13.3 Mantle melting models

Volcanoes located on continental crust often exhibit complex ²³⁰Th evolution patterns, probably because mantle-derived magmas become trapped during their rise through low-density sialic basement. In contrast, oceanic volcanoes might be expected to show simpler behaviour, since oceanic crust is easily punctured by rising magma. Therefore, oceanic volcanics provide a window to study Th isotope fractionation processes in the mantle.

The first detailed U-series measurements on oceanic volcanics were made by Oversby and Gast (1968) on recent ocean island lavas. This study revealed disequilibrium between isotopes of the ultra-incompatible elements, radium and thorium. Oversby and Gast suggested that these fractionations were probably inherited from a melting event in the mantle source of the magmas. ²³⁰Th activities were observed to be higher than ²³⁸U activities, suggesting that thorium was a more incompatible element than uranium. This conclusion was supported more than ten years later (Condomines et al., 1981) in studies of MORB magma genesis (see below).

In view of the short half-life of ²²⁶Ra, Oversby and Gast attributed disequilibrium of this species to rapid ascent of ocean island magmas from the source area (< 10 000 yr). This conclusion has also been supported by radium analysis of MORB (section 13.3.5). In addition, rapid ascent of ocean island magmas has been confirmed by studies of their Th isotope chemistry over time. For example the volcanoes of Mauna Kea (Hawaii), Marion Island (SW Indian Ocean) and Piton de la Fournaise (Fig. 13.15) all show constant initial ²³⁰Th/²³²Th ratios (within error) over the last 250 kyr (Newman et al., 1984; Condomines et al., 1988). This suggests that transport of magma from the melting zone to the surface probably occurred within a few thousand years, and without storage in a deep crustal reservoir, which would have perturbed the observed ratios. Therefore, the calculated initial Th isotope ratio for each eruption is probably very close to the source value.

Fig. 13.15. Plot of erupted (initial) Th activity ratios against time for Piton de la Fournaise volcano (Reunion Island) showing constant magma composition over time, within error. After Condomines et al. (1988).

13.3.1 Melting under ocean ridges

Mid ocean ridges present the minimum crustal thickness which must be traversed by ascending mantle-derived magmas. Therefore, in this environment we should have the best opportunity to see back through the processes of magma evolution during ascent, to study source processes and chemistry. However, some workers (e.g. O’Hara and Mathews, 1981) have suggested that MORB magmas spend many eruptive cycles in periodically re-filled, periodically tapped magma chambers under the ridge, which then grossly perturb the incompatible element and isotopic signatures of the product magmas. In this case, they argued, it would be almost impossible to ‘invert’ the data (see section 7.2.3) to reconstruct the source chemistry.

The short half-life of ²³⁰Th has provided a powerful tool to test these models of MORB magma evolution. In the first detailed study of MORB samples, Condomines et al. (1981) found that fresh, young crystalline basalts and glasses from the ‘FAMOUS’ area on the Mid Atlantic Ridge (37 ^oN) had a narrow range of ²³⁰Th/²³²Th and U/Th activity ratios. Because these samples were all less than 5 kyr old, their present Th activity ratios can be taken as initial ratios at the time of eruption.

When plotted on a U)Th isochron diagram, the FAMOUS data fall well to the left of the equiline, showing them to be far from isotopic equilibrium. This U)Th disequilibrium must have been inherited during the melting process (Fig. 13.16), because U and Th are both ultra-incompatible elements, and cannot be fractionated from each other during Raleigh crystallisation in a magma chamber. If the residence time of magma in such chambers was more than a few tens of kyr, U)Th activities would again reach equilibrium (Fig. 13.16). Because this has not happened, we can deduce that the transport of magma from the melting zone to the surface was relatively rapid, which is not consistent with prolonged evolution in an open-system magma chamber. This conclusion has subsequently been supported by evidence of isotopic disequilibrium of even shorter-lived U-series nuclides in MORB glasses (section 13.3.5).

Fig. 13.16. U)Th isochron diagram showing activity ratios in young lavas from the FAMOUS area of the Mid Atlantic Ridge, to the left of the equiline. Arrows show the effects of partial melting and radioactive decay. After Condomines et al. (1981).

In addition to the FAMOUS area, Condomines et al. (1981) showed that other young ridge basalts and OIB also fell on the left-hand side of the equiline (Fig. 13.17). Hence, in all of these cases, melts were enriched in Th/U relative to the source. This implies greater incompatibility of Th over U during melting. Allegre and Condomines (1982) expressed this Th/U fractionation during melting by the quantity ‘k’:

(²³⁸U/²³²Th)_magma

k = ))))))))) [13.10]

(²³⁸U/²³²Th)_source

However, it is more useful to express this ratio as its reciprocal, termed ‘r’, as used by McKenzie (1985a). In addition to facilitating the algebra, this formulation avoids confusion of ‘k’ with kappa (the atomic ²³²Th/²³⁸U ratio):

(²³⁸U/²³²Th)_source

r = ))))))))) [13.11]

(²³⁸U/²³²Th)_magma

Since the source is assumed to be on the equiline, its ²³⁸U/²³²Th activity is equal to its ²³⁰Th/²³²Th activity. Furthermore, if the analysed sample was extracted from the source in less than a few thousand years, the source Th isotope activity is equal to that measured in the magma:

(²³⁸U ) (²³⁰Th) (²³⁰Th)

()))) = ()))) = ()))) [13.12]

(²³²Th)_source (²³²Th)_source (²³²Th)_magma

Hence, by substituting into equation [13.11], we obtain:

(²³⁰Th/²³²Th)_magma (²³⁰Th)

r = ))))))))) = ()))) [13.13]

(²³⁸U/²³²Th)_magma (²³⁸U )_magma

This is represented in Fig. 13.17 by the gradient of lines projecting from the origin. Hence we can determine U/Th fractionation during melting from a U-series analysis of the magmatic product.

Fig. 13.17. U)Th isochron diagram showing fields for MORB and OIB relative to the Th/U fractionation factor during melting (r). Modified after Allegre and Condomines (1982).

Corroboration of the Mid Atlantic Th isotope results came from a similar study on the East Pacific Rise by Newman et al. (1983). These data lie to the left of the equiline, and fall within error of unaltered basalts from the FAMOUS area, but with more scatter, particularly in ²³⁸U/²³²Th activity. Since U and Th are both ultra-incompatible elements, Newman et al. recognised that it was very difficult to generate the required U/Th fractionations at the degrees of melting normally expected for MORB (ca. 10%). Hence, they suggested that under these conditions a U)Th-rich accessory phase might be required to explain the data.

Thompson et al. (1984) reversed this problem, arguing that the incompatible element signatures of MORB rocks, including U)Th disequilibrium data, could only be generated by very low degrees of mantle melting. They noted that such an explanation was consistent with observations for other isotope systems on MORB glasses (e.g. Cohen et al., 1980), which showed the observed Rb/Sr, Sm/Nd and U/Pb ratios in MORB magmas to be fractionated relative to the ratios required in the source to generate observed isotope compositions (see section 6.2.2).

13.3.2 The effect of source convection

This line of argument was developed by McKenzie (1985a), who performed calculations to determine the maximum percentage of partial melting that was consistent with the observed U/Th fractionations. For this purpose he assumed that Th was perfectly incompatible (i.e. its bulk distribution coefficient between solid and liquid, D, is zero), and that there was no magma residence time in a ridge chamber before eruption. In order to generate a ²³⁰Th/²³⁸U enrichment (r) of 1.25 using a batch melting model and a D value of 0.005 for uranium, the maximum degree of melting permitted was 2%. However, this result is not consistent with major element considerations, which require MORB to be a large degree (ca. 15%) melt of the mantle. Hence, McKenzie ruled out the simple batch melting model for MORB genesis, and adopted instead the dynamic melting model of Langmuir et al. (1977).

In the dynamic melting model, melts are extracted simultaneously from a vertical thickness of perhaps 60 km of mantle (horizontal lines in Fig. 13.18). The melts ascend quickly to the surface in a conduit, mixing as they go (solid vertical lines in Fig. 13.18). Meanwhile the source itself moves slowly upwards through the melting zone (dashed vertical lines). At any given point the source contains less than 2% melt (termed the ‘porosity’), but as it moves upwards and melts are tapped off, the source becomes more and more depleted in incompatible elements. If melts mix equally from the whole melting zone, the effect of dynamic partial melting on incompatible element abundances is similar to that of batch melting. This is because (in the extreme case) the source is completely exhausted of these elements by the time it reaches the top of the melting zone. In other words, incompatible element extraction is 100% efficient. However, for short-lived nuclides, the two melting models can yield quite different results.

Fig. 13.18. Schematic view of a dynamic melting model for the generation of MORB, involving fast ascent and mixing of magmas, with slow ascent of the source. After McKenzie (1985a).

If the rate of mantle upwelling is rapid relative to the half-life of the nuclide in question (e.g. ²³⁰Th), then this nuclide behaves like a stable element. In that case, dynamic melting will yield an aggregate melt similar to batch melting, and the 15% melt fraction necessary to explain major element data cannot satisfy the Th activity data. However, if the rate of mantle upwelling is very slow relative to the half-life of ²³⁰Th, then ²³⁰Th which is removed from the source at the base of the melting column is replenished in the source as it ascends, by decay from residual uranium (which is less incompatible than thorium). Consequently, as upwelling progresses, the ²³⁸U/²³²Th activity of the source increases, but it remains on the equiline. After extraction of all U and Th from the source (15% total melt) the ²³⁸U/²³²Th activity of the aggregate melt (star in Fig. 13.19) will be the same as that of the initial source, but the ²³⁰Th/²³⁸U activity ratio (r) is still the same as in the first increment of melting at the base of the melting zone.

Fig. 13.19. Consequences of very slow mantle upwelling under the ridge for the Th activity systematics of MORB magmas. Note that the rate of magma upwelling is very rapid relative to the ²³⁰Th half-life.

In between these two extremes (simple batch and dynamic melting), it is possible to determine the rate of mantle upwelling which will yield the observed r value in MORB, given the bulk distribution coefficients (D) for U and Th. Williams and Gill (1989) presented these relationships in diagrammatic form, based on the equations developed by McKenzie (1985a). This information is shown in Fig. 13.20. The values of D chosen by McKenzie (1985a) lead to a calculated mantle upwelling rate of only 1 cm/yr. In contrast, Williams and Gill (1989) argued for a much higher D value for uranium (Fig. 13.20). This implies a more rapid rate of upwelling (ca. 7 cm/yr).

Fig. 13.20. Diagram showing the relationship between calculated mantle upwelling rate (cm/yr) and bulk distribution coefficients (D) for U and Th, assuming a dynamic melting model with 2% porosity and yielding a ²³⁰Th/²³⁸U activity (r) of 1.2 in MORB. After Williams and Gill (1989).

These two different upwelling rates make very different predictions about mantle processes under the ridge. A value of 1 cm/yr is less than the rate of plate motion, which led McKenzie (1985b) to argue that the melting zone under the ridge is funnel-shaped. Trace elements are then extracted from a wide swath of mantle near the base of the funnel, while major elements are dominated by the melt extracted from the apex of the funnel (Fig. 13.21a). Because the trace element extraction zone is larger, this lower domain dominates the U)Th systematics of the melt, which acts like a small-degree batch melt of the original mantle source.

Fig. 13.21. Predicted and observed distribution of melting zones under a mid ocean ridge. a) model predicted by Galer and O’Nions (1986); b) cross section of the East Pacific Rise based on results of the MELT seismic experiment. After Forsyth et al. (1998).

In contrast, with the higher upwelling rate of Williams and Gill (1989), melt extraction occurs from a vertical slice under the ridge, yielding a result closer to the simple dynamic model. However, the consequence is that the ²³⁰Th/²³²Th activity of the erupted products is substantially higher than the source (Fig. 13.19), while the ²³⁸U/²³²Th activity is similar to the source. O’Nions and McKenzie (1993) pointed out that in this case, the Th/U ratio (kappa value) of the source (sections 6.3.3 and 13.3.7) should be determined, not from the Th isotope ratio of MORB (equation [13.12] above), but directly from the elemental U/Th ratio of MORB. Hence, this model predicts that short-lived isotopes are fractionated by the melting process under ridges, but stable incompatible elements are not fractionated under these conditions.

The real situation may be somewhere between the two extremes described above; however, several lines of evidence tend to support the slow upwelling model. Perhaps the most important piece of evidence comes from the so-called Mantle Electromagnetic and Tomography (MELT) experiment, which used geophysical methods to image the distribution of partial melt zones under the East Pacific Rise (Forsyth et al., 1998). Seismic evidence collected in this experiment showed that the zone of incipient melting under the ridge extended to depths of over 150 km, and to a width of nearly 800 km, matching the shape of the melting zone predicted in Fig. 13.21a but having an extent 3 to 4 times greater in each direction (Fig. 13.21b). Other lines of evidence in support of slow upwelling with an extended zone of incipient melting are the continuing need to explain the trace element signatures of long-lived isotopic systems (section 6.2.2), and evidence for preferential melting in the garnet stability zone, to be discussed below.

13.3.3 The effect of melting depth

As noted above, ²³⁰Th/²³⁸U enrichment (increased r) is only possible if thorium is more incompatible than uranium. Therefore, to model Th/U fractionation more accurately it was necessary to refine the determinations of the crystal/melt distribution coefficients for U and Th. Since the only mineral phases that host significant inventories of U and Th are clino-pyroxene (cpx) and garnet, these minerals have been the focus of attention.

In the first detailed work on this subject, Beattie (1993a) measured solid/liquid partition coefficients (D) for cpx that were greater for Th than U, implying that melting in the spinel peridotite stability field (above 70 km depth) could not generate the observed Th/U fractionations. On the other hand, Beattie (1993b) showed that garnet has solid/liquid partition coefficients which are capable of generating the observed ²³⁰Th/²³⁸U enrichments. This was confirmed by LaTourrette et al. (1993), who determined D_Th/D_U values of 0.1 for garnet. Hence, it was concluded that the Th/U fractionations observed in MORB must originate from melting at greater than 70 km depth, and the resulting liquids must be transported to the surface quickly, before substantial decay of ²³⁰Th can occur.

These conclusions were questioned by Wood et al. (1999) based on modelling the pressure dependance of cpx/liquid partition coefficients for U and Th. With increasing pressure, cpx becomes more aluminous, shrinking the size of the M2 cation site where U and Th are housed. This should favour the smaller uranium ion, causing the ratio of U/Th partition coefficients between cpx and liquid to increase with pressure. Wood et al. predicted that at pressures slightly above 1 GPa (=10 kbar, equivalent to 35 – 50 km depth) the D_U/D_Th ratio should rise above unity, allowing Th/U excesses to be generated by MORB melting in the spinel peridotite field. These predictions were confirmed by experimental work (Landwehr et al., 2001), and their possible consequences are shown in Fig. 13.22.

Fig. 13.22. Predicted excess ²³⁰Th activity as a function of melting depth, based on measured cpx/liquid and garnet/liquid partition coefficents for U and Th, and assuming a porosity (incremental melt fraction) of 0.001%. Note the change in scale on the y axis. After Landwehr et al. (2001).

This plot shows the excess ²³⁰Th activity that can be generated by partial melting of lherzolite in the plagioclase-, spinel- and garnet-peridotite stability fields. These results show that significant Th isotope excesses can be generated in the spinel-peridotite field, but only at extremely low porosity. In fact, the excess ²³⁰Th values presented in Fig. 13.22 were calculated assuming a porosity of 10^-5, equivalent to a melt fraction of only 0.001%! A somewhat more realistic porosity of 0.1% yields D_Th/D_U values for cpx that are 75% as large as those shown, but these values are still only half the value obtained in the Garnet stability field. In conclusion therefore, these findings do permit limited Th isotope excesses to be obtained at shallower depths than the garnet stability field, but melting in the garnet zone is still likely to be the major source of such disequilibrium.

Further light is thrown on the question of melting depths under ridges by the observation of a relationship between U-series activity ratios and ridge depth. In a study of MORB glasses from the Azores plateau, Bourdon et al. (1996a) demonstrated an inverse correlation between ²³⁰Th/²³⁸U activity ratio and water depth above the axis of the Mid Atlantic Ridge. This correlation was subsequently extended by Bourdon et al. (1996b) to other ridge segments (Fig. 13.23). However, in view of the great sensitivity of Th/U disequilibrium to melting porosity, one would not expect to see the greatest disequilibrium in samples from the shallowest part of the ridge, which has the highest melting rate.

Fig. 13.23. Plot of ²³⁰Th/²³⁸U activity (‘r’) for MORB against depth to the ridge axis. ( ! ) = Mid Atlantic; ( Î ) = Gorda, JDF; ( " ) = EPR; ( <> ) = Australia-Antarctic. After Bourdon et al. (1996b).

The observation of an inverse correlation between isotope disequilibrium and depth led Bourdon et al. (1996a,b) to suggest that the main control on Th/U disequilibrium across the Azores plateau must be the depth at which melting is initiated. If melting is initiated at greater depths, the longer melting column leads to greater overall melt fractions, but the longer melting interval within the garnet zone increases Th/U disequilibrium. Bourdon et al. attributed the greater melting depth across the Azores plateau to increased heating associated with the mantle plume. An alternative explanation is enhanced contamination of the mantle by eclogite or garnet pyroxenite from the plume (Hirschmann and Stolper, section 9.2.4). However, Bourdon et al., argued that this could not account for the Azores observations, since Th/U excesses do not correlate with isotopic or trace element evidence for source enrichment.

Data from Iceland are an exception to the generally good correlation between ridge depth and isotopic disequilibrium, since they lie well below the main trend. However, Iceland obviously represents an extreme example of plume contamination of a ridge, since the ridge actually emerges above sea-level. Therefore, Bourdon et al. attributed this anomalous behaviour to the much larger upwelling velocity under Iceland. This was confirmed by a more detailed study of Iceland and the Reykjanes Ridge (Peate et al., 2001). Data for Iceland itself were again found to lie well below the main array. However, samples from greater than 1km depth on the Reykjanes Ridge south of Iceland exhibited a positive correlation between excess Th activity and depth, consistent with the rest of the MORB array.

13.3.4 The effect of source composition

The relative importance of source composition versus melt fraction as a control of isotope disequilibium has continued to be a matter of debate. Sigmarsson et al. (1998) investigated this question by plotting ²³⁰Th/²³⁸U activity ratios (‘r’ values) against ²³²Th/²³⁸U activity ratios. The latter can be converted to kappa (6) by multiplying by the ratio of the half-lives (3.134). The 6 value is in turn almost identical to the overall Th/U weight ratio. This plot (Fig. 13.24) is actually equivalent to the Th/U ‘alternative isochron’ plot (section 12.4.3) which was also used for presenting Ra/Th isotope data (section 13.1.2); however, that is not the purpose here. Sigmarsson et al. argued that the correlation between r values and 6 values showed that Th isotope disequilibrium is caused by variations in source composition. However, since the apparent 6 value can itself be fractionated by the melting process, this could be a circular argument.

Fig. 13.24. Plot of ²³⁰Th/²³⁸U activity (‘r’) against ²³²Th/²³⁸U activity (or Th/U concentration, 6) to show sub-linear arrays for different ocean ridge and ocean island suites, lying between the fields for garnet-pyroxenite and garnet-peridotite melts. After Sigmarsson et al. (1998).

A more conclusive determination of the effect of source composition on U-series disequilibrium is to compare Th isotope data with long-lived isotope tracers that are known to be affected by source variations. Lundstrom et al. (1999) made such a study on the East Pacific rise in the vicinity of the Siqueiros Fracture Zone, northwest of the Galapagos Islands. Based on trace element data and long-lived isotope signatures (Sr – Nd) they identified magmas from an enriched source (E-MORB), a depleted source (D-MORB), and mixtures between these components (N-MORB). These three types of sources also gave rise to distinct differences in Th isotope disequilibrium, with E-MORB exhibiting excess ²³⁰Th activities, whereas D-MORBs were essentially in secular equilibrium (Fig. 13.25a). Hence, Lundstrom et al. concluded that E-MORBs were sampling garnet-bearing veins that were distributed in a source with ‘marble cake’ structure (section 6.1.5), whereas D-MORBs sampled the garnet-free peridotite ‘host’. N-MORBs were then attributed to mixing between these two end members.

Unfortunately, further study of this area (Sims et al., 2002) suggested that melting processes were more complex than previously realised. Sims et al. analysed a suite of samples collected from the axial graben of the East Pacific Rise, just north of the Siqueiros Fracture Zone studied by Lundstrom et al. (1999). On the plot of Th isotope disequilibrium ‘r’ (²³⁰Th/²³⁸U activity) against 6, they found that their axial graben samples lay on the mixing line between the E-MORB and D-MORB of Lundstrom et al. (Fig. 13.25a). However, on a plot of Th isotope disequilibrium (‘r’) against long-lived isotope tracers, they found that the axial graben samples did not lie on mixing lines between the E-MORB and D-MORB end-members defined by the Siqueiros Fracture Zone (Fig. 13.25b). Sims et al. therefore concluded that variations of U-series isotope activities were due to polybaric melting of a homogeneous source, rather than mixing between melts from compositionally distinct sources.

Fig. 13.25. Plots of isotope data for the axial graben of the East Pacific Rise ( solid ) compared with D-MORB and E-MORB samples from the Siqueiros Fracture Zone ( open ). a) Th activity ratios; b) Th activity as a function of Sr isotope ratio. Modified after Sims et al. (2002).

This interpretation is problematical because it contradicts nearly twenty years’ work on the origin of Pacific MORB, which suggested that the homogeneous signatures of long-lived isotope tracers are due to magma mixing under the ridge, rather than the sampling of a homogeneous mantle source (section 6.1.4). However, a re-examination of the Sims et al. paper suggests that basalts from the Lamont Seamounts (Fornari et al., 1988) are a much better indicator of the nature of D-MORB in the axial graben segment studied by Sims et al. than the basalts of the Siqueiros Fracture Zone. Firstly, the Lamont Seamounts are much closer to the study area than the Siqueiros Fracture Zone, and secondly, Pb isotope data from the axial graben samples actually form an array that falls within the larger envelope of the Lamont Seamount array (not shown here). The Lamont Seamounts have Sr isotope signatures indicative of a more depleted source (Fig. 13.25b) which would much better explain the compositions of the axial graben samples by mixing with E-MORB. Hence it appears that, as proposed by Lundstrom et al. (1999), axial graben samples of the East Pacific Rise are indeed the products of mixing between isotopically heterogeneous magmas from a ‘marble cake’ or ‘plum pudding’ mantle.

13.3.5 Evidence from short lived species

Observations of ²²⁶Ra/²³⁰Th disequilibrium in MORB place even tighter constraints on melting models beneath ridges than those provided by Th/U data. Measured ²²⁶Ra/²³⁰Th activity ratios in MORB glasses are as high as 2.5, despite the short (8000 yr) equilibration time of ²²⁶Ra. In principle, the dynamic melting model of McKenzie (1985a) can explain the Ra)Th data at very low porosities, assuming a Ra distribution coefficient of zero, because it assumes instantaneous melt extraction from all levels in the melting column. In this model, most of the radium must come from the base of the melting column, because ultra-incompatible elements are very efficiently extracted at low degrees of melting. Chabaux and Allegre (1994) showed that this model is applicable to OIB, whose small ²²⁶Ra excesses may be preserved in a rapidly upwelling plume. This generates a positive correlation between ²²⁶Ra/²³⁰Th and ²³⁰Th/²³⁸U activity ratios, which is expressed as an inverse correlation on the ‘reverse’ plot of ²³⁰Th/²²⁶Ra versus ²³⁰Th/²³⁸U activity ratio used by Chabaux and Allegre (Fig. 13.26).

Fig. 13.26. Reverse plot of ²³⁰Th/²²⁶Ra versus ²³⁰Th/²³⁸U activity ratios, showing a correlation for OIB magmas, consistent with a simple melting model. After Chabaux and Allegre (1994).

Unlike OIB magmas, it seems unlikely that MORB melts can ascend from 80 km depth with sufficient velocity to avoid decay of the excess ²²⁶Ra inventory of the magma. Therefore, Spiegelman and Elliott (1993) proposed that small melt fractions cannot easily escape from the base of the melting zone, but only ascend slowly to the surface by a mechanism they termed ‘equilibrium porous flow’ (EPF). They proposed that this process was also accompanied by an increase in the porosity of the melting system, from a value of zero at the base of the melting column to a maximum of ca. 0.5 % at the top of the melting column. This model has the effect of holding back the complete release of Th, which can then decay to Ra as the source ascends. The ²²⁶Ra extracted from these shallower levels in the melting column can then reach the surface without undergoing significant decay. This model gives mathematically acceptable solutions to the Th)U and Ra)Th data, but it is questionable whether melt extraction can begin at the porosities of less than 0.1% required in this model. An alternative approach (Rubin and Macdougall, 1988; Qin, 1992) is to invoke disequilibrium melting.

A disequilibrium melting model differs from all of the models discussed above, in which the inventory of trace elements within each mineral grain undergoing melting is believed to be homogenised by diffusion before any melt is removed from the surface of the grain. Hence, in an equilibrium melting model, ultra-incompatible elements can be stripped out from the entire grain by very small degrees of melting. However, Qin argued that if the melting rate is of the same order of magnitude as the volume diffusion rate of cations in mineral grains (e.g. garnet and cpx), then incompatible elements will be stripped out from grains in layers, like the shells of an onion.

Qin (1992) argued that disequilibrium melting is almost unavoidable in the generation of ²²⁶Ra excesses, since the secular equilibration time of this nuclide (8000 yr) is comparable with the 10⁴ yr diffusional equilibration time for cations in a mineral grain at the temperature of basaltic melting (section 6.1.2). Qin took this argument further, by suggesting that differing rates of volume diffusion for different cations could cause diffusional fractionation of U-series nuclides and other incompatible element couples. However, this overlooks the fact that the source spends a minimum of 100 kyr in the melting zone, for a 50 km-deep melting zone upwelling at 5 cm/yr. These figures suggest that disequilibrium melting cannot be maintained over the whole depth of the melting column under ridges, but might occur at the base of the column in such as way as to hold back complete release of ultra-incompatible elements into the melt.

Kelemen et al. (1995) took a different approach, by examining the petrology of ophiolite complexes for evidence of the type of magma flow mechanisms that might have occurred under ocean ridges. They suggested that dunite pods, which make up 5 – 15% of the Oman ophiolite (Fig. 13.27), were formed by the partial equilibration of basic magmas with upper mantle harzburgite, causing the replacement of pyroxene by olivine. Hence, these pods seem to represent ‘fossilised’ melt conduits, up which magma migrated by porous flow, and possibly also by channel flow. Evidence for porous flow is provided by the pervasive replacement of pyroxene, which requires magma – wall-rock interaction. On the other hand, evidence of focussed channel flow is provided by the occurrence of chromitite rafts within the dunite pods. Because of the relatively low solubility of Cr in basaltic melts, Kelemen suggested that the chromitites must have scavenged Cr from over 300 times their own mass of liquid. This implies that the dunite pods experienced time-integrated melt/rock ratios over 300, consistent with a function as magma conduits.

Fig. 13.27. Idealised reconstruction of the magma conduit system under a Mid Ocean Ridge, based on the distribution of dunite pods in the Oman ophiolite. Stream lines show the direction of solid-state flow of the peridotite source material. After Kelemen et al. (1995).

Evidence that places tighter constraints on the alternative models of dynamic partial melting (channel flow) or EPF (porous flow) comes from a comparison of excess ²²⁶Ra and ²³⁰Th activities. Beginning with the work of Volpe and Goldstein (1993) it was observed that ²²⁶Ra/²³⁰Th activity ratios appeared to be inversely correlated with ²³⁰Th/²³⁸U activities in MORB. However, because of the very short half-life of ²²⁶Ra, it could not be proven that the ²²⁶Ra/²³⁰Th activity ratios measured in the early studies were initial ratios at the time of eruption. In contrast, the samples analysed by Lundstrom et al. (1999) and Sims et al. (2002) from the axial graben of the EPR provided the first conclusive evidence of initial ²²⁶Ra/²³⁰Th activity ratios. These samples were collected by submersible rather than dredge (used in most previous studies). This allowed very young samples to be precisely selected from the narrow axial graben, in part from an eruption that was actually in progress on the sea floor in 1992. In addition, Po – Pb dating of other samples also indicated ages of less than 200 yr (Rubin et al., 1994).

An inverse correlation between ²²⁶Ra/²³⁰Th and ²³⁰Th/²³⁸U activity ratios from the axis of the EPR (Fig. 13.28) suggests that these magmas were produced by mixing between D-MORB and E-MORB end-members with distinct origins. The latter have large ²³⁰Th excesses but little excess ²²⁶Ra, indicating an origin from deep melting in the garnet zone, whereas the former have large ²²⁶Ra excesses, but little excess ²³⁰Th, implying a shallow origin from a source that did not lose its radium inventory at depth. Hence, Lundstrom et al. (1999) suggested that E-MORBs were derived principally by a channel flow melting process, whereas D-MORBs were generated by a porous flow melting process. These two processes must have been going on at the same time under the ridge, and could simply reflect heterogeneity in the melting process. For example, garnet pyroxenite veins melt preferentially to form ²³⁰Th-enriched E-MORB melts. These rise to the surface along channels that begin as zones of porous flow (hence extracting a ²²⁶Ra-enriched D-MORB fraction from their wall-rocks). As melt focussing increases, a few of the zones of porous flow probably evolved into open magma conduits (Kelemen et al., 2000).

Fig. 13.28. Plot of ²²⁶Ra/²³⁰Th versus ²³⁰Th/²³⁸U activity ratios to show an inverse correlation in MORB, attributed to mixing between D-MORB and E-MORB melting processes. ( solid ) = EPR; ( triangle ) = JDF–Gorda; ( o ) = Siqueiros Fracture Zone. After Sims et al. (2002).

13.3.6 Evidence for mantle upwelling rates

Lundstrom et al. (1998) argued that if most MORBs are the result of mixing between more depleted and less depleted sources, the average amount of Th isotope enrichment (‘r’) observed on a ridge segment might not be a fundamental property of that ridge, but could merely reflect the chance selection of more or less depleted samples. For example, the correlation between ridge depth and the average ‘r’ value on a ridge segment (Bourdon et al., 1996a,b) should be expected to be a very noisy correlation. On the other hand, Lundstrom et al. argued that the slope of the ‘disequilibrium trend’ on the U–Th isochron (‘equiline’) diagram might be a more fundamental property of a particular ridge segment.

When Lundstrom et al. (1998) plotted the slope of this U–Th ‘disequilibrium trend’ against the half-spreading rate for seven ridge segments, they observed a good correlation for all examples except the Azores plateau (Fig. 13.29). They attributed this correlation to the effect of mantle upwelling velocity. Thus, on a fast-spreading ridge, the limited time for Th ingrowth during the ascent of the source through the melting zone leads to limited excess Th, whereas on slowly spreading ridges the slow ascent of the source allows maximum Th ingrowth. This appears to support the EPF model, where Th ingrowth is the main source of isotopic disequilibrium. However, on the equiline diagram, most of the disequilibrium trends pivot round the E-MORB field, rather than the D-MORB end-member proposed by Lundstrom et al. (1998), so their argument is not conclusive.

Fig. 13.29. Plot of the slope of the ²³⁰Th ‘disequilibrium trend’ against half spreading rate (= model upwelling rate), showing a positive correlation for different ridge segments in the East Pacific. Subsequent work (Lundstrom, 2003) has added more points near the origin. After Lundstrom et al. (1998).

Analysis of both protactinium and thorium allows the effects of mantle upwelling rate to be evaluated at the same time as the effect of source composition (Fig. 13.30). Bourdon et al. (1998) used this figure to compare the degrees of source enrichment and upwelling rate in MORB with different plume sources. Plumes exhibit a lower ²³¹Pa/²³⁰Th activity ratio than MORB, attributed to a greater fraction of garnet in their sources. However, plume-derived lavas appear to reflect more variable upwelling rates, even within a single hot-spot. For example, Hawaii and Iceland have very variable upwelling rates, from ca. 2 cm/yr to 30 cm/yr. On the other hand the Grande Comore plume exhibits a more consistent but lower upwelling rate, coupled with an enriched source. In a more detailed study of the Hawaiian plume, using combined Pa–Th analysis, Sims et al. (1999) calculated upwelling rates as high as 20 – 80 cm/yr for Kilauea and Mauna Loa, but only 2 – 6 cm/yr for Hualalai and Mauna Kea. They attributed these variations in upwelling velocity to the radial distances of these volcanoes from the centre of upwelling, believed to lie under the southeast coast of the main island.

Fig. 13.30. Plot of Excess ²³¹Pa activity against excess ²³⁰Th activity to compare MORB (solid) with different ocean islands: ( o ) = Hawaii; (triangles) = Iceland; (diamonds) = Grande Comore. Lines represent constant ²³¹Pa/²³⁰Th activity ratios (in boxes) and are labelled with upwelling rates in cm/yr, modelled assuming a melting porosity of 0.1% and an integrated melt fraction of 4%. After Bourdon et al. (1998).

13.3.7 Evidence from Th–Sr and Th–U mantle arrays

U-series isotopes can be used in conjunction with long-lived isotope systems such as Rb–Sr and U–Pb to yield additional information about long-term mantle enrichment processes. However, before examining the question of long-term mantle evolution, it is important to re-examine the mantle melting process using a combination of U–Th and Rb–Sr evidence.

Condomines et al. (1981) first demonstrated that MORB and OIB samples formed a strong mantle array on a Th activity ratio versus Sr isotope ratio plot which is analogous to the Nd versus Sr isotope mantle array. Downward displacements of data from this array can be caused by prolonged magma evolution in the crust, as seen in Iceland and in the Canaries. On the other hand, some altered ocean floor basalts from the FAMOUS area of the Mid Atlantic Ridge fall above the Th)Sr isotope array due to contamination with ²³⁰Th-enriched seawater. If these types of samples are removed from the data array, we can then examine the residual data to see whether ²³⁰Th/²³²Th or ²³⁸U/²³²Th activities (Fig. 13.19) are better correlated with Sr isotope ratios. This can help to test the alternative models of dynamic melting and equilibrium porous flow.

If Th isotope ingrowth during source upwelling is the principal origin of excess Th activities, the Th/U (6) value of the source should be best determined from the ²³⁸U/²³²Th activity ratio of the products (Fig. 13.31b). On the other hand, if U/Th fractionation during partial melting in the garnet zone is the principal origin of excess Th activities, the 6 value of the source should best be determined from the ²³⁰Th/²³²Th activity ratio of the products (Fig. 13.31a). Both of these U-series activity ratios are compared with the Sr isotope ratios of MORB and OIB samples in Fig. 13.31. The best correlation is observed in Fig. 13.31a, which supports the dynamic melting (garnet source) model rather than the ingrowth (EPF) model. However, most of the correlation line is defined by OIB rather than MORB, so the test is strictly relevant only to OIB. Since most plumes have greater upwelling rates than MORB, the EPF model is not in any case expected to provide a good fit for plumes.

Fig. 13.31. Comparison between the strength of Th–Sr isotope mantle arrays from a) ²³⁸U/²³²Th activities, and b) ²³⁰Th/²³²Th activities, against [atomic] Sr isotope ratio for MORB and OIB. Canary Island samples are anomalous, due to their long pre-eruptive history. After Condomines and Sigmarsson (2000).

U)Th isotope data yield an ‘instantaneous’ 6 value for the source; in other words the value pertaining in the source at the time of volcanism. However, we can also calculate a ‘time integrated’ 6 value for a given reservoir, such as the upper mantle, from Pb isotopes (section 6.3.3). The ‘time-integrated’ ratio is the average ratio over Earth history for a sample from that reservoir. OIB lie on a ‘mantle array’ (Fig. 13.32) between MORB and the U)Th geochron (representing the Bulk Earth). It is thought that the enriched plumes sampled by OIB buffer the MORB reservoir, which has a relatively short Pb residence time (section 6.3.3).

Williams and Gill (1992) proposed that one of the enriched reservoirs which buffers the U)Th systematics of OIB and MORB is sub-continental lithosphere. They argued that the signature of this component is exemplified by alkali basalts from Nyamuragira volcano in Eastern Zaire and Gaussberg volcano, Antarctica (see also Williams et al., 1992). Both of these volcanoes display low ²³⁰Th/²³²Th activity ratios, yielding instantaneous 6 values of ca. 5, well above the Bulk Earth value, but within the Mantle Array defined by oceanic volcanics (Fig. 13.32). In contrast, basalts from the Craters of the Moon volcanic field (Idaho) fall far from the mantle array of OIB samples (Reid, 1995). This cannot be explained by crustal contamination or in situ decay, but can be explained by a uranium enrichment event which was too recent to affect Pb isotopes, yet sufficiently ancient for ²³⁴U to decay to ²³⁰Th. This enrichment event may have been caused by CO₂ metasomatism associated with the Yellowstone Plume. A similar model was proposed by Williams and Gill (1992) to explain less extreme U enrichment of the source of Nyiragongo volcano.

Fig. 13.32. Plot of time integrated 6 (Pb) against instantaneous 6 (Th) for oceanic and continental volcanics in the Mantle Array, along with the Craters of the Moon volcanic field ( o ), which lies off the array. After Reid (1995).

13.3.8 Evidence for crustal melting and contamination

Work on Icelandic lavas by Sigmarsson et al. (1991) has shown that Th isotope data can also be used to investigate the genesis of felsic rocks in oceanic environments. Two alternative models for these rocks involve either direct fractionation of mafic magmas or partial melting of pre-existing mafic crust. However, because of the young age of this crust, conventional radiogenic tracers such as Sr and Nd cannot resolve these models. In contrast, the short half-life of ²³⁰Th may allow the solution of this problem.

Rift-zone tholeiites from Iceland are displaced to the left of the equiline by partial melting, but after 0.5 Myr, when their excess ²³⁰Th activity has decayed back to secular equilibrium, they are displaced downwards to a different range of Th activity ratios on the equiline (Fig. 13.33). Consequently, historical-age felsic melts produced by anatexis of Icelandic crust will have a lower ²³⁰Th/²³²Th activity than direct magmatic differentiates of juvenile basic magma. Sigmarsson et al. found that dacitic volcanics from the Hekla volcano in southern Iceland had ²³⁰Th/²³²Th activities too low to be derived from contemporaneous mantle-derived magmas (horizontal single arrows), but consistent with the melting of older crust (double arrow). Hekla rhyolites were then modelled by magmatic fractionation of the dacite melts (Fig. 13.33).

Fig. 13.33. U)Th isochron diagram showing the consequences of fractional crystallisation (F.C.) versus crustal anatexis (C.A.) for the production of felsic melts in Hekla volcano, Iceland. After Sigmarsson et al. (1991).

Th isotope studies of volcanic systems in Iceland have also been able to show the effect of contamination of basic magmas by crust a few Myr old (Hemond et al., 1988; Sigmarsson et al., 1992). In major volcanic centres, where the oxygen isotope composition of the pre-existing crust has been overprinted by meteoric hydrothermal convection, Th activity ratios also correlate with *¹⁸O. An example of this behaviour is shown in Fig. 13.34 for contaminated quartz tholeiites from the active rift zones of Iceland.

Fig. 13.34. Diagram of Th activity ratio against *¹⁸O (relative to SMOW) showing the effect of contamination of mafic magmas by young crust. ( ! ) = olivine tholeiite; ( " ) = quartz tholeiite. After Hemond et al. (1988).

13.3.9 Sources of continental magmas

The evidence that excess ²³⁰Th activities require the presence of garnet except at very low melting porosities (section 13.3.3) has provided a basis for understanding U-series systematics in young continental lavas. Asmerom and Edwards (1995) demonstrated this approach in comparing young (< 10 kyr) basalts from the Pincate volcanic field of the Basin and Range province in Mexico, with the ‘San Francisco’ volcanic field of the Colorado Plateau.

Nd isotope and geochemical data are consistent with an asthenospheric origin for basalts of the Basin and Range, but a lithospheric origin for those of the Colorado Plateau. U-series analysis was performed to see whether basalts from these different sources would possess different ²³⁰Th signatures, reflecting melting at different depths. The results showed that magmas regarded as asthenospheric had excess ²³⁰Th activities typical of MORB magmas (r = 1.2 – 1.35), whereas those attributed to lithospheric melting had no excess ²³⁰Th activity (r = 0.99 – 1.02). Two possible explanations for equilibrium ²³⁰Th/²³⁸U activity ratios are large degrees of mantle melting or slow ascent to the surface. However, both of these possibilities were ruled out by the observation of large excess ²³¹Pa activities in these rocks (²³¹Pa/²³⁵U activity = 2.0). Melting in the spinel peridotite field can generate excess ²³¹Pa, but cannot generate significant excess ²³⁰Th activity (section 13.3.3). Therefore Asmerom and Edwards suggested that alkali basalts of the Colorado Plateau were probably generated by shallow melting of subcontinental lithosphere within the spinel peridotite field, whereas Basin and Range magmas were produced by deeper asthenospheric melting in the garnet field (Fig. 13.35).

Subsequent work (Asmerom et al., 2000) widened this study to include two samples from the Rio Grande Rift (RGR). The Zumi Band tholeiite is on the margin of the RGR and is attributed to a lithospheric source under the Colorado Plateau, whereas the Potrillo basalts are located in the southern central part of the RGR and attributed to an asthenospheric source. U-series data (Fig. 13.35) are consistent with these predictions. All of the alkali basalts have large excess ²³¹Pa activities, consistent with small degree melting and rapid magma ascent. In contrast the tholeiite has a smaller excess, due to either a larger degree of melting or slower ascent. On the other hand, excess ²³⁰Th activities are again grouped according to source type, with the asthenospheric suite yielding large excess activities, whereas the lithospheric suite yields data within error of the equiline.

Fig. 13.35. Plot of excess ²³¹Pa activity against excess ²³⁰Th activity showing distinct signatures in lithospheric (solid) and asthenospheric (open) magmas from the western USA. (lower solid point) = tholeiite. Curve shows the result of simple batch melting of spinel or garnet peridotite at different melt fractions, using reasonable partition coefficients. After Asmerom et al. (2000).

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