d of rising, the m o r e c o n c e n t r a t e d s o l u t i o n p r o d u c e d b y c r y s t a l l i z a t i o n d e s c e n d e d along the walls to a c c u m u late on t h e f l o o r w h e r e it p o n d e d a n d stratified (Fig. 5). T h e b e h a v i o r of this d e s c e n d i n g l a y e r was n o t s i m p l y a reversed analog of t h e rising o n e p r o d u c e d in t h e earlier stages o f the e x p e r i m e n t . It d i f f e r e d in t h a t its m o t i o n h a d the same d i r e c t i o n as t h a t o f t h e d e s c e n d i n g t h e r m a l b o u n d a r y layer, and c o u n t e r f l o w was n o t a factor. As a c o n s e q u e n c e , the c o m p o s i tional l a y e r was m o r e distinct, a n d s h o w e d little t u r b u l e n c e , even t h o u g h it h a d a slightly higher v e l o c i t y . T h e division o f the b o d y into t w o s e p a r a t e l y l a y e r e d z o n e s (Fig. 6) c o r r e s p o n d s c r u d e l y to the d e v e l o p m e n t of the m a j o r p a r t s o f t h e S k a e r g a a r d I n t r u s i o n , a m a i n L a y e r e d Series t h a t crystallized f r o m t h e f l o o r u p a n d an U p p e r B o r d e r G r o u p t h a t crystallized f r o m t h e roof down. MODELING CALC-ALKALINE MAGMAS T h e t a n k used in e x p e r i m e n t s m o d e l i n g calc-alkaline s y s t e m s is illustrated in Fig. 7. In m o s t respects, its c o n s t r u c t i o n r e s e m b l e s t h a t o f the t a n k used in t h e e x p e r i m e n t s j u s t d e s c r i b e d . It m e a s u r e s a b o u t 40 b y 10 c m b y 60 c m

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Fig. 6. a. Major z o n e s p r o d u c e d in the tank after the main liquid had first m e l t e d its walls and then declined in temperature and began to crystallize ice. The t w o z o n e s remained distinct as t h e y c o n t i n u e d to c o o l and crystallize, b. A schematic sketch illustrates these z o n e s and the nature of the f l o w that produced them.

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1:2 high and has t r a n s p a r e n t wails o n the f r o n t and back. The s o l u t i o n (:an t-~, c o o l e d or h e a t e d in a variety of c o n f i g u r a t i o n s by circulating liquid t h r o u g h brass c h a m b e r s at the r o o f , walls, or floor. T u b e s t h r o u g h the r o o f permii~ m o n i t o r i n g o f t e m p e r a t u r e s and c o m p o s i t i o n s during the course of an ex. p e r i m e n t , and an access p o r t at tI:e base can be used to inject new liquids. f'orrnatio~z o f an u p p e r z o n e

In a t y p i c a l e x p e r i m e n t , the t a n k was filled with a s o l u t i o n s a t u r a t e d at r o o m t e m p e r a t u r e . T h e t o p a n d sides were t h e n c o o l e d in such a w a y t h a t the t e m p e r a t u r e was l o w e s t at the a p e x and increased slightly with d e p t h . When crystals o f Na2CO3 began to f o r m on the cooling surface, a thin film o f liquid o f low d e n s i t y a n d refractive i n d e x c o u l d be seen rising over the crystals and s t r e a m i n g u p w a r d (Fig. 8}. With t i m e , this light liquid a c c u m u -

13

Fig. 8. a. The rising buoyant boundary layer next to the wall has a thin laminar zone next to the growing crystals and a wider turbulent zone where the fractionated liquid back-mixes with the descending undifferentiated liquid of the interior, b. As the lightfractionated liquid accumulates, the interface between the upper and main zones forms a bright line caused by the difference in refractive index of the two liquids. With time, this interface moves downward as the volume of the upper zone increases. Width of view in (a) is 1.5 cm;in (b) it is 25 cm. lated u n d e r the r o o f , and the originally h o m o g e n e o u s solution separated into t w o separate gravitationally stable zones, each c o n v e c t i n g i n d e p e n d e n t ly and at d i f f e r e n t rates. A s t r o n g d i f f e r e n c e in refractive index defining the interface b e t w e e n the t w o zones was displaced d o w n w a r d with time as the b u o y a n t f r a c t i o n a t e d liquid c o n t i n u e d to a c c u m u l a t e . At the same time, double-diffusive c o n v e c t i o n within the u p p e r zone caused the segregated liquid to b e c o m e t h e r m a l l y and c o m p o s i t i o n a l l y stratified (Fig. 9) in the m a n n e r described b y T u r n e r ( 1 9 8 0 ) and T u r n e r and Gustavson (1981). Meanwhile, the lower zone c o n v e c t e d o n a larger scale and r e m a i n e d thermally and c o m p o s i t i o n a l l y h o m o g e n e o u s . The t e m p e r a t u r e and d e n s i t y profiles o f the u p p e r z o n e were displaced d o w n w a r d as b u o y a n t f r a c t i o n a t e d liquid c o n t i n u e d to rise and a c c u m u late u n d e r the r o o f (Fig. 10). The lightest ( m o s t dilute) liquid flowing directly over crystals o n the wall rose directly to the t o p o f the u p p e r zone, while i n t e r m e d i a t e c o m p o s i t i o n s w e n t to lower levels a p p r o p r i a t e for their respective densities. We a t t r i b u t e the linear c o m p o s i t i o n a l profile to t u r b u lent b a c k - m i x i n g w h i c h we observed b e t w e e n the rising c o m p o s i t i o n a l

14

Fig. 9. S t r a t i f i c a t i o n ()iT the u p p e r z o n e can be revealed by injecting an initially vertical line of dye d o w n the c e n t e r and margins and allowing it to be d e f o r m e d by conveetiw~ flow. S t r a t i f i c a t i o n o f this kind results from a c o n d i t i o n in which two c o m p o n e n t s of d e n s i t y have very d i f f e r e n t diffusivities and are o p p o s e d in such a way t h a t one, in this case, the c o m p o s i t i o n a l gradienl, tends to stabilize the liquid, while a n o t h e r , which in this case is t e m p e r a t u r e , tends ~o destabilize, i~

boundary layer and the less differentiated liquid of the interior. This effect was most pronounced in the zone of counterflow where a descending thermal boundary layer is adjacent to the ascending compositional layer. F u r t h e r evotu tion o f the u p p e r z o n e

The progressive change in the profile and downward displacement of the interface with time resulted from two effects. First, dilute liquid rising along the wall back-mixed with progressively more depleted interior liquids as the upper zone became thicker and more evolved. Hence, the fractionated character of the rising liquid was better preserved than when it rose through liquids of more primitive compositions. Second, as crystallization continued along the walls and roof of the upper zone, the liquid in equilibrium with crystals at any particular level became cooler and hence more dilute. Thus, the composition and density of liquid in the interior of the upper zone were governed by the temperature of the wall at any given level. The

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20

Fig. 10. With time, the gradients of temperature and density (or composition) are displaced downward. Hatched lines indicate the level of the interface. In detail, these gradients are not linear but are stepped on a small scale as indicate in Fig. 9.

detailed d i s t r i b u t i o n o f c o m p o n e n t s in the u p p e r z o n e t o o k a variety o f d i f f e r e n t forms, d e p e n d i n g o n the n a t u r e o f flow in the b o u n d a r y layer and t h e m a n n e r in w h i c h the liquids equilibrated with the walls, as discussed in Part III o f this series (Baker a n d McBirney, 1 9 8 5 ) . A t the same time t h a t c r y s t a l l i z a t i o n at the wall w o r k s to increase the a m o u n t o f d i f f e r e n t i a t e d liquid, transfer o f c o m p o n e n t s across the horiz o n t a l interface t e n d s to o f f s e t this effect. T h o u g h we c a n n o t assess the rates o f these t w o c o m p e t i n g processes in m a g m a s , we can anticipate, in a qualitative w a y , their influence o n d i f f e r e n t i a t i o n . A t high rates o f cooling, greater c r y s t a l l i z a t i o n at the walls should a c c e n t u a t e the c o m p o s i t i o n a l c o n t r a s t b e t w e e n the u p p e r and main z o n e s and increase the rate o f acc u m u l a t i o n and p r o p o r t i o n s o f d i f f e r e n t i a t e d liquids. Slower c o o l i n g and greater e x c h a n g e o f c o m p o n e n t s across the interface b e t w e e n the u p p e r and main zones s h o u l d have the o p p o s i t e effect. It seems likely, t h e r e f o r e , t h a t liquid f r a c t i o n a t i o n s h o u l d cause a s t r o n g e r degree and m o r e rapid rate o f d i f f e r e n t i a t i o n in shallow intrusions t h a n in d e e p e r ones -- the reverse

16 of what would be expected from crystal settling or static crystallizatio~l without liquid fractionation. Although the composition and density of the liquid at a given level o:t' the upper zone has the same composition and density as the liquid next to crystals growing at the same level, the temperature far from the wall may be higher than the saturation value if the influx of heat from hotter convecting liquid below is more than enough to offset losses through the roof. If this happens, the liquid in the interior of the upper zone may become slightly superheated. Small crystals that form near the roof and settle through this undersaturated liquid tend to dissolve, and, depending on the relative rates of crystallization at the margins and solution of crystals in the interior, the liquid at a given level may increase or decrease in its content of Na~COL~. These conditions have a number of possible analogs in magmatic systems. Crystal-free obsidians of the kind found in many basalt-rhyolite complexes may be superheated liquids drawn from the upper zone of a body in which a high rate of heat transfer across the interface results from the strong temperature contrast between a rhyolitic upper zone and a hotter underlying mass of convecting mafic magma. With somewhat weaker transfer of heat into the base of the upper zone, crystals settling from the roof would be only partly resorbed and might resemble the disequilibrium assemblages of phenocrysts that are so c o m m o n in many zoned pyroclastic rocks of felsic compositions. As the thermal gradient is reduced even further, crystals may nucleate and grow in the upper zone and could form crystalrich siliceous rocks, such as those of many large ignimbrites. Cooling to a eutectic

If cooling and crystallization continued long enough, the solution in the upper zone of the tank eventually reached its eutectic and began to crystallize ice. At this unique temperature and composition, the density of the liquid reached a minimum, and thermal and compositional profiles through the upper zone became more uniform. The composition and density approached a nearly constant eutectic condition throughout the upper zone, and any transfer of sodium carbonate by diffusion and convection from the main zone was offset by crystallization at the upper walls and roof. Further cooling led only to more crystallization; the composition of the liquid did not change. The result of an experiment carried to this point (Fig. 11) was to produce a much smaller gradient of composition and density in the upper zone and a sharp step at the interface at its base. By analogy, we infer that siliceous magmas that reach a eutectic.like condition would tend to become uniform with decreasing amounts of compositional zoning once they reach this limit in their major element evolution. This would not, of course, restrict their zoning of excluded trace elements, which could continue to accumulate.

17

Structural consequences

The redistribution of mass resulting from differentiation and accumulation of liquids of low density under a roof could change the gravitational stability of a magma with respect to its surroundings. An intrusion that was originally emplaced at a level where it was in hydrostatic equilibrium in the crust should become increasingly unstable, if the density of the upper zone falls below that of the overlying rocks. When the force exerted by this b u o y a n t mass on the roof becomes great enough to exceed the lithostatic D e n s i t y , g cm-3 1.06 1.07 108 l

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Fig. 11. Crystallization to the eutectic c o n d i t i o n at w h i c h ice and s o d i u m carbonate precipitate together eventually leads to a nearly c o n s t a n t c o m p o s i t i o n in the u p p e r z o n e e v e n though the temperature in the center o f the z o n e increases d o w n w a r d . A stratified b o t t o m z o n e d e v e l o p e d in t h i s e x p e r i m e n t w h e n c r y s t a l s s a n k from the r o o f and w e r e resorbed in a h o t t e r z o n e o n the floor.

IX

load and strength of the overlying crust, the upper zone could be mobilized and either intrude its roof or erupt at the surface. Such a mechanism could be the cause of doming leading to large caldera-forming eruptions of siliceous magmas and may also account for the rise of siliceous domes from highly evolved sub-volcanic reservoirs.

Effects of injecting new liquids Most reservoirs below active volcanic vents must be replenished at frequent intervals by injections of new magma, perhaps in combination with withdrawal of equivalent volumes by periodic eruptions. Depending on the type of magma and its stage of differentiation, the density of the new injection may be either greater or less than that of the main body it enters. If lighter, the new liquid would rise toward a level of gravitational equilibrium within the column; if denser, it would pond on the floor. The main possibilities that could arise from these density relations have been outlined by Sparks, Huppert, and their coworkers (Sparks et al., 1980; Huppert and Sparks, 1980a, b). They show that new magma can mix effectively with the main body only if it is less dense and rises turbulently to a high level in the chamber. If it is denser and ponds on the floor, it contributes little to the composition or density of the main magma. Even large volumes entering the chamber at high velocities quickly lose m o m e n t u m to the inertia of the overlying liquid and are unlikely to rise high enough to penetrate the main body of earlier magma (Turner, 1973, pp. 173--176). They can, however, contribute heat to the system and thereby affect its convective behavior and course of differentiation. In order to model this latter case, which is the most likely one in calcalkaline intrusions, we injected dense hot liquid into the base of the tank after the original solution had reached an advanced stage of evolution. Being denser, the new liquid formed a b o t t o m zone beneath the earlier formed main and upper zones. The immediate effect was to interrupt the course of cooling, but with time the temperature fell and crystallization of Na~CO3 was resumed. The effect was more pronounced if the new liquid was injected after the upper zone had reach the eutectic and was crystallizing both Na2CO3 and ice. With a large influx of heat, crystallization was interrupted, and the two-phase crystalline assemblage under the roof began to melt. Because ice melts more readily than crystals of sodium carbonate dissolve, the crystals became disaggregated, and sodium carbonate dropped toward the floor leaving behind a very dilute liquid enriched in melt water. Meanwhile, falling crystals of sodium carbonate began to dissolve as they entered the hotter liquid at the base. Thus, the upper liquid became more dilute, while the lower one became more concentrated. The process observed here was essentially one of incongruent melting resulting from the differing kinetics of melting of the phases in the crystal-

19 line assemblage at the roof. It is interesting to speculate on the possibility that such a process might be capable of producing liquids of unusual compositions b e y o n d the limits imposed by eutectic-like phase relations. If, for example, rocks consisting of quartz, feldspar, and ot her phases were partially melted by an intrusion of high-temperature magma, those crystals that melt most readily would cont r i but e a di sproport i onat e a m o u n t to the first melt, while phases that melt more slowly might settle to deeper levels before melting or reacting with h o t t e r more basic magma. In the case just described, redistribution of c o m p o n e n t s was achieved by mass transfer when crystals d r o p p e d from the upper level of the chamber into h o t t e r liquid below. As crystals were resorbed, the density of the lower liquid increased and accentuated the interface between the zones. This b o t t o m zone of very dense liquid may be analogous to the basal zones o f certain types of igneous complexes in which layered ultramafic rocks underlie a main gabbroic zone, which in turn is overlain by an upper zone of felsic differentiates.

Effects of bottom crystallization The process just described can continue only so long as the main zone is n ot saturated with the crystals that enter it from above; eventually, of course, the t e m p e r a t u r e must fall until the lower liquid becomes saturated. We tested this possibility in an e x p e r i m e n t that was carried to the point at which the t e m p e r a t u r e on the floor of the main zone reached the saturation level and crystals began to form on the floor. When this condi t i on was reached, we n o t e d a sharp acceleration of convection in the main zone. We attribute this acceleration to the decrease in compositional density of the liquid as it flowed over crystals growing on the floor. Narrow plumes of b u o y a n t fluid began to stream upward in the center of the reservoir, and the velocity of circulation was greatly enhanced t h r o u g h o u t the entire b o d y o f the main zone. As a result, the rate of c onvect i on was m uch greater when the base was cooling than when the t e m p e r a t u r e of the basal layer was maintained by new injections of h o t liquid. It is significant that this form of compositionally driven convection resulting from cooling of the floor is so much stronger than thermally driven convection as it is conventionally visualized in a magma that loses heat mainly through its roof. At the same time t hat convection was accelerated by crystallization on the b o t t o m , the compositional contrast between the u pp er and main zones began to decline, and their interface eventually disappeared. Two effects brought this about. First, the fractionated liquid p r o d u c e d by crystallization on the floor was n o t transferred to the upper zone through boundary-layer flow but spread t h r o u g h o u t the vigorously convecting main zone and t h e r e b y reduced the compositional contrasts between zones. In addition, the enhanced rate of convection led to increased mixing at the interface and by eroding the base of the upper zone eventually d e s t r o y e d it.

20 We conclude from these observations that the convective regime in talcalkaline magmas may chm~ge dramatically when new injections of hot. dense magma come to an end and crystallization begins on the bottom of the reservoir. If the upper zone disappears, as it did in the model, little evidence of it would be preserved in the solidified body. It is not surprising, therefore, that plutons rarely have a sharply defined interface separating a felsic upper zone from a more mafic zone below.

SYNTHESIS OF EXPERIMENTAL RESULTS The results of these experiments have implications for both volcanic and plutonic magmas with different types of density variations. Volcanic rocks

Some of the c o m m o n l y observed volcanic phenomena that may be ascribed to processes similar to those described here have already been mentioned. Chief among these are the following. (a) The volumes and degrees of differentiation of highly evolved magmas observed in large mature igneous centers may be the result of liquid fractionation accompanying modest amounts of side-wall crystallization. (b) The fact that voluminous eruptions of felsic magmas are most characteristic of those series in which density declines with increasing differentiation indicates that only b u o y a n t liquids are likely to be segregated into the upper levels of sub-volcanic reservoirs. The scarcity of intermediate compositions in m a n y tholeiitic volcanic suites must be due to their greater density and tendency to pond on the b o t t o m rather than rise through liquids and crustal rocks of lower densities. (c) The close association in time and space of basic magmas with the products of their own crystallization requires a mechanism of differentiation in which liquids of contrasting composition can coexist in gravitationally stable zoned magma chambers. Zoned and bimodal magmas erupted from the same or nearby vents could come from such bodies. (d) Correlations between the duration of periods of dormancy and the volumes and compositions of felsic magmas erupted after long periods of repose provide a measure of the rates of accumulation of differentiated magmas by liquid fractionation. The fractionated magma may range from a crystal-rich to superheated liquid, depending on its heat balance with respect to the main zone and cooling margins. (e) Accumulation of light liquids under a roof can lead to an unstable condition in which the force exerted by the b u o y a n t magma exceeds the strength and weight of overlying rocks. Once this critical limit is exceeded, the magma may be mobilized and erupt, either as viscous domes or explosive ejecta, depending on its volatile c o n t e n t and temperature.

21

Plu tonic rocks By c o m b i n i n g the observations m a d e in tank e x p e r i m e n t s , o n e can construct a possible s e q u e n c e o f events that might f o l l o w e m p l a c e m e n t and s u b s e q u e n t c o o l i n g o f sub-volcanic intrusions at shallow depths in the crust. We postulate four separate phases (Fig. 12).

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22

Stage 1 -- Initial in trusion The initial e m p l a c e m e n t of a body into the crust may be followed by a brief period during which temperatures at the margins are high enough to melt felsic wall rocks. When modeled in our tank, melting was seen to p ro d u ce a b u o y a n t dilute liquid that rose to the u p p e r m o s t levels under the roof. R e f r a c t o r y crystals separated from the disaggregating wall " r o c k s " settled into h o t t e r liquid and t ended to dissolve at lower levels where they accentuated the compositional contrast. The result was a rapid division of the initially h o m o g e n e o u s liquid into two zones, an upper one p r o d u c e d by accumulation o f the b u o y a n t partial melt, and a main zone of h o t t e r denser liquid enriched in the c o m p o n e n t s of resorbed crystals that sink from higher levels.

Stage H -- Cooling, crystallization, and accumulation o f fractionated liquid Melting absorbs such large am ount s of heat that it c a n n o t continue for long w i t h o u t f r e q u e n t influxes of h o t magma. When the intrusion cools and begins to crystallize on its walls and under its roof, a compositional boundary layer may sink and p o n d on the floor if its density exceeds that of its parent. If its density is less, it can rise to accumulate under the roof. If, in the latter case, the flow of this compositional b o u n d a r y layer is at least partly turbulent, the fractionated liquid will back-mix with its parent and p ro d u ce linear compositional variations in the upper zone.

Stage III --Periodic eruption and replenishment with fresh magma In calc-alkaline magmas, new liquid injected into a still fluid intrusion will probably be denser and h o t t e r than the more evolved liquids of the main and upper zone; if so, it will tend to p o n d on the floor as a b o t t o m zone and may become even denser if it resorbs crystals entering it from above. Owing to its greater density, it is unlikely to mix with earlier liquids. In tholeiitic magmas, new injections are more likely to be lighter and rise to a higher level; t hey may even pass through the denser, more evolved magmas to er u pt at the surface. Whether or n o t the new magmas mix with the earlier ones, t he y tend to sustain weak thermally driven convection in the main zone.

Stage I V -

Crystallization, homogenization and inward solidification

As the t e m p e r a t u r e of the b o d y falls and replenishment becomes less frequent, crystallization must eventually begin on the floor. When this happens in calc-alkaline magmas, convection of the main zone is no longer drive by simple thermal effects alone but also but a much larger decrease in density resulting from crystallization on the floor. Convective circulation

23 o f the main z o n e is t h e n a c c e l e r a t e d b y the c o m b i n e d effects o f these rei n f o r c i n g processes and, if s t r o n g e n o u g h , m a y sweep a w a y t h e resing c o u n t e r f l o w n e x t to the crystallizing walls. T h e u p p e r z o n e will t h e n cease to g r o w and, at the same time, t h e c o m p o s i t i o n a l c o n t r a s t b e t w e e n the u p p e r a n d main zones will gradually decline. These h o m o g e n i z i n g processes are less i m p o r t a n t in tholeiitic bodies in w h i c h liquids b e c o m e denser as t h e y evolve. F r a c t i o n a t e d liquids d e s c e n d to the f l o o r where t h e y p o n d and crystallize with little e f f e c t o n the c o n v e c t i v e behavior o f the main b o d y o f m a g m a above. When the c o m p o s i t i o n a l differences b e t w e e n the u p p e r and main zone o f calc-alkaline bodies b e c o m e slight e n o u g h for the a u g m e n t e d c o n v e c t i v e f l o w to e r o d e t h e base o f the u p p e r zone, the interface b e t w e e n the t w o zones rises, b e c o m e s progressively m o r e indistinct, and e v e n t u a l l y disappears. The b o d y t h e n c o n v e c t s as a single unit as c r y s t a l l i z a t i o n p r o c e e d s i n w a r d a n d the b o d y solidifies. In Part II, we e x a m i n e several q u a n t i t a t i v e aspects o f these processes in greater detail, and in Part I I I we discuss s o m e o f the c o m p o s i t i o n a l effects t h e y w o u l d be e x p e c t e d t o p r o d u c e . ACKNOWLEDGEMENTS We are very appreciative o f critical reviews by D. B o s t o k , C.F. Chen, Harry Hardee, H e r b e r t H u p p e r t , Bruce D. Marsh, and R.S.J. Sparks, all o f w h o m read earlier versions o f the m a n u s c r i p t and c o n t r i b u t e d materially to its i m p r o v e m e n t . This w o r k was b y N S F G r a n t E A R 8 1 2 1 0 6 1 .

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24 Huppert, H.E. and Sparks, R.S.J., 1980b. The fluid dynamics of a basaltic magma chamber replenished by influx of hot, dense, ultrabasic magma. Contrib. Mineral. Petrol., 75: 279--289. Huppert, H.E. and Sparks, R.S.J., 1984. Double-diffusive convection due to crystallization in magmas. Annu. Rev. Earth Planet. Sci., 12: 11--37. Loewinson-Lessing, F., 1911. The fundamental problems of petrogenesis. Geol. Mag., pp. 248--257 and 289--297. Loewinson-Lessing, F., 1954. A historical Survey of Petrology, Oliver and Boyd, Edinburgh, 112 pp. McBirney, A.R., 1980. Mixing and unmixing of magmas. J. Volcanol. Geotherm. Res., 7: 357--371. McBirney, A.R. and Noyes, R.M., 1979. Crystallization and layering of the Skaergaard Intrusion. J. Petrol., 20: 487--554. Murase, T. and McBirney, A.R., 1973. The properties of some common igneous rocks and their melts at high temperatures. Geol. Soc. Am. Bull., 84: 3563--3592. Nilson, R.H., McBirney, A.R. and Baker, B.H., 1985. Liquid fractionation. Part If: fluid dynamics and quantitative implications for magmatic systems. In: B.H. Baker and A.R. McBirney (Editors), Processes in Magma Chambers. J. Volcanol. Geotherm. Res., 24: 25-54. Norton, D. and Taylor, H.P., 1979. Quantitative simulation of the hydrothermal systems of crystallizing magmas on the basis of transport theory and oxygen isotope data: an analysisof the Skaergaard Intrusion. J. Petrol., 20: 421--486. Sartorius yon Wa]tershausen, W., 1853. Ueber die vulkanischenGesteine in Sizilienund Island und ihre submarine Umbildung.G6ttingen. Shaw, H.R., 1974. Diffusion of 1120 in granitic liquids. Part If. Mass transfer in magma chambers. In: A.W. Hoffmann, B.J. Giletti, H.S. Yoder, Jr., and R.A. Yund (Editors), Geochemical Transport and Kinetics. Carnegie Inst. Washington,Publ. 634, pp. 155-170. Simkin, T., Siebert, L., McClelland, L., Bridge, D., Newhal], C. and Latter, J.H., 1981. Volcanoes of the World. Hutchinson Ross, Stroudsburg, Pa., 233 pp. Smith, R.L., 1979. Ash-flowmagmatism. Geol. Soc. Am. Spec. Pap., 180: 5--27. Sparks, R.S.J., Meyer, P. and Sigurdsson, L.B., 1980. Density variation amongst midocean ridge basalts: implications for magma mixing and scarcity of primitive lavas. Earth Planet. Sci. Lett., 46: 4] 9--430. Spera, F.J. and Crisp, J.A., 1981. Eruption volume, periodicity, and caldera area: relationships and inferences on development of compositional zonation in silicic magma chambers. J. Volcanol. Geotherm. Res., 11: 169--188. Stolper, E. and Walker, D., 1980. Melt density and the average composition of basalt. Contrib. Miner. Petrol., 74: 7--12. Thorarinsson, S., 1954. The eruption of Hekla 1947--1948, II. The tephra-fall from Hekla on March 29th, 1947. Visindafelag Islendinga, 68 pp. Turner, J.S., 1973. Buoyancy Effects in Fluids. Cambridge Univ. Press, 368 pp. Turner, J.S., 1980. A fluid dynamical model of differentiation and layering in magma chambers. Nature, 285: 213--215. Turner, J.S. and Gustavson, L.B., 1981. Fluid motions and compositional gradients produced by crystallization or melting at vertical boundaries. J. Volcanol. Geotherm. Res., 11: 93--125. Walker, G.P.L., 1975. A new concept of the evolution of the British Tertiary intrusive centres. J. Geol. Soc., 131: 121--141. Wilcox, R.E., 1954. Petrology of Paricutin Volcano, Mexico. U.S. Geol. Surv. Bull., 965-C: 281--353.