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 The present work reports multiple collector inductively coupled plasma mass spectrometry (MC-ICP-MS) measurements of the isotopic compositions of Hf and Pb in the first 3 km of the deep core retrieved by the Hawaii Scientific Drilling Project. The measurements cover all the samples from the standard geochemical reference set, glasses from the deep hole, and replicates from the pilot hole. Both Hf and Pb are less radiogenic in Mauna Loa compared to Mauna Kea. The transition between Mauna Kea and Mauna Loa lavas in the deep core is progressive for εHf and 208Pb/204Pb, but a sharp discontinuity is observed for 208Pb*/206Pb*. There is no correlation between the alkalinity of the samples and isotopic composition. In detail, the Hf isotope compositions of samples from the pilot hole are not all identical to those of the HSDP-2 core for samples retrieved from a similar depth, suggesting that steep topography existed at the time of emplacement or that a different eruptive sequence was recorded. The strong correlation between 208Pb*/206Pb* and 3He/4He (He data from M. D. Kurz et al. (Rapid helium isotopic variability in Mauna Kea shield lavas from the Hawaiian Scientific Drilling Project, submitted to Geochemistry Geophysics Geosystems, 2002)) requires the episodic incorporation of a component that resembles the basalts erupted by either Kilauea or the Loihi eruptive centers (this component is referred to as K/L). The data suggest that some 500 kyr ago, Mauna Kea was tapping a mantle source similar to that tapped by Kilauea today. Isotopic variability of Pb and He cannot be accounted for by radiogenic ingrowth in a closed system, but requires the mixing of mantle source components with distinct outgassing histories. The time series of isotopic and concentration data in Mauna Kea samples spanning about 350,000 years of age indicate the recurrence of geochemical patterns in the melting column. Ignoring the most recent alkalic samples, we find that the dominant fluctuations of εHf and 207Pb/204Pb correspond to a period of 50,000 years. For La/Yb, Zr/Nb, 87Sr/86Sr, 206Pb/204Pb, 207Pb/206Pb, and 208Pb/206Pb, a dominant period of ca. 18,000 years is obtained. Once provision is made for the existence of harmonics, the consistency between the isotopic spectrum of the pilot hole and the HDSP-2 core is very good. The input of the K/L component does not seem to be periodic. We use these recurrence intervals in conjunction with the upwelling rate deduced from buoyancy flux and seismic evidence of the maximum dimension of scatterers to constrain the radius of the Hawaiian plume conduit to be in the range of 10–50 km and the upwelling velocity to be in the range of 0.13–3 m/yr. Plausible vertical length scales of heterogeneities in the conduit are 6.5–160 km.
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 Although numerous important scientific results were obtained from the geochemistry of the HSDP pilot hole lavas, this relatively short core did not make it possible to use the geochemical analyses, in particular those of radiogenic isotopes, as time series because the time window was not sufficiently broad to be of geophysical significance with respect to hot spot dynamics [e.g., DePaolo et al., 2001]. In the present contribution to the HSDP initiative, we use a comprehensive time series of combined high-resolution, high-precision Hf and Pb isotope data for the continuous 3 km sequence of Mauna Kea lavas to set constraints on the nature of the Mauna Kea mantle sources and how they varied through time. Before reaching Mauna Kea by drilling, ca 250 m of lavas from the currently active Mauna Loa volcano had to be traversed, and here we also present the Hf and Pb isotope data for this suite of samples. The petrology and geochemistry of modern Hawaiian lava flows offer a two-dimensional view of the hot spot activity which has been used to infer cross sections of melt extraction [Ribe and Christensen, 1999] and mantle heterogeneities in the plume conduit [DePaolo et al., 2001]. One of the most important goals of a high-resolution series of samples covering a significant interval of the lifetime of a volcano is to provide geochemical time series (assuming a reliable timescale for the stratigraphic column) that allow the geochemical cross sections inferred from the modern eruptions to be tested. The present results for the Mauna Kea and Mauna Loa volcanoes have allowed us to deduce aspects of the chemical and physical structure and the dynamics of the Hawaiian plume beneath Mauna Kea, examine how the plumbing systems of different volcanoes may interact, and make inferences about the relationships of Mauna Kea with its neighboring volcanoes, notably Mauna Loa, Kilauea, and Loihi.
2. Samples and Analytical Techniques
2.1. Hf Isotope Analyses
 We report 155 Hf isotope analyses of 123 different samples from Mauna Loa (19 samples) and Mauna Kea (104 samples) from the second Hawaii Scientific Drilling Project core (HSDP-2) (Table 1). The Hf isotopic compositions were analyzed by MC-ICP-MS (the VG Plasma 54 instrument in Lyon) during the period of January 2000 to April 2001. Hafnium purification and mass spectrometry followed the procedures described by Blichert-Toft et al. . To avoid ambiguity between measured isotopic variations and potential chemistry problems or machine drift during long run sessions (as required by the large number of samples analyzed), samples were routinely randomized for both Hf separation chemistry and mass spectrometric analysis. Furthermore, in order to monitor machine performance, the JMC-475 Hf standard was run systematically in between every second or third sample throughout the entire project. Hf total procedural blanks routinely were less then 25 pg.
Table 1. Hf and Pb Isotope Compositions of Mauna Loa and Mauna Kea Samples from the HSDP-2 Core
mbsl, meters below sea level.
Hf and Pb isotopic compositions measured by MC-ICP-MS (VG Plasma 54).
176Hf/177Hf normalized for mass fractionation to 179Hf/177Hf = 0.7325. 176Hf/177Hf of JMC-475 Hf standard = 0.28216 ± 0.00001 (i.e., 2σ external reproducibility = 0.0035% or 35 ppm as also seen from the sample replicate analyses). Hf standard run every second or third sample.
Uncertainties reported on Hf measured isotope ratios are in-run 2σ/√n analytical errors in last decimal place, where n is the number of measured isotopic ratios.
NBS 981 Pb standard run after every two samples. The 2σ standard error on NBS 981 on a typical day of analysis was 142, 120, and 125 ppm, respectively, for 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb. Average individual errors on Pb isotopic analyses (two standard deviations) were 0.0048 for 205Tl/203Tl, 0.0204 for 208Pb/204Pb, 0.0186 for 207Pb/204Pb, and 0.0190 for 206Pb/204Pb. Reproducibility of replicate analyses, including leaching, was 0.6 permil (relative difference) or 0.025 for 208Pb/204Pb, 0.008 for 207Pb/204Pb, and 0.010 for 206Pb/204Pb.
Hand-picked glass as opposed to the rest of the samples, which are powders from the standard geochemical reference sample set.
 The analyzed sample suite spans the entire depth interval from sea level to current coring depth with the deepest sample coming from 3069 mbsl. One hundred and nineteen of these samples are powders from the 119-sample standard geochemical reference set, while four samples are hand-picked glasses from Mauna Kea from the depth interval between 2200 and 2400 mbsl. Based on major element data (J. M. Rhodes and M. J. Vollinger, Composition of basaltic lavas sampled by phase 2 of the Hawaiian Scientific Drilling Project: Geochemical stratigraphy and magma types, submitted to Geochemistry Geophysics Geosystems, 2002; hereinafter referred to as J. M. Rhodes and M. J. Vollinger, submitted manuscript, 2002), this particular depth interval may represent a unique excursion of increased alkalinity in the middle of several kilometers of basalts with a strong tholeiitic character. We considered it important to investigate this feature in more detail by undertaking the additional glass analyses. Nineteen of the samples from the reference suite are from Mauna Loa (sea level down to 246 mbsl) and 100 of the samples are from Mauna Kea (between 246 and 3098 mbsl, the coring depth at the time of writing).
 In order to verify the external reproducibility for Hf isotopic measurement of 0.35 epsilon units, as indicated by the JMC-475 Hf standard analyses, six samples from Mauna Loa and 20 samples from Mauna Kea were analyzed in duplicate. Some of these samples were chosen for repeat measurement because their in-run errors were greater than the external reproducibility as judged from the analyses of JMC-475. Three additional samples from Mauna Kea were further analyzed in triplicate in order to certify their measured Hf isotopic composition. The excellent reproducibility of all replicate analyses (Table 1) and the consistency of Hf isotopic compositions between consecutive samples, which, as noted above, were not analyzed in successive order, indicate that our error assignment is conservative. In order to further check for potential analytical bias between Hf isotopic measurements for HSDP-1 (the first Hawaii Scientific Drilling Project pilot core) and HSDP-2, four samples from the bottom of HSDP-1 (which overlaps with HSDP-2) were reanalyzed simultaneously with samples from HSDP-2 (Table 1). The results for the HSDP-1 replicates are identical within error to the original analyses carried out by Blichert-Toft and Albarède , thus allowing direct comparison between the two cores.
2.2. Pb Isotope Analyses
 All the samples measured for Pb isotopic composition were processed in the clean laboratory at Université Libre de Bruxelles. The samples were leached with 6 N HCl, as described by Weis and Frey , in order to remove a maximum of secondary alteration products. Lead was subsequently separated by a single passage through an anion-exchange column. Total blanks for the entire procedure were 100–200 pg, which is negligible with respect to the Pb of the samples analyzed (∼100–300 ng). The Pb isotopic compositions were measured on the MC-ICP-MS VG Plasma 54 in Lyon from June 2000 to June 2001. Thallium spike was added to all samples and standards to monitor mass fractionation [White et al., 2000]. The total Pb ion beam intensities varied from 0.6 to 8 V, but only results for samples with an intensity exceeding 2 V of total Pb were used in order to have sufficient precision on the isotopic ratios. Furthermore, because the Tl/Pb ratio appears to be critical to the accuracy of the Pb isotope results, especially for 207Pb/204Pb, only results for samples with Tl/Pb < 0.5 were retained. Almost all the samples from the standard geochemical reference set were analyzed. Among these, 19 are duplicates and two are triplicates. Nineteen samples are from Mauna Loa and 95 samples are from Mauna Kea. As done for Hf, samples were processed randomly for both Pb separation chemistry and mass spectrometric analysis. Because the NBS 981 standard is run systematically after every two samples as a reference to calculate the sample isotopic ratios, no single value of this standard can be reported that would be an independent test of machine accuracy. However, it has been shown by White et al.  that the method used in this study reproduces thermal-ionization Pb isotope results on basaltic samples very accurately. It is worth reemphasizing here that the current technique does not assume that Pb and Tl have similar mass biases, but rather that the biases of these two elements maintain a constant ratio over the time period of a few runs. The good performance of the Plasma 54 was further substantiated by the measurement of multiple NIST 981-NIST 982 mixtures (B. Nelson and F. Albarède, unpublished data): 207Pb/206Pb and 208Pb/206Pb are precise to better than 50 ppm, while 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb typically are precise to within 100 ppm per atomic mass unit.
 The Pb isotope results and a comparison with triple-spike Pb isotope data (J. Eisele et al., The long-term Pb isotope evolution of Mauna Kea lavas from the HDSP-2 drill core, submitted to Geochemistry Geophysics Geosystems, 2002; hereinafter referred to as J. Eisele et al., submitted manuscript, 2002) on a subset of samples from the Mauna Kea section of the deep core (HSDP-2) is presented in Figure 1. Except for 207Pb/204Pb, for which the Plasma 54 data are clearly significantly more noisy than the triple-spike data, the agreement between the MC-ICP-MS and the triple-spike values is remarkable, especially when taking into account the down core isotopic variations. The cause for the noise on the 207Pb/204Pb measurements by MC-ICP-MS is not yet understood. Although matrix left after elution may alter mass fractionation to some extent, it is our experience that Pb isotope measurements on solutions with a relatively heavy matrix reproduce well within the stated errors. Memory should not be a significant issue since the Plasma 54 of Lyon never sees any 204Pb or 207Pb spike, while the 207Pb/204Pb ratios of the bracketing standard (NIST 981) and the samples are nearly identical. J. Eisele et al. (submitted manuscript, 2002) observe a lack of reproducibility of 207Pb/204Pb measurements on some subaerial basalts from the HSDP pilot core and ascribe it to contamination by particles transported with groundwater. Because our leaching procedure is somewhat less severe than the procedure used in Mainz, we may be seeing a similar effect. A last option is that our HCl-based chemistry fractionates Pb isotopes on anion-exchange resin. Such a process has been previously documented for Zn, Cu [Maréchal et al., 1999; Maréchal and Albarède, 2002] and Fe [Anbar et al, 2000] and has been tested here for Pb by eluting a few micrograms of NIST 981 on an anion-exchange column. The surprising result of this experiment (mass fractionation on 207Pb/204Pb in excess of 2000 ppm across the elution peak) is described in Appendix A. A similar experiment with similar outcome was described by Baker and Waight . Unfortunately, it has not been possible to assess the yield of our Pb purification chemistry for the HSDP-2 samples, which were all run prior to this experiment and for which Pb concentrations are not precisely known. However, the observation that the Pb isotope partition coefficients between the anion-exchange resin and HCl may change by as little as 40 ppm per mass unit from 204Pb to 208Pb may account for some of the noise observed in our HSDP-2 data. Natural variations in 206Pb/204Pb and 208Pb/204Pb are an order of magnitude larger than the 207Pb/204Pb variations: the impact of potential analytical artifacts is therefore less critical on the first two ratios.
3.1. Hf Isotopes
 Hf isotopic compositions for Mauna Loa lavas from the deep core (HSDP-2) have 176Hf/177Hf that varies from 0.283051 to 0.283115, corresponding to εHf = +9.9 − +12.1 (Table 1; Figure 2). This is similar to, though slightly more variable than observed for Mauna Loa lavas from the pilot core (HSDP-1) (εHf = +10.5 − +11.6 [Blichert-Toft and Albarède, 1999]). Samples from the top of the Mauna Loa section are the least radiogenic, with successive samples becoming progressively more radiogenic with depth except for a small wiggle at about 125 mbsl and an abrupt excursion to less radiogenic values at about 200 mbsl. Samples following this excursion gradually become more radiogenic during the remaining 50 m leading to the contact with Mauna Kea (Figure 2). The range of 176Hf/177Hf for the HSDP-2 Mauna Kea section (0.283087–0.283152 or εHf = +11.1 − +13.4) likewise is indistinguishable from that of the HSDP-1 Mauna Kea section (εHf = +11.4 − +13.1 [Blichert-Toft and Albarède, 1999]). However, between 500 and 750 mbsl, Hf in HSDP-2 is offset systematically with about 0.5 epsilon units toward more radiogenic values relative to HSDP-1 (Figure 3b). The discrepancy in Hf isotopic composition for this part of the overlapping depth interval between the two cores cannot be due to an analytical artifact as the four duplicate analyses from HSDP-1 analyzed together with the new samples from HSDP-2 came out identical within error to the first set of analyses by Blichert-Toft and Albarède  (Table 1). It would of course have been preferable to duplicate the Hf isotope measurements in the section where the two cores are isotopically distinct. We consider, however, that the reproducibility of HSDP pilot core data acquired on the same samples three years apart and the overall consistency of the multiple replicates of HSDP-2 analyses make it unlikely that an analytical bias may account for the Hf isotope discrepancy between the two cores. Despite the two holes having been drilled just a few kilometers apart and the similarity of one particular alkaline flow in each core (SR131 and R177 as pointed out by S. Huang and F. A. Frey (Trace element abundances of Mauna Kea basalt from phase 2 of the Hawaii Scientific Drilling Project: Petrogenetic implications of correlations with major element content and isotopic ratios, submitted to Geochemistry Geophysics Geosystems, 2002; hereinafter referred to as S. Huang and F. A. Frey, submitted manuscript, 2002)), it seems clear that stratigraphic correlations cannot be retrieved from the depth in the core alone.
 As observed previously for the pilot core [Blichert-Toft and Albarède, 1999], Hf isotope compositions of Mauna Kea lavas in the HSDP-2 core (εHf ∼ +12.3 ± 0.9) are overall more radiogenic than those of Mauna Loa lavas (εHf ∼ +11.0±0.9) (Figure 2). While the transition from Mauna Kea to Mauna Loa lavas in the pilot core is abrupt with a drop of about one εHf unit [Blichert-Toft and Albarède, 1999], it is preceded in the HSDP-2 core by a conspicuous gradual decrease of almost two εHf units over the top 200 meters of Mauna Kea flows (Figure 2). Hafnium in the flows between 500 and 1500 mbsl generally seems to be more radiogenic than in the flows at the bottom of the core. Hf isotope compositions oscillate with only few observed breaks that exceed error bars (Figure 3b). The hyaloclastite sample SR0705-0.15 (at 1823.2 mbsl), analyzed in triplicate to verify its aberrant (with respect to neighboring samples) isotopic composition, is clearly anomalous (Figure 2) and will not be discussed further. The four hand-picked glasses from the depth interval of 2200 to 2400 mbsl were leached and also analyzed for their Hf isotopic compositions. Their εHf values are indistinguishable within error from those of the corresponding whole rock powders from the standard geochemical reference set (Figure 2). The glasses define a distinct trend of increasingly radiogenic 176Hf/177Hf (or increasing εHf) with decreasing depth that overlaps the identical trend defined by the whole rock powders.
3.2. Pb Isotopes
 Lead isotopic compositions for the Mauna Loa part of the deep core (HSDP-2) vary between 18.061 and 18.250 for 206Pb/204Pb and 37.804 and 37.995 for 208Pb/204Pb (Table 1; Figure 1). Whereas 206Pb/204Pb and 207Pb/204Pb do not show systematic variability down core, 208Pb/204Pb increases more or less systematically between 9.5 and 242 mbsl, the latter depth defining the contact with Mauna Kea. For the Mauna Kea section of HSDP-2, 206Pb/204Pb varies between 18.408 and 18.670 and 208Pb/204Pb between 37.933 and 38.248. In a 208Pb/204Pb (and 207Pb/204Pb) versus 206Pb/204Pb plot, there is no overlap between the Mauna Loa and Mauna Kea data (Figure 4). The lavas in the upper part of the Mauna Kea section are characterized by slightly less radiogenic Pb isotopic compositions than typical for deeper Mauna Kea lavas and cluster in the least radiogenic part of the Mauna Kea field in a Pb-Pb diagram.
 While 208Pb/204Pb, like 176Hf/177Hf, displays some continuity between Mauna Kea and Mauna Loa samples, the transition between the two volcanoes for 206Pb/204Pb, 207Pb/204Pb, and 208Pb*/206Pb* is marked by a sharp discontinuity (Figure 1). Relative to Mauna Loa, Mauna Kea is characterized by more radiogenic Pb and a lower source Th/U (208Pb*/206Pb*) ratio, the latter showing an overall increase with depth. Nine samples from middepth, notably from the interval 1973.8 to 2123.7 mbsl and from 2321.6, 2467.3, 2503.5, and 2654.1 mbsl, which all have a less negative alkalinity than the bulk of Mauna Kea lavas (Figure 3a), have distinctly higher 208Pb*/206Pb* ratios. For reasons to be explained in the Discussion, we will hereafter refer to these samples as the K/L group. As mentioned above, in a 207Pb/204Pb versus 206Pb/204Pb plot (Figure 4b), the difference between Mauna Kea and Mauna Loa stands out, but in contrast with the results of Abouchami et al. [2000a] on the pilot core, no fine structure can be defined within the data. We ascribe this to the larger errors on 207Pb/204Pb associated with the thallium-spike method used here with respect to the triple-spike method employed by Abouchami et al. [2000a]. Another reason may be a variable efficiency of Pb contamination removal by acid leaching (see J. Eisele et al., submitted manuscript, 2002). As also remarked above, the same contrast between Mauna Kea and Mauna Loa shows up in a 208Pb/204Pb versus 206Pb/204Pb plot with the more alkaline K/L Mauna Kea samples plotting with unusually high 208Pb/204Pb for a given 206Pb/204Pb (Figure 4a). Despite the potential analytical limitations on 207Pb/204Pb, we used a 3-D rotated Pb projection to attempt to demonstrate that most Mauna Kea data fall within a plane, whereas the more alkaline K/L samples plot distinctly above this plane (Figure 5).
4.1. Interaction Between Mauna Kea Basalts and the Pacific Lithosphere
 The field of combined Hf and Pb isotope compositions for the HSDP-2 samples is very similar to that of the pilot hole and we will not repeat here the discussion presented elsewhere for Hf [Blichert-Toft and Albarède, 1999; Blichert-Toft et al., 1999; S. Huang and F. A. Frey, submitted manuscript, 2002] and Pb [Abouchami et al., 2000a]. We note, however, that the present Pb and Hf isotope compositions plot on the general hyperbolic array that Blichert-Toft et al.  used to infer that the East Pacific plate is not involved as a significant component in Hawaiian basalts (Figure 6). This point is discussed by Z. Wang et al. (An examination of the roles of plume, lithosphere, and edifice in Hawaiian shield-building magmatism based on oxygen isotope date from the second HSDP core, submitted to Geochemistry Geophysics Geosystems, 2002; hereinafter referred to as Z. Wang et al., submitted manuscript, 2002) who emphasize that the εHf of Pacific MORB and Mauna Kea basalts overlap. The histogram shown as an inset in Figure 6 does indeed show some overlap and it may be argued that some Mauna Kea basalts may have incorporated particularly infrequent E-type (enriched) lithospheric material, e.g., similar to MORB from the Siqueiros fracture zone [Sims et al., 2002]. As a whole, however, the Pacific plate remains a very unlikely depleted end-member of Hawaiian basalts.
4.2. Transition Between Mauna Loa and Mauna Kea
 Although Hf and Pb isotopic data allow a clear distinction to be made between lavas from Mauna Loa and Mauna Kea, there is a tendency for the uppermost 200 meters of Mauna Kea lavas to show isotopic compositions intermediate to those of the two volcanoes (Figures 1–3). The series of 207Pb/204Pb and 208Pb/204Pb ratios are virtually continuous across the transition, while the series of 206Pb/204Pb ratios shows a gap but no discontinuity of the trend. In contrast, the 208Pb*/206Pb* ratios show both a gap and an abrupt discontinuity of the trend. Only the most recent (topmost) of these transitional lavas are alkaline (Figure 3a), which confirms the observation from the pilot core that there is no overall correlation between alkalinity and Hf (or Pb) isotopic composition [Blichert-Toft and Albarède, 1999]. Hafnium in the most alkaline samples from the uppermost Mauna Kea flows in the HSDP-2 core is substantially less radiogenic than in the alkaline samples from the same depth interval in the pilot hole [Blichert-Toft and Albarède, 1999] (Figure 3b). Were it not for 208Pb*/206Pb*, the HSDP-2 core Hf and Pb isotope data would support a transitional regime between Mauna Kea and Mauna Loa indicative of a mixed source of interacting batches of magmas, probably reflecting the gradual invasion of the plumbing system of Mauna Kea by that of Mauna Loa. This observation contrasts with the sharp discontinuity between the two volcanoes observed in the Hf and Pb isotope data from the pilot hole [Blichert-Toft and Albarède, 1999; Abouchami et al., 2000a]. The distinctive properties of the two cores are further illustrated by the significantly more radiogenic character of Hf in the lava flows of the HSDP-2 core between 500 and 750 mbsl relative to those of the pilot core. These discrepancies suggest that, at equivalent depths, the two drill holes did not sample the exact same lava piles, indicating either a lateral shift in stratigraphy between the two cores over the ca 2 km that separate them or the accumulation of different lava flow sequences at the two locations, perhaps caused by steep topography at the time of eruption. In contrast, Mauna Loa lavas have identical εHf versus depth relationships in the two cores. As for Pb isotopes, no samples from the pilot hole were analyzed by MC-ICP-MS, thus preventing direct comparison between the two cores. However, the agreement between the Pb isotopic compositions obtained for HSDP-2 in the present study by MC-ICP-MS and those obtained by triple spike for the HSDP-1 core [Abouchami et al., 2000a] is good.
4.3. Mauna Kea Source Heterogeneity
 In order to evaluate which isotopic properties may be correlated, we first ran our own Hf and Pb isotope data together with the Sr and Nd isotope data produced by J. G. Bryce et al. (manuscript in preparation, 2003) and the He isotope data produced by M. D. Kurz et al. (Rapid helium isotopic variability in Mauna Kea shield lavas from the Hawaiian Scientific Drilling Project, submitted to Geochemistry Geophysics Geosystems, 2002; hereinafter referred to as M. D. Kurz et al., submitted manuscript, 2002) on the same samples through a Principal Component Analysis (PCA) software. PCA is a method used to identify the orthogonal directions of maximum variability and is described in a number of different textbooks [e.g., Johnson and Winchern, 1992; Albarède, 1995; Reyment and Jöreskog, 1996]. The three components obtained for 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb, respectively, account for 46.3, 24.2, and 13.0 percent of the variability. There is hardly any correlation between the Pb isotopic ratios and other isotope compositions, since, as demonstrated by Blichert-Toft et al. , such mixing relationships are strongly nonlinear. One exception stands out, however: 208Pb*/204Pb* and 3He/4He plot next to each other in the space of the first three components (Figure 7) which indicates that they are strongly correlated [Eiler et al., 1998]. We surmise that the odd position of 87Sr/86Sr along the axis of the third component may signal the occasional presence of a seawater component, either as a contaminant in the lava pile or as a real mantle component. The position of the εHf and 206Pb/204Pb axes in the plane of the first two components confirms that, although three components are necessary to describe the overall isotopic variability of Hawaiian basalts, two components seem to be enough to describe the relationship between εHf and 206Pb/204Pb [Blichert-Toft et al., 1999].
 The systematics of Pb isotopic compositions, particularly in 208Pb/204Pb-206Pb/204Pb space (Figure 4a), require that more than two components be involved in the Mauna Kea lavas. As indicated in section 3, the middepth K/L samples as a group and the rest of the Mauna Kea samples have different Pb isotopic compositions. The K/L samples, which J. M. Rhodes and M. J. Vollinger (submitted manuscript, 2002) refer to as type-3 basalts, are readily identified by their high values of 208Pb/204Pb for a given value of 206Pb/204Pb, but also stand out by their less negative alkalinity, high Ca, Ti, and Nb contents, and low silica (Figure 8). Although J. M. Rhodes and M. J. Vollinger (submitted manuscript, 2002) found these lavas very similar to Loihi basalts, Frey and Rhodes  list these features as characteristic of lavas from Kilauea with respect to Mauna Loa. The 3He/4He ratios of the Mauna Kea samples reach values of up to 25 (M. D. Kurz et al., submitted manuscript, 2002) which would be more diagnostic of Loihi basalts if it was not because 3He/4He values in excess of 20 are also known from Kilauea [Kurz et al., 1996]. More extensive sampling of Kilauea may turn up even less radiogenic He. The Sr, Nd [Garcia et al., 1995], and Hf [Blichert-Toft et al., 1999] (Figure 6) isotope compositions of the two volcanoes are not distinguishable from each other. The isotopic ratio for which the overlap between Loihi and Kilauea data is minimal is 208Pb*/204Pb*, with Loihi values being higher. However, evidence from conventional TIMS data [Staudigel et al., 1984; Garcia et al., 1993, 1995] that these two volcanoes do not overlap in Pb isotope space is not very strong and a better case must await full publication of high-precision triple-spike Pb isotope data [Abouchami et al., 2000a]. By referring to a K/L component, it is not our intention to suggest that a common Kilauea-Loihi component exists which lumps together the properties of these two distinct volcanoes but rather that, based on the available data, one volcano may be as appropriate a reference as the other. With respect to the chronological relationships discussed below, we simply point out here that assigning the K/L (type-3) basalts to a Loihi stage in the evolution of the Mauna Kea volcano requires strengthening of existing arguments.
3He/4He usually is observed to be decoupled from nonvolatile isotopic systems [e.g., Valbracht et al., 1996] but Eiler et al.  demonstrated that, in Hawaiian basalts, there is a strong correlation between 3He/4He and some combination of Pb isotopic ratios that we wish to elaborate further on here. As expected from the PCA results, there is a strikingly positive correlation between 3He/4He and 208Pb*/206Pb* for Mauna Kea (Figure 8a). The K/L samples represent the high-3He/4He and high-208Pb*/206Pb* end-member of this correlation. It can be shown by writing the equation for radiogenic ingrowth that this correlation is not due to mere radiogenic ingrowth of 4He in a closed system:
in which the subscript 0 refers to modern values, T0 is the age of the Earth and λi stands for the decay constant for the nuclide i. Likewise, the radiogenic ingrowth of the 208Pb*/206Pb* ratio is given by
Upon elimination of the Th/U ratio, the last two equations can be combined as:
This relationship indicates that radiogenic ingrowth in a closed system with a broadly uniform 238U/3He ratio but a variable Th/U ratio would lead to a negative correlation between 208Pb*/206Pb* and 3He/4He, which is the opposite of what we observe for the Mauna Kea data (Figure 8a). The trend observed in this figure shows that it is not the variation of the Th/U ratios in the source that creates the observed correlation but mixing between two mantle components with a distinct fractionation/outgassing history: the relatively undegassed K/L component with high 3He/4He (low integrated 238U/3He) happened to have a high source Th/U while the relatively degassed component with a “normal” (7–15) 3He/4He (higher integrated 238U/3He) happened to have a lower Th/U ratio. We are therefore not observing a real correlation between 3He/4He and the U-Th-Pb isotopic system [Eiler et al., 1998] but rather a simple mixing relationship between the 3He/4He and the U/He ratios of two variably outgassed mantle components with different Th/U ratios. In other words, the conundrum of He isotope decoupling from nonvolatile systems is yet to be resolved. This decoupling, which may reflect the decoupled dynamics of volatiles and magmas [Valbracht et al., 1996], probably explains why 3He/4He is so variable in the HSDP-2 samples whereas their εHf is relatively constant.
 The bulk of Mauna Kea samples do not separate into two distinct groups, but rather form a trend that shows that each Mauna Kea sample contains different proportions of a Kilauea-like mantle source (as an example we have singled out the “intermediate Mauna Kea” group as shown in Figure 8). The Kilauea “flavor” is dominant in the nine K/L samples that, according to the age model of D. J. DePaolo et al. (manuscript in preparation, 2003), should be 496–532 kyr old. Kilauea is the youngest aerial Hawaiian volcano. The oldest dated Kilauea sample is only 341 kyr [Quane et al., 2000], but, from the growth model established on Mauna Kea, DePaolo and Stolper  inferred that Kilauea is probably as old as 600 kyr. Because essentially all middepth Kea samples contain some proportion of the K/L component, it is unlikely that the HSDP-2 core inadvertently sampled isolated Kilauea lava flows. As first suggested by Abouchami et al. [2000b], this rather indicates that the young Mauna Kea was tapping a mantle source similar to the source Kilauea is tapping today.
4.4. Time Series Analysis
 With reliable age information, a relatively long core, such as the HSDP-2 core, becomes a prime source of information for the length scales of heterogeneities in the mantle and the timescales of melting processes. One limitation, however, is the possible presence of hiatuses in the volcanic activity at the location of the drill core. The survival time of volcano surfaces (resurfacing time) is, however, known to be a Poisson process. It has been demonstrated that the ages of Hawaiian surface elements are exponentially distributed with, for Kilauea, a mean resurfacing time of about 500 years [Holcomb, 1987], an estimate that also seems to hold for Mauna Loa [Kauahikaua et al., 1995]. The HSDP-2 core counts about 1000 flow units, most of which erupted over a period of about 350 kyr, suggesting an average resurfacing time of 350 years, i.e., not very different from estimates for other volcanoes. Assuming time-invariant resurfacing with an exponential distribution of resurfacing times, the number of lava flows within a given time interval Δt is Poisson-distributed with, for Mauna Kea, a mean value of Δt/350 and a standard deviation of (Δt/350)1/2. An estimate of the maximum error on age assignment at the 1σ level for the entire core is therefore on the order of (1000)1/2*350 ≈ 10,000 years, an uncertainty smaller than that associated with K-Ar ages. Consequently, although basalt production by Mauna Kea probably declined over its lifetime, we can argue that random hiatuses are unlikely to introduce a major bias in the time analysis of the geochemical data.
 The ages in the stratigraphic column have been established by fitting the existing Ar-Ar dates (W. D. Sharp et al., manuscript in preparation, 2003), which are few and have relatively large error bars. Because the samples are irregularly spaced down core, we cannot use standard FFT (Fast Fourier Transform) techniques, as interpolation is known to produce spurious peaks. Instead, we used the method of periodograms specifically designed for unevenly spaced data [Lomb, 1976; Scargle, 1982; Albarède, 1995; Abouchami et al., 2000a] and which is nothing more but a fit of the data by a periodic function of prescribed frequency. For the purpose of not creating spurious peaks at very low frequencies, an appropriate background (i.e., the secular trend) must first be removed. This background was evaluated here by smoothing the data with a Gaussian filter, which is a running mean with weights normally distributed around the point to be smoothed (Figure 9). The standard deviation of 50,000 years chosen here for this filter ensures there is no significant bias in the high-frequency range. Other values of the standard deviation were tested with no or only very little consequence to the well-constrained part of the spectrum, but our option was that peaks beyond 50,000 years are insufficiently constrained within the considered time window and were therefore ascribed to the secular trend. Once normalized to the standard deviation of the analyzed variable, the peak heights can be associated with significance levels allowing for the probability that the peak is not a false alarm to be estimated [Scargle, 1982].
Tables 2 and 3 presents the results of the periodogram analysis before and after removal of the secular trend for the isotopic compositions of Hf, Pb, Nd, Sr (Nd and Sr data from J. G. Bryce et al. (manuscript in preparation, 2003)), and He (from M. D. Kurz et al., submitted manuscript, 2002), for the incompatible element ratios La/Yb (from S. Huang and F. A. Frey, submitted manuscript, 2002) and Zr/Nb, and for alkalinity (two latter both from J. M. Rhodes and M. J. Vollinger (submitted manuscript, 2002)) in Mauna Kea flows. The results for Pb and Hf isotopic data after removal of the secular trend are shown in Figure 10. These results report the frequency at the peak, the power (height of the peak), the period (one over the frequency), and the confidence level. Only peaks with confidence levels in excess of 50 percent have been considered. As it is clear that some of the peaks are harmonics of lower frequency (longer period) fluctuations, we plotted the base-two logarithm of the peak heights obtained after applying the Gaussian filter (Figure 11). In this base, two peaks differing by one unit are harmonics of each other (multiplication by two). The strongest peaks characterizing the trace element ratios and alkalinity signal are less significant than those characterizing the isotopic ratios, which strongly suggests that melting blurs the signal of source heterogeneity. Two families of peaks emerge that differ by a factor of four and therefore are double harmonics of each other. These two groups of peaks (one at 4500–5000 years, the other at 17,000–19,000 years) may not represent fundamental periods but the HSDP-2 core is currently too short to allow for the identification of potentially longer periods. These two groups involve the incompatible element ratios La/Yb and Zr/Nb, 87Sr/86Sr, 206Pb/204Pb, 207Pb/206Pb, 208Pb/206Pb and at a lower confidence level 176Hf/177Hf. In addition to the stable 19,000 years period, the unfiltered data show strong 10 kyr peaks consistent with the 206Pb/204Pb peak found by Abouchami et al. [2000a] on the pilot core and by J. Eisele et al. (submitted manuscript, 2002) for the HSDP-2 samples, but this feature appears to be an intermediate harmonics that disappears after removal of the secular trend. Slower and very significant fluctuations are observed for 207Pb/204Pb (48,000 years), probably in phase and harmonic relationships with those of Hf (50,500 and 115,000 years) and reproduce the strong peak observed at 48,000 years by Abouchami et al. [2000a] on the pilot core. The 208Pb*/206Pb* peak has a low confidence level (0.59) and its position moves from 714,000 to 96,000 upon removal of the secular component (Tables 2 and 3). Neither 3He/4He nor εNd variations seem to have a periodic component in that time window. Input of the K/L component does not seem to be a periodically recurring phenomenon.
Table 2. Most Significant Peaks of the Lomb Periodograms Before Removal of the Secular Trend
Period T, ka
S. Huang and F. A. Frey (submitted manuscript, 2002).
J. G. Bryce et al. (manuscript in preparation, 2003).
J. M. Rhodes and M. J. Vollinger (submitted manuscript, 2002).
DePaolo  discussed the existence of recurring geochemical patterns in the pilot core with the help of a chromatographic model. A particularly interesting application is the possibility of relating the phase separation between the various isotopic patterns to the hydrodynamic dispersivity of the porous flow. The chromatographic model, however, assumes Henry's law behavior for all the melt components, and hence a complete decoupling of trace and major elements. It is therefore required that incompatible elements, such as Nd and Hf, move faster than the major elements which make up the melt itself [Albarède, 1995, p. ∼517]. Although the assumption that the mobile phase is inert with respect to the stationary phase is acceptable for column chromatography in the laboratory, it is inadequate for basaltic melts that may react with the porous peridotite matrix. Consequently, we consider that the recurring character of the isotopic patterns in the HSDP-2 core reveal source characteristics rather than hydrodynamic features.
4.5. Size of Mantle Heterogeneities
 With rare exceptions [Nataf and VanDecar, 1993], plume conduits away from ridge axes are too thin to be observed by seismic waves. It is usually assessed that an upper limit of the conduit diameter is the Fresnel zone of body seismic waves, i.e., the interval between two objects that scattering at the P and S wavelengths does not allow to separate. It is therefore assumed that plume conduits must be narrower than this wavelength, i.e., on the order of a few tens of kilometers, a diameter confirmed by geodynamic modeling [Loper and Stacey, 1983; Olson et al., 1993].
 The shape and volume of the mantle source in the plume conduits that Hawaiian volcanoes actually tap is unclear. Consequently, the shape of isotopic heterogeneities becomes relevant to the interpretation of their record in volcanic time series. Ribe and Christensen  assumed that melt is extracted vertically at steady state and considered that, when moving across the plume conduit over their lifetime (approximately 1 My), Hawaiian volcanoes tap a disk-shaped volume centered on the summit. They estimated the instantaneous eruption rate Qe as the integral of the melt supply rate q (x, y) of the plume conduit over the area of a disk of radius r as:
where x is the coordinate on the lithosphere along the volcanic chain axis, y the transverse coordinate, V the plate velocity, and ρc the basalt density. They determined that a value of r = 33.6 km accounts for the typical volume of a single volcano. We can likewise determine the instantaneous concentration of a particular element in the erupted lava as:
This complex formula expresses the rather trivial statement that a basalt has the composition of its constitutive melt packets weighted by their respective sizes. The model used by DePaolo et al.  uses a geometry similar to that of Ribe and Christensen  and a steady state melting column to constrain the melt supply rate q(x, y) and then inverts the set of geochemical data on Hawaiian volcanoes to produce C(x, y) maps and their isotopic analogs. Both Ribe and Christensen  and DePaolo et al.  therefore assume that the geochemical cross section of the plume conduit is time invariant. A similar assumption was used by J. Eisele et al. (submitted manuscript, 2002) to model their time series of Pb isotopes: these authors view heterogeneities as very long filaments stretched parallel to the plume axis such that fluctuating isotopic compositions exclusively reflect the density of filaments across the plume conduit.
 However, whether volcanic successions record a horizontal compositional gradient across the plume conduit at the successive locations of the volcano summit or vertical heterogeneities in the plume conduit is arguable (Figure 12). If we ignore the upward broadening of the plume conduit, the equation for advective transport in two dimensions can be formulated as
where vz is the upwelling velocity. For a hot spot the strength of Hawaii, modeling predicts centerline vertical velocities of about 1 m/yr [Loper and Stacey, 1983; Olson et al., 1993; Schubert et al., 2001], which indicates that the vertical component of heterogeneity gradients cannot be neglected with respect to the radial components. Two factors will therefore contribute to increase the relative importance of the second term on the right-hand side of the above equation with respect to the first term: (i) the plate velocity V is likely to be smaller than the upwelling velocity vz, and (ii) cross-sectional heterogeneities (as measured by ∂C/∂x) will be horizontally averaged by magma extraction.
 The size and shape distribution of heterogeneities is largely unknown since numerical experiments of continuum mechanics, such as those used by Farnetani and Richards , Ribe and Christensen , and Farnetani et al.  must mesh the mantle using elements with a dimension still fairly coarse (10–20 km) with respect to the radius of the conduit and the source disk. Stretching in plume conduits is, however, potentially significant, although far less important than in plume heads [Farnetani et al., 2002]. With stretching simply reflecting velocity gradients, its effect on bulk compositions is minimized by the mere fact that the very slow outer conduit layers will have a very small contribution to the overall material budget of the plume. The reason why heterogeneities stretched along the conduit walls are unlikely to contribute significantly to the magma budget is the same as that accounting for the apparent lack of entrained upper mantle in the source of hot spot basalts [Farnetani and Richards, 1995; Ribe and Christensen, 1999]: temperature dependence of viscosity in a strong temperature gradient confines plume flow to a well-defined high-velocity conduit with a rather sharp, efficiently “lubricated” edge, and with piston flow as the best analogue. We do not claim here that the plume-conduit cross section is geochemically homogeneous (“striped” plume), and the very existence of contrasting Kea and Loa trends is there to illustrate it. However, ignoring the vertical component of heterogeneities along the conduit is bound to result in inadequate description of the plume.
 If the observed peaks in our periodograms (Figure 11) are fundamental and not harmonic modes of much slower fluctuations, they may be taken as indicating that the diameter of the mantle plume is at least on the order of a few kilometers to a few tens of kilometers. Davies [1988, 1999] and Sleep  argued that the Hawaiian swell, i.e., the area of shallower seafloor depth around the hot spot, is due to upwelling of hot and therefore light material. In contrast, Phipps Morgan et al.  argued that a large part of the buoyancy flux may be due to the depletion of the upwelling material. From the geometry of the Hawaiian swell and the assumption that the excess buoyancy is entirely of thermal origin, the flux of plume material Qp was inferred to range from 7.5 km3/yr [Davies, 1988] to 9.5 km3/yr [Sleep, 1990], which Ribe and Christensen  reduced to less than 4 km3/yr. The magma production of the recent Hawaiian volcanoes is of about 0.1–0.2 km3/yr [Swanson, 1972; Clague and Dalrymple, 1987; Moore, 1987; Watts and ten Brink, 1989] but may drop to a mean value of 0.03 km3/yr or less when integrated over the entire volcanic chain [Clague and Dalrymple, 1987; Davies, 1999]. Such a value corresponds to 1–5 percent of the hot spot upwelling rate, a number consistent with the degrees of melting inferred from petrological and geochemical arguments.
 For isotopic fluctuations modulated by plume flux, it is possible to evaluate the amount of plume material upwelling between two surges of a particular component and elaborate on characteristic length scales associated with isotopic heterogeneities. Hafnium isotope and 207Pb/204Pb fluctuations come in “cycles” of T = 50,500 years and therefore, using Ribe and Christensen's  value of 4 km3/yr, are associated with packets of mantle with a volume ΔV = QpT (Figure 13) of about 202,000 km3. The range of plume conduit radii and upwelling velocities must be consistent with continuum mechanics constraints [Schubert et al., 2001]. If we assume a maximum radius R of the hot spot conduit of about 50 km (as suggested by the width of the Fresnel zone of P and S waves), the layers with a same mean isotope composition must be separated by an interval Δl = ΔV/4πR2 of about 6.5 km and the upwelling velocity vz = Δl/T must be 13 cm/yr. Such a low velocity is equivalent to the plate velocity and therefore is at odds with the apparent fixity (or near fixity) of the Hawaiian hot spot over most of the Cenozoic. With a conduit radius R = 10 km, the separation Δl would increase to 160 km and the upwelling velocity vz to 3 m/yr, a value more consistent with the hot spot remaining fixed in the upper mantle circulation. All these results are contingent on the assumption that we successfully identified the fundamental mode and not the harmonics: if, as suggested by J. Eisele et al. (submitted manuscript, 2002), the strongest Pb isotope period is 100 kyr rather than 50 kyr, the length scale of heterogeneities should be modified accordingly. Only future deepening of the HSDP-2 drill hole may resolve this ambiguity.
Appendix A:: Evidence for Pb Isotope Fractionation on Anion-Exchange Columns in HCl Medium
 This experiment, carried out in the clean laboratory in Lyon, was designed to elucidate whether incomplete yields of Pb elutions can account for significant isotope fractionation during chemical processing of samples. Twenty micrograms of NIST 981 Pb standard were evaporated, loaded in 2.5 N HCl on 1ml AG1-X8 200-400 mesh anion-exchange resin, and then eluted with the same acid. The 208Pb signal and the Pb isotopic composition of each fraction were measured on the Plasma 54. We found that 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb were fractionated by several permil across the elution peak (Figure 14) and that isotopic fractionation was mass dependent (Figure 15). We used the same procedure, essentially a fit of the elution curve of each isotope by an error function, as in the work of Maréchal and Albarède , to retrieve the partition coefficient of each isotope. We found that a partition coefficient of 30, which is consistent with the classical results of Kraus and Nelson , and a variation of the partition coefficients of 40 ppm per mass unit account extremely well for the observed results. We then integrated the isotopic ratios of the individual fractions collected up to a certain yield (Figure 16) in order to evaluate the potential isotopic bias introduced by incomplete recovery of sample Pb. Although the conditions used to establish mass-dependent fractionation of Pb isotopes on the column are slightly different from those used for sample elution, notably a larger column volume and a weaker HCl normality, they illustrate that a chemistry yield of less than 100 percent may introduce a mass bias that could be mistaken for a mass spectrometry artifact.
 We thank Philippe Télouk for assistance with the Plasma 54 and the French Institut National des Sciences de l'Univers through the program Intérieur de la Terre and the Belgian Fonds National de la Recherche Scientifique for financial support. Reviews by Wafa Abouchami, Al Hofmann, Don DePaolo, Fred Frey, and Bill White and discussions with Cinzia Farnetani and Yanick Ricard helped improve the manuscript considerably.