Journal of Petrology Advance Access originally published online on February 4, 2005
Journal of Petrology 2005 46(5):973-997; doi:10.1093/petrology/egi007
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Mantle Preconditioning by Melt Extraction during Flow: Theory and Petrogenetic Implications
SCHOOL OF EARTH, OCEAN AND PLANETARY SCIENCES, CARDIFF UNIVERSITY, CARDIFF CF10 3YE, UK
RECEIVED JANUARY 4, 2004; ACCEPTED DECEMBER 8, 2004
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ABSTRACT |
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TOP
ABSTRACT
INTRODUCTIONMantle preconditioning may be defined as the extraction of small melt fractions from mantle asthenosphere during its flow to the site of magma generation. Equations may be written for mantle preconditioning, assuming that the mantle comprises enriched ‘plums’ in a depleted matrix. The equations take into account variations in mass fraction of plums, the relative rate of melting of plums and matrix, the temperature and pressure of melt extraction, the mass fraction of melt extracted, the extent of chemical exchange between plums and matrix, and the efficiency of melt extraction. Monitoring mineralogical changes and variations in partition coefficients along the inferred P–T–t path of the mantle asthenosphere allows the equations to be correctly applied to the conditions under which melt extraction takes place. Numerical experiments demonstrate the influence of petrogenetic variables on the shape of melt extraction trajectories and provide new criteria for distinguishing between melt extraction and mixing as the cause of regional geochemical gradients. Representative examples of arc–back-arc systems (Scotia), continental break-up (Afar) and plume–ridge interaction (Azores) indicate that the compositions of the mantle sources of mid-ocean ridge basalts and island arc basalts may be determined, at least in part, by the melt extraction histories of their asthenospheric sources.
KEY WORDS: geochemical modelling; mantle flow; isotope ratios; trace elements
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INTRODUCTION |
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The requirement for conservation of mass leads to the development of pressure gradients that drive horizontal asthenospheric flow on a variety of scales. Thus, asthenosphere must flow towards ocean ridges and regions of active lithospheric extension where material is being removed, but flow away from plumes where material is being added. In addition, asthenosphere must flow obliquely away from converging or colliding continents because the lithospheric keels of the continents act as barriers to flow and prevent return flow in the direction of convergence. At subduction zones, asthenosphere should flow into mantle wedges because of the removal of mantle beneath the arc and above the underlying subducting plate (Davies & Stevenson, 1992
). This inflow rate will increase if the slab is rolling back or sinking (Dvorkin et al., 1993). The greatest flow rates are probably from adjacent regions of positive and negative pressure, such as from plumes to ridges (plume–ridge interaction), plumes to incipient oceans (volcanic rifted continental margins) or collision zones to marginal basins (mantle extrusion).
The significance of pressure-driven asthenosphere flow for magma genesis has been recognized for some time through identification of geochemical gradients or geochemical discontinuities. Most of the early work (e.g. Schilling, 1969, 1973) and much recent work (e.g. Douglass et al., 1999; Haase, 2002; Thirlwall et al., 2004) focuses upon the geochemical ‘spikes’ along the mid-ocean ridge system and the concept of mixing between flowing plume mantle and ambient mid-ocean ridge basalt (MORB) mantle. Over the past decade, however, there has been a growing realization that melt extraction during mantle flow could also play a significant role, and perhaps even the dominant role, in generating regional geochemical gradients. In particular, McCulloch & Gamble (1991) and Woodhead et al. (1993) proposed that asthenosphere flowing into the mantle wedge above subduction zones loses a small melt fraction in the back-arc region before melting beneath the volcanic arc, and Phipps Morgan et al. (1995) argued that asthenosphere moving from plume source to near-ridge sink would encounter thinner and thinner lithosphere and so lose melt to off-axis volcanism before the ridge itself was reached. Others, such as Yu et al. (1997) presented geochemical models relating the mantle reaching mid-ocean ridges to melt extraction during flow of plume material towards the ridge.
There have been many proposed refinements to the basic model of melt extraction during mantle flow. Phipps-Morgan & Morgan (1999) proposed that the asthenosphere may be supplied by the melt residues from plumes, rather than by a fertile plume mantle, and that it is these that subsequently melt to form MORB. Niu et al. (1999) pointed out that the flowing mantle could lose melt to the overlying mantle lithosphere by infiltration of small melt fractions and thus that off-axis volcanism is not a prerequisite for melt extraction. Haase & Devey (1996) and Harpp & White (2001) emphasized that two types of asthenospheric flow could affect magma genesis: shallow, shear-driven flow caused by movement of the overlying lithospheric plate, and deeper pressure-driven flow caused by plume-to-ridge pressure gradients. Pan & Batiza (1998) noted that melt extraction during mantle flow may be accompanied by entrainment of the mantle above and below the asthenospheric conduit. Murton et al. (2002) presented a model of polybaric melt extraction during mantle flow.
The likely mechanism of melt extraction from the mantle has been termed ‘dynamic melting’ by Langmuir et al. (1977) to denote fractional melting with a trapped melt fraction. The studies outlined above imply that dynamic melting may take place in two settings: during asthenospheric flow to the principal site of magma generation, and at the principal site of melt generation itself (in the melting column). The mantle itself need not ‘see’ this distinction as it loses its incompatible elements in a broadly similar way during both processes. However, for the extracted magma, there is an important difference as only the melt fractions extracted within the melting column have the opportunity to contribute to the pooled melt produced at the site of magma generation.
Kincaid & Hall (2003) usefully distinguished between these two settings of melt extraction by describing melt extraction during flow to the site of magma generation as ‘preconditioning’, the terminology adopted for this paper. Kincaid & Hall (2003) specifically investigated arc–basin systems, in which mantle may be preconditioned by loss of melt fractions in the back-arc before undergoing melting beneath the arc front. However, mantle may be preconditioned in any setting if its temperature exceeds its solidus during flow to the eventual site of magma genesis—as illustrated in Fig. 1. Thus it is possible that the mantle source region for any asthenosphere-derived magma will reflect not just the provenance of its source, or mixture of sources, but also its history of preconditioning by melt extraction.
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This paper examines the potential relationships between asthenosphere flow and mantle composition, with particular emphasis on the geochemistry and petrology of preconditioning and the implications of preconditioning for magma genesis in a range of tectonic settings.
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MANTLE PRECONDITIONING BY MELT EXTRACTION: THEORY |
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The fundamental assumption in modelling mantle preconditioning is that the mantle comprises a mixture of enriched and depleted components (e.g. Sleep, 1984
; Zindler et al., 1984; Allègre & Turcotte, 1986). Much of this work treats the mantle as a two-component system, made up of enriched ‘plums’ embedded within a depleted matrix (Phipps Morgan, 1999), although it will also demonstrate that the same approach applies to multi-component systems. It is the preferential removal of these plums during melt extraction that provides the distinctive geochemical features of mantle preconditioning.
Phipps Morgan (1999) first laid out the basic principles for discriminating between mixing and melt extraction for explaining geochemical gradients between plume and depleted MORB mantle. He defined ‘melt extraction trajectories’, or ‘METs’, as trajectories in element-isotope space resulting from progressive extraction of melt from a heterogeneous source. He demonstrated that they could have the superficial appearance of mixing trajectories, but found that melt extraction and mixing could be distinguished in ‘two component, two element + isotope systems’. This paper takes his approach as the starting point, retaining also his symbols (Ti and Ii for trace element concentration and isotope ratio for element i and Ti/j for the trace element ratio i/j) and extends it to permit the use of numerical experiments to study the effect of varying the different melt extraction parameters.
The first stage of the preconditioning model is to define the starting composition of the mantle asthenosphere (A) as a two-component mixture of ‘plums’ (P) and matrix (M) containing a mass fraction MP of plums, and hence a mass fraction (1 – MP) of matrix. Making a small approximation by ignoring the fact that the element in the isotope ratio has two different masses, the trace element ratio, T2/1, and isotope ratio, I1, of the asthenosphere can be expressed as mixing equations, corresponding to equation (1) of Phipps Morgan (1999):
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modelled his melt extraction trajectories by allowing the two components to change their compositions by undergoing sequential increments of dynamic melting. His key assumptions are that plums melt independently of the matrix component (as they must do in part, at least if melt extraction trajectories are to have isotope gradients) and that the plum and matrix components each lose a different mass fraction of melt.
This work extends his formulation. It first defines the mass fraction of melt lost from the plum component relative to the mass of the plum component as FP and the mass fraction of melt lost from the matrix component relative to the mass of the matrix component as FM. This means that, after extraction of a total melt fraction FL from a mass fraction MP of plums plus a mass fraction (1 – MP) of matrix, the total mass will be 1 – FL made up of a mass fraction 1 – FP of plums and 1 – FM of matrix. The mass fractions of plums and matrix remaining will then be given by 
and 
, respectively.
The basic equations for trace element ratios (T2/1) and isotope ratios (I1) in preconditioned mantle asthenosphere following a given episode of melt extraction can thus be expressed, again using mass balance, as
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 | (4) |
fractional melting equation, and porosity can be taken into account by calculating bulk distribution coefficients that include trapped melt with D = 1 (see Appendix A for details).
Because the plums and matrix probably melt at different rates, it is useful to define a relative rate of melting, r, such that r = FM/FP. Thus, r = 0 if only the plums are melting and r = 1 if plums and matrix melt at the same rate. Also, r may approximate to a constant during preconditioning because the amount of melt extracted is low, although it may vary considerably once the solidus for the pure matrix is exceeded at the higher degrees of melt extraction found within a melting column (Phipps Morgan, 2001). FP and FM can be expressed in terms of MP (the mass fraction of plums in the starting material), FL (the total mass fraction of melt extracted from the asthenosphere during flow) and r (the relative contribution of plum melt to total melt). By mass balance
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Substitution for FP and FM into equations (3) and (4) gives general equations for mantle preconditioning by melt extraction during flow in which FL, r and MP are the principal variables:
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Figure 2 illustrates the geochemical principles of mantle preconditioning using equations (5) and (6) by examining some hypothetical melt extraction trajectories on plots of isotope ratio against trace element ratio. Two projections are shown: (a) isotope ratio, I1, against trace element ratio, T2/T1, in which T1 is more incompatible than T2 (e.g. 143Nd/144Nd against Yb/Nd or Sm/Nd, or 176Hf/177Hf against Lu/Hf); (b) isotope ratio, I1, against trace element ratio, T2/T1, in which T1 is less incompatible than T2 (e.g. 143Nd/144Nd against La/Nd or 176Hf/177Hf against Nb/Hf).
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In Fig. 2a, the initial composition lies at ao on a mixing trend between plums and matrix. Because of the common denominators in the ratios used in the two axes, this mixing trend will be linear (Langmuir et al., 1977
). Both plums and matrix will then become relatively depleted in the more incompatible trace element with progressive melt extraction. As T1 is more incompatible than T2, the T2/T1 ratios of both matrix and plums will increase and, because the plums melt the more rapidly, the T2/T1 ratios of the plums will increase more rapidly than those of the matrix. The isotope ratio will move towards the ratio of the component that melts out less rapidly; that is, towards the ratio of the matrix in this case. The bulk asthenosphere composition must then lie on tie-lines joining the residual matrix and residual plum compositions. Thus, in this model, the residual asthenosphere composition will lie at a1 on tie-line m1–p1 after extraction of the first mass fraction of melt, at a2 on tie-line m2–p2 after extraction of a second mass fraction, and so on. The melt extraction trajectory is the line a0–a3. Eventually, the plums will either melt out or become so depleted that they make no effective contribution to the bulk composition. The melt extraction trajectory will then flatten at the isotope ratio of the matrix (as shown in Fig. 2a)—unless there has been isotopic exchange between plums and matrix, in which case it will flatten at an isotope ratio between that of the matrix and that of the plums as discussed later.
On the second isotope–trace element projection (Fig. 2b), the ratio T2/T1 decreases with progressive melt extraction as T1 is now less incompatible than T2. The resulting melt extraction trajectory is concave rather than convex and converges on a trace element ratio of zero rather than diverges towards infinity.
The essential characteristic of preconditioned ‘plum-pudding’ mantle in which plums undergo preferential melting is therefore a convergence on the isotopic composition of the matrix coupled with trace element ratios that converge to zero or infinity depending on which element is the more incompatible. This simple model does, however, assume a single plum composition while ignoring entrainment of other mantle compositions, equilibration between the plum and matrix components and efficiency of melt extraction. The next sub-sections consider the effects of these complexities.
Preconditioning of multi-component mantle
Although this paper focuses on the simple case of a two-component (melt + matrix) mantle, the method can be extended to multi-component mantle. Mathematically, the various single plume contributions to the trace element and isotope budgets in equations (5) and (6) must be modified by substituting multiple plum contributions. For example, for a residual asthenosphere containing a number of plum components, 
, with FPi/FL = zi, the term 
in equation (5) must be replaced by 
.
Figure 3a illustrates the effect of adding a second plum component to the melt extraction equations for the case of I1 against T2/1 where T1 is more incompatible than T2 (as in Fig. 2a). In this example, the second plum, Q, melts twice as fast as P, although both melt faster than the matrix. The bulk plum composition evolves along trajectory p0–p3, converging isotopically upon the type of plum that melts less rapidly, namely P. The composition of the residual asthenosphere must then lie on tie-lines between the residual matrix composition and the residual bulk plum composition at the points determined by two-component (residual bulk plum–residual matrix) mixing. The resulting melt extraction trajectory, a0–a3, will then be the locus of residual asthenosphere compositions. In this case, the plums are more similar in composition to each other than to the matrix, so the trajectory for multi-component mantle resembles that of two-component mantle. Phipps Morgan (1999) reached the same conclusion from examining the isotopic consequences of melting mantle containing a range of plum components (e.g. HIMU, EMI, EMII) melting at different rates. He found that melt extraction from a multi-component system can produce a tube-like MET in isotope space. He also noted that melt extraction may provide a better explanation than multi-component mixing for ocean island isotope systematics.
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Preconditioning with entrainment
Flowing asthenosphere may entrain overlying lithosphere or underlying mesosphere in addition to undergoing melt extraction. If so, then the models require modification. Entrainment at any point on the melt extraction trajectory simply moves the asthenosphere along a linear mixing trend towards the entrained composition. It can be modelled by iterating mixing and melt extraction equations.
Figure 3b illustrates combined preconditioning and entrainment, again for the case of I1 against T2/1 where T1 is more incompatible than T2. The gradient will be affected in different ways according to the precise composition of the mixing component. For example, entrainment of matrix will shift the melt extraction trajectory towards the matrix composition. Conversely, entrainment of the starting asthenosphere composition will usually shift the trajectory towards the plum composition. This latter process is likely to be important if preconditioned asthenosphere has the opportunity to mix with deeper asthenosphere that has not risen above its solidus and so had no history of preconditioning.
Preconditioning with chemical exchange between plums and matrix
A recent study by Kogiso et al. (2004) concluded that partial melts segregate from the mantle without significant diffusive equilibration between the melt and their peridotite residues. However, although it is possible that the plums and matrix behave as completely independent and isolated units during preconditioning and melting, it is still important to evaluate the possibility that some form of chemical exchange takes place. Given the evidence that diffusion is too slow, this work focuses on mass transfer to effect chemical exchange between plums and matrix.
The approach adopted here is to assume that, during each episode of melt extraction, a small mass fraction of the pooled melt is retained by both plums and matrix. This pooled melt will have isotope ratios and element concentrations between those of the two end-members and so allow isotope and element redistribution between plums and matrix: the matrix will be enriched in incompatible elements while the plums are depleted. Of course, chemical exchange will really be more complicated than this. For example, in a flowing, decompressing system, the upper part of the asthenosphere might be expected to be invaded by melts from deeper in the asthenosphere (e.g. Murton et al., 2002). However, the method proposed (addition of trapped melt after melt extraction) provides a convenient way to model variable chemical exchange between matrix and plums. It requires that the extraction equations be modified by adding a trapped melt component to the trace element and isotope budgets in equations (5) and (6), as described in Appendix A.
Figure 3c illustrates the effect of including chemical exchange in the melt extraction models. Essentially the ‘plums’ converge isotopically on the matrix composition during flow, while the matrix converges on the plum composition. The change in the slope of the melt extraction trajectory is small, but there is a significant change in the isotope composition reached when plums have effectively been removed. Thus, if r < 1, the greater the proportion of trapped melt, the lower the final isotope ratio of the preconditioned mantle.
Preconditioning and efficiency of melt extraction
Efficiency of melt extraction is an important variable in the application of the melt extraction equations. It can be modelled simply as the mass fraction of melt (
) that accumulates prior to melt extraction. This appears in the equation for the bulk distribution coefficient (see Appendix A). When the mantle releases melt immediately upon reaching the solidus (efficient melt extraction), is small and the bulk distribution coefficient for the most incompatible elements is little affected. However, if significant melt accumulates before extraction so that is large (inefficient melt extraction), then the bulk distribution coefficient for the most incompatible elements will be significantly increased. In Fig. 3, a large value of would mean that the more highly incompatible element, T1, is retained to a greater extent by the mantle residue. The T2/T1 ratio (where DT2 > DT1) is therefore depleted less rapidly. The net effect is that the melt extraction trajectory is displaced to the left and steepened.
Melting of preconditioned mantle
Mantle that has undergone preconditioning during flow will eventually reach the site of melting (the melting column) to produce the observed, erupted lavas (Fig. 1a). As noted in the Introduction, dynamic melting of heterogeneous mantle may take place both during preconditioning and within the melting column. The melting column processes may thus, to a first approximation, be modelled in the same way as preconditioning using equations (5) and (6). The mantle composition will, therefore, continue to follow a preconditioning trajectory as it releases melt fractions to the pool of segregating melt in the melting column. It may not, however, be a perfect extrapolation of the preconditioning trajectory as the relative rates of melting of matrix and plums, r, may change markedly as melting proceeds (Phipps Morgan, 2001). In addition, the different plum components may vary in importance as melting proceeds, giving discontinuities on isotope–isotope plots and, to a lesser extent, on isotope–trace element ratio plots (Phipps Morgan, 1999).
The relationship between the primitive magma emerging from the melting column and the composition of the mantle entering the column will then depend on (1) initial mantle heterogeneities caused by variable mixtures of the components, (2) the extent of, and variability in, preconditioning, and (3) the extent of pooling of the various melt fractions. Figure 4 illustrates the principles underlying the dynamic melting of preconditioned mantle. It again focuses on the projection of isotope ratio (I1) against trace element ratio (T2/T1), where element T1 is less incompatible than T2 (see Fig. 2a), although the principles apply to all projections.
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Figure 4a illustrates the melting of uniformly preconditioned mantle, in which the initial asthenosphere at a0 has lost melt fractions to reach a3 prior to reaching the melting column; a3 then lies on the tie-line between depleted matrix at m3 and depleted plums at p3. The melting process can be viewed as melting of m3 and p3 followed by mixing of the melt fractions generated by each in proportions defined by r, the relative rates of melting of matrix and plums, and MP, the mass fractions of plums. Mass balance dictates that the overall mass fraction of melt, F, is made up of F(1 – MP)r/[r + (1 – r)MP] of matrix-derived melt and FMP/[r + (1 – r)MP] of plum-derived melt. Thus, in Fig. 4a, the plum melt contribution follows the trend pl1–pl3–p3 and the matrix melt contribution follows the trend ml1–ml3–m3, while the pooled melt follows a trajectory l1–l3–a3. At any given degree of melting, the pooled melt, li, will lie on a tie-line joining the plum and matrix melts, pli and mli. If, as is likely, r < 1, the early melts will have more plum-like isotope ratios and the pooled melt trajectory will be convex. Appendix A gives the expression for calculating these pooled melt compositions.
Figure 4b extends this principle to the melting of variably preconditioned mantle, in which four parts of an initial mantle asthenosphere at a0 have lost melt fractions to reach a1, a2, a3 and a4 so that the melting column is fed by a mantle source with preconditioning-induced heterogeneities. If each mantle composition then undergoes pooled fractional melting, the melt extracted from each will form a series of trajectories, each similar to that in Fig. 4a. If the degree of melting is similar in each case, a trajectory can be drawn to link the compositions of the extracted melt, l1–l4. For DT1 < DT2, as here, the overall pooled melt trajectory will lie to the left of, and be steeper than, the melt extraction trajectory. If DT2 < DT1, the equivalent trajectory will lie to the right of the melt extraction trajectory.
It should be noted that trajectories such as that in Fig. 4b also apply to dynamic melting within the melting column when melt fractions are imperfectly pooled. However, the variations in isotope and trace element ratios in lavas produced by mantle dynamic melting of two-component mantle should still be much less than those achieved by preconditioning in most cases—although there may be exceptions as Elliott et al. (1991) demonstrated for Iceland. This is because the individual melt increments are always pooled to some extent. However, the net effect is that both preconditioning and dynamic melting may contribute to observed melt extraction trajectories.
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MANTLE PRECONDITIONING BY MELT EXTRACTION: MELTING PARAMETERS |
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In flowing from its original site of matrix–plum mixing to its eventual site of melting and magma generation, the asthenosphere will follow a P–T–t path. If this path intersects its solidus, then melt will be generated and may satisfy physical criteria for extraction. This may be a single event, but could take place over a wide pressure interval, and could involve more than one episode of extraction or continuous extraction. This means that the mineralogical and chemical compositions of the asthenosphere must be tracked along the P–T–t path so that the correct bulk distribution coefficients are used in the modelling. To track these changes simply, this work uses experimental mineral compositions plotted in CaO–Al2O3 space. Given that the mantle components may behave differently from plums, it tracks separately the peridotite matrix and two types of plum: pyroxenite/eclogite and hybrid mantle. Having established the mineral composition, it is then possible to calculate partition coefficients and mineral reaction coefficients appropriate for the pressures, temperatures and compositions along the melt extraction (preconditioning) path. For reasons of space this paper focuses on the elements Nd (T1) and Yb (T2), but the principles can be applied to any elements.
Tracking matrix mantle mineralogy
Figure 5a illustrates the method used here to model matrix mantle. It is difficult to identify actual samples of matrix mantle as all mantle may contain, or have contained, a plum component. None the less, a good starting point will be mantle that will act as a source for depleted magma such as normal (N)-MORB, either a synthetic material such a MORB pyrolite or a natural occurrence of an unmelted and unenriched peridotite. The majority of potential matrix compositions fall in the range of CaO = 3·5 ± 0·25 and Al2O3 = 4·25 ± 0·25. This range also encompasses many of the experimental peridotite compositions used to investigate the anhydrous peridotite solidus. The mean is very similar to Tinaquillo peridotite with its inferred 7% melt loss ‘restored’, and to the Kettle River Peridotite used in the experiments of Walter (1998). This paper therefore uses CaO = 3·5 and Al2O3 = 4·25 (point M in Fig. 5a) for modelling and uses published experiments on mantle similar to this composition to define the compositions of the host minerals at the various pressures and temperatures.
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The mineral proportions for any point on a P–T–t path along the solidus of M may be represented graphically in CaO–Al2O3 space by the location of M within the polygon formed by the component phases. If (as for 4–6 GPa in Fig. 5a) there are three phases, the proportions may be determined uniquely as there are two variables (CaO and Al2O3) and two degrees of freedom (three mass fractions summing to unity). If there are four phases (as for 1–3 GPa in Fig. 3a) the mass fraction of one of these must be determined independently before the proportions of the remainder can be computed from CaO and Al2O3 concentrations.
Figure 5a shows that only olivine, clinopyroxene and garnet are present for matrix melting from 6 GPa to about 3·3 GPa (Walter, 1998). The principal change is then the increasing Al content of clinopyroxene with decreasing pressure that leads to a small increase in the ratio of clinopyroxene to garnet as pressure falls. Once pressures are sufficiently low that orthopyroxene becomes a solidus phase (<3·3 GPa for M), the principal change with falling pressure is the increase in Ca content of clinopyroxene that leads to a decrease in the proportion of clinopyroxene (and increase in proportion of orthopyroxene) as pressure falls.
When the garnet–spinel transition is reached (2·8 GPa for MORB pyrolite: Robinson & Wood, 1998), residual garnet will react with olivine to form two pyroxenes and spinel. At this pressure, both orthopyroxene and clinopyroxene have moderately Al-rich compositions. With falling pressure, the Ca content of the clinopyroxene increases, causing the proportion of clinopyroxene to decrease and the proportion of orthopyroxene to increase. At the same time, both pyroxenes become less Al-rich and the proportion of spinel increases to retain Al mass balance.
Appendix B gives the equations that allow the mass fractions of phases to be computed. Above 3·3 GPa, where only garnet, clinopyroxene and olivine are present, the equation is a straightforward manipulation of the simultaneous equations for CaO and Al2O3 mass balance. Between 3·3 and 2·8 GPa, however, where olivine, clinopyroxene, orthopyroxene and garnet are all present, the phase proportions have to be obtained by first estimating the mass fraction of garnet. For spinel lherzolites, at pressures <2·8 GPa, olivine, clinopyroxene, orthopyroxene and spinel are all present and the phase proportions have to be obtained by first estimating the mass fraction of spinel.
If melt is extracted at any pressure, CaO and Al2O3 will be lost from the asthenosphere. Before any further calculation is made of mineral proportions, new CaO and Al2O3 concentrations of the residue must be calculated using melt reaction coefficients. This is illustrated in Fig. 5d. The recalculation procedure is also described in Appendix C. For simplicity, the assumption made here is that melting changes the position of M but not the mineral compositions. Clearly, this is not the case, but the small fractions extracted have only a small effect on mineral composition compared with the large effects of pressure and temperature. However, more detailed modelling could be carried out by varying mineral compositions and using all the major elements in calculating phase proportions.
Tracking plum mineralogies
Tracking plum mineralogies is difficult because there are so many potential types of plum and because plum extraction may be a single-stage event (direct extraction of melt from the plum) or a two-stage event (plum-derived melt reacts with the matrix to form a hybrid peridotite, which then subsequently melts). This distinction is highly significant in modelling melt extraction: for example, the relative rates of melting of matrix and plums (r) will be much smaller for a single-stage event. In the single-stage model (Hirschmann & Stolper, 1996; Pertermann & Hirschmann, 2003), eclogite and pyroxenite plums release melt in response to decompression over a large depth range beginning some 150°C below the dry peridotite solidus. In a two-stage model (Yaxley & Green, 1998; Yaxley, 2000), the melt generated in this way reacts with the matrix to form a hybrid peridotite. Melting then takes place at the solidus of the hybrid peridotite, which is at only a slightly lower temperature than that of the matrix itself.
The variability in plum type was discussed by Pertermann & Hirschmann (2003), who demonstrated that naturally occurring eclogites and pyroxenites may occupy a large part of CaO–Al2O3 space. One reason for this large spread in composition is that they may have many sources, including: (1) recycled oceanic crust (basalts and gabbros); (2) recycled sedimentary materials; (3) alkali basalt veins; (4) vein-wall cumulates. The CaO and Al2O3 ranges of these are illustrated in Fig. 5b. Mid-ocean ridge basalt and gabbro typically have CaO and Al2O3 of 13 ± 3 and 15 ± 3 wt %, respectively. Alkali basalt veins that are recycled via subducted oceanic lithosphere (Niu et al., 2002) or entrained within the asthenosphere during plume melting (Le Roex et al., 2002) form from near-primary, low-degree melts. Thus they typically have lower CaO than MORB and so lie below the MORB field (Kushiro, 2001). Cumulates have a wide range of compositions depending on which minerals predominate. High-pressure vein cumulates, such as those of Beni Bousera (Pearson et al., 1993), have slightly lower CaO and Al2O3 than MORB whereas low-pressure cumulates typically have low Al2O3 and variable CaO. Recycled volcanogenic sediments (not shown in Fig. 5b) commonly plot close to the MORB field, but pelagic sediments vary greatly according to the original proportions of carbonates (CaO rich) and clay minerals (Al2O3 rich).
Whatever their origin, eclogite and pyroxenite plums have solidi that, even under anhydrous conditions, lie well below the peridotite matrix solidus in the 6–1 GPa region. Most experiments indicate that plums can undergo high degrees of melting before the peridotite matrix solidus is reached. For example, Pertermann & Hirschmann (2003) estimated that plums at 3 GPa will undergo 60% of batch melting, although fractional melting would not give such a high value. Experimental melting of eclogites and pyroxenites at high temperatures and pressures consistently demonstrates that the first melts extracted contain low amounts of CaO, becoming more CaO rich as melting proceeds. The residue, in contrast, becomes more CaO rich. Garnet melts at a greater rate than clinopyroxene although the difference may be small (e.g. Yasuda et al., 1994): in other words, the increasing CaO content of the plums is matched by an increasing CaO content of the residual clinopyroxene. This work makes the same assumption as Hirschmann & Stolper (1996) to model eclogite and pyroxenite plums; namely, that the process approximates to modal melting and that partition coefficients do not vary as melting proceeds. This may seem a considerable simplification, but varying the parameters has little effect on the projection modelled here. For more detailed studies, and different projections, a more detailed model may be needed.
Hybrid peridotite plums are, as defined above, the reaction or impregnation products of eclogite/pyroxenite-derived melt and the peridotite matrix. The product of eclogite or pyroxenite melting is silica-rich and so reacts with the surrounding mantle to generate a hybrid pyroxene-rich peridotite. The composition of the hybrid mantle can be calculated, or determined graphically, by mixing of matrix and eclogite-derived melt. In the three garnet pyroxenites or eclogites for which high-pressure, anhydrous experiments have been performed (Yaxley & Green, 1998; Klemme et al., 2002; Pertermann & Hirschmann, 2003), CaO increases with degree of melting, whereas Al2O3 varies only slightly. Figure 5c shows the garnet clinopyroxenite melting trend from the experiments of Pertermann & Hirschmann (2003), where GC is the starting composition and GC20 and GC50 are the compositions for 20 and 50% melting, respectively. Mixing lines can be drawn from mantle M to the chosen point on the melting trend and the hybrid composition calculated by mass balance using the component compositions and the chosen mass fraction of added melt.
The hybrid peridotites can be tracked in the same way as the matrix peridotites, by using the techniques illustrated in Fig. 5a. The main problem is how to estimate the mineral compositions. However, Yaxley & Green (1998) demonstrated that, if the melt:matrix ratio is low, the minerals in the hybrid mantle have very similar compositions to the minerals in the matrix and that assumption is made here. Clearly, however, a small shift to higher CaO and Al2O3 will take place and could be taken into account for more precise modelling.
Tracking reaction coefficients and partition coefficients for peridotites
Melt reaction coefficients are the proportions of phases contributing to the melt and are used to calculate P in the melting equations (Appendix A). The melt reaction coefficients used to model mantle preconditioning (Table 1) are those that are most applicable to near-solidus melting. Values at low pressure (1–1·5 GPa) are taken from Kinzler & Grove (1992), Baker & Stolper (1994), Walter & Presnall (1994), Robinson et al. (1998) and Walter (1999). Those at intermediate pressure (2–3·5 GPa) additionally incorporate values of Walter et al. (1995) and Walter (1999). Those at high pressure (
3·5 GPa) are based on values of Walter (1998). It should be noted that, for melt extraction at high presssure during flow in which degrees of melting are low, orthopyroxene will not be a product at the solidus; instead, it will appear as the degree of melting increases. In consequence, the orthopyroxene reaction coefficients used here are lower than those in the compilation made by Longhi (2002), because those apply to high degrees of melting (and thus a polybaric melting column) but not small amounts of melt extracted from the base of a melting column.
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For the partition coefficients, the partitioning experiments of Salters & Longhi (1999)
and Salters et al. (2002) are most directly applicable to this study. Unfortunately, they refer to temperatures that are some 100°C above both Hirschmann's (2000) and Herzberg et al.'s (2000) best-fit mantle solidi and do not extend to pressures beyond 3·4 GPa. However, good fits with other experimental data indicate that their parameterizations are more robust. To obtain clinopyroxene–melt and garnet–melt partition coefficients appropriate for low-degree melts of fertile mantle peridotites over the pressure range of 1–6 GPa, this paper uses the parameterizations published by Salters et al. (2002) and then applies them to the few experiments in which degrees of melting are within the range 2–12 wt % and for which both melt and mineral compositions are published. Figure 6 illustrates the relationship between partition coefficient and pressure at the solidus, and Table 1 gives the values used in this study for Nd and Yb. Errors (2
) on regression lines are typically about 0·1 log units.
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Table 1 shows that the bulk distribution coefficients for Nd generally decrease with increasing pressure along the anhydrous, peridotite solidus, although there is a plateau at intermediate pressures. For Yb, there is a balance between the increase in proportion of garnet with depth and the decrease in partition coefficient resulting from changes in P, T, and melt and mineral compositions. The greatest bulk partition coefficients for Nd are at shallowest depths, but the greatest values for Yb are at intermediate depth (3·5 GPa).
A key question is whether these partition coefficients are also valid at ultra-low degrees of melting, when minor hydrous phases may contribute significantly to the melt. Robinson et al. (1998) discovered that melt compositions for <3% melting of MORB pyrolite at 1·5 GPa have high Si and Na and low Mg and Ca, although melt compositions for low degrees of melting of the depleted Tinaquillo peridotite have ‘normal’ values. Parameterization of their data for experiments with 0·8–0·9 degrees of melting MORB pyrolite gives clinopyroxene–melt partition coefficients of 0·71 for Yb and 0·42 for Nd, well above the values of 0·4 for Yb and 0·18 for Nd listed in Table 1. Blundy et al. (1998) obtained a clinopyroxene–melt partition coefficient >1 by direct measurement on a c. 1% melt at the same pressure. On the other hand, the values cited in Table 1 almost exactly match the parameterizations of data obtained for 2·4 wt % melting at 1 GPa (Schwab & Johnson, 2001) and for <1 wt % melting at 5 GPa (Herzberg & Zhang, 1996). Gaetani (2004) explained that it is the first melts of fertile mantle at low pressure that give unusually high partition coefficients because the high Na and Al depolymerize the melt. These details will need to be incorporated into more sophisticated models, as will the role of water in low-degree melts. However, varying partition coefficients on this scale has little effect on the shapes of melt extraction trajectories, principally because much of the melt extraction takes place at higher pressures where Na and Al concentrations of low-degree melts are not so high.
Tracking reaction coefficients and partition coefficients for eclogites and pyroxenites
For a given clinopyroxene:garnet ratio, reaction coefficients should vary slightly with pressure down to the pressure at which garnet begins to break down, clinopyroxene entering the melt slightly faster than garnet at high pressure and garnet entering the melt slightly faster than clinopyroxene at low pressure (e.g. Yasuda et al., 1994). For this paper, both minerals are assumed to contribute equally to the melt over the full range of eclogite stability. As the lower limit of garnet stability may be of the order of 1·5–2·0 GPa (Yasuda et al., 1994; Hirschmann & Stolper, 1996), this eclogite mineralogy has been retained throughout melt extraction for pressures above 1·5 GPa. Studies of Beni Bousera suggest that the typical low-P breakdown product is a corundum-bearing websterite (Kornprobst et al., 1990). However, this is unlikely to be relevant, as the plums will normally be ultra-depleted in incompatible elements through melt extraction by this stage.
For the garnet–melt partition coefficients, Hirschmann & Stolper's (1996) compilation (for P <3 GPa) gives DYb = 6·4 [by interpolation using the approach of Wood & Blundy (1997)] and DNd = 0·052, and the data of Klemme et al. (2002) gives (at 3 GPa) DYb = 7·1 and DNd = 0·035 (by interpolation). Equivalent values for clinopyroxene compilations are respectively DYb = 0·44 and DNd = 0·187, and DYb = 0·64 and DNd = 0·17. For higher pressures, the experimental data of Yasuda et al. (1994) at 5 GPa, parameterized according to Salters et al. (2002), give DYb = 7·9 and DNd = 0·12 for garnet, and DYb = 0·48 and DNd = 0·186 for clinopyroxene. These data are insufficient to indicate any pressure, composition or temperature dependence. However, the contrast between compatible Yb and incompatible Nd is so great that it masks possible errors in the individual Nd and Yb coefficients in most models. This paper uses the same values throughout: DYb = 7·0 and DNd = 0·07 for garnet; and DYb = 0·45 and DNd = 0·18 for clinopyroxene.
A note of caution is that van Westrenen et al. (2001) found that eclogites and garnet pyroxenites with >19 mol % Ca on the garnet X-site could have markedly different D values, notably higher coefficients for Nd. It is, therefore, likely that some eclogites do exhibit different partition coefficients from those used in this study although, again, the principal conclusions are not affected.
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NUMERICAL EXPERIMENTS ON MANTLE PRECONDITIONING |
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The equations developed in this paper coupled with the values of the melting parameters listed in Table 1 allow numerical experiments on mantle preconditioning to be carried out for the plot of 143Nd/144Nd vs Yb/Nd (I1 vs T2/1, where 1 indicates Nd and 2 indicates Yb). The method is first to define compositions of the matrix mantle (M) and plums (P) prior to preconditioning. Here, the matrix has arbitrary values of 1 ppm Nd, 0·4 ppm Yb and 143Nd/144Nd = 0·5132, and the plums (P) are hybrid plums (mantle metasomatized by plum melts) containing 5 ppm Nd, 0·5 ppm Yb, and 143Nd/144Nd = 0·5126. The pressure at which the mantle crosses its solidus is next defined. The matrix and plum mineralogies at this pressure are then calculated using the equations in Appendix B, and the corresponding partition and reaction coefficients calculated. The composition of the residual asthenosphere is then calculated from equations (A3) and (A4) for the chosen values of mass fraction of plums (MP), relative rate of plum melting (r), mass fraction of trapped melt (FT) and efficiency of melt extraction (
). It should be noted that these experiments are based on melt extraction at a single pressure. For multiple episodes of melt extraction, the mineralogy would need to be recalculated as described in Appendix C and the process repeated.
Figure 7 depicts some of the key results. It depicts models in which the variables are initially fixed at MP = 0·3, r = 0·1, FT = 0 (no chemical exchange between plums and matrix), plum composition P from Fig. 5d, melt extraction at 2·5 GPa throughout, and an efficiency of melt extraction () of 0·02. The various parts of Fig. 7 then highlight the effect of varying each of the parameters in turn.
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Figure 7a illustrates the effects of variable r; that is, variable rate of melting of matrix with respect to rate of melting of plums. As r decreases from unity (matrix and plums melt at equal rates) to 0·001 (almost entirely plums melting), the melt extraction trajectories become steeper and a plateau is reached at progressively lower Yb/Nd ratios. For r = 0·001, when the plum component dominates melting, the extraction trend is only just to the right of the mixing line before converging on the matrix composition. This distinctive trend results because the matrix composition scarcely changes whereas the plums become progressively depleted in incompatible elements until they no longer contribute significant Nd to the bulk mantle composition. This has the interesting consequence that even apparently simple mixing trends between two end-member components could be explained by preconditioning with very low values of r.
Figure 7b illustrates the effect of variable MP; that is, variable mass fractions of plums. Each trajectory again follows a positive slope ending in a plateau. As the mass fraction of plums decreases, the Nd contribution from the plums decreases more rapidly to ‘background’, and the bulk mantle composition reaches its plateau at lower ratios of Yb/Nd.
Figure 7c illustrates the effects of different plum mineralogies. The effect of mineralogy is illustrated by varying the proportion of clinopyroxene while retaining the ratio of olivine to orthopyroxene. As the mass fraction of clinopyroxene in the plums increases, the bulk distribution coefficient for Yb increases and Yb is more strongly retained in the residue from melt extraction whereas Nd is much less affected. Thus, the greater the mass fraction of clinopyroxene, the more rapid the increase in Yb/Nd ratio for a given melt loss and the shallower the melt extraction trajectory.
Figure 7d illustrates the effects of depth of melt extraction during mantle flow. At high temperatures and pressures, melt extraction begins well within the garnet lherzolite facies whereas, at lower temperatures, melt extraction begins within the spinel lherzolite facies. The consequence is flatter trends for the higher temperatures and pressures, because melting in garnet lherzolite facies causes Yb to be retained relatively strongly in the melt extraction residue. Subsequent partial melting of such a mantle source therefore yields basalts with high Yb/Nd ratios.
Figure 7e illustrates the effects of chemical exchange between plums and matrix during melt extraction. The variable is FT, the retained melt expressed as a mass fraction of the residual mantle: the higher the value of FT, the lower the plateau value of the Nd isotope ratio. The retained melt is treated as pooled fractional melt from the related melt extraction episode.
Figure 7f illustrates the effects of efficiency of melt extraction. The variable is , the extent of melting required before melt can be extracted from the flowing asthenosphere. The higher the value of , the less rapid the depletion of Nd in the mantle and hence the steeper the melt extraction trend and the earlier the plateau is reached.
It should be noted also that Fig. 7 is based on only two components, a MORB mantle component with high Yb/Nd and high Nd isotope ratio and a plum component with low Yb/Nd and low Nd isotope ratio. It is, as Fig. 3a demonstrates, equally possible to model other types of plum, or mixture of plums, although (as will be seen) the scenario chosen best simulates natural systems. This particular projection of 143Nd/144Nd against M/Nd (where M is any incompatible element) is sensitive not only to the composition of the plums, but also to their age and hence their residence time in the mantle. For example, Yb/Nd correlates with Sm/Yb, so the compositions of plums (and matrix) will evolve with time and the precise Nd isotope ratios will depend on both the initial isotope ratio and the residence time in the mantle before melting. This is clearly important if the plums represent old, recycled material. For example, the pyroxenite veins of Beni Bousera (Pearson et al., 1993), often cited as examples of the plums in a plum-pudding mantle, have very high Yb/Nd ratios but low Nd isotope ratios. They could melt to produce magma with low Yb/Nd ratios, which would react with mantle to yield hybrid plums of the required composition. However, if recycled through the Earth, the veins would rapidly evolve to very high Nd isotope ratios and therefore represent unsuitable compositions.
Overall, therefore, the numerical experiments demonstrate that melt extraction trajectories differ from mixing trends in both the gradient of plum removal and the presence of a plateau. The gradient becomes increasingly shallow (and increasingly divergent from a mixing gradient) for higher pressures and temperatures of melt extraction, for lower rates of plum melting compared with matrix melting, for plums with high proportions of garnet and clinopyroxene, for high proportions of plums relative to matrix and for efficient melt extraction. The position of the plateau depends on the isotope composition of the matrix, the extent of chemical exchange between plums and matrix, and the isotope composition of the plums. Moreover, although the overall trajectories do not resemble mixing lines, almost all lavas are derived from mantle with Yb/Nd <0·8. Most of the modelled trajectories are close to linear over this range. Thus, it cannot be assumed without further evaluation that linear trends on this type of plot must result from source mixing, as melt extraction could give the same outcome.
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SOME POSSIBLE EXAMPLES OF MANTLE PRECONDITIONING |
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There are many examples that could be used for comparison with the theoretical models. For reasons of space, this paper focuses on the one projection of 143Nd/144Nd against Yb/Nd and three areas: one representative of possible preconditioning in a back-arc setting, one representative of possible preconditioning during continental break-up, and one representative of possible preconditioning during plume–ridge interaction. In all examples, isotope data have been normalized to La Jolla of 0·511858 or BCR-1 of 0·512643. Where standard data have been reported, trace element data are normalized to recommended values.
Preconditioning by mantle flow into an arc–basin system: Bouvet–Scotia Sea
The compositional relationships between lavas from the South American Antarctic Ridge (SAAR), East Scotia Ridge (ESR) back-arc spreading centre and South Sandwich Islands (SSI) island arc (Fig. 8) provide a good test of the models presented here. Pearce et al. (1995) have already demonstrated that the depleted nature of the South Sandwich arc lavas supports the hypothesis of McCulloch & Gamble (1991) and Woodhead et al. (1993) that the mantle reaching the arc front has been preconditioned by melt loss in the back-arc. Leat et al. (2000, 2004) and Fretzdorff et al. (2002) additionally found that lavas at the edges of the basin were more enriched in incompatible elements than those in the centre and so supported models for flow of enriched mantle into the back-arc from both north and south. Pearce et al. (2001) further demonstrated that the lavas from the East Scotia Ridge form trends in isotope space that point towards the composition of Bouvet Island; thus they belong to the Bouvet mantle domain, which includes the SAAR, the southernmost Mid-Atlantic Ridge and the western part of the South-West Indian Ridge. A. P. Le Roex et al. (1983, 1985) and P. J. Le Roex et al. (2002)