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Journal of Petrology Advance Access originally published online on April 28, 2007
Journal of Petrology 2007 48(6):1119-1154; doi:10.1093/petrology/egm012
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© The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Origin of CFB Magmatism: Multi-tiered Intracrustal Picrite–Rhyolite Magmatic Plumbing at Spitzkoppe, Western Namibia, during Early Cretaceous Etendeka Magmatism

R. N. Thompson1,*, A. J. V. Riches1,{dagger}, P. M. Antoshechkina2, D. G. Pearson1, G. M. Nowell1, C. J. Ottley1, A. P. Dickin3, V. L. Hards4, A.-K. Nguno5 and V. Niku-Paavola5,{ddagger}

1Department of Geological Sciences, Durham University, South Road, Durham DH1 3LE, UK
2Division of Geological and Planetary Sciences, California Institute of Technology, MC 170-25, Pasadena, CA 91125, USA
3Department of Geology, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1
4British Geological Survey, Keyworth, Nottingham NG12 5GG, UK
5Geological Survey of Namibia, 1 Aviation Road, Private Bag 13297, Windhoek, Namibia

RECEIVED FEBRUARY 22, 2006; ACCEPTED FEBRUARY 27, 2007


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 SPITZKOPPE DYKE SWARM
 PETROGRAPHY AND PICRITE...
 GEOCHEMISTRY
 DISCUSSION OF DYKE GEOCHEMISTRY
 FOCUS ON THE PICRITES
 IMPLICATIONS FOR ETENDEKA...
 SUMMARY
 SUPPLEMENTARY DATA
 APPENDIX
 REFERENCES
 
Early Cretaceous tholeiitic picrite-to-rhyolite dykes around Spitzkoppe, western Namibia, are part of the extensive Henties Bay–Outjo swarm, penecontemporaneous with ~132 Ma Etendeka lavas ~100 km to the NW. Although only intermediate to rhyolitic dykes contain clinopyroxene phenocrysts, the behaviour of Ca, Al and Sc in the dyke suite shows that liquidus clinopyroxene—together with olivine—was a fractionating phase when MgO fell to ~9 wt %. Both a plot of CIPW normative di–hy–ol–ne–Q and modelling using (p)MELTS show that a mid-crustal pressure of ~ 0·6 GPa is consistent with this early clinopyroxene saturation. Sr, Nd, Hf and Pb isotope variations all show trends consistent with AFC contamination (assimilation linked to fractional crystallization), involving Pan-African Damara belt continental crust. The geochemical variation, including isenthalpic AFC modelling using (p)MELTS, suggests that the picrites (olivine-rich cumulate suspensions) were interacting with granulite-facies metamorphic lower crust, the intermediate compositions with amphibolite-facies middle crust, and the rhyolitic dykes (and a few of the basalts) with the Pan-African granites of the upper crust. The calculated densities of the magmas fall systematically from picrite to rhyolite and suggest a magmatic system resembling a stack of sills throughout the crust beneath Spitzkoppe, with the storage and fractionation depth of each magma fraction controlled by its density. Elemental and isotopic features of the ~20 wt % MgO picrites (including Os isotopes) suggest that their parental melts probably originated by fusion of mid-ocean ridge basalt (MORB) source convecting mantle, followed by limited reaction with sub-continental lithospheric mantle metasomatized just prior to the formation of the parental magmas. Many of the distinctive features of large-volume picritic–basaltic magmas may not be derived from their ultimate mantle sources, but may instead be the results of complex polybaric fractional crystallization and multi-component crustal contamination.

KEY WORDS: flood basalts; Spitzkoppe; picrite; trace elements; hafnium isotopes; Etendeka


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 SPITZKOPPE DYKE SWARM
 PETROGRAPHY AND PICRITE...
 GEOCHEMISTRY
 DISCUSSION OF DYKE GEOCHEMISTRY
 FOCUS ON THE PICRITES
 IMPLICATIONS FOR ETENDEKA...
 SUMMARY
 SUPPLEMENTARY DATA
 APPENDIX
 REFERENCES
 
Attempts to understand the genesis and evolution of magmas can be subdivided into: (1) determining the physical and chemical conditions of magma genesis; (2) understanding the processes that have affected the magmas between their genesis and final solidification. Researchers interested in the first process are inclined to see the second one as little more than a nuisance, standing between them and their objectives. For this reason it is common for such students of magmas to focus on samples, techniques or datasets that appear to them to evade the ‘problem’ of post-genesis processes. The flood basalts of large igneous provinces (LIPs) in general, and the early Cretaceous Paraná–Etendeka province in particular, have been and remain favourite battlefields for differing views about the relative importance of the two processes. The many publications that attempt to discern the ultimate sources of these magmas are split between favouring either the sub-continental lithospheric mantle (SCLM) or the underlying convecting mantle, with or without a contribution from either delaminated SCLM or older subducted material. Recent examples of such studies are those by Peate (1997Go), Ewart et al. (1998aGo, 2004aGo), Gibson et al. (2000Go, 2005Go), Marsh et al. (2001Go), Thompson et al. (2001Go), Trumbull et al. (2004aGo) and Tuff et al. (2005Go).

All these studies acknowledge the probability that hot upwelling magmas will react with and absorb relatively fusible continental crust. Some studies attempt to make allowances for such crustal contamination, usually by comparing the predicted chemical effects of a likely crustal contaminant, such as the local granite basement, with geochemical trends observed in the magmatic suite. Most published studies assume a priori that any such crustal contamination takes place by a process of assimilation linked to the fractional crystallization of the melt (AFC), such that magmas become progressively more contaminated with falling liquidus temperature. Hence, they routinely reverse this reasoning and propose that the best shortcut to identifying magmas that have undergone little or no reaction with continental crust is to focus only on those with relatively high MgO contents, and hence high liquidus temperatures.

This is difficult to do in the Paraná–Etendeka province. For example, the compendium of data by Peate (1997Go) shows almost no Paraná lava analyses with >7 wt % MgO. Likewise, Marsh et al. (2001Go) and Ewart et al. (2004aGo) showed that relatively few Etendeka lavas—excluding the basal ferropicrites (Gibson et al., 2000Go)—have >9 wt % MgO. Even this higher MgO content falls far short of the lowest value calculated for melts to be in equilibrium with a peridotite mantle. Primary magmas do not fall below 13–14 wt % (Thompson et al., 2005Go) and rise to values above 20 wt % MgO. Therefore all arguments that the elemental and isotopic variations in ‘more Mg-rich’ Paraná–Etendeka lavas are inherited from their mantle sources and unaffected by subsequent polybaric fractional crystallization and concomitant crustal contamination (e.g. Erlank et al., 1984Go, and many subsequently) are, to some extent, acts of faith.

This study is concerned with a picrite–rhyolite suite of dykes exposed within the Etendeka igneous province, south of the lavas. They are approximately contemporaneous with the Etendeka extrusive rocks and often taken to be their hypabyssal equivalents (e.g. Marsh et al., 1997Go; Trumbull et al, 2004aGo). All but one of these dykes shows clear geochemical evidence, detailed below, of reaction between the melts and the local continental crust. The only possible exception is one dyke with ~20 wt % MgO. The AFC reactions involved at least three distinctive crustal rock-types, at upper-, middle- and lower-crustal depths. Clinopyroxene precipitated, deep in the crust, when MgO in these fractionating melts reached ~9 wt % MgO. The combined effects of this process and the crustal contamination strongly affected many inter-element ratios in the magmas (including some routinely used to classify Paraná–Etendeka magma types), together with isotopes of Sr, Nd, Hf and Pb. This confirms other recent studies, which showed that, even when dealing with Mg-rich basalts and picrites (e.g. Kent et al., 2002Go; Yaxley et al., 2004Go; Saal et al., 2005Go; Harlou et al., 2006Go; Zhang et al., 2006Go), post-genesis interactions between the upwelling melts and their surroundings are common.


    SPITZKOPPE DYKE SWARM
 TOP
 ABSTRACT
 INTRODUCTION
 SPITZKOPPE DYKE SWARM
 PETROGRAPHY AND PICRITE...
 GEOCHEMISTRY
 DISCUSSION OF DYKE GEOCHEMISTRY
 FOCUS ON THE PICRITES
 IMPLICATIONS FOR ETENDEKA...
 SUMMARY
 SUPPLEMENTARY DATA
 APPENDIX
 REFERENCES
 
The dyke swarm exposed in the Spitzkoppe area (Fig. 1) is part of the major Henties Bay–Outjo (HB–O) swarm (Lord et al., 1996Go; Trumbull et al., 2004aGo). The HB–O swarm mostly trends between NE–SW and NNE–SSW, and extends inland for at least 500 km from the continental margin. It forms part of the southern Etendeka Igneous Province (Marsh et al., 2001Go). Whereas most Etendeka lavas are preserved in a belt adjacent to the Atlantic coast, dyke swarms and intrusive sub-volcanic centres extend inland within the Late Proterozoic to Cambrian Damara orogenic belt, along the southern margin of the Congo craton (Fig. 1, inset). The Cretaceous extension and magmatism of this region is generally considered to be an integral part of the igneous event that produced the Paraná–Etendeka lavas, more deeply eroded than the coastal belt (e.g. Milner & le Roex, 1996Go; le Roex & Lanyon, 1998Go; Marsh et al., 1997Go, 2001Go; Wigand et al., 2003Go). Trumbull et al. (2004aGo, fig. 1) defined the HB–O swarm as ~70 km wide in the vicinity of Spitzkoppe. To the NW there is a relatively narrow (~25 km) dyke-poor zone before reaching the dense parallel dyke swarm between the Cretaceous Brandberg and Messum intrusive complexes (Thompson et al., 2001Go). For most of its length the HB–O dyke swarm is emplaced in metamorphic rocks—mica schists, migmatites, calc-silicates and marbles—and granites (sensu lato) of the Pan-African Damara belt but, north of Outjo, it enters the Archaean–Proterozoic Congo Craton (Fig. 1, inset).


Figure 1
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Fig. 1. Sketch map of the area around Spitzkoppe, western Namibia. Geology simplified after Geological Survey of Namibia (1997Go) and Frindt et al. (2004bGo). Areas of surficial cover (mostly pediment gravels and dune sands) are omitted, notable south of Klein Spitzkoppe. Numbered filled squares mark sampled dykes (apart from VB12 basement granite). Average trend of most sampled dykes is NNE. All sample numbers have the prefix VB. The Black Range picrite dyke forms a prominent topographic ridge SSW of sample VB32. Inset shows the location of the Henties Bay–Outjo (HB–O) dyke swarm, stippled, and some of the main early Cretaceous Etendeka intrusive complexes. M, Messum; B, Brandberg; OY, Okenyenya.

 
At first sight the possible maximum age of the HB–O dykes is only constrained geologically to be post-Damara, whereas their minimum age is constrained by the radiometric dates of the Cretaceous plutonic complexes that intersect them (Fig. 1, inset). Dykes of the Jurassic Karoo igneous province do not occur in central and NW Namibia. The closest Karoo dykes are at the NW extremity of the 179 Ma (Ar–Ar dates) Okavango giant dyke swarm, which terminates in NE Namibia—about 750 km NE of Spitzkoppe—and trends at a right angle to the HB–O swarm (Le Galle et al., 2002Go). Trumbull et al. (2004aGo) discussed the age of the HB–O dykes in detail and noted that their only published radiometric dates were obtained using the K–Ar method and mostly fall in the range 116–143 Ma. All the HB–O dyke samples chemically analysed to date form a single coherent tholeiitic picrite–rhyolite suite (Marsh et al., 1997Go; Trumbull et al., 2004aGo; this paper). The picrite–intermediate compositions also occur in the abundant dykes SW of Brandberg and in the Huab and Horingbaai areas (Fig. 1, inset), where they intersect 133 Ma southern Etendeka basal lavas. Both they and the lavas are transected by the 131 Ma Brandberg intrusive complex (Thompson et al., 2001Go). Immediately NE of Spitzkoppe the HB–O dykes are transected by the large Erongo central volcanic and intrusive complex (Fig. 1, inset), dated at 133–130 Ma (with errors ±0·8–1·9 Ma) by Wigand et al. (2003Go) using both Ar–Ar biotite and U–Pb zircon methods.

The Spitzkoppe swarm dykes cut Damara basement in the relatively flat surroundings of the prominent peaks formed by the Gross and Klein Spitzkoppe granite stocks (Fig. 1). They vary in width from 1 m to 10 m and their trends range from 10° to 90°, with most falling between 30° and 50°. Two of the picrites (VB19 and 32) occur as dykes between 20 m and >30 m thick; both form prominent topographic ridges.

Frindt et al. (2004aGo) and Trumbull et al. (2004bGo) both noted that felsic dykes are more common around Spitzkoppe than elsewhere in the HB–O swarm, although they have the same trends as their mafic neighbours. On a regional scale, the Spitzkoppe granites appear to transect all the dykes and thus post-date them. Nevertheless, Frindt et al. (2004aGo) have shown that several of the mafic regional dykes penetrate the marginal granite. Within the granite, the mafic dykes have irregular margins and are cut by late-stage granitic veins. One mafic dyke also locally forms a zone of pillow-like enclaves within the granite. The chilled cuspate margins of the enclaves are typical of liquid–liquid magmatic contacts elsewhere and leave no doubt that the basic and acid melts coexisted (Frindt et al. 2004aGo; S. Frindt, personal communication, 2005). The whole-rock Rb–Sr isochron age of the Gross Spitzkoppe stock is 124·6 Ma ± 1·1 Ma (MSWD = 2·5), with initial 87Sr/86Sr = 0·7134 (Frindt et al., 2004bGo) but this may be lower than the true emplacement and original cooling age, as a result of subsequent hydrothermal redistribution of Rb (S. Frindt, personal communication, 2005). A clear example of this hydrothermal redistribution of Rb in a pluton is the Beinn an Dubhaich granite, Skye, NW Scotland. Dickin (1980) obtained an Rb–Sr whole-rock isochron age for this pluton of 53·5 ± 0·8 Ma (2SD), whereas its zircon U–Pb age (M. A. Hamilton, D. G. Pearson & R. N. Thompson, unpublished data) is 55·89 ± 0·15 Ma (2SD). It therefore remains uncertain whether the Spitzkoppe dyke swarm was emplaced at ~125 Ma or a few million years earlier, such as the ~132 Ma date for similar mafic dykes in the Brandberg, Huab and Horingbaai areas to the north and the nearby Erongo complex (Wigand et al., 2003Go). The weight of evidence regionally clearly favours the 132 Ma date.


    PETROGRAPHY AND PICRITE MINERALOGY
 TOP
 ABSTRACT
 INTRODUCTION
 SPITZKOPPE DYKE SWARM
 PETROGRAPHY AND PICRITE...
 GEOCHEMISTRY
 DISCUSSION OF DYKE GEOCHEMISTRY
 FOCUS ON THE PICRITES
 IMPLICATIONS FOR ETENDEKA...
 SUMMARY
 SUPPLEMENTARY DATA
 APPENDIX
 REFERENCES
 
The thick picrite dykes are coarse and gabbroic. Their abundant olivines enclose only small chromites, whereas the plagioclase and clinopyroxene are intergrown. Small orthopyroxenes are scattered around the margins of the olivines and there are traces of interstitial biotite. Basalt dykes are finer grained and either aphyric (intergrown olivine, plagioclase and clinopyroxene) or contain small olivine phenocrysts. Intermediate dykes (5·4–1·7 wt % MgO) have sparse plagioclase phenocrysts; some euhedral and others rounded. Early pigeonite has been identified optically in VB8. The groundmass becomes progressively finer grained until it is devitrified glass in the felsic dykes. The dominant phenocrysts in the felsic dykes are quartz and turbid sericitized feldspar. Clinopyroxene phenocrysts are extremely scarce (two out of 32 samples). The picrites are almost devoid of visible low-temperature alteration but reaction of ferromagnesian minerals to chlorite ranges from ~10% to >80% in some of the less Mg-rich dykes. Our geochemical tests of the effects of this alteration are described below.

Picrite mineral compositions
Samples from two thick picrite dykes were studied by electron probe microanalysis at Manchester University [see Thompson et al. (2005Go) for method].

Olivine
Representative olivine analyses are given in Table 1. Figure 2 shows individual microprobe analyses as functions of the Mg-number of the host dyke. Rock Mg-number was calculated with 10% of total Fe as Fe3+ (Thompson & Gibson, 2000Go). Two values of Kd for the distribution of Fe2+ and Mg between olivine and melt are plotted: 0·30 is appropriate for equilibria between picrites and their olivines at 1 atm, whereas 0·31 applies at 0·5 GPa pressure (Ulmer, 1989Go). Garcia et al. (1995Go) and Garcia (1996Go) showed how some Hawaiian basalts and picrites from Mauna Loa and Mauna Kea are in equilibrium with their olivines, whereas others are best explained as cumulates because their olivines plot to the right of the equilibrium Kd (i.e. the bulk composition is more magnesian than would be appropriate to precipitate the olivines it contains). Using this reasoning, the olivine phenocrysts in both VB18 and 32 are clearly accumulative. The Spitzkoppe picrites therefore appear to be suspensions of olivine phenocrysts in basaltic liquids, rather than originally picritic melts. Olivines from the nearby (~100 km to the north) Horingbaai suite are also plotted in Fig. 2 for comparison (Thompson et al., 2001Go). An obvious difference between the two suites is the lack of very magnesian olivine macrocrysts in the two Spitzkoppe picrites studied. Of course, the possibility of some post-crystallization re-equilibration of these olivines in the thick dykes cannot be ruled out but, if this has not happened, then the VB32 olivines must have been precipitated from a melt with Mg-number ~60 and the VB18 olivines from an even more Fe-rich melt.


Figure 2
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Fig. 2. Mg-number of olivine phenocrysts in two Spitzkoppe picrites (VB18 and 32) vs Mg-number of the rocks containing them. Individual olivine analyses are shown as short horizontal bars. Similar data from contemporaneous Horingbaai dykes in the Brandberg–Huab area (Fig. 1, inset) are summarized as grey vertical bars, for comparison (Thompson et al., 2001Go). Given Kd values of 0·30–0·31 for Fe2+–Mg partitioning at equilibrium between basic melts and olivine (Ulmer, 1989Go), the phenocrysts in VB18 and 32 must be accumulative (see text).

 

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Table 1: Representative electron microprobe mineral analyses in Spitzkoppe picrite dykes

 
Chromite
Euhedral chromites up to a few millimetres in size occur within the olivines in both picrites. Representative analyses are given in Table 1. Cr2O3 varies between about 6 and 26 wt %, and Al2O3 between 2·7 and 6·0 wt % in both samples but a few points show Al2O3 values up to 15 wt %.

Clinopyroxene
This phase is clearly late-crystallizing in the picrites as it tends towards large poikilocrysts, enclosing both olivines and plagioclases. Typical analyses are given in Table 1.

Orthopyroxene
This mineral forms small subhedra, mostly close to the margins of olivines, and larger poikilitic crystals. Two analyses are given in Table 1.

Biotite
Small interstitial crystals of biotite are visible in trace quantities within both picrites, especially VB32, and an analysis is given in Table 1. Without analysis for fluorine, it cannot be certain that this biotite is necessarily hydrous and therefore indicative of a wet magma (see below).

Alkali feldspar
Element maps show that alkali feldspar also occurs interstitially in VB32.


    GEOCHEMISTRY
 TOP
 ABSTRACT
 INTRODUCTION
 SPITZKOPPE DYKE SWARM
 PETROGRAPHY AND PICRITE...
 GEOCHEMISTRY
 DISCUSSION OF DYKE GEOCHEMISTRY
 FOCUS ON THE PICRITES
 IMPLICATIONS FOR ETENDEKA...
 SUMMARY
 SUPPLEMENTARY DATA
 APPENDIX
 REFERENCES
 
Methods
Analytical methods are described in Electronic Appendix A, available for downloading at http://www.petrology.oxfordjournals.org.

Results
Element and oxide variation
The analyses (Table 2) show wide ranges of MgO (20·1–0·1 wt %) and SiO2 (46·0–68·2 wt %). Additionally, five acid dykes from around the Gross Spitzkoppe granite stock, analysed by Frindt et al. (2004aGo) are plotted in the following diagrams where appropriate. Samples with >12 wt % MgO are called picrites in this paper (Le Bas, 2000Go). On a plot of (Na2O + K2O) vs SiO2 (TAS; Le Maitre, 2002Go) the new analyses plot along the same trend as published data for the HB–O swarm dykes (Trumbull et al., 2004aGo, fig. 3), through the fields basalt, andesite, dacite and rhyolite but adjacent to the boundary with the basalt–trachyte suite.


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Table 2: Whole-rock analyses of dykes from the Spitzkoppe swarm and Damara Belt crustal rock-types

 
A plot of selected oxides (wt %) and trace elements (ppm) vs MgO (Fig. 3) in the Spitzkoppe picrite–rhyolite dykes shows that both Cr and Ni fall progressively with MgO. Although the variations of SiO2, Cr and Ni with MgO are smooth curves in Fig. 3, the behaviour of the other major oxides and Sc in this diagram is more complex. Trend lines have been drawn (by eye) to illustrate qualitatively the extent to which each plot is described by an inflected trend, such as may occur during fractional crystallization of melts by the addition of a new mineral to the separating phases. Such inflected trend-lines describe the behaviour of CaO, Al2O3 and Sc well (Fig. 3). In the Fe2O3, TiO2 and P2O5 plots there is a handful of points lying far above the trends fitting the other data. Thin sections of the samples showing these relatively high Fe2O3, TiO2 and P2O5 values have visible populations of titanomagnetite and apatite microphenocrysts that may be accumulative.


Figure 3
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Fig. 3. Variations of selected oxides and Sc in the Spitzkoppe dykes as functions of MgO. {blacksquare}, Spitzkoppe picrite–rhyolite dykes (Table 2); {square}, Spitzkoppe acid dykes (Frindt et al, 2004aGo). Separate symbols (• and {triangleup}) are used for all the dykes in the Cr–Ni plot, for clarity. Trend lines are drawn by eye. High- and low-Ti Etendeka lava fields from Marsh et al. (2001Go).

 
The trend inflections for Fe2O3 and TiO2 in Fig. 3 correspond approximately to the appearance of titanomagnetite in thin sections, as MgO falls to ~3·5 wt %. Likewise, the inflection of the P2O5 trend at ~3·0 wt % MgO marks the appearance of apatite microphenocrysts. The inflection at ~6·5 wt % MgO in the Al2O3 plot corresponds to the appearance of plagioclase as a phenocryst. In contrast, the inflections at ~9·0 wt % MgO in the CaO and Sc trends do not correspond to the first appearance as phenocrysts of any mineral, such as Ca-rich clinopyroxene, that might remove these two elements together from a melt. The only visible phenocryst in dykes with MgO contents on both sides of this inflection is olivine (sometimes with chromite inclusions), a mineral poor in both Ca and Sc. Clinopyroxene is conspicuously absent as phenocrysts in the Spitzkoppe basic and intermediate dykes.

The two fields drawn on the TiO2–MgO plot (Fig. 3) encompass >1000 analyses of lavas and hypabyssal intrusions from throughout the Etendeka Igneous Province (Marsh et al., 2001Go), showing how they divide into low-Ti and high-Ti magmatic suites. Between these fields a group of 12 analyses has been omitted for clarity. These are the Tafelkop basalts of Marsh et al. (2001Go), known by others as ‘LTZ.H’ (Ewart et al., 1998aGo) or ferropicrites–basalts (Gibson et al., 2000Go). It should be noted that, although the two fields in Fig. 3 and their subdivisions were described as mafic by Marsh et al. (2001Go), and most of the subdivisions are formally named ‘basalts’, the analyses defining the two fields include compositions with MgO as low as 3 wt %. The Spitzkoppe dykes clearly form part of the Etendeka low-Ti suite.

The array of patterns produced by rare earth element (REE) variation in the Spitzkoppe dykes (Fig. 4) is qualitatively concordant with the data on Fig. 3. The progressive increase in all the REE, except Eu, from picrites to rhyolites is consistent with a fractional crystallization process creating this magma suite. Apart from aphyric basalts VB20 (no Eu anomaly) and VB24 (small positive Eu anomaly), all the samples have negative Eu anomalies. These are approximately constant throughout dykes that lack plagioclase phenocrysts and increase in plagioclase-phyric intermediate and acid dykes (see Fig. 14 below).


Figure 4
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Fig. 4. Chondrite-normalized rare earth elements in the Spitzkoppe dyke samples.

 
Isotopes
The radiogenic isotopic ratios of the Spitzkoppe dykes show large variations (Tables 3 and 4) and these rule out the possibility that their range of elemental compositions could be due to closed-system fractional crystallization of a basic magma. The isotopic ratios are corrected to an emplacement age of 132 Ma, for reasons explained above.


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Table 3: Sr, Nd, Hf and Pb isotopes in Spitzkoppe dykes and Damara Belt crustal rock-types

 

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Table 4: Osmium isotopes in olivine phenocrysts of Spitzkoppe picrites

 
Tests for effects of low-temperature alteration and very small-scale sample isotopic heterogeneity. The isotope data for dykes in Table 3 can be used to test the effects of low-temperature hydrothermal alteration because samples analysed at McMaster were all first leached in acid whereas those analysed at Durham were not. Eight dyke samples were analysed for Pb isotopes in both laboratories. Excluding the rhyolite sample VB30, the R2 value for the regression between the two sets of 206Pb/204Pb data (the ratio with the largest range of values) is 0·999. Rhyolite VB30 falls slightly off this regression (R2 drops to 0·994) and this may be due to the turbid hydrothermal alteration of its predominant alkali feldspar.

There are small significant differences between 87Sr/86Sr for the McMaster and Durham analyses of picrites VB18 and 32. Although these could be alteration related, they are not both in the same direction. There is also a significant difference between the results of the two laboratories for 143Nd/144Nd in VB18, discussed in detail in Electronic Appendix A. It is generally accepted that the latter are unlikely to be related to the slight alteration of this sample. These data suggest small-scale isotopic variability within the picrites—as might be expected from the crustal assimilation model to be developed below. Although lava samples are usually isotopically homogeneous at the hand-specimen level, it is becoming clear that this homogeneity is illusory, in that glass inclusions within the olivine phenocrysts of some crustally contaminated continental picrites are extremely heterogeneous in both elements and isotopes (e.g. Yaxley et al., 2004Go; Harlou et al., 2006Go). Such inhomogeneity should logically eventually be expected to occur between aliquots from a powdered individual olivine-phyric hand specimen, and samples VB18 and 32 appear confirm this point. Clearly, this matter requires more research.

Sr, Nd and Hf isotopes. On a plot of 87Sr/86Sr vs {varepsilon}Nd (Fig. 5) the picrite–intermediate dykes form a steep continuous array. The picrites have {varepsilon}Nd values just above and just below zero, within the field of ocean island basalts (OIB), whereas {varepsilon}Nd values for the intermediate and rhyolite dykes fall in the range from –5 to –10. New analyses of crustal rocks comprise: Damara granite VB12, which crops out within the dyke swarm [Frindt et al. (2004bGo) analysed another Damara granite sample, SF17, ~1·5 km SE of VB12, Fig. 1]; Damara granite (VB38) and associated aplite (VB39) and pegmatite alkali feldspar (VB37), which crop in the Horingbaai mafic dyke swarm, south of the Brandberg intrusive complex (Thompson et al., 2001Go); Damara phyllite (VB41) and metasedimentary schist (VB42) between the Brandberg and Huab areas (Fig. 1). Some of these crustal rocks tend to enlarge the Sr–Nd isotopic fields for Damara granites and metasediments plotted by Frindt et al. (2004bGo). A mixing curve between picrite dyke VB32 (highest {varepsilon}Nd) and the local Damara granite (VB12/SF17) does not pass through the dyke data. The field for pre-Damara basement in the Spitzkoppe area is speculative and follows the suggestion of Frindt et al. (2004bGo) and others that the Damara belt may be underlain by the same Archaean–Proterozoic gneisses as form the Congo–Angola craton in Kaokoland, NW Namibia (Seth et al., 1998Go). If this is so, such a deep-crust basement would form a suitable crustal end-member for a mixing curve passing through the picrite and basalt dyke data in Fig. 5. Tangible isotopic evidence for a deep-crust basement of this composition is provided by rhyolites from the Cretaceous Paresis sub-volcanic complex, NE of Spitzkoppe (Fig. 1, inset), which have Sr–Nd isotopic ratios (Fig. 5) very similar to those of the Kaokoland gneisses (Mingram et al., 2000Go). In this paper we use Paresis rhyolite PA19 (Mingram et al., 2000Go) as a geochemical proxy for partial melts of acid–intermediate lower crust in the Damara region. This is obviously less satisfactory than having lower crust samples available.


Figure 5
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Fig. 5. Initial 87Sr/86Sr and {varepsilon}Nd in the Spitzkoppe dykes and Damara belt granites and metasediments (at 132 Ma). VB data points from Table 2; SF data points from Frindt et al. (2004aGo). Fields for southern Etendeka lavas and dykes from Thompson et al. (2001Go), Goboboseb quartz latites (GL) after Ewart et al. (1998bGo), and Paresis rhyolites from Mingram et al. (2000Go). LTZ is ‘Low Ti-Zr’ (Ewart et al., 1998aGo). Other fields modified after Frindt et al. (2004bGo). [See text for sources of the mafic potassic dykes (stars in filled circles).] Dashed line is a bulk-mixing curve between picrite VB32 and Damara granite VB12. Details are given in the text of the ticked continuous lines showing modelled AFC processes (using pMELTS) for a model picrite with MgO ~15 wt % and crustal acid rocks PA19 (Paresis rhyolite; Mingram et al., 2000Go) and VB12 (Table 2). The model adds 1 g of crust per increment to 100 g of initial picrite and then calculates the outcome isenthalpically.

 
Table 3 and Fig. 6 show the first Hf-isotope data published for both Etendeka igneous rocks and Damara belt crustal rocks. The dyke data show covariation of {varepsilon}Nd and {varepsilon}Hf, such that the picrites and basalts fall in the OIB field whereas the intermediate and rhyolite dykes have similar Nd–Hf isotope ratios to the local Damara belt exposed crust. The MgO content of each Spitzkoppe dyke is marked in Fig. 6, so that the overall correlation between MgO and Nd–Hf isotopic ratios in the dykes can be seen.


Figure 6
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Fig. 6. {varepsilon}Nd and {varepsilon}Hf in the Spitzkoppe dykes and Damara belt granites and metasediments (at 132 Ma). Symbols and data sources as in Fig. 5. Mantle array and fields for MORB and OIB from Nowell et al. (1998Go), Chauvel & Blichert-Toft (2001Go), Graham et al. (2006Go) and references therein. Dashed vectors indicate the field of ancient sub-continental lithospheric mantle (SCLM) peridotites (Pearson et al., 2003Go).

 
Pb isotopes. When it became clear that Pb isotope variation in the Spitzkoppe dyke swarm is complex, we analysed sample sets at both Durham and McMaster, so as to maximize the data and also to provide interlaboratory cross-checks (Table 3). At first sight, Pb isotopes in the Spitzkoppe dykes (Table 3) behave in much the same way as their Sr–Nd–Hf isotopes, in that the picrites and Mg-rich basalts form a linear array, with a good correlation between Pb isotopes and MgO in the 20–9 wt % range (Fig. 7). However, the rhyolite dyke VB30, and also dyke SF11d of Frindt et al. (2004bGo) show a major difference. Instead of continuing the trend of the mafic dykes to lower 206Pb/204Pb ratios, they have relatively high 206Pb/204Pb and 208Pb/204Pb ratios and thus, in terms of Pb isotopes, appear to be unrelated to the picrites and basalts. The Mg-poor basalts and intermediate dykes (MgO ~8–3 wt %) divide between these Pb isotopic groups; the majority have relatively low 206Pb/204Pb, combined with slightly higher 208Pb/204Pb than the Mg-rich basalts (Fig. 7), but two Mg-poor basalts, VB14 and 16, cluster with the rhyolite dykes in terms of their Pb isotopes. The field for Damara S-type granites (Frindt et al., 2004bGo) must be enlarged slightly to incorporate our new Pb-isotope data for these rock-types (Table 3 and Fig. 7) and the Spitzkoppe rhyolite dykes plot within the enlarged fields. They also lie close to the Gross Spitzkoppe granite field (Frindt et al., 2004bGo). The field for southern Etendeka LTZ lavas and dykes incorporates data for so-called continental flood basalt (CFB)-like dykes in the nearby Brandberg area (Thompson et al., 2001Go; Fig. 1, inset). This field has been redefined in Fig. 7 by reanalysis of key samples (Table 3). After such standardization, it becomes clear in Fig. 7 that the elongation of this field is collinear with Pb isotopic variation in the Spitzkoppe picrites and Mg-rich basalts. The most Mg-rich Spitzkoppe picrites have 206Pb/204Pb >19·0, which is higher than values of this ratio in both Tristan da Cunha and Walvis Ridge lavas, and also in previously studied Damaraland Cretaceous picrite–basalt dykes (Thompson et al., 2001Go; Gibson et al., 2005Go).


Figure 7
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Fig. 7. Initial 206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb in Spitzkoppe dykes and Damara belt granites and metasediments (at 132 Ma). Symbols and data sources as in Fig. 5. The dotted lines show trends in Pb isotopic ratios in the dykes. Polygonal fields are from Thompson et al. (2001Go), Ewart et al. (2004aGo) and Frindt et al. (2004bGo). Average Damara belt metasediments from McDermott & Hawkesworth (1990Go). GSG, Gross Spitzkoppe granite; GL, Goboboseb quartz latites. Northern Hemisphere Reference Line (NHRL) from Hart (1984Go). Vectors illustrate the 132 Ma correction for different values of µ and {kappa}.

 
Os isotopes. Osmium isotopes were determined on separated olivine phenocrysts from picrites VB18 and 32, to see whether this early crystallizing phase might have trapped oxides or sulphides before the magmas were exposed to crustal contamination. The separates were made by hand-picking, with fragments containing opaque inclusions left in the separate, rather than removed. Using an emplacement age of 132 Ma, the initial 187Os/188Os ratios of the picrite olivines (Table 4) are 0·126248 (VB32) and 0·124262 (VB18). The significance of these results will be discussed below in the section ‘Focus on the picrites’.


    DISCUSSION OF DYKE GEOCHEMISTRY
 TOP
 ABSTRACT
 INTRODUCTION
 SPITZKOPPE DYKE SWARM
 PETROGRAPHY AND PICRITE...
 GEOCHEMISTRY
 DISCUSSION OF DYKE GEOCHEMISTRY
 FOCUS ON THE PICRITES
 IMPLICATIONS FOR ETENDEKA...
 SUMMARY
 SUPPLEMENTARY DATA
 APPENDIX
 REFERENCES
 
Open-system fractional crystallization but at what depth?
The element and oxide data summarized in Figs 3 and 4 make a strong qualitative case for fractional crystallization as the mechanism that produced the wide range of rock-types in the Spitzkoppe dykes, and the isotopic data suggest that this was an open-system (AFC) process. The composition of the parental magma is difficult to determine. All the most Mg-rich dykes in the suite are rich in olivine phenocrysts. Electron probe microanalyses of these in two of the picrites (Fig. 2) has shown that this olivine is not unusually forsteritic and therefore the high MgO of the rocks is clearly due to olivine accumulation. The most direct way to identify a likely parental composition is therefore to focus on the aphyric dyke with the highest MgO content. This is VB26 (Table 2), with 11·1% MgO.

Judging from Fig. 3, such a parental melt would have accumulated olivine phenocrysts to form the picrite suite and then evolved to the basalts, intermediate compositions and rhyolites by fractional crystallization of the following assemblages: olivine alone; ol + cpx; ol + cpx + plag; plag + cpx (ol disappears from thin sections at 5·0–5·5 wt % MgO); plag + cpx + Fe–Ti oxide; plag + cpx + oxide + apatite. The main phenocrysts observed in the rhyolites are alkali feldspar and quartz. This chemistry-based story of fractional crystallization is complicated by two items of evidence: (1) all the basalts that appear, from geochemical considerations, to have fractionated Ca-rich clinopyroxene lack phenocrysts of this mineral; (2) Sr, Nd, Hf and Pb isotope variation in the suite all imply that the fractional crystallization was open-system, with concomitant dissolution of crust in the melts.

The relative stabilities of olivine and Ca-rich clinopyroxene crystallizing from a basaltic magma are very sensitive to pressure. The most direct way to show this is by using experimental melting studies of rocks to determine the crystallization behaviour of a basic–intermediate magmatic suite as a function of pressure. After noting the ‘cryptic clinopyroxene fractionation’ phenomenon during 1 atm phase-equilibria studies of basic and associated lavas (Thompson, 1972Go), Thompson (1974Go) studied the Palaeocene alkali olivine basalts and hawaiites of Skye, NW Scotland, using polybaric experimental phase equilibria and showed that they had undergone extensive ‘cryptic’ fractionation of Ca-rich clinopyroxene (aluminous sub-calcic augite in that case) at pressures around 0·9 GPa, despite the lavas being almost devoid of augite phenocrysts in thin section. The effect of pressure on the relative stabilities of liquidus olivine and Ca-rich clinopyroxene in basaltic melts and their fractionation residua can be seen clearly in a plot of CIPW-normative ol–di–hy–ne-Q (Fig. 8). Although this projection ignores plagioclase, it is useful for illustrating the crystallization behaviour of olivine tholeiite suites such as the Spitzkoppe dykes. Parts of several cotectics are marked in Fig. 8a. They are all for the equilibrium assemblage (ol + plag + cpx + basaltic melt). The 1 atm curve was compiled by Thompson et al. (2001Go) from several sources. The 0·9 GPa curve was constructed by Thompson (1982Go) from the results of experimental melting PT studies on olivine tholeiites, alkali basalts and hawaiites that precipitated ol, plag and cpx cotectically on their liquidi at ~0·9 GPa. The 0·2 and 0·8 GPa curves are from melting experiments on mid-ocean ridge basalt (MORB) by Grove et al. (1992Go), analysing progressive residual liquids. The 0·7 GPa curve is for experimental fractional crystallization of a tholeiite (Villiger et al., 2007Go). A single point, marked M in Fig. 8a, is available for a Columbia River Plateau basalt (Martindale, from Helz, 1980Go) that shows experimental cotectic liquidus precipitation of ol + plag + cpx at 0·35 GPa, a mid-crust pressure.


Figure 8
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Fig. 8. CIPW normative diopside, olivine, hypersthene, nepheline and quartz in Spitzkoppe dyke samples and comparisons. All data are calculated with 10% of total iron as Fe2O3. (Thompson & Gibson, 2000Go). Cotectics at 1 atm, 0·2, 0·7, 0·8 and 0·9 GPa for the equilibrium [ol + plag + cpx + basaltic liquid] are from Thompson (1982Go), Grove et al. (1992Go), Villiger et al. (2007Go) and the data of Sack et al. (1987); arrows mark directions of falling temperature. The continuous-line 1 atm cotectic is the best fit to the experimental data; all of the latter fall between the dashed lines. The pMELTS cotectic for AFC involving Damara granite VB12 (see text) is from pMELTS modelling in this paper. (a) Spitzkoppe dykes (MgO >3·0 wt %) and southern Etendeka Tafelberg lavas and LTZ-L lavas and dykes (Erlank et al., 1984Go; Ewart et al., 1998aGo; Thompson et al., 2001Go). MgO contents are marked beside dyke points. (b) Horingbaai dykes (Thompson et al., 2001Go). MgO contents are marked beside most points.

 
All of these cotectics show consistent migration away from the Cpx apex of Fig. 8a with rising pressure. This means that a fractionating olivine tholeiite magmatic system could undergo cotectic separation of olivine and clinopyroxene in the deep crust, but any remaining clinopyroxene phenocrysts might redissolve during the subsequent uprise of the melts, so that chemical study of the suite would indicate ‘cryptic’ clinopyroxene fractionation. Thompson (1987Go) showed how the olivine tholeiite lavas of Kilauea, Hawaii, behave on this diagram just as would be expected for a magmatic suite fractionating within the upper crust, and therefore controlled by the 1 atm cotectic. Likewise, the ~132 Ma Horingbaai dyke swarms, immediately NW of Spitzkoppe (Thompson et al., 2001Go) conform closely on this diagram (Fig. 8b) to the expected behaviour of olivine tholeiite magmas fractionating within the upper crust. In contrast, the Spitzkoppe dykes behave very differently (Fig. 8a). Picrites and basalts with >9 wt % MgO form a fan-shaped array, as would be appropriate for compositions controlled by accumulation or removal of olivine. The trend for dykes with lower MgO contents is scattered. Although MgO generally falls as the Spitzkoppe dyke compositions migrate towards the Qz apex of the diagram, this relationship is not a close one. The non-picritic dyke analyses give the overall impression in Fig. 8a that they lie scattered along a cotectic (or bundle of cotectics) at similar depths to, or perhaps a little deeper than, the one at 0·35 GPa (~14 km depth) marked by the Martindale basalt liquidus phase equilibria (Helz, 1980Go). This places the likely site or sites for the evolution of the Spitzkoppe dykes within the lower crust. Furthermore, they appear to have evolved at depths less than the ~30–35 km of the Moho in this area (Green, 1983Go; Miller, 1983Go; Gladczenco et al., 1997Go; Bauer et al., 2000Go) because the compositions do not trend towards alkalic residua, as has been shown experimentally to occur at 0·8–0·9 GPa (Thompson, 1982Go; Grove et al., 1992Go). Although some of the natural cotectics for Spitzkoppe dykes seem to be further from the Cpx apex of Fig. 8a than predicted by the closed-system fractional crystallization experimental results of Villiger et al. (2007Go), modelling using pMELTS indicates that this phenomenon appears to be caused by AFC processes involving granitic (sensu lato) crust (Fig. 8b and see below). The lavas of the Snake River Plain, Idaho, behave in the same way (Thompson et al., 1983Go, fig. 1b).

When the radiogenic isotope data are viewed in this light, the trends of the Spitzkoppe dyke analyses in Figs 5–7GoGo can be interpreted with more confidence. Relatively low 143Nd/144Nd (negative {varepsilon}Nd), 87Sr/86Sr and 206Pb/204Pb are all characteristic of the high-grade metamorphic rocks that are thought to form the lower half of most continental crust (Moorbath et al., 1975Go; Dickin, 1981Go; Scherer et al., 1997Go; Rudnick & Gao, 2003Go; Dickin, 2005Go). The trends for picrite and some of the basalt data in Figs 5 and 7 are therefore clearly compatible with AFC processes at lower-crust depths in the Spitzkoppe dyke suite, as will be discussed further below.

Rhyolite melt evolution in the upper crust?
When their elemental compositions alone are considered, the rhyolite dykes in the Spitzkoppe swarm appear to be part of the same magmatic suite as their picrite–intermediate companions (Figs 3 and 4). The plot of Nd–Hf isotope ratios shows the same relationship (Fig. 6) but the situation becomes subtly different when Sr isotopes are considered. The rhyolite dykes [Table 3 and Frindt et al. (2004bGo)] have considerably higher 87Sr/86Sr ratios (Fig. 5) than can be fitted by any plausible mixing curve passing through the data for the picritic–basalt dykes. Instead, the rhyolite dykes have 87Sr/86Sr ratios in the same range as the metasediments and extensive S-type granites of the Damara belt (McDermott et al., 1989Go, 1996Go; McDermott & Hawkesworth, 1990Go; Jung et al., 2003Go), the regional rock-types into which they are emplaced. Lead isotopes (Fig. 7) show a subtly different relationship. Both the rhyolitic and two of the accompanying Mg-poor basaltic dykes lie within the compositional fields of the Damara S-type granites and metasediments. Figures 5 and 7 also show how relatively high 87Sr/86Sr and 208Pb/204Pb separate the Spitzkoppe rhyolite dyke compositions from those of the granites in the penecontemporaneous Gross Spitzkoppe stock, around which they are emplaced. The simplest way to interpret these isotopic relationships is to deduce that the picritic–magnesian basalt magmas of the Spitzkoppe swarm evolved within the lower or middle crust and the rhyolite melts developed by extreme AFC at upper-crust levels. Nevertheless, localized wholesale upper-crustal melting cannot be ruled out. The Mg-poor and intermediate dyke magmas followed a complicated series of individual paths through the sub-Spitzkoppe continental crust.

Modelling the fractional crystallization
Open-system fractional crystallization in the Spitzkoppe magma system can be confirmed by means of modelling calculations using MELTS, pMELTS and Adiabat_1ph (Smith & Asimow, 2005Go), as detailed in the Appendix. Apart from traces of interstitial biotite (Table 1) in the thickest picrite dykes—with the volatiles probably inherited from traces of hydrous minerals in the SCLM (see below)—the mineralogy of all the Spitzkoppe dykes is anhydrous. The only exception is a trace of interstitial blue–green amphibole in rhyolite VB30. It therefore seems a reasonable approximation to treat the Spitzkoppe magma system as anhydrous until further research clarifies its water content.

Method. All the picrite dykes are olivine-phyric and limited microprobe study suggests that the olivine is accumulative (Fig. 2). Attempts to model fractional crystallization using the original version of MELTS, however, predicted extensive liquidus orthopyroxene. It is known (Table 1) that at least picrites VB18 and 32 contain small amounts of interstitial orthopyroxene; their bulk compositions are thus not far from saturation with this phase. The original MELTS algorithm overestimated the relative stability of orthopyroxene compared with olivine (Hirschmann et al., 1998Go) and it is perhaps unsurprising that this systematic bias is enough to stabilize the ‘wrong’ phase. Although it is intended for calculations at >1 GPa, and for peridotite compositions only, pMELTS sometimes captures the behaviour of MgO-rich basaltic melts (sensu lato) more closely than MELTS (e.g. Smith et al., 2003Go). Hence, we repeated the calculations using pMELTS, which gave olivine as the liquidus phase. We stress that because (with the exception of the 1 GPa result) the calculated trends lie outside the calibrated range of the pMELTS model, the quantitative results should be taken with some caution.

The most MgO-rich aphyric dyke sample in this suite is VB26 (11· 09 wt % MgO) although, as discussed in the ‘Focus on the picrites’ section below, the real parental melts at Spitzkoppe may have had as much as 15–20 wt % MgO. The usual way in which algorithms such as (p)MELTS are employed to model fractional crystallization is to select a putative parental composition from the samples in the magmatic suite, such as VB26, and then to use the software to predict how this might undergo fractional crystallization, or AFC if required, under various PT regimes. This approach means that elemental abundances in the calculated evolving melt are forced to be the observed values and any mismatch between parameterized and actual phase compositions must be taken up by the solid phases only, which sometimes causes the predicted melt to evolve to extreme compositions. In contrast, when (p)MELTS is used for melting calculations, the bulk composition is imposed and any mismatches between actual and predicted phase compositions are distributed over all the phases present. Consequently, rather than using the natural dyke chemical analysis of VB26 as the starting composition for fractional crystallization modelling, it was preferable to use pMELTS to generate a picrite ‘model parental melt’, which (according to pMELTS) could then fractionate olivine alone until it closely resembled VB26.

Extensive trial-and-error mantle fusion calculations with pMELTS produced a suitable ‘model primary melt’. This aggregated fractional melt, with ~20 wt % MgO, was generated by isentropic decompression melting under a relatively thin lithospheric lid. For Os-isotope reasons explained below, depleted mantle compositions such as those from McKenzie & O’Nions (1991Go, 1995Go) and Workman & Hart (2005Go) were tried and the best fit was achieved by using the former with the potential temperature (Tp) of the mantle set to ~1500°C. The ‘model parental melt’ was derived by subtracting olivine fractionally from the ‘model primary melt’ until MgO reached ~15 wt % (the lower limit of the estimated primary magma range, with a calculated equilibrium olivine of Fo90). The actual trace-element abundances and isotopic ratios of VB19 were attached to ‘model VB19’ (Table 2). Of the three picrite dykes with similar MgO contents, VB19 was chosen for its wide range of isotope determinations and because its trace-element abundances were close to the average values of the other two (i.e. VB3 and 18).

It is conceivable that parental magmas were transported laterally as dykes from a location near the axis of the Proto-Atlantic rift, where the lithosphere would have been thinner (e.g. Bauer et al., 2000Go), but obviously the pMELTS starting model cannot be used to discuss in detail the ultimate origin of the Spitzkoppe picrites. It is simply a device to let the pMELTS algorithm interact with a ‘starting composition’ that it ‘recognizes’ as having been originally in equilibrium with a lherzolite mantle.

AFC
Bowen (1928Go) concluded that, because upwelling magma is generally porphyritic, most magmas are saturated and carry little or no superheat. Therefore heat for dissolving country rock comes from that released during crystallization of the melt. As his detailed phase-diagram approach demonstrated, however, the reaction progression depends on the complicated interactions of temperature-dependent phase stability fields. Hence, AFC is ideally suited for analysis with a thermodynamically based model, such as MELTS, and we have applied the Adiabat_1ph front-end here also.

For the Spitzkoppe suite it has been necessary to modify the procedure in several ways and new features were added to the public version of Adiabat_1ph in the process; details are given at www.gps.caltech.edu/~asimow/adiabat and in the Appendix. This included an implementation of isenthalpic calculations together with a means to specify the thermal state of the assimilant. The initial crustal temperature was taken as 500°C after considering Cretaceous palaeogeothermal gradients derived from lherzolite mantle xenolith PT equilibria from Okenyenya (Baumgartner et al., 2000Go) and near Swakopmund (Whitehead et al., 2002Go), the two nearest appropriate localities. The starting situation was 100 g of ‘model VB19’ at its liquidus, and fifty 1 g increments of either VB12 or PA19 acid crust (see Fig. 9 legend) were added.


Figure 9
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Fig. 9. Variations of CaO, Al2O3, Fe2O3 and SiO2 in the Spitzkoppe dykes as functions of MgO. Also plotted are closed-system fractional crystallization and AFC trends modelled using pMELTS. Details of the modelling are given in the text; each trend-line is based on ~310 modelling steps for fractional crystallization and ~50 steps for AFC. Closed-system modelled fractionation curves at various anhydrous pressures are labelled in the Al2O3 plot. The 0·6 GPa curve (bold continuous line) gives the best fit to the dyke CaO and Al2O3 analyses. The AFC modelled trend using Damara granite VB12 (Fig. 1) is shown as a bold dashed line; the trend using Paresis rhyolite PA19 approximately overlies this one.

 
Reiners et al. (1995Go) incorporated the original software of Ghiorso & Sack (1995Go) into a quantitative model of heat-balanced AFC and showed that the ratio of the rates of assimilation and fractional crystallization, r, could vary dramatically as a typical magma evolved. Naturally, cooling and magma transport rates can strongly affect the r value (e.g. Kuritani et al., 2005Go) and very complex models of magma chamber processes, such as the EC-E'RA{chi}FC model of Spera & Bohrson (2004Go), can be developed if all likely factors are included. Here a relatively simple equilibrium model was used and the calculations were undertaken in two stages, which represented extreme cases. First, the magmatism was treated as closed-system fractional crystallization of a cooling dry parental magma. Second, the thermal evolution during AFC was constrained by balancing the heat released during fractional crystallization with that required to melt and incorporate plausible country rock. This latter case is approximately equivalent to the ‘maximal contamination’ end-member of Spera & Bohrson (2004Go) and assumes no heat loss by conduction.

Results. Using the procedure described above, pMELTS calculated the closed-system fractional crystallization trends shown in Fig. 9. Examples at pressures between 0·5 and 1· 0 GPa are plotted and compared with the Spitzkoppe dyke data. The variation in the calculated MgO–CaO inflexion with pressure is relatively small and thus the inferred pressure is only loosely constrained, especially given our caveat about extrapolating pMELTS. It is encouraging, however, that the bold continuous line corresponding to a pressure of 0·6 GPa, which is in the middle of the range inferred qualitatively from Fig. 8 (~0·35–0·8 GPa), falls closest to most of the Spitzkoppe data for CaO and Al2O3. At higher anhydrous pressures, spinel precipitated in the pMELTS models (see Fig. 9) and this phase is not observed in any Spitzkoppe dykes.

For comparison, the model results for adding granitic crust VB12 during AFC of ‘model VB19’ at 0·6 GPa are shown (dashed line) in Fig. 9. Results for adding Paresis rhyolite PA19 (Mingram et al., 2000Go), the proxy for lower-crust partial melt used in this paper, are almost identical. For most oxides the data fall between the closed-system and open-system curves, suggesting that AFC processes dominated the dyke evolution but that the r value was lowered by conductive heat loss. This is particularly clear in the FeO* plot, which shows that Fe–Ti oxides reached saturation below ~7 wt % MgO in the dyke magma and AFC models but not in the closed-system models, in agreement with the experiments of Villiger et al. (2007Go). With the exception of Al2O3, the fit to all oxides (including P2O5 and TiO2, which are not shown) is good and reinforces our confidence in the ability of pMELTS to describe Mg-rich basalt evolution. We tested the possibility that small amounts of water in the parental melts—such as might be held in the minerals of nominally anhydrous mantle (Hauri et al., 2006Go)—was the reason for the poor Al2O3 fit by re-running the 0·6 GPa calculations using pHMELTS and H2O contents up to 1 wt %. The misfit for Al2O3 became worse and therefore remains unexplained. This is clearly a limitation to the complete success of the modelling.

The success of pMELTS in modelling the isotopic consequences of AFC is clear in Fig. 5. The model curves are marked with increments of added crust in grams (see the Appendix). This is close to, but not identical to, added crust marked as percentages. Starting from ‘model VB19’, the AFC curve in Fig. 5 involving Paresis rhyolite PA19 (Mingram et al., 2000