3.1. Crustal Processes
 The major element systematics of the high-MgO Theistareykir magmas (> 8 wt% MgO) (Figure 2) are affected by crystal fractionation and/or accumulation of olivine (ol). Combined major and trace element relationships (Figures 2 and 9) show that clinopyroxene (cpx) or combined ol-cpx fractionation [Maclennan et al., 2001], in general, does not exert a major control on magma composition. Also, significant amounts of plagioclase (plag) fractionation (> 5%) (Figure 9b) have not occurred in samples with MgO > 8 wt%, although the increasing scatter in variation diagrams (Figure 2) observed for samples with MgO of about 8 wt% may be attributed to either plag accumulation (samples with plag phenocrysts and high Al2O3: sample 9359, 9385, 9389 from Storavitishraun and sample 9383 from Theistareykirhraun) or incipient plag and cpx (along with ol) fractionation (samples with low Al2O3 and CaO contents: sample 9353 and 9393 from Langavitihraun; Figure 2, Table 1).
Figure 9. (a) CaO/Al2O3 versus V and (b) Al2O3/TiO2 versus Sr. Both V and Sr behave as incompatible elements during melting (Sr somewhat more so), and are compatible in clinopyroxene and plagioclase, respectively. Experimental evidence shows that CaO/Al2O3 increases with increasing degree of melting and decreasing pressure of melting [see, e.g., [Falloon et al., 1988; Kinzler and Grove, 1992b; Hirose and Kushiro, 1993; Kushiro, 1996]. Thus, the negative correlation between CaO/Al2O3 and V and the lack of correlation between CaO/Al2O3 and Sc (not shown, Sc ranges from 35 to 52ppm; Table 1) show that partial melting rather than clinopyroxene crystallization (at any pressure) is responsible for the positive MgO-CaO/Al2O3 relationship (Figure 2d). Although compatible with the major element systematics alone, fractional crystallization of wherlite (orange arrow) [Maclennan et al., 2001], cannot explain the inverse relationship between CaO/Al2O3 and V and can only be explained by relatively large amounts of combined ol and cpx fractionation (> 30% ol), which is inconsistent with the major element systematics (Figure 2). Al2O3/TiO2 decreases with increasing pressure of melting and similar to CaO/Al2O3 versus V, the negative relationship between Al2O3/TiO2 and Sr at Theistareykir suggest that plagioclase fractionation (or combined olivine-plagioclase and olivine-plagioclase-clinopyroxene fractionation) is expected to be of minor importance, and that the Al2O3/TiO2 versus Sr relationship is controlled by melting, not fractionation. Arrows indicate fractional crystallization of olivine (ol), plagioclase (plag) and clinopyroxene (cpx), starting from a lava very similar to sample 9394 (90 ppm Sr, 240 ppm V). Dol from Kennedy et al. , Dcpx from Hart and Dunn , Dplag from White  and references therein. Symbols as in Figure 2, excluding the Draugarhraun basalts.
Download figure to PowerPoint
 The size (up to 3 mm) and abundance of ol phenocrysts (up to 20%; see Table 1 and Slater ) in the most MgO-rich lavas (MgO > 18 wt%) as well as Ni contents greater than those in most “primary” magmas (Figure 10a) suggest that at least these magmas have accumulated ol. Petrographic evidence for ol accumulation in the other samples (< 18 wt% MgO) is elusive, and ol phenocryst compositions [Slater, 1996] are similar to calculated equilibrium compositions. The whole rock MgO-FeO systematics also do not clearly support ol accumulation for the basalts with less than 18 wt% MgO (Figure 10b; see also Albarède et al. ). However, the amount of accumulated or fractionated ol ultimately depends on the inferred or estimated composition of the parental or “primary” magma, which is model-dependent [Hart and Davis, 1978; Korenaga and Kelemen, 2000].
Figure 10. Plots of MgO versus Ni and FeO. (a) Shown are the linear MgO-Ni relationship in the Theistareykir basalts and calculated olivine fractionation curves (adjustment of DNi [Kinzler et al., 1990] after each 0.1% step of olivine crystallization, starting from sample 9390 (MgO about 20 wt%), and sample 9356 (MgO about 14 wt%), respectively). Curves show the range of compositions inferred for “primary” mantle melts according to Korenaga and Kelemen  (labels olNi = 2500–3500 indicate melts with equilibrium olivine with 2500–3500 pmm Ni). Following the model of Hart and Davis  and Kinzler et al. , a linear relationship between MgO and Ni, such as that at Theistareykir (see Figure 10a) is evidence for olivine accumulation and the calculated MgO content of the “primary” Theistareykir lavas is approximately 10–10.5 wt%, indicating that all Theistareykir samples with MgO > 10 wt% would have accumulated olivine. However, for melt compositions with MgO > 9 wt%, olivine fractionation also results in a nearly linear MgO-Ni relationship (Figure 10a). Therefore, the linear MgO-Ni relationship of the Theistareykir basalts cannot be taken as definitive evidence for olivine accumulation (see also Korenaga and Kelemen ), and MgO contents of about 10–10.5 wt% are not a reliable estimate for the primary MgO content of the Theistareykir lavas. Korenaga and Kelemen  suggest that equilibrium olivine in primary melts have Ni contents within the range of Ni contents in olivine from peridotites (∼2500–3500 ppm) and that lower Ni contents in equilibrium olivines are caused by olivine fractionation (Figure 10a). Most Ni contents in equilibrium olivines calculated for the Theistareykir melts are lower than those in peridotites, and would therefore suggest that olivine fractionation, rather than accumulation as predicted by the Hart and Davis model [Hart and Davis, 1978], is the more important process (Figure 10a). Estimating “primary” melt compositions following the approach of Korenaga and Kelemen  requires that olivine is added until the Ni content in equilibrium olivine reaches 2500–3500 ppm (the range of Ni contents in olivines in peridotites). For a Ni concentration in the equilibrium olivine of 3000 ppm, resulting “primary” melt compositions have MgO contents clustering between 13 and 15 wt%, although the total range is between 11.5 and 18 wt%. (b) MgO-FeO systematics in the Theistareykir basalts. Lines labeled Fo94-Fo90 indicate position of melts in equilibrium with olivine with fosterite contents 94–90. Points labeled ol94-ol86 indicate composition of olivine with fosterite contents 94–86. Olivine accumulation trends form linear trends between the composition of the accumulated olivine (e.g., ol90) and the line for melts in equilibrium with that olivine composition (e.g., Fo90; see e.g., Albarède ). Except for the samples with MgO > 18 wt% such trends are not readily apparent and the MgO-FeO relationship in the Theistareykir basalts provides no clear evidence supportive of olivine accumulation. See text for further details. Bold line between Fo88 and Fo92 represents the range of ol-phenocryst composition of the Theistareykir basalts [Slater, 1996; Slater et al., 2001]. Symbols for the Theistareykir basalts as in Figure 2.
Download figure to PowerPoint
 Following the model of Hart and Davis  and Kinzler et al. , the calculated MgO content of the “primary” Theistareykir lavas is approximately 10–10.5 wt%. However, because it is difficult to discriminate between ol accumulation or ol crystallization processes based on the MgO-Ni relationship alone, the 10–10.5 wt% estimate is ambiguous (see Figure 10a for details). Following the approach of Korenaga and Kelemen  (see Figure 10 for details) “primary” melt compositions for the Theistareykir lavas have MgO contents clustering between 13 and 15 wt%, and ol fractionation, rather than accumulation as predicted by the Hart and Davis model [Hart and Davis, 1978], appears to be the more important process for lavas with MgO < 15 wt% (Figure 10a). Therefore, owing to the high MgO content of the Theistareykir magmas and the inferred MgO of ∼14 wt% in the primary magmas, the amount of ol accumulation and fractionation is minor even for the most MgO–rich and MgO-poor lavas (< about 20%, see Figure 2).
 Positive correlations between CaO/Al2O3 and Al2O3/TiO2 and MgO (Figure 2) clearly show that ol fractionation/accumulation processes alone cannot explain all of the major element variability at Theistareykir, which is confirmed by the large range in trace element concentrations and ratios (Figures 3–5). In this context, the correlations between major element parameters and radiogenic isotope ratios (Figure 8) are a striking feature that bears on the origin of the major element variations. Especially the correlation between Mg# (MgO) and radiogenic isotopes (see Table 3) poses the question whether the amount of differentiation is somehow linked to source variations, or if inferred source signatures (e.g., Sr, Nd, Hf, Pb isotopes) are affected by crustal processes driven by crystal fractionation (e.g., assimilation fractional crystallization processes (AFC)) as has recently been proposed [Eiler et al., 2000]. Numerous observations confirm that AFC-type processes do not play a defining role for the chemistry and isotopic composition of the Theistareykir melts [e.g., Elliott et al., 1991], see detailed discussion in appendix A2). Is it likely then that magmas originating from different sources (as reflected in different isotopic composition) have a systematically different fractionation history? Or, alternatively, is the major element chemistry not disturbed to such an extent by fractionation processes that it still provides reliable information about partial melting and/or source heterogeneity?
 Correlations between parameters such as CaO/Al2O3, Al2O3/TiO2, K2O/TiO2, and also FeO and radiogenic isotope ratios are not influenced by ol fractionation or accumulation, regardless of the exact primary magma composition (in detail, some scatter in the correlations between Al2O3/TiO2 or Na2O/TiO2 and the various isotope ratios could be caused by plag accumulation or incipient plag fractionation; see Figures 4 and 8). Furthermore, correcting the major element compositions back to “primary” melt compositions using the approaches of either Hart and Davis  or Korenaga and Kelemen  shows that the sense and quality of the correlations of “corrected” major element abundances and ratios with isotope ratios is unaffected by these exercises (Table 3) with the exception of MgO (back-correcting all lavas to a certain MgO content eliminates all correlations with MgO). This suggests that the major element systematics are not substantially obscured by high-level fractionation after the magmas leave the mantle and that the correlations between major elements and isotope ratios are a near-primary feature of partial melting and source heterogeneity. Combined major and trace element systematics confirm this notion (e.g., CaO/Al2O3 versus V and Al2O3/TiO2 versus Sr; Figure 9).
3.2. Melting Processes
 In the preceding discussion, we have established that the fundamental major and trace element variations observed at Theistareykir are primary or near-primary signatures resulting from partial melting of the mantle - and we know, based on the isotopic variations in the Theistareykir and Icelandic rocks in general, that the mantle source is heterogeneous. In principal, partial melting and source heterogeneity can affect the major and trace element chemistry in two ways: (1) melting of different sources produces melts with distinct isotopic composition and different major and trace element chemistry or (2) the major and trace element chemistry is largely a function of pressure (P) and degree (F) of melting, implying that isotopically different parts of the source are sampled systematically as a function of pressure and degree of melting.
 The sub-Icelandic mantle is anomalously hot compared to other portions of the Mid-Atlantic ridge (MAR; ΔT about 200°C, [Sleep, 1990; Schilling, 1991]) and melting beneath Iceland is expected to start deeper than is typical for submerged portions of the MAR. Furthermore, because of the thinner lithosphere, melting beneath Iceland continues to shallower depths than at most other ocean islands. It is reasonable to expect, therefore, that variations in the pressure (P) and extent of melting (F) will have a comparatively important influence on Icelandic melt compositions (it is important to note that, in most melting models, P and F are physically coupled such that low-F melts at a single locality derive from higher average P than high-F melts). What are the basic features that originate from different P and F of melting and are these features compatible with the major and trace element chemistry of the Theistareykir suite?
 On the basis of melting experiments [e.g., Falloon et al., 1988; Kinzler and Grove, 1992a, 1992b; Langmuir et al., 1992; Hirose and Kushiro, 1993; Baker and Stolper, 1994; Baker et al., 1995; Kushiro, 1996; Lesher and Baker, 1996; Longhi and Bertka 1996; Longhi and O'Connell, 1996; Kinzler, 1997; Walter, 1998] and thermodynamic calculations with MELTS [Ghiorso, 1994; Ghiorso and Sack, 1995], the effects of pressure and degree of melting are such that high-P, low-F melts have higher TiO2, K2O, FeO, and lower CaO/Al2O3, CaO/Na2O, Al2O3/TiO2 than low-P, high-F melts produced by melting a similar source. High-P, low-F melts also have higher incompatible element concentrations and higher ratios of more to less incompatible trace elements ratios (e.g., higher (La/Sm)N, (Dy/Yb)N, δ(Lu/Hf) ratios [e.g., Salters and Hart, 1989; Salters, 1996]) and lower compatible trace element concentrations than low-P, high-F melts from a similar source. The major (possibly excluding MgO) and incompatible trace element variations in the Theistareykir basalts (Figures 5 and 8) are therefore both qualitatively and quantitatively [Slater et al., 2001] consistent with those expected to be produced by continuous melting of a homogeneous peridotite source with the picrites representing the low-P, high-F melts and the incompatible element enriched tholeiites representing the high-P, low-F melts.
 We know, however, that the source is not homogeneous and that source effects on melt composition must also be considered, especially in light of the good correlations observed between radiogenic isotope ratios and major and trace elements in the Theistareykir basalts (Figure 8). Calculations using MELTS show that melts from more fertile peridotites have higher TiO2 and Na2O, and lower MgO, CaO, CaO/Al2O3, CaO/Na2O and Al2O3/TiO2 ratios, than melts of less fertile peridotite at similar F (we used three peridotite compositions, in order of increasing “fertility”: DMM [Wasylenki et al., 1996; Hirschmann et al., 1998, 1999], MM3 [Baker and Stolper, 1994], and HK66 [Hirose and Kushiro, 1993]; see Asimow et al. [1995, 1997] and Hirschmann et al. [1998, 1999] for further details of modeling melting with MELTS). Furthermore, in the context of a single melting column, melt from fertile peridotite will be substantially more enriched in incompatible trace elements than melts produced from the less fertile peridotite higher in the column (at a given local F). Unfortunately, then, the effects of source heterogeneity are very similar to those resulting from variation in the pressure and degree of melting; to a large extent, the effects are additive, and, in general, it is difficult to disentangle the respective roles of source heterogeneity and partial melting on the major and trace element systematics. The depleted character of the Theistareykir melts, however, and the combination of major and trace element and isotopic data allow a more detailed assessment of the respective roles of melting and source composition.
 The overall depleted character of Icelandic tholeiites and their similarity to N-MORB in terms of both their isotopic and major and trace element composition suggests a volumetrically dominant role for a depleted, and roughly MORB-like (see discussion in section 3.3) source material. Note, for example, that even in case of melting of a depleted mantle source, very high degrees of melting (> 15–20%, depending on the preferred melting model and partition coefficients, see Figure 4) are required in order to produce the low absolute trace element abundances of the Theistareykir melts. In addition, only experimental melts from the most depleted starting compositions (e.g., Tinaquillo lherzolithe [Falloon et al., 1988]) have similarly low TiO2, Na2O and high CaO, and CaO/Na2O, CaO/Al2O3, similar to the results using MELTS and the Theistareykir major element variations are parallel to melting trends (experimental or using MELTS) from single sources. Because of the apparent dominance of the depleted material, it appears likely therefore that the major elements are substantially more sensitive to the pressure and degree of melting than they are to the presence of enriched source material and thus are best explained in the context of polybaric or dynamic melting (effectively, the extraction of melts that integrate over different pressure intervals within the melting regime [see, also, Wood et al., 1979; Wood, 1979, 1981; Elliott et al., 1991; Slater et al., 2001]. Klein and Langmuir [Klein and Langmuir, 1987, 1989; Langmuir et al., 1992] also concluded that “local” variations of Na8 and Fe8 with ridge depth at several localities along the MAR (including Iceland [Klein and Langmuir, 1987, 1989; Langmuir et al., 1992]) are not caused by source heterogeneity and are instead a function of degree and depth of partial melting.
 Slater et al.  have shown that the trace element variations in both lavas and melt inclusions in the Theistareykir basalts are quantitatively consistent with incomplete mixing of instantaneous fractional melts from a homogeneous source. This, however, requires a source that is slightly more enriched than the depleted MORB source, contrary to other evidence for a dominant depleted source (see above and section 3.3). Moreover, trace element concentrations and ratios are more sensitive to the influence of source heterogeneity than to variations in the F and P of melting compared to the major elements. The variation in isotopic composition of Sr, Nd, Pb, and Hf must reflect source heterogeneity, and the correlations between trace elements and radiogenic isotopes in the Theistareykir basalts therefore show that a significant part of the trace element variation must be due to source heterogeneity. Melting and mixing calculations show that only small amounts of enriched source material (< about 20% in case of PUM [McDonough and Sun, 1995]; see also Slater et al. ) is necessary to produce the variations in the Theistareykir basalts. In detail, it is difficult to model the process due to the lack of knowledge of appropriate partition coefficients for heterogeneous sources and the lack of knowledge of the number and composition of enriched components and the mixing process. However, because of the depleted nature of the Theistareykir melts, it appears safe to conclude that melts from the enriched portions of the source contribute only a small fraction relative to melts from the depleted source material.
 In contrast to the trace elements, major element variations reflect mainly different P and F of melting. Correlations between major elements and isotopes suggest that different sources are sampled systematically as a function of P and F of melting. This is most easily explained in the case where the enriched material has a lower solidus T. Often, isotopically enriched mantle source material is thought to be produced by intramantle migration of fluids or melts, or subduction of basalt, sediment, or other crustal material. Such material would have a more mafic composition than depleted peridotite and is indeed likely to have a lower solidus temperature, and may also have a narrower melting interval than “less enriched” or “depleted” upper mantle peridotite (i.e., MORB source material [see, e.g., Sleep, 1984; Zindler et al., 1984; Prinzhofer et al., 1989; Hirschmann and Stolper, 1996; Stracke et al., 1999]). Therefore an enriched source with a mafic mineralogy is likely to melt to a larger degree and be consumed in a relatively shorter time and depth interval following the onset of melting than is depleted peridotite. This causes the influence of the isotopically enriched component to be more pronounced in melts which derive from higher pressures. A similar effect, however, would be expected from melting more enriched peridotite. Compared to depleted peridotite, melting of enriched peridotite is also expected to start at higher pressure but is likely to continue melting to similar pressures as depleted peridotite. Therefore, unless partial melting of mafic compositions results in characteristic and identifiable chemical compositions of these melts, the effects of melting mafic and enriched peridotite is expected to be difficult to distinguish, and it is premature to make a definitive conclusion whether the enriched source material consists of enriched peridotite or more mafic compositions.
 In summary, melting beneath Theistareykir integrates over a large range of pressures, is characterized by extraction and incomplete aggregation of instantaneous melts with aggregated melts representing low to very high degrees of melting, and is dominated by melting of depleted peridotite (similar to N-MORB source material). An enriched source component is required but appears to be volumetrically minor. Despite the large influence of P and F of melting, trace element concentrations are substantially affected by source heterogeneity. In contrast, because of the dominance of the depleted component, major element variations are little influenced by source heterogeneity and are mainly controlled by dynamic melting. Therefore correlations between radiogenic isotope ratios and major and trace elements indicate that sampling of isotopically distinct components of the Icelandic source is not a random process but occurs systematically as a function of both the pressure and extent of melting. The most enriched melts in terms of their isotopic and trace element compositions are derived from the highest mean pressure of melting, and represent the smallest degrees of partial melting (Figures 5 and 8). This is most readily explained by a lower solidus temperature of the enriched component(s).
 Furthermore, at other ocean islands, as at Iceland, an isotopic distinction is commonly observed between tholeiites, alkali basalts and silica-undersaturated magmas (e.g., Hawaii and Samoa). Even at mid-ocean ridges, the observed degree of isotopic variability decreases as the scale of melting, or rate of processing of mantle material (as measured by spreading rate), increases (Figure 11). These observations suggest that the scale on which enriched and depleted materials are intermingled in the mantle is small compared to the maximum dimension over which melts are produced and mixed beneath ridges.
Figure 11. Isotopic variability in global MORB as a function of spreading rate. The isotopic variability in global MORB increases with decreasing spreading rate, while the average isotopic composition for each ocean basin is independent of the spreading rate. The MORB data include combined Sr, Nd, and Pb isotope data for about 490 samples from the Atlantic (MAR), 325 for Pacific (Pacific ridges) and 130 samples from the Indian ocean spreading centers (SEIR, South East Indian ridge, SWIR, South West Indian ridge). Data have been compiled from the Lamont Doherty petrological database (LDEO petrological database at http://petdb.ldeo.columbia.edu/petdb). (a) Nd and Pb isotopic variability versus spreading rate. The isotopic variability is simply the 2σ scaled to the analytical error, which is assumed to be ±0.00002 for 143Nd/144Nd, and 0.015 and 0.035 for 206Pb/204Pb, and 208Pb/204Pb, respectively. (b) Average 143Nd/144Nd, 206Pb/204Pb, and 208Pb/204Pb for each spreading ridge plus 2σ as shown in Figure 11a.
Download figure to PowerPoint