Journal of Petrology Advance Access published online on November 27, 2008
Journal of Petrology, doi:10.1093/petrology/egn059
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The Internal Magma Reservoir of Large Intrusions Revealed by Multiphase Rayleigh Fractionation
Department Of Geosciences, University Of Massachusetts, 611 North Pleasant Street, Amherst, Ma 01003-9297, USA
Received June 14, 2008; Revised typescript accepted October 16, 2008
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONSYSTEMATICSROLE OF TRAPPED LIQUIDAPPLICATIONSHOW DOES IT WORK?ADDITIONAL EFFECTSNATURE OF THE INTERNAL...CONCLUSIONSREFERENCES |
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The fractionation progress of a crystallizing basaltic magma is recorded in the changing mineral compositions of binary solutions that form a part of plagioclase, olivine, and augite. When such compositional data are plotted against an independent measure of progress such as volume, they can often be described by a Rayleigh equation that reveals details of the crystallization history. A binary solution crystallizing by itself follows a path determined by the Rayleigh exponent (D – 1) where D is the partition coefficient X1S/X1L (X is mole fraction, 1 is low-melting component, L is liquid, S is solid). In company with another phase, however, such a binary solution may follow a wide range of paths in an envelope about (D – 1), ranging from (a) f
(D – 1) to (b) (D – 1)/f, where f is the fraction of the active phase—the binary solution under consideration. The upper limiting curve, an extended fractionation path, is given by (a) above, whereas a full X2 depletion path (b) defines the lower limit. This range of alternatives is here codified and supplemented by considerations of residual porosity. The result is a Rayleigh equation in five variables that can illuminate magmatic history, including the probability of the existence of an internal reservoir that damps the depletion effect. The range of paths can help to identify evidence for, and causes of, leading-edge fractionation of ascending magma, small packet crystallization, pressure variations, off-cotectic excursions, and oscillating modal variation. KEY WORDS: Magma reservoir; Rayleigh paths; binary solutions; Kiglapait; Skaergaard
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONSYSTEMATICSROLE OF TRAPPED LIQUIDAPPLICATIONSHOW DOES IT WORK?ADDITIONAL EFFECTSNATURE OF THE INTERNAL...CONCLUSIONSREFERENCES |
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Multiphase Rayleigh fractionation (MRF) of binary solutions in multicomponent systems was discussed in an earlier contribution (Morse, 2006
). For fractional crystallization, MRF treats the reaction progress of an active phase (the binary solution of interest) in company with one or more phases that are indifferent to the progress of the active phase, but whose removal from the liquid by crystallization reduces the fraction of remaining liquid. In the original paper, much was made of the disagreement between MRF, which produced an extended path of fractionation, and the MELTS routine (Ghiorso & Sack, 1995), which gave only the path of a binary solution crystallizing by itself, without additional components. It became clear that something was missing in the MRF development, and possibly in the MELTS routine as well.
Here, with the aid of Paul Asimow, the missing part of the development is found and identified in the MELTS calculation. The missing feature is a depletion path, followed by a binary solution when its phase components are present in small quantity, when the refractory component is rapidly depleted simply because it is scarce. This is the path found by MELTS when the crystallization of an inactive phase is prevented. MELTS does not as yet treat explicitly the case of an extended path, but does so implicitly, because the depletion path and the extended path cancel each other out to yield the binary solution path by itself, as found by MELTS and shown in fig. 5 of Morse (2006).
In short, there are three harmonious paths of multiphase Rayleigh fractionation: the binary itself, the extended path, and the depletion path. The purpose of this paper is to explain and codify the three paths, to show how they may imply a reservoir internal to the magma body but capable of being isolated from the crystallization zone, and to suggest the existence of such reservoirs in large magma bodies. Moreover, it is shown that repeated or oscillating involvement of, or isolation from, the reservoir can produce much of the scatter or systematically repeated variations in mineral compositions seen in layered intrusions, including the sawtooth or cyclic patterns sometimes found up-stratigraphy. The effects of depletion also appear in the basal reversals of mineral compositions often seen in mafic intrusions, and they explain the principle of leading-edge fractionation of ascending magmas, when small packet crystallization occurs and depletion paths are followed.
The recognition of the depletion path in MELTS is due to Paul Asimow (personal communications in autumn 2006), who turned off plagioclase crystallization in an artificial mixture of OL30, PL70 and found the Fo content of olivine strongly depleted as a result.
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SYSTEMATICS |
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TOPABSTRACTINTRODUCTIONSYSTEMATICSROLE OF TRAPPED LIQUIDAPPLICATIONSHOW DOES IT WORK?ADDITIONAL EFFECTSNATURE OF THE INTERNAL...CONCLUSIONSREFERENCES |
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Review
Recapitulating the development in the earlier paper (Morse, 2006
), we have the treatment of binary solutions given by the principle of linear partitioning, as follows. For many binary solutions, and especially many of those of petrological interest, the (mole, weight, atomic) partition coefficient D1 = X1S/X1L obeys a linear relationship
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| (1) |
). The first formal derivation was given at p. 472 of Morse (1997), where KD was defined and expanded as the exchange coefficient. A derivation using the Gibbs energy was then given at pp. 2309–2311 of Morse (2000), where a full discussion of the interrelationships of the partition coefficients for the two end-members of a binary solution was given, with graphical illustrations. That paper also explored pronounced failures of linearity in certain boiling mixtures, along with many examples of convincing linearity, for both continuous binary solutions and azeotropes. Further thermodynamic implications were explored at pp. 2317–2318 of Morse (2000), including the interesting results that the exchange reaction may be nearly isentropic at constant pressure, and nearly isochoric at constant temperature. The form of equation (1) is useful for calculating fractional crystallization with the Rayleigh equation discussed below. By this convention we track the fractionation progress of the low-melting liquid component X1 = C as it increases from an initial value toward C = 1· 0. Then the composition of the solid is found from the partitioning relation. Figure 1 illustrates the linear partitioning relationship for a system with KD = 0·30. Hereafter the subscript (1) on D will be omitted as being understood.
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The general Rayleigh equation (Rayleigh, 1896
) that describes the concentration C of an end-member in a binary solution with decreasing fraction of the initial system F is
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| (2) |
), or weight fraction, or another conserved property. The quantity F refers to liquid (FL) on crystallization or to solid (FS) on melting. The behavior of Rayleigh fractionation with crystallization is usefully illustrated in a log–log plot (Fig. 2) of an idealized system of olivine, Fo–Fa. In this figure, F is taken as the fraction of the system present as liquid, FL, running down from left to right (as with time). The corresponding per cent solidified, PCS = 100(1 – FL), is plotted at the base of the diagram. Figure 2 shows the evolution of the liquid composition from the bulk composition C0 as a function of the fractionation progress represented by decreasing FL. It is seen that the liquid composition follows a curve that is asymptotic to the pure component 1 = Fa, and that this curve is driven by successive tangents to the liquid composition. These tangents describe the collection of evolving values of fictive C0 that are used in precise stepwise calculations (e.g. Morse, 1997).
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For binary solutions in multicomponent systems, which may contain more than one crystal species, we now modify the Rayleigh equation for multiphase fractionation by introducing (Morse, 2006
) a multiplier f on the Rayleigh exponent (D – 1), as follows:
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| (3) |
is the fraction of the active crystal phase relative to total crystals, and D is the partition coefficient X1S/X1L as defined in equation (1). By active crystal phase (here ) is meant that phase (or possibly combination of phases) that causes C to evolve, all other phases being passive in that respect, but nevertheless removing mass from the liquid and hence diminishing FL by their crystallization. The beginnings of this treatment were applied to the fractionation of olivine at p. 1049ff of Morse (1996). A complete derivation of equation (3) was given at pp. 228–229 of Morse (2006), followed by a proof at pp. 229–230.
New developments
The effect of the operator f when its value is less than 1· 0 is to damp the evolution of C so that the fractionation path is extended to a flatter slope than that of the pure binary, for which f 
1· 0. The smaller the value of f, the flatter the slope, hence the multiphase effect is more pronounced for a less abundant phase such as olivine than for a more abundant phase such as plagioclase, when the two crystallize in cotectic proportions that we may simulate as 30:70. For example, when this flattening for olivine with f = 0·3 was compared with the pure binary in fig. 5 of Morse (2006), it was shown that the crystal composition reached Fo68 at 80 PCS in comparison with Fo25 for the pure binary system Fo–Fa. However, in the same figure, it was also shown that the calculation from MELTS fell almost exactly on the binary, and this led to further discussion at the end of that paper.
The conflict between the multiphase Rayleigh fractionation (MRF) result was given further consideration by Paul Asimow, as noted above, in which with MELTS he turned off the plagioclase in the artificial 30:70 system and found a very strong depletion path (so called because the Fo content of the liquid was rapidly exhausted), which happened simply because the olivine component was scarce. This led to the general understanding that the depletion path and the extended path taken together generated the binary path, and hence when MELTS plotted on the binary, it ‘recognized’, in principle, the existence of both the depletion path and the extended path. More precisely, of course, we knew that the extrema cancelled each other out to give the binary. Armed with this awareness, it was a simple matter to deduce that the equation for the depletion path must be the inverse of the equation for the extended path, and therefore that the depletion path was given by the Rayleigh exponent
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| (4) |
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| (5) |
Therefore, in fact, there are three legitimate paths in MRF: the original upper or extended path, the lower depletion path, and the resultant cotectic path, which is exactly that of the pure binary. Moreover, each of the two limiting (outer) paths implies the other, so one may imagine a development starting with a value of f = 1· 0 and decreasing to values <1· 0, generating an expanding envelope of conjugate upper and lower paths disposed symmetrically about the binary. These curves are shown in Fig. 3, for several values of f. The exponent f(D – 1) lifts the upper curves away from the binary, and the exponent (D – 1)/f draws the depletion curves down from the binary. For all f 
1· 0, the cotectic still resides exactly on the binary because the two opposing exponents and their curves cancel each other.
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The depletion function
We now need a further development to understand the full meaning of the depletion path and the upper path. To do this, we define the depletion function g such that f
g 1· 0 and write the exponent
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| (6) |
and 1· 0. Next, we ask what meaning could be attached to the case g = 1· 0, and reason that, to avoid depletion, all we need is the presence of a reservoir connected to the crystallizing region being studied. Equations (4)–(6) all simply respond to the empirical discovery that the depletion path found by Asimow is generated by dividing the Rayleigh exponent by the fraction of the active phase instead of multiplying it. This principle is given no formal derivation, but instead is an intuitive step. However, a retrospective derivation can be made along the lines of the development cited above in appendix A of Morse (2006). The physical attributes of the reservoir could be highly variable and need not concern us here in detail. In principle, however, we may classify the reservoir as either internal to the system (the magma body) or external to it (conventional magma recharge). For reasons to be discussed, the internal reservoir is required here, with interesting consequences, and we may consider it to be quasi-infinite. It is assumed that the reservoir is not contained within the crystallization zone but is in potential communication with it.
The role of the depletion function is illustrated in Fig. 4a for equimolar olivine (i.e. Fo50 liquid) in the case of a bulk composition OL30 PL70 with KD = 0·30. Here olivine crystallizing by itself follows the path g = f. Olivine crystallizing both in the pure binary and on the cotectic also follows the middle path, and the upper cotectic path is generated by the involvement of the internal reservoir with g = 1· 0. The cotectic results given by the MELTS calculation plot essentially on the binary. The region between the binary and the upper curve is the cotectic region, occupied by the ensemble of layered intrusions discussed by Morse (2006). These characteristics are emphasized again in Fig. 4b, where the exponents are shown, along with arrows showing the motion of the upper and lower curves as g 
; 1· 0.
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The cotectic region lying between the binary and the upper curve can be contoured on g, as in Fig. 5. This result gives a quantitative physical meaning to g, which is a measure of the approach of the system to that of an internal reservoir. Scatter of natural data near the curve for g = 1· 0 can be taken as evidence for imperfections in the degree of approach to the infinite reservoir, with excursions into the reservoir followed by the crystallization of small packets that have become isolated from the reservoir, and therefore become rapidly depleted.
A further comparison of MRF and MELTS is given in Fig. 6 for the case of bulk composition KIBC3, a simplified analogue of a plausible parent magma of the Kiglapait intrusion studied experimentally by Morse et al. (2004). Here the two depletion curves are close together at the beginning, but the MELTS curve steepens away from the MRF path, probably because the MELTS calculation sees the effect of pyroxene, which is not assumed by the MRF calculation.
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Reservoir probability
Clearly, if the natural data plot on or near the binary there is no evidence for an internal reservoir, and we may assign the probability that such a reservoir is present as P(ir) = 0. However, if the natural data plot above the binary we may infer the presence of a reservoir with P(ir) > 0. The value of P(ir) may be calculated explicitly as follows, after a brief recapitulation of the case so far.
The operators on the Rayleigh exponent (D – 1) are a multiplier 0 f 1 and a divisor f g 1. When the multiplier is absent (the phase is suppressed) and the divisor g = f, fractionation occurs on the depletion path, for which the refractory component is depleted to the maximum extent and the evolved component is enriched to the maximum extent. When both operators are present, the ratio f/g runs the fractionation. This ratio runs from 1· 0 at the binary to f at the extended path, and the value of g becomes a measure of the presence of an internal reservoir. The probability P(ir) of the presence of an internal reservoir is found when g – f is taken relative to the value 1 – f:
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| (7) |
the probability of a reservoir is zero, and when g = 1, the probability of a reservoir is unity. However, g also may serve as a fitting parameter, with which we may inquire whether a Rayleigh fractionation function can be found to fit a set of observed data. In this case, values of g > 1· 0 may be entertained in computation as a quick substitute for fitting by reducing the value of f.
Range of fractionation
The possibilities of fractional crystallization run from these limiting cases: (1) fully depleted in the refractory component, (D – 1)/g, where g = f; (2) past the binary f(D – 1)/g (D – 1); (3) to fully extended in the evolved component, f(D – 1), where g = 1. Similar principles hold for fractional melting, a process not considered here.
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ROLE OF TRAPPED LIQUID |
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TOPABSTRACTINTRODUCTIONSYSTEMATICSROLE OF TRAPPED LIQUIDAPPLICATIONSHOW DOES IT WORK?ADDITIONAL EFFECTSNATURE OF THE INTERNAL...CONCLUSIONSREFERENCES |
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Trapped liquid in a cumulate nominally has D = 1· 0 for all components and so can be accounted for very simply by letting D(trapped liquid) = pr, where pr is the residual porosity representing the effective amount of unmodified parent magma left in the cumulate by burial and isolation before all adcumulus exchange could be effected (e.g. Morse, 1986
). Such an isolated liquid must eventually crystallize the components of more evolved phases as well as zoning (plagioclase) or modifying (olivine) the resident cumulus crystals.
The residual porosity is best quantified from the presence and modes of excluded phase components that are not part of the cumulus assemblage. It is also distinctively revealed and quantified by zoning in plagioclase, where present. In the Kiglapait intrusion, the value of pr was estimated from the residual amounts of excluded modal phase components of augite, Fe–Ti oxides, sulfide globules, and apatite, leading to a mean value described by pr = 0·14FL0·9 (Morse, 1979b). This result in turn was compared with the range of zoning 
An in plagioclase, obtained in grain mounts, to give the relation 100 pr = 1· 9 An – 3·9. In turn, this result was used successfully to distinguish between intercumulus and cumulus apatite in the pr-rich Upper Border Zone of the intrusion (Morse & Allison, 1986). It is therefore supposed from such a success that the estimates of pr in the Lower Zone are robust.
Trapped liquid has two effects: secular and local. The secular effect changes the fractionation path of the magma by damping the forward evolution of the conserved component, hence also damping the depletion of the refractory component of the binary solution, whereas the local effect modifies the resident crystal mode and composition within the cumulate rock.
Secular effect
The Rayleigh evolution of the liquid ratio C/C0 is given, as usual, by the fraction of liquid FL raised to the exponent (D – 1) in the general case. Here we discuss the modification of the exponent by the presence of trapped liquid. For multiphase Rayleigh fractionation we have as before the multiplier f on the exponent and we assume for the moment nothing about the divisor g. The variable partition coefficient D, as given by the linear partitioning or any other relationship, must now be modified by adding the residual porosity pr, but only that part of the porosity attributed to the active phase, hence the quantity added must be (f x pr). Therefore we write for the whole Rayleigh exponent f[D + (f x pr) – 1]. Using as an example a case where f = 0·3, D = 0·5, pr = 0·2, and FL = 0·1, the unmodified result will be
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| (8) |
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| (9) |
as for olivine, the secular effect is very powerful. For example, in one calculation with a moderately large but decreasing residual porosity, the olivine composition at 90 PCS without the secular effect is Fo27, whereas with the extended path of the secular effect it is Fo51. For larger values of f as for plagioclase, the effect is much milder. It should be noted that in the above, the formulation tacitly assumes that the depletion function g = 1· 0, consistent with an internal reservoir. The secular trapped liquid effect operates on the evolving liquid composition by slowing its evolution as the bulk effective D tends toward 1· 0. The presence of an internal reservoir does not erase this effect. Instead, the absence of an internal reservoir tends to erase the effect, by causing an opposing depletion in the refractory component.
Local effect
The local effect, once the liquid is sequestered in the cumulate by solidification or burial, is to react with the resident crystals by adding evolved, excluded phases and components. Thus the cumulus crystals of, say, plagioclase and olivine are changed in some degree toward Ab and Fa, respectively, and according to their abundance in the cumulate and in the liquid. In general, the cotectic ratio of cumulus crystals is not the same as that of their components in their parent liquid, because in general the liquid path is curved and the cumulate (the instantaneous solid composition) is tangent to the liquid path. However, in the case of olivine and plagioclase, the cotectic has a small curvature and the tangent path can be considered similar to the liquid composition without serious error. Therefore, one may use the notation f both as the fraction of the active phase separating from the liquid, and as that of the phase component within the local liquid.
The residual porosity pr adds low-melting component to the crystal according to the fraction of the active phase and value of pr. Where C is the amount of low-melting component in the liquid, X1L, the amount X added to the resident crystal is
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| (10) |
and pr are involved.
As an example, the rather large pr = 0·32 inferred for the base of LZa in the Skaergaard intrusion (Morse, 1979b), applied to cumulus crystals Fo72 at f = 0·35 (taken as olivine + augite), with liquid C = XFa (wt) = 0·632 and XMg (liquid, molar) = 0·459, results in a final crystal composition of Fo66, a difference of –0· 06 in XMg.
The trapped liquid effects on the effective partition coefficient are illustrated in Fig. 7 for the Skaergaard and Kiglapait intrusions.
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APPLICATIONS |
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TOPABSTRACTINTRODUCTIONSYSTEMATICSROLE OF TRAPPED LIQUIDAPPLICATIONSHOW DOES IT WORK?ADDITIONAL EFFECTSNATURE OF THE INTERNAL...CONCLUSIONSREFERENCES |
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Olivine at Kiglapait and Skaergaard
The olivine trends in both these layered intrusions were treated in an earlier paper (Morse, 2006
), but here we can add more details. First, the effect of trapped liquid will be applied, and then the paths of the cotectic = binary and depletion will be shown for comparison. The value of g can be explored in conjunction with the choice of normative olivine in the crystal mixture. As with all calculations with mafic phases, the Rayleigh fractionation procedure is chosen to operate on mass units instead of volumes, but the compositions of the crystals are recalculated to mole units for comparison with the field data.
Kiglapait
Figure 8 shows the solution for the Lower Zone and early Upper Zone of the Kiglapait intrusion. The upper continuous black line shows the uncorrected solution for g = 1· 0 with a fictive initial olivine composition taken as Fo74. This curve may be taken as a fair approximation of the mean path through the data. A path for the true liquidus (i.e. cumulus) compositions represented by the upper limit of the data points would be better served by a fictive starting point at Fo76. The dashed curve in Fig. 8 shows the result of including the trapped liquid effect with residual porosity ranging from 0·14 at 0 PCS to 0· 02 at 88 PCS, as found by Morse (1979b). This curve serves the mean path through the data somewhat better than the continuous line. The value of g = 1· 0 needed to find a curve matching the data implies the presence of an internal reservoir above the 40 PCS level.
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Of perhaps greater interest are the two paths for cotectic and depletion fractionation. Clearly, these paths give access to the scattered Fe-richer compositions, but can they really operate to do so? The answer in the first (cotectic) case is clearly yes; if the value of g locally becomes minimal, hence equal to f
, then the fractionation will follow the cotectic = binary curve. From this result it would appear that the probability of the presence of an internal reservoir was more often zero than any other value in the range 
15–40 PCS. The depletion curve can become active at any time when small packet crystallization occurs, as in local excursions of magma into the olivine field without crystals of plagioclase. Such excursions are clearly recorded in the abundance of olivine-rich or dunite layers in the range 0–15 PCS found in the intrusion, and are clearly permitted by the well-known low barrier to nucleation of olivine relative to plagioclase. This effect, combined with the high probability of leading-edge fractionation, can explain all of the olivine data in this basal reversal, as discussed below under a classification of the effects accessible to the principles of this study.
Skaergaard
In the previous treatment of the Skaergaard olivine (Morse, 2006) the starting composition was taken as Fo69, and it was found that the combined fraction of olivine plus augite taken as f was required to be set at 50% to match the data. With the recognition of the depletion function, a more realistic choice of f = 0·35 is permitted, as shown in Fig. 9. Here the fictive starting point is set at Fo72 and the residual porosity is varied with the crystal composition from values 0·35 at 10 PCS to 0· 03 at 90 PCS, with the result that the path adjusted for the local effect of trapped liquid passes reasonably well through the data when a value of g = 0·65 is assumed. Here is an example of how the values of g and f can be adjusted as fitting parameters, because as shown above they operate on each other. In this case, the probability of the presence and involvement of an internal reservoir at any given time is, from equation (7), P(ir) = 0·46.
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Plagioclase
Kiglapait
The partitioning of plagioclase with liquid varies with pressure to such an extent that at high crustal or low mantle pressures the values of XAn in the two compositions merge and may even become reversed. Relevant experimental data for anorthositic parents and the Kiglapait intrusion are shown in Fig. 10. The value of KD rises strongly with P, and that correlation in turn affects the shape of the binary loop and the values of D used to drive the MRF calculation. The result is a family of curves, calculated for fpl = 0·70, shown in Fig. 11. Data for Kiglapait Lower Zone plagioclase compositions are shown in Fig. 12 along with two curves from the previous figure. The upper curve is calculated for 8 kbar and the lower curve for 5 kbar. However, the Kiglapait intrusion was emplaced at a pressure of about 2·5 kbar referred to the present erosion level (see review by Morse et al., 2004
), so these limiting curves are not directly relevant.
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Various schemes were used to find solutions to MRF that would match the data from the rocks. To reflect the decreasing importance of plagioclase in the crystal assemblage, the values of fpl were taken as the total CIPW-normative feldspar in the rock models described in table 5 of Morse (1981b
); these values rise from fpl = 0·51 to 0·72 at 20 PCS, then fall to 0·44 at 90 PCS. From the olivine results, the depletion function was set at g = 1· 0. A starting composition of An67 was assumed to derive a mean path through the data. The value of KD was set at 0·50. The residual porosity was varied from 0·14 to 0· 02 as for olivine, and used for both the secular and local effect on fractionation. No very satisfactory solution was found using a value of g = 1· 0, for which the curve fell near the lower limit of the data for PCS levels above 40.
The assumed constant value of KD then came into question. The maximum stratigraphic thickness of the Kiglapait intrusion is 8400 m, corresponding to a pressure of 5 kbar at the base, for which the value of plagioclase KD is well determined at 0·52 (Morse et al., 2004). The most secure value at 1 atm is that for the system Di–An–Ab, for which KD = 0·26, giving a non-trivial potential variation of 0·26 in KD over the pressure range 0–5 kbar. Assuming as a limiting condition a full magma body, the depth relation r over time is easily scaled as r = 8400 FL1/2 m from fig. 1 of Morse (1988), and hence the pressure can be scaled as well. The pressure range from 0 to 90 PCS would be from 5020 to 3297 bars, with a corresponding variation in KD from 0·52 to 0·43. The width of the binary loop varies inversely with the value of KD, so with decompression the loop becomes wider, and for a given liquid composition the crystal becomes more refractory and hence drives the evolution of the liquid more strongly. Conversely, for a narrower loop the evolution of the liquid is slower. If the pressure decreases with time, one should find an initial shallower trend followed by a steeper one.
The calculation as described above was repeated using the full range of variable KD, and the result is rather surprisingly good, as seen in Fig. 13. The bold curve finds the mean path through most of the data, and the dashed curve shows the less successful calculation with constant KD. Data plotting below the bold curve can be interpreted as a partial loss of the internal reservoir, hence g < 1· 0. As with olivine, many of the low An values at stratigraphic levels below 40 PCS can be reached by the depletion curve, but those below 20 PCS must signify leading-edge fractionation of incoming magma (discussed below). A starting composition of An69 would accommodate the cumulus compositions very well, as can be approximated by lifting the bold continuous curve by 2% An (dotted curve in Fig. 13).
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It is not likely that the crystallization of plagioclase actually took place at the maximum pressure indicated by the total thickness of the present intrusion, but it is at least realistic that much of the differentiation could be driven by the dominantly adcumulus solidification of floor cumulates. The bold curve shown in Fig. 13 is clearly an upper limiting condition for the starting point at An67, but it does suggest a role for pressure in the fractionation of plagioclase.
The discussion above treats only the range 0–90 PCS, beyond which the variation of plagioclase composition becomes more complicated. From 90 to 95 PCS the data follow a very steep path (Fig. 14). Within this interval the over-production of augite declines from a maximum at 42% in the mode to the equilibrium value near 19% (Morse, 1979b fig. 12). It appears probable that the steep variation of plagioclase composition in this stratigraphic interval is a response to the preferential extraction of CaAl by excess augite (e.g. Morse & Ross, 2004, table 7). The steep path resembles a depletion curve, so a model fractionation path was calculated using a full depletion mode with pr = 0 and g = fpl, hence a Rayleigh exponent of (D – 1)/g, again varying KD with pressure. The result falls adequately within the data (Fig. 14).
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Beyond 94–95 PCS the data follow a much flatter slope, because here the feldspars become increasingly ternary, and a full treatment will need to incorporate the full effect of potassium throughout, leading to an end point at the ternary feldspar minimum. The code for ternary solutions requires careful rewriting from the binary solution code and is at present still under construction.
This exercise helps to illustrate the flexibility of multiphase Rayleigh fractionation in finding viable solutions to the stratigraphic behavior of a binary solution. The free parameters of the depletion function g, the variable fraction of the active phase, the value of the exchange coefficient KD and the residual porosity pr permit a fruitful search for a path through the data. Once achieved, such a path may not be unique, but it may serve as a valid exercise in discovery. The result may illuminate the effect of the varying mode of another phase, as here with respect to augite, which evidently produced an offset in what might otherwise have been a smooth curve of evolution if augite had not crystallized in excess. That this represents a depletion mode and hence the apparent absence of an active internal reservoir is illusory, for in fact the over-production of augite is considered to represent a wholesale dump of augite previously sequestered in the internal reservoir (Morse, 1979b). In this case the depletion mode may be seen as a proxy for some other combination of circumstances.
Skaergaard
New data for plagioclase cores and rims in the Skaergaard Layered Series are available in a comprehensive report by Toplis et al. (2008) and shown in Fig. 15, plotted against volume per cent solidified as calculated from table 1 of Nielsen (2004). Two features of this array are of special interest. First, the data show a pronounced concave-up trend, and, second, there is a distinctive temperature–stratigraphic height shelf from LZc to MZ. Liquidus temperatures retrieved from this plagioclase dataset have been presented and discussed by Morse (2008), where the shelf is inferred to be an actual liquidus shelf (Wyllie, 1963) caused by the incoming of abundant Fe–Ti oxide minerals and their attendant release of latent heat (Holness et al., 2007).
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These data are initially analyzed to investigate the steep trend at the early stages of fractionation below 60 PCS in Fig. 15. As shown by the continuous curve in this figure, the data in this region closely fit a pure plagioclase binary with KD = 0·4, a value based on the assumed pressure of the intrusion, and using a fictive intercept of An = 70·5 at 0 PCS. However, as shown by the dashed curve in the figure, the data may also be fitted equally well to a Rayleigh calculation using a value of g = 0·65 (as found for olivine, Fig. 9), and using residual porosity pr = 0·25 FL0·9, which is then multiplied by the fraction of plagioclase fpl, which in turn is allowed to vary from 0·68 to 0·50 in the interval 0–80 PCS according to the relation fpl = –0·2637(–log FL) + 0·675. This relation loosely characterizes the CIPW norms of the Skaergaard rocks in this part of the intrusion. The reason the two curves match so well at these early stages is that the value of g = 0·65 is close to the value of the fraction of plagioclase, so that fpl/g approximates to 1· 0 and therefore the Rayleigh exponent approximates to (D – 1), as for the pure binary. Nevertheless, the chosen values of g, fpl, and pr are realistic as opposed to an assumption of fpl = 1· 0.
It is important to note that the value of g = 0·65 found for olivine implies a considerable deviation from the binary where the fraction of ‘olivine’ is small, 0·35, compared with 1· 0 for an extended trend. In the olivine case, the probability of communication between the crystallization zone and an internal reservoir could be represented as (0·65–0·35)/(1· 0–0·35) = 0·46, whereas for the case of plagioclase, and assuming an average value of fpl = 0·65, the relevant estimate of probability is zero for the lower stratigraphic levels. We therefore have the interesting implication that the Skaergaard LZ olivine ‘sees’ the internal reservoir, but the plagioclase does not. This dichotomy deserves further discussion, as given elsewhere below under the heading ‘Diffusion’ in the section ‘Additional effects’.
The two fractionation curves in Fig. 15 diverge as fpl falls to low values at higher PCS, and both fall far below the data for PCS > 65. However, the multiphase relation can be brought to a flatter slope by increasing g to 1· 0 for the region >65 PCS [hence P(ir) = 1· 0], and putting the secular effect of pr into the exponent, as shown in Fig. 16. Here the value of pr is more closely modeled to the zoning data of Toplis et al. (2008) as given in fig. 5 of Morse (2008), and varies as indicated in the caption. The value of fpl is kept constant at 0·5 above 80 PCS. The result satisfactorily matches the data to 97 PCS and beyond with a realistic choice of variables.
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This exercise shows that at low values of PCS there is no evidence for an internal reservoir, which, however, becomes fully involved [with g = 1· 0 and P(ir) = 1· 0] at the LZc–MZ boundary near 65 PCS. The curve still falls below the MZ shelf, which we regard as an anomaly consequent upon the copious crystallization of magnetite and augite in MZ. The boundary is almost precisely where Holness et al. (2007
) inferred from the discontinuous jump in textural maturation a major, discontinuous jump in the fractional latent heat. Evidently this heat effect and the increasingly mafic nature of the cumulate brought the evolution of plagioclase composition nearly to a standstill, from which it eventually recovered to embark on a new fractionation path.
Potassium in plagioclase
Minor components such as K and Rb in plagioclase and Cr and Mn in mafic minerals are expected to ride piggy-back on the evolution of their major mineral carrier phases. Here as an example we examine the case for K in Kiglapait plagioclase.
As long ago argued (e.g. Morse, 1981a, fig. 10), the low values of the partition coefficient DKfsp/l, if operating in nature with K treated as an independent trace element, would send any normal mafic magma screaming off into granitic K-space by 90 PCS, contrary to our observation, hence the effective partition coefficient for K in plagioclase must be much closer to 1· 0 than indicated by experiment. We can find the value of that effective partition coefficient by another route.
If instead of following the rule of K as an independent trace element, we make the reasonable assumption that it travels with the Ab component of feldspar, we may simply find the relationship between K and Ab in natural feldspars and use that to follow the behavior of K with fractionation, in which Ab is the conserved component in the liquid and the recalculated crystal. The result is shown in Fig. 17, along with the algorithm relating ppm K to plagioclase XAb in the ensemble of natural Kiglapait feldspars. The correlation is good to 92 PCS, after which the sharp increase toward ternary feldspar takes over. The full MRF treatment of ternary solutions, still under construction, should allow the good fit to be extended further, but the forward modeling treatment does involve use of the experimental partition ratio as found by Morse et al. (2004). In the present exercise, the effective partition coefficient is bypassed altogether, and although it could be calculated, it is not needed for the result sought.
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Based on this evidence that K does NOT behave as an independent trace element, but as an essential component of ternary feldspar linked to Na, it appears safe to say that multiphase Rayleigh fractionation with an internal reservoir resolves the potassium dilemma in layered intrusions and anorthosites.
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HOW DOES IT WORK? |
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Overview
We may now review the general principles of multiphase Rayleigh fractionation. Small packets of magma can fractionate only on the binary or below, to the limit of the depletion curve. They fractionate on the binary when only a single phase is crystallizing, or when an active phase crystallizes in cotectic company with one or more indifferent phases. When a second phase component is abundant in the magma, but does not locally crystallize, the active phase may fractionate the magma on the depletion curve. The entire graphical space from the depletion curve to the binary is thus available to the magma in the absence of an internal reservoir. These generalities are usefully considered by an analysis and review of specific cases that might apply to mafic magma bodies.
Case 1: stable equilibria
Cotectic
Mafic phase. In normal magmas, the cotectic mafic phase or phases will be formed in lesser amount, with f < 0·4 in most cases. If g = f the fractionation (for example of the Mg ratio) follows the binary. If g is small but greater than f then the fractionation runs close to the binary but above it, on a slightly extended path. If g is intermediate, f < g < 1, then the departure from the binary is significant because the span 1 – f is relatively large. Finally, when g = 1, the fractionation path is maximally flattened, and this effect is more pronounced than for the felsic phase.
Felsic phase. All the above arguments are reversed because the span 1 – f is small, perhaps <0·4, compared with the mafic cotectic case. Hence the effect of g is smaller than for the mafic phase.
Case 2: metastable equilibria
Off-cotectic, felsic
Mafic phase. The mafic phase is subordinate, and therefore vulnerable to the depletion effect, hence may fractionate faster than in the cotectic case.
Example. In the Upper Critical Zone of the Bushveld Complex, there are small-scale cycles between relatively felsic and mafic cumulates, interpreted as the result of crystal sorting. In the felsic cumulates, the Mg-number of the pyroxenes is routinely smaller than in the mafic cumulates where pyroxene is dominant. The opposite effect may occur for plagioclase in the more mafic cumulates, but it is less noticeable (see Cawthorn & Mbalaka, 2007).
Felsic phase. The felsic phase is dominant and therefore the value of f is greater than normal and the fractionation is nominally closer to the binary. However, the involvement of a reservoir will counteract this tendency, and if g rises in company with f extended fractionation will result.
Example. All massif anorthosite bodies with large volumes of plagioclase-rich rocks having limited evidence of fractionation belong to this category. In such cases, the limited composition range invites the presumption of adcumulus growth, a reservoir, and P(ir) 1. This case might involve suspension of plagioclase (Hess, 1960) buffered to a constant composition because of its overabundance, whereas mafic phases sink, as in the Middle Banded Series of the Stillwater Complex (McCallum, 1996).
Off-cotectic, mafic
Mafic phase. The mafic phase is dominant and the fractionation is nominally closer to the binary, but the involvement of a reservoir counteracts this tendency. The local effect is that the mafic layers in layered intrusions tend to be more refractory in mafic mineral compositions than the same minerals in felsic layers because mafic layers are more likely than felsic layers to solidify by adcumulus growth aided by compositional convection. The secular effect is that the refractory composition fed into the cumulate during adcumulus growth is balanced by a rejection of evolved components, leading to an eventual enrichment of the residual liquid in low-entropy components, as in normal fractional crystallization. Does this rejected solute stay in the crystallization zone or may it feed back into the reservoir?
Felsic phase. The felsic phase is subordinate and therefore vulnerable to the depletion effect, hence may fractionate faster than in the cotectic case.
Case 3: leading-edge fractionation and basal reversals
The margins and early cumulates of many intrusions are more evolved in composition than younger injections or overlying layers. This phenomenon leads to basal reversals in stratigraphic composition profiles. The leading edge of an intrusive magma body is an example of small packet crystallization for which there is no internal reservoir, but instead a frequent absence of one crystal phase or another in the ascending magma, which is subject to modal oscillations caused by variable barriers to nucleation. This environment favors strong depletion in refractory components, particularly for the more easily nucleated mafic phases.
Because dry mafic magmas must crystallize mafic minerals on decompression, the leading edge of intrusive mafic magmas must in general be fractionated in Mg-number. Because the delayed nucleation of plagioclase then occurs in an off-cotectic felsic-rich liquid, this mineral is subject to the depletion effect and so also is more evolved than in later generations. The observation of basal reversals and leading-edge fractionation of early magma inputs is an inevitable consequence of magma emplacement into the crust. It is not a hypothesis subject to falsification, but a result of simple physical principles in the gravitational field of a planetary body.
When leading-edge fractionation becomes defeated by the more rapid influx of fresh magma, the newly resident magma will become more refractory in composition, to the limit of the primary mantle source magma. Any early crystals deposited by the more fractionated magma will be overlain stratigraphically by more refractory crystals, causing the basal reversals of olivine compositions often found in layered intrusions, strikingly so in the Kiglapait intrusion and many others described by Cawthorn (1996). This compositional profile marks the continuation of fractionation along the binary, still with the possibility of excursions toward the depletion curve, resulting in scatter of the mineral compositions. Plagioclase is also subject to this compositional reversal, as it crystallizes in small packets or in full cotectic ratio along or below its own binary.
In summary, the eventual main body of magma will cap the reversal with a compositional maximum followed by a prolonged fractionation history. By the same token, the chilled margin of a mafic intrusion can be expected to be more evolved than the main magma, which is ordinarily prevented from chilling. However, unevolved magma may leak out and chill in unexpected places. Chill zones must, therefore, be studied with care if they are to yield reliable information.
Sawtooth or cyclic profiles
Oscillation about a cotectic as a result of crystal sorting. P(ir) > 0, oscillation between g 1· 0 and 1· 0 > g > f (see Fig. 18).
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Examples. Examples include olivine Fo cycles in the South Kawishiwi intrusion of the Duluth Complex, as modeled in fig. 13 of Lee & Ripley (1996
), and cycles in Bushveld An, Fo, Mg-number and Sr0 (Tegner et al., 2006). The Bushveld cycles described by Tegner et al. (2006) are characteristically floored by thin magnetitite layers, suggesting only a transient influence of an internal reservoir at the base of the cycle. The Bellevue drill core studied by Ashwal et al. (2005) shows 13 density reversals, only one of which has a compositional reversal. Similar thin oxide-rich layers occur in the Kiglapait intrusion leading up to the Main Ore Band at 93·5 PCS, but it is not known if they have overlying compositional effects. Such centimeter-scale oxide layers are apparently off-cotectic mafic excursions buffered by an internal reservoir. |
ADDITIONAL EFFECTS |
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Here we may speculate on how the principles discussed in this paper might bear on features found or imagined to occur in real rocks. The following remarks may serve as a tutorial on practical applications of the methods here developed, although leaving room for other, equally valid approaches to the field evidence.
Residual porosity
This effect can be large for crystal phases in low abundance but smaller for abundant cotectic phases. It is larger for orthocumulates and smaller for adcumulates, reaching zero for perfect adcumulates. The local effect is accounted for by adding the residual porosity times the fraction of the active phase to calculated cumulus composition, thereby increasing the value of C, the conserved low-melting component. The secular effect, independent of the expression of the local effect, is accounted for by adding the residual porosity times the fraction of the active phase to the partition coefficient D within the Rayleigh exponent. The choice of whether to include either or both of these effects amounts to a free parameter in attempting to model a specific set of measured data.
Systematically variable modes
These occur in most systems and are dealt with by using the best available natural data and calculating the modal variation of active phases as a function of FL. Mass units (e.g. CIPW normative results) should be used especially for mafic minerals in preference to volume units such as oxygen units, for the calculation of fractionation. However, the output of binary solution compositions is conveniently given in mole units. Modal variation responds to the curvature of cotectic field boundaries in compositional hyperspace. This curvature is small and nearly pressure-independent for plagioclase–olivine, but may be large for more complex assemblages.
Internal boundary layer
Such a layer is inferred to exist between the crystallization zone and the internal reservoir. Such a compositional and even P–T boundary layer might be transient at early stages, varying to more durable at intermediate stages, and erased at late stages of fractionation, particularly following the stirring effects of large-volume production of Fe–Ti oxide minerals.
Diffusion
This probably plays a role in the extent of communication between a crystallization zone and an internal reservoir, separated by a boundary layer. The evidence from the Skaergaard olivine and plagioclase data and their Rayleigh models, discussed above, suggests that at early (LZ) stages, the olivine communicates with a reservoir half the time, whereas the plagioclase does not. This difference might reasonably be expected from the relevant polymerization of the two types of components in the melt, minimal for mafic components that are less polymerized and maximal for more polymerized felsic components, assuming an associated range of diffusivity. These differences may well lead to differing values of the depletion function g.
Minor components
These tend to ride ride piggy-back on the evolution of their major mineral carrier phases, as calculated for K above. The principles of multiphase Rayleigh fractionation allow the enlightened treatment of trace elements that have major element crystal-chemical roles.
Stratigraphic isotopic variations
These have commonly been ascribed to periodic contamination from external sources, usually involving more radiogenic isotopic ratios of, most commonly, Sr and Pb. However, one examination of Sr-isotopic data for the Kiglapait intrusion showed a steady Rayleigh-type increase of radiogenic Sr above the 90 PCS level (Morse, 1983), and a similar case was discussed for Sr and Nd in the Rum intrusion (Morse, 1988). The relationships are amenable to an interpretation involving an internal reservoir that contains an early introduced component of radiogenic material from an older magmatic residue, or from wallrock contamination, retained in the reservoir until gradually being incorporated into the crystallization zone as the reservoir became more involved. In any case, a carrier component was hypothesized as related to the polymerized K-rich residue, now regarded as stored in the reservoir.
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NATURE OF THE INTERNAL RESERVOIR |
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Physical aspects
The physical nature of the postulated and indicated internal reservoir has been ignored in all the foregoing, leaving the evidence compositional, and the physical configuration purposely unspecified. However, certain general constraints can be specified. The reservoir does not exist in any outer shells, for these cool to the walls and floor instead of through the roof. It does not belong to any scheme of zoned magma chambers involving liquid layers, because fractionation will make overlying layers denser, and underlying dense layers will shield the accumulation zone from local recharge, not to mention adcumulus growth. Diffusive density gradients are unstable to adcumulus growth with compositional convection (Morse, 1986
). From the compositional evidence the reservoir is durable over great time scales of order 105 years. The reservoir is therefore internal, bounded by a compositional, thermal and pressure-sensitive boundary layer.
Evidence for an internal reservoir
An internal reservoir was postulated for two main reasons, the improbability of external recharge of fractionated residua, and the physical presence of metastable gradients in arriving mineral modes up-stratigraphy. If the Lower Zone of the Kiglapait intrusion took 400–800 kyr to crystallize (Morse, 1979a), then frequent delivery of just the right magma composition at just the right place to account for the extended trends of olivine and plagioclase by external recharge becomes an exercise in special pleading, invoking magma fractions evolved elsewhere to the same degree as within the body, a hypothesis impossible to defend. If, however, the reservoir is the main body of magma itself, and crystallization is normally confined to a boundary sheath along the roof, walls and floor of the intrusion, periodic or continuous access to the reservoir is assured. Moreover, recurrent or local events involving more or less input from the reservoir will easily account for random oscillations or variations in mineral compositions, and these may be triggered by random physical instabilities in the magma body.
Slow arrivals
The notion of an internal reservoir at Kiglapait was developed specifically to explain the ‘slow arrivals’ of the new (cotectic) cumulus phases augite, Fe–Ti oxides, and immiscible sulfide globules (Morse, 1979b). The modal abundance of these three phases is a strong function of stratigraphic height in the intrusion. The ranges in meters over which these slow arrivals occur are shown in Table 1, derived from fig. 1 of Morse (1988). The table shows that the disturbance of modal abundances, from background through maximum to recovery at the equilibrium cotectic value, ranges in stratigraphic thickness from 1· 3 to 2 km, or 16–24% of the entire intrusion. After the deposition of the Main Ore Band at 93·5 PCS, the entire system reached a uniform, well-mixed equilibrium state, as shown by the very sharp arrival of apatite at 94 ± 0·3 PCS.
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These relationships were interpreted (Morse, 1979b
) as implying an internal reservoir that escaped perfect mixing, but contributed steadily to the crystallization zone and thereby became depleted in refractory components. The conserved components were then released over long periods of time to the crystallization zone, leading to slow modal increases, over-production, and relaxation to the equilibrium value. Because of the relationship FL to time (Morse, 1988; Fig. 1), and assuming 1 Myr for the crystallization of the intrusion, then the drawdown of this reservoir may have taken as much as 235 kyr (from the middle entry of the last column in Table 1). Even half that time is a long time for the preservation of a liquid–(liquid + crystals) interface. It was proposed (see Morse, 1979b, fig. 19) that the internal reservoir resided in the core of a toroidal convection system, around which the crystallization sheath circulated with only trivial interaction.
Supporting evidence from Skaergaard
In addition to the slow arrivals in the Kiglapait intrusion, spikes in cumulate maturation at the arrivals of augite, magnetite and apatite have been described from the Skaergaard intrusion by Holness et al. (2007). These spikes coincide with demonstrated overshoots in modal abundances, as in Kiglapait, and are interpreted as metastable excursions into off-cotectic compositional space, followed by rapid relaxation to the abundance consistent with cotectic saturation. Such excursions may be considered to imply physical evidence for the presence of an internal reservoir.
Discussion of reservoir properties
The invocation of an internal reservoir in a hot magma body may seem to be at great variance with conventional fluid dynamical estimates based on Rayleigh numbers calculated using the length scale of the entire magma depth and therefore implying vigorous turbulence and perfect stirring. However, if the crystallization zone is thin and defines the length scale of the local Rayleigh number, the implication of turbulence is lessened. In either case, the concept of an active sheath surrounding a passive core is hardly unfamiliar in the science of the Earth, where cold-core rings in the ocean can survive as much as 7 months before dissipating into a warm environment such as the Sargasso Sea. These rings are cylindrical boundary layers of kilometer-scale wall thickness, and they may have diameters as large as 300 km and depths of some 3·5 km, so they have an aspect ratio of order 100 and the viscosity of water without crystals. Layered intrusions have aspect ratios ranging from 3 to perhaps 55 for the Bushveld Complex, and viscosities 100–1000 times that of water, but they may ‘dissipate’ (i.e. crystallize) over time scales up to 1·7 x 106 as long. Putting that into another perspective, a cold-core ring may heat up by mixing a few degrees C/yr, but the magma may cool as slowly as 10–4 or 10–5 deg/yr. Separation into durable, adjacent flow and more passive regimes in such magmas requires no great leap of faith.
The high aspect ratio of the Bushveld Complex suggests the possibility of multiple reservoirs, perhaps in a multicellular arrangement, and possibly interacting or not interacting with each other over time and space.
Mass-balance issues
The extended path of fractionation implies that the crystallization zone is a feeding zone from the internal reservoir. In that case all the composition range between the extended path and the binary represents evolved components that have remained within the reservoir. This material should eventually appear in the overlying rocks. If it does not, there may be a discrepancy in mass balance. If it does, we still may not know how the remnants of the reservoir are partitioned over the stratigraphy. In the Kiglapait case, the modal evidence suggests that the stirring event of the Main Ore Band at 93·5 PCS must have completely mixed the remaining reservoir into the resident magma, so that by 94 PCS the apatite arrived suddenly everywhere. Before that last stirring, the modal evidence of Fe–Ti oxides shows a rise starting at 80 PCS (Table 1 here; Morse, 1979b, fig. 4), suggesting the start of wholesale mixing into the feeding zone. Before that time, the reservoir presumably retained a composition relatively rich in excluded components left behind from the feeding process. Therefore the best place to look for the addition of these components would be between 80 and 93·5 PCS, after which they were, from the evidence, completely mixed.
In the case of Kiglapait plagioclase and olivine, most of the compositional array below 45 PCS falls below or near the binary, so that does not require balancing. Compositions above 90 PCS fall well below the fractionation model and, along with the compositions from 0 to 20 PCS, tend to compensate for the refractory components stored in the main extended array. However, the full range of compositions shown in figs 9 and 10 of Morse (1979a) appear from inspection insufficient to balance the refractory components. Some or perhaps all of the balance can be found in the Upper Border Zone, where the residual porosities rich in excluded components are very high (Morse, 1995), but the original size of the UBZ is unknown and is hence a free parameter that may be possible to resolve by seeking a quantitative balance for the refractory components.
When any extended binary fractionation path occurs in a closed system, the summation from the top down over all the rocks may yield a true bulk composition for the intrusion, but any partial summation will encounter displaced compositions and therefore cannot be used as intermediate liquid compositions unless they lie outside the zone of displacement. Thus the most reliable liquid compositions from summation will occur in uppermost levels above Ap+ or Mt+, and again near the base of the intrusion, perhaps near 0–20 PCS.
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CONCLUSIONS |
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The extended cotectic path of MRF matching the natural data of some layered intrusions testifies to the existence of durable, quasi-infinite reservoirs in large magma chambers. The close match of Rayleigh fractionation paths through the data of the Skaergaard and Kiglapait intrusions, at various values of the depletion function, not only allows quantitative statements to be made about the presence or absence of such reservoirs, but also indicates the quality of the volume estimates. In particular, the exact match of the LZ Skaergaard data for plagioclase composition with the Rayleigh solution for the binary-cotectic suggests that the relative Nielsen (2004
) volumes are realistic. The fact that the olivine data in both intrusions can be matched by the Rayleigh calculations, and particularly that the data never fall systematically above those calculated curves suggests that the data validate the theory and make it practical. The chief difficulty in applying this principle to natural occurrences will often be found in the estimation of volume relations. These appear to be reasonably good in the two intrusions, disparate in size, examined here. One way of approaching this problem might be to look at the data and models for any other body and, with appropriate constraints from field evidence, invert the procedure and solve for the volumes from the data and the theory.
Once the plausibly off-and-on buffering capacity of an internal reservoir is recognized, a rich array of possibilities is revealed for interpreting stratigraphic compositional relations. Some of these may make more sense than the conventional invocation of external magma recharge, which may range from the demonstrable and obvious to the questionable.
Above all, it is the theme of this exercise that mineral compositional evidence can and often should be treated in the context of binary solutions, and that the close examination of such data with end-member models may reveal much about the history of large magma bodies. Conversely, any physical models for magmatic fractionation must be able to stand the test of compositional modeling.
Computational analysis of interpenetrating and otherwise circulating fluids in the gravitational field is now coming into practice and may find a fertile field of application to crystallizing magma bodies. With such codes it should be possible to make increasingly realistic fluid-dynamical models in which internal boundary layers between crystal-bearing and crystal-free regions can be tested for various flow fields, geometries and durability. One mark of success in such an enterprise might be the ability to detect an internal reservoir from first principles.
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ACKNOWLEDGEMENTS |
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My dept to Paul Asimow for pursuing the dialogue that produced the depletion function and the symmetry of fractionation about the binary is, clearly, very great. I think it has broken open a new door into the workings of melting and crystallization in the Earth. The manuscript has benefited from an especially thorough and perceptive review by Dave Walker, and a rigorous anonymous review. Comments by E. M. Ripley and Mehmet Keskin were also helpful.
*Corresponding author. Fax: 413-545-1200. E-mail: tm{at}geo.umass.edu
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REFERENCES |
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Ashwal LD, Webb SJ, Knoper MW. Physical and mineralogical properties of Bushveld rocks: Magnetic susceptibility, density and mineral chemistry in the 2950 m Bellevue drillcore, Northern Lobe. South African Journal of Geology (2005) 108:199–232.
Banks DC, Morse SA, Brady JB. OL–PLAG reaction to Al-CPX + OPX + SP + LIQ at 13 kb and the partitioning of PLAG/L. EOS Transactions, American Geolphysical Union (2002) 83:S365–S366.
Cawthorn RG, ed. Layered Intrusions (1996) Amsterdam: Elsevier. 441–483.
Cawthorn RG, Mbalaka W. Modal layering in the cyclic units of the Upper Critical Zone of the Bushveld Complex, South Africa. Frontiers in Mineral Sciences 2007, Programme and Abstracts (2007) 229. Available at www.minersoc.org.
Fram MS, Longhi J. Phase equilibria of dikes associated with Proterozoic anorthosite complexes. American Mineralogist (1992) 77:605–616.[Abstract]
Ghiorso MS, Sack RO. Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid–solid equilibria in magmatic systems at elevated temperatures and pressures. Contributions to Mineralogy and Petrology (1995) 119:197–212.[Web of Science]
Hess HH. Stillwater Igneous Complex, Montana, a quantitative mineralogical study. Geological Society of America, Memoirs (1960) 80.
Holness MB, Tegner C, Nielsen TFD, Stripp G, Morse SA. A textural record of solidification and cooling in the Skaergaard Intrusion, East Greenland. Journal of Petrology (2007) 48:2359–2377.
Lee I, Ripley EM. Mineralogic and oxygen isotopic studies of open system magmatic processes in the South Kawishiwi intrusion, Spruce Road area, Duluth Complex, Minnesota. Journal of Petrology (1996) 37:1437–1461.
McBirney AR. The Skaergaard Intrusion. In: Layered Intrusions—Cawthorn RG, ed. (1996) Amsterdam: Elsevier. 147–180.
McCallum IS. The Stillwater Intrusion. In: Layered Intrusions—Cawthorn RG, ed. (1996) Amsterdam: Elsevier. 441–483.
Morse SA. Kiglapait geochemistry I: Systematics, sampling, and density. Journal of Petrology (1979a) 20:555–590.
Morse SA. Kiglapait geochemistry II: Petrography. Journal of Petrology (1979b) 20:591–624.
Morse SA. Kiglapait geochemistry III: Potassium and rubidium. Geochimica et Cosmochimica Acta (1981a) 45:163–180.[CrossRef][Web of Science]
Morse SA. Kiglapait geochemistry IV: The major elements. Geochimica et Cosmochimica Acta (1981b) 45:461–479.[CrossRef][Web of Science]
Morse SA. Strontium isotope fractionation in the Kiglapait intrusion. Science (1983) 220:193–195.
Morse SA. Convection in aid of adcumulus growth. Journal of Petrology (1986) 27:1183–1215.
Morse SA. Motion of crystals, solute, and heat in layered intrusions. Canadian Mineralogist (1988) 26:209–244.[Web of Science]
Morse SA. Kiglapait Upper Border Zone: a complete but liquid-rich mirror image of the floor. Terra Abstracts (1995) 7:300.
Morse SA. Kiglapait mineralogy III: Olivine compositions and Rayleigh fractionation models. Journal of Petrology (1996) 37:1037–1061.
Morse SA. Binary solutions and the lever rule revisited. Journal of Geology (1997) 105:471–482.[Web of Science]
Morse SA. Linear partitioning in binary solutions. Geochimica et Cosmochimica Acta (2000) 64:2309–2319.[CrossRef][Web of Science]
Morse SA. Multiphase Rayleigh fractionation. Chemical Geology (2006) 226:212–231.[CrossRef][Web of Science]
Morse SA. Toward a thermal model for the Skaergaard liquidus. American Mineralogist (2008) 93:248–251.
Morse SA, Allison JP. Correlation between roof and floor cumulates of the Kiglapait intrusion, Labrador. Geophysical Research Letters (1986) 13:1466–1469.[Web of Science]
Morse SA, Ross M. Kiglapait mineralogy IV: The augite series. American Mineralogist (2004) 89:1380–1395.
Morse SA, Brady JB, Sporleder BA. Experimental petrology of the Kiglapait Intrusion: cotectic trace for the Lower Zone at 5 kbar in graphite. Journal of Petrology (2004) 45:2225–2259.
Nielsen TFD. The shape and volume of the Skaergaard Intrusion: implications for mass balances and bulk composition. Journal of Petrology (2004) 45:507–530.
Rayleigh JWS. Theoretical considerations respecting the separation of gases. Philosophical Magazine (1896) 42:493–498.
Rayleigh JWS. On the distillation of binary mixtures. Philosophical Magazine, Series 6 (1902) 4:521–537.
Tegner C, Cawthorn RG, Kruger FJ. Cyclicity in the Main and Upper Zones of the Bushveld Complex, South Africa: Crystallization from a zoned magma sheet. Journal of Petrology (2006) 47:2257–2279.
Toplis MJ, Brown WL, Pupier E. Plagioclase in the Skaergaard intrusion: Part 1: Core and rim compositions in the Layered Series. Contributions to Mineralogy and Petrology (2008) 155:329–340.[CrossRef][Web of Science]
Wyllie PJ. Effects of the changes in slope occurring on liquidus and solidus paths in the system diopside–anorthite–albite. In: International Mineralogical Association, Papers and Proceedings of the Third General Meeting, Mineralogical Society of America Special Paper—Fisher DJ, Frueh AJ, Hurlburt CS, Tilley CE, eds. (1963) 1:204–212.
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