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 We analyzed Pb isotopic compositions of 50 samples from the HSDP-2 drill hole, covering the time interval 180 to 550 kyr B.P. in the stratigraphic record of Mauna Kea. All analyses were corrected for instrumental bias using a triple-spike technique. The aims of this study are to document temporal changes in sources contributing to Mauna Kea and to investigate how these may relate to the chemical structure of the Hawaiian plume. Lead isotopic compositions of the lavas have 206Pb/204Pb ratios ranging from 18.41 to 18.63, 207Pb/204Pb from 15.47 to 15.49, and 208Pb/204Pb from 37.97 to 38.22. In 207Pb/204Pb-206Pb/204Pb space, the samples display a broad linear array, while three distinct arrays are found in 208Pb/204Pb-206Pb/204Pb space. These arrays can clearly be distinguished by their 208Pb/204Pb ratios and are referred to as “Kea-lo8,” “Kea-mid8,” and “Kea-hi8.” The 206Pb/204Pb isotope ratios exhibit rapid shifts by ∼0.2 over 100 m depth intervals, and jumps from one Pb isotope array to another and back in less than ∼100 m depth. Despite these rapid Pb isotope fluctuations, a particular Pb isotope array dominates over periods of several tens to hundreds of kiloyears. We interpret the Pb isotope arrays found in HSDP-2 in terms of mixing of end-members lying along the radiogenic and unradiogenic extensions of the arrays. At the radiogenic extension the three HSDP-2 arrays converge to a common end-member. The lower extensions of the arrays diverge in three directions, each with different 208Pb/204Pb ratios. This topology suggests that the HSDP-2 arrays were produced by mixing of at least four end-members. The origin of these end-members was investigated using Monte Carlo simulations of a Pb isotope evolution model. The simulations suggest that the common radiogenic end-member of the three Pb isotope arrays contains material with elevated μ values and has a relatively young age (<1.5 Ga). Such a signature can be plausibly interpreted in terms of the presence of recycled oceanic crust in the source. The HSDP-2 Kea-lo8, Kea-mid8, and Kea-hi8 Pb isotope arrays dominate over different time periods and can be related to the displacement of Mauna Kea relative to the plume center over time. The Kea-lo8 array is present between ∼180 and 370 ka and samples more peripheral parts of the plume, while the Kea-mid8 and Kea-hi8 arrays occur in the deeper parts of the core (∼370 to 550 kyr ago), when Mauna Kea was closer to the plume center. Over the time intervals when each array dominates, we derive corresponding “lengths” of materials in the source by integrating the estimated upwelling velocity across the plume. These calculations suggest Pb isotope heterogeneities of at least several tens of kilometers in vertical length within the Hawaiian plume. The Pb isotope arrays may correspond to relatively small-scale heterogeneities derived from the D″ layer in the lower mantle.
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 Lead isotopic compositions of Hawaiian volcanoes are particularly interesting because they form linear arrays in 208Pb-207Pb-206Pb-204Pb isotope space [e.g., Tatsumoto, 1978]. The slopes of the arrays in 207Pb/204Pb-206Pb/204Pb space carry age information if interpreted as isochrons [Tatsumoto, 1978; Chase, 1981]; alternatively, these arrays may be interpreted in terms of binary mixing [Tatsumoto, 1978; Abouchami et al., 2000a]. Since there are three radiogenic Pb isotope ratios, this allows identification of mixing processes in three-dimensional isotope space. High-precision triple-spike Pb isotopic compositions of Mauna Kea lavas from the pilot hole of the Hawaiian Scientific Drilling Project (HSDP-1) [Abouchami et al., 2000a] together with those of other Hawaiian volcanoes [Abouchami et al., 2000b] demonstrate the existence of linear arrays in Pb isotope space for each volcano.
 The HSDP-2 drill hole record provides an unprecedented means for looking at the long-term Pb isotope fluctuations of a single Hawaiian volcano, and thus allows drawing inferences regarding the Pb isotope structure of the Hawaiian plume. Here we report Pb isotope data for fifty samples from HSDP-2, obtained using a triple-spike technique [Galer, 1999], which show the presence of three distinct Pb isotope arrays in the long-term record of Mauna Kea lavas. We interpret these Pb isotope arrays in terms of mixing, and investigate the pre-eruptive history of the mixing end-members using Monte Carlo simulations of a three-stage Pb isotope evolution model. Using a time series analysis, we examine the possible length scales and distribution of Pb isotope heterogeneities within the Hawaiian plume.
 Lead isotopic compositions were determined on fifty Mauna Kea lavas and one Mauna Loa sample from HSDP-2. These samples cover a depth range from 125 to 3068 meters below sea level (mbsl). The data set also includes Pb isotopic compositions of seven samples from the HSDP-1 pilot hole reanalyzed here, analyses of two HSDP-2 drilling mud samples, and results of leaching experiments on sample R-365. Analytical methods are described in Appendix A, and the Pb isotope data are summarized in Table 1. Fourteen of the HSDP-2 analyses were duplicated, six of which were replicate runs on the same dissolution and eight of which were duplicate dissolutions. The external reproducibility on Pb isotope measurements is discussed in Appendix B and illustrated in Figure 1. The two sigma deviation from a mean value on 14 duplicate analyses of HSDP-2 samples is 0.0019 (100 ppm) for 206Pb/204Pb, 0.0020 (130 ppm) for 207Pb/204Pb and 0.0060 (160 ppm) for 208Pb/204Pb (Figure 1; Table 1) (see also Appendix B).
Pb isotope ratios in italics are from Abouchami et al. [2000a]. The age model is from DePaolo et al. (submitted manuscript, 2003). The 2σ values are the last significant decimals of the given ratio. The 208Pb*/206Pb* is defined as ([208Pb/204Pb]sample − 29.475)/([206Pb/204Pb]sample − 9.307).
 Lead isotope ratios of HSDP-2 Mauna Kea samples range from 18.41 to 18.63, 15.47 to 15.49 and 37.97 to 38.23, for 206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb ratios, respectively (Table 1, Figures 2a and 2b). The single Mauna Loa sample analyzed in this study has the following Pb isotope composition: 206Pb/204Pb = 18.22, 207Pb/204Pb = 15.46 and 208Pb/204Pb = 37.96. The lead isotope variations are resolved at about 120, 10 and 40 times the external precision for the 206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb ratios, respectively, as inferred from duplicate measurements.
 In 207Pb/204Pb-206Pb/204Pb space (Figure 2b), the samples form a broad band, whereas the 208Pb/204Pb-206Pb/204Pb relationships (Figure 2a) clearly show the presence of three separate groups having distinct 208Pb/204Pb ratios for a given 206Pb/204Pb ratio. Because the three arrays converge as the 206Pb/204Pb ratio increases, a unique assignment for the most radiogenic samples to a specific array is difficult. We nevertheless subdivided the samples into three groups and assigned each of the samples to a specific array. In the following, we will refer to these arrays as “Kea-lo8,” “Kea-mid8” and “Kea-hi8,” corresponding to the sample groups with the lowest, intermediate and highest 208Pb/204Pb ratios, respectively (Figure 2a). The samples defining the Kea-hi8 group have been referred to elsewhere as “type-3” basalts (J. M. Rhodes and M. J. Vollinger, Composition of basaltic lavas sampled by Phase-2 of the Hawaii Scientific Drilling Project: Geochemical stratigraphy and magma types, submitted to Geochemistry Geophysics Geosystems, 2003) and “K/L samples” [Blichert-Toft et al., 2003].
 Sample SR0222-2.00 could conceivably be assigned to either the Kea-lo8 or Kea-mid8 arrays. However, on the basis of its stratigraphic position (see below), we chose to incorporate it into the Kea-lo8 array. The most radiogenic sample of the data set - SR0855-0.10 - falls close to the Kea-hi8 array, and is thus attributed to this group rather than to the Kea-mid8 array.
 We performed linear regressions on the three arrays, using the method of Williamson  and the results are summarized in Table 2. In 207Pb/204Pb-206Pb/204Pb space, the Kea-lo8 regression line, including sample SR0222-2.00, yields a slope of 0.082 ± 6, corresponding to a Pb-Pb model age of 1.25 ± 0.14 Ga. However, these results are strongly dependent upon this one data point, because excluding it would modify the slope to 0.0067 ± 8, resulting in a negative model age. The regression lines of the Kea-mid8 and Kea-hi8 arrays in 207Pb/204Pb-206Pb/204Pb space have relatively shallow slopes of 0.0797 ± 30 and 0.0973 ± 36, corresponding to Pb-Pb model ages of 1.19 ± 0.08 and 1.57 ± 0.07 Ga, respectively (Table 2). Omitting sample SR0855-0.10 from the Kea-hi8 array does not significantly alter the regression results (slope = 0.0952 ± 96 and age = 1.53 ± 0.19 Ga). The reduced chi-square values (χ2red.) are greater than 1 (Table 2), indicating that the average deviation of the samples from a linear regression model is greater than the analytical precision. These observations suggest that the arrays in Pb isotope space are not strictly linear in a statistical sense, and the data do exhibit some real residual scatter. A possible origin for this scatter is discussed below and in Appendix B.
Regressions were performed using the Williamson  method. Errors are reported at 95% confidence (2σ). χ2red., reduced chi-squared (MSWD); τ, model age.
2.2. Lead Isotope Comparison Between HSDP-1 and HSDP-2
 The range in Pb isotopic compositions measured in HSDP-2 lavas is broadly similar to that found in HSDP-1 samples [Abouchami et al., 2000a]. In particular, the Kea-lo8 array samples share strong similarities with HSDP-1 samples [Abouchami et al., 2000a] - both groups have relatively low 208Pb/204Pb ratios and form arrays in 208Pb/204Pb-206Pb/204Pb space with slopes that are identical within error (Figure 3a). However, the Kea-lo8 samples extend to less radiogenic 207Pb/204Pb and 208Pb/204Pb ratios than the “normal Kea” array from HSDP-1 [Abouchami et al., 2000a]. The variation in 207Pb/204Pb of HSDP-2 lavas is about half that found in HSDP-1 lavas, and the data points lie between the “normal” and “anomalous” Kea arrays of Abouchami et al. [2000a] (Figure 3b). To explore the possible reasons for this difference, we reanalyzed some samples from HSDP-1 (Figure 3). The latter show an offset similar to that observed between HSDP-1 and HSDP-2 samples. The possible reasons for this result are discussed in detail in Appendix B, but it appears that the offset is most likely due to variable subaerial contamination of the samples.
 The relationships in 208Pb/204Pb-206Pb/204Pb space show that HSDP-1 samples lie along the Kea-lo8 array, suggesting that they belong to the same group (Figure 3a). This is also consistent with the stratigraphic range covered by the HSDP-1 hole and the occurrence of Kea-lo8 samples at shallower levels in the HSDP-2 hole (Figure 4). For a given 206Pb/204Pb ratio, 207Pb/204Pb ratios vary by ∼0.01 within the Kea-lo8 array (Figure 2). This variation is equivalent to the difference observed between the “normal” and “anomalous” HSDP-1 Mauna Kea arrays [Abouchami et al., 2000a]. Re-evaluation of the HSDP-1 data in the light of the HSDP-2 results suggests that the existence of two distinct Pb isotope arrays within the Mauna Kea section is questionable. It is important to note, however, that the sampling density of HSDP-2 is greater than HSDP-1 and, with the exception of the Kea-lo8 samples, the rest of the HSDP-2 data fall within the range defined by the HSDP-1 and Kea-lo8 arrays. For clarity and internal consistency, only samples analyzed in this paper from the main HSDP hole (HSDP-2) will be considered further when discussing the 207Pb/204Pb-206Pb/204Pb and 208Pb/204Pb-206Pb/204Pb relationships of Mauna Kea lavas.
2.3. Lead Isotope Stratigraphy
 The Pb isotope stratigraphy of HSDP-2 is shown in Figure 4 and displays the following features: (1) relatively small overall isotopic variability in 206Pb/204Pb ratio of ∼0.25, (2) rapid shifts in 206Pb/204Pb ratio by ∼0.2 within 100 m depth intervals (for example, at ∼1400 mbsl and at ∼2600 mbsl), (3) no unidirectional isotopic trend toward higher or lower 206Pb/204Pb ratios, and (4) jumps from one Pb isotope array to another and back again in less than ∼100 m depth intervals.
 Lavas belonging to the Kea-lo8 Pb isotope array are found systematically at depths less than 750 mbsl. A possible exception is sample SR0222-2.0, which we have placed into the Kea-lo8 group, but could also be part of the Kea-mid8 array. Samples from the Kea-mid8 array occur throughout the whole HSPD-2 core, in the depth range from 750 mbsl to 3068 mbsl. Kea-hi8 array samples are mainly confined at two depth intervals, from 1973 to 2123 mbsl and from 2321 to 2503 mbsl, but also appear as several intercalated lavas at depth below 2500 mbsl (see Figure 4). One of these intercalated lavas is sample SR0855-0.10, for which it is unclear whether it belongs to the Kea-mid8 or Kea-hi8 group.
 The three Mauna Kea Pb isotope arrays can also be distinguished by their different radiogenic 208Pb*/206Pb* ratios (Figure 4b). The radiogenic 208Pb*/206Pb* ratio represents the time-integrated 232Th/238U ratio since formation of the Earth and is defined as ([208Pb/204Pb]sample − 29.475)/([206Pb/204Pb]sample − 9.307) [Galer and O'Nions, 1985]. Although there is some overlap in 208Pb*/206Pb* ratio between the different sample groups, the Kea-lo8 array clearly exhibits the lowest 208Pb*/206Pb* ratios of 0.933 ± 3, the Kea-mid8 has intermediate 208Pb*/206Pb* ratios of 0.939 ± 5, while the Kea-hi8 array has the highest 208Pb*/206Pb* of 0.949 ± 9 (means and 2σ variation).
 The Pb isotope stratigraphy of the HSDP-1 and HSDP-2 cores agree with one another to 750 mbsl depth (Figures 4c and 4d), and this is also supported by the similarities of the Kea-lo8 and HSDP-1 samples observed in Pb isotope space (see Figure 3). At depths greater than 750 mbsl, some HSDP-2 samples have lower 206Pb/204Pb ratios (at 800–900 mbsl) (Figure 3c). However, in Pb-Pb space, it remains unclear whether the two HSDP cores have different Pb isotopic compositions at depths greater than 750 mbsl, because most available data were obtained by conventional TIMS [Lassiter et al., 1996], with the exception of three triple spike analyses [Abouchami et al., 2000a]. The latter three analyses lie at the intersection of the Kea-lo8 and Kea-mid8 arrays (Figure 3), making it difficult to assess whether Kea-mid8 array lavas are present in the HSDP-1 core as well.
 The HSDP-1 and HSDP-2 drill holes are located about 1.2 km apart, but cannot be correlated on the basis of flow units. However, the overall similarity of HSDP-1 and HSDP-2 Pb isotope systematics in the upper 1200 m (Figure 2) implies some lateral compositional continuity between the two cores. For example, both cores have low 206Pb/204Pb ratios of ∼18.43 at about 300 m depth and increase up to ∼18.53 at about 600 m depth (Figure 4c). From this, we conclude that there is no fundamental discrepancy between the two compositional depth profiles. The 208Pb*/206Pb* stratigraphy shows rapid short-term oscillations, making this parameter unsuitable for correlating the two holes (Figure 4d).
3. Interpretation of the Pb Isotope Arrays
3.1. Contamination Issues
 The Pb isotopic compositions of basalts are susceptible to alteration after eruption by contamination from dust, seawater alteration and subaerial weathering, as well as by contamination during sampling and sample processing [see, e.g., McDonough and Chauvel, 1991; Thirlwall, 2000]. Because of recent improvements in analytical precision, previously undetectable contamination effects may be significant and may not have been totally eliminated by the standard leaching procedure adopted. They probably represent the limiting factor for the accuracy of Pb isotope analyses (see Appendix B). This problem potentially applies to the HSDP-2 Pb data presented here. However, two observations suggest that the Pb isotope differences between the three Kea arrays found in HSDP-2 represent variations in the lavas themselves and not variable degrees of contamination. First, the absolute variation in the measured 207Pb/204Pb ratio is very small (∼0.02), while there are larger differences in slopes and relative positions of the arrays in 208Pb/204Pb-206Pb/204Pb space (Figure 2). Since potential contaminants can be expected to possess 207Pb/204Pb and 208Pb/204Pb ratios distinct from those of the Mauna Kea lavas [Abouchami et al., 2000a], contamination should influence both the 207Pb/204Pb and 208Pb/204Pb ratios of a given sample. Second, duplicate dissolutions of eight HSDP-2 samples had reproducible Pb isotope compositions (Figure 1). Overall, we consider the three different Pb isotope arrays to reflect primary magmatic signatures.
 The three groups of samples of HSDP-2 lavas do not strictly form linear arrays within analytical precision in Pb isotope space, as shown by linear regression (see Table 2). Consequently, the Pb isotope arrays cannot be considered as purely binary mixtures, and an additional process is necessary to explain the residual scatter. These slight deviations from strictly linear relationships may be due either to variable degrees of contamination, or imply that more than two source end-members (asthenospheric or lithospheric) are present. However, the fact that the different linear arrays are still recognizable (Figure 2a) indicates that binary mixing is the dominant process, and that contribution from a third end-member must be relatively minor.
3.2. Isochrons Versus Mixing Lines
 Linear arrays in Pb isotope space can be interpreted as either isochrons or binary mixing lines. Abouchami et al. [2000a] suggested an approach for distinguishing between these two possibilities. Their argument was based on the comparison of the κ ((232Th/238U)today), as calculated from the regression lines in Pb isotope space, with the measured 232Th/238U ratio κ* of the lavas. If κ* is significantly different from κ, the Pb isotope arrays are unlikely to represent isochrons, and are better interpreted as mixing lines (see Abouchami et al. [2000a] for details). These authors also showed that the κ calculated from the slope of the Pb isotope arrays in 208Pb/204Pb-206Pb/204Pb space is relatively insensitive to the differentiation “age.”
 The κ values inferred for the Kea-lo8, Kea-mid8 and Kea-hi8 arrays are 3.88 ± 0.06, 1.80 ± 0.03, and 0.90 ± 0.03, respectively (Table 2). These values are significantly different from the 232Th/238U ratios (= κ*) of 3.21 ± 0.23 recalculated from the measured concentration ratio (Th/U = 3.10 ± 0.23) in HSDP-2 glasses [Jochum et al., 2000; Amini et al., 2002]. Thus, the best interpretation of the three HSDP-2 arrays is that they correspond to binary mixing lines.
3.3. Principal Component Analysis
 We performed a Principal Component Analysis (PCA) of the HSDP-2 Pb isotope data set to complement that already presented for the HSDP-1 pilot hole samples [Abouchami et al., 2000a]. The methods follow closely those already described (see Allègre et al. , Albarède , and Abouchami et al. [2000a] for details). In brief, PCA of three independent variables results in the definition of three orthogonal eigenvectors (v1, v2 and v3) and associated eigenvalues λ1, λ2 and λ3. The vector v1 lies along the direction of maximum variance in the data set, while v3 represents the least variance. In addition, the eigenvalues correspond to the proportions of the data set variance that can be ascribed to each eigenvector. By plotting the data set projected onto the v1-v2 plane (i.e., perpendicular to v3), for example, the data can be illustrated in 2-D, corresponding to the directions of maximum variance in 3-D. Thus, the aim here is primarily to facilitate a better appreciation of how the data are distributed in 3-D Pb isotope space, since this is often hard to “visualize” using conventional Pb isotope plots (see Figure 2).
 The eigenvectors calculated for the HSDP-2 Pb isotope data set are: v1 = (0.6562, 0.1714, 0.7349), v2 = (0.6135, 0.4458, −0.6518) and v3 = (0.4393, −0.8786, −0.1874). They are shown projected perpendicular to each of the three eigenvectors in turn in Figures 5a, 5b, and 5c. The eigenvalues λ1, λ2 and λ3, corresponding to v1, v2 and v3, are 2.146, 0.754 and 0.100 (summing to 3.0), from which it follows that 71.5% of the data set variance can be accounted for by v1, 25.1% by v2, and only a very minor amount (3.3%) by v3, respectively. Thus, v1 and v2 together represent ∼97% of the variance present, implying that the HSDP-2 data can be well approximated by a plane in 3-D Pb isotope space (see Figure 5).
 The distinction between the Kea-lo8, Kea-mid8 and Kea-hi8 arrays can be seen quite clearly in Figure 5a, in the plot of v1 versus v2. Figures 5b and 5c show the HSDP-2 data set viewed from two complementary directions at right-angles to that depicted in Figure 5a. Eigenvector v1 lies roughly along the Kea-mid8 array, while v2 defines the “offset” between the three arrays. This offset is mostly in the 208Pb/204Pb direction, as can be appreciated from the location of the projected 208Pb/204Pb axis in Figure 5c.
Figure 6 shows the projected HSDP-2 data together with available triple-spike Pb isotope data from Mauna Kea lavas from the HSDP-1 pilot hole (Table 1) [Abouchami et al., 2000a]. Most of the HSDP-1 data lie close to the HSDP-2 Kea-lo8 array (Figure 6a), which is to be expected given that the Kea-lo8 array is found in the upper parts of the HSDP-2 core where stratigraphic overlap of the two cores should occur. Figures 6a and 6c suggest, in addition, that some of the HSDP-1 lavas may share affinities with the Kea-mid8 and Kea-hi8 arrays.
4. Mauna Kea End-Members and Th-U-Pb Differentiation
4.1. Mauna Kea End-Members
 The three Pb isotope arrays are interpreted in terms of mixing between end-members that must lie along the radiogenic and unradiogenic extensions of the arrays (Figures 7a and 7b). Here we assess the number and composition of end-members involved in the formation of these arrays. The 95% confidence intervals of the regression lines are shown in Figures 7a and 7b.
 The “radiogenic extensions” of the HSDP-2 regression lines broadly converge toward a single end-member. The intersection field of the regressions at the 95% confidence level has a 206Pb/204Pb ratio between 18.60 and 18.75 and a 208Pb/204Pb ratio between 38.20 and 38.26 (Figure 7a). The 207Pb/204Pb ratio of the common intersection field lies between 15.48 and 15.50 (Figure 7b). The fact that an intersection point exists may mean that all lavas share a “common” radiogenic end-member with this composition. The intersection field differs from the “Kea component” proposed by Eiler et al.  in that it has more radiogenic 207Pb/204Pb and 208Pb/204Pb ratios (Figure 7). The presence of a common radiogenic end-member is also supported by the PCA projections of the HSDP-2 data set illustrated in Figure 5, which show the Kea-lo8, Kea-mid8 and Kea-hi8 arrays converging to a common point in 3-D Pb isotope space.
 Assuming that each of the three HSDP-2 arrays predominantly represents binary mixing, then at least four components are required to explain the Pb isotope systematics of Mauna Kea – a common radiogenic end-member and three independent unradiogenic end-members lying at the lower extensions of the 208Pb/204Pb-206Pb/204Pb arrays (Figure 7a). In principle, it is possible to explain multiple linear arrays lying in a plane by mixing only three end-members [Douglass and Schilling, 2000]; however, this scenario would require rather special circumstances of premixing between two end-members in specific proportions (e.g., premixing Kea-hi8 and Kea-lo8 end-members to create the Kea-mid8 array) [Abouchami et al., 2000a].
 Regardless of the exact number of end-members involved, it is clear that there is considerable heterogeneity in Mauna Kea lavas, requiring not one or two, but several end-members heterogeneously distributed in the Hawaiian plume. The Pb isotope end-members of HSDP-2 have been compared with the Pb isotope arrays found for other Hawaiian volcanoes [Abouchami et al., 2000b]. The end-member on the lower extension of the Kea-hi8 array shares similarities with Loihi lavas, while the Kea-mid8 array as a whole is similar to Kilauea lavas [Abouchami et al., 2000b; W. Abouchami et al., Long-lived heterogeneities and asymmetry of the Hawaiian plume, manuscript in preparation, 2003 (hereinafter referred to as Abouchami et al., manuscript in preparation, 2003)]. Thus, we disagree with the assessment of Blichert-Toft et al.  that there is a common “Kilauea-Loihi component” present.
4.2. Pb Isotope Character and Evolution of Mauna Kea End-Members
 In Pb isotope space, the depleted character of Mauna Kea lavas is manifested by relatively low 207Pb/204Pb and 208Pb/204Pb ratios for a given 206Pb/204Pb ratio when compared with other OIB (Figures 7c and 7d) [Thirlwall, 1997]. Such compositions suggest relatively low μ values (≡(238U/204Pb)today) in the early history of the source, together with relatively low Th/U ratios. The HSDP-2 Pb isotope arrays have substantial differences in the 208Pb/204Pb ratios of the end-members involved, and also show small variations in their 207Pb/204Pb ratios (Figure 7). Such characteristics can be explained by calling upon relatively recent differentiation of the source materials. Indeed, recent Th-U-Pb differentiation would only cause subtle differences in the present-day 207Pb/204Pb ratios, because 235U is virtually extinct at present, while variations in 206Pb/204Pb and 208Pb/204Pb ratios could still occur.
4.3. Pb Isotope Evolution Model for the End-Members: A Monte Carlo Approach
 The Pb isotope systematics of HSDP-2 suggest little variation in the 207Pb/204Pb ratios of the end-members, while four end-members with distinct 208Pb/204Pb ratios are needed to explain the relationships in 208Pb/204Pb-206Pb/204Pb space (Figure 7). Pb isotope evolutions that could have generated such a geometry in Pb isotope space are investigated using two-stage Pb isotope evolution models with variable initial Pb isotope composition, and variable timing and extent of U/Pb and Th/U fractionation.
 Three example evolutions for the HSDP-2 end-members are plotted in Figure 8. All three evolutions start at 3.7 Ga, but with a variable initial composition, which we call the “Archean box.” The terrestrial Pb isotopic composition at 3.7 Ga is constrained by the compositions of Pb ores in the oldest terrestrial rocks in the Isua Belt, as well as by model compositions [Stacey and Kramers, 1975; Galer and Goldstein, 1996; Kramers and Tolstikhin, 1997] (see Appendix C for further explanation). From this initial composition, the Pb isotope ratios evolve in a second stage to time t2, when the U/Pb and Th/U ratios are fractionated (Figure 8). The Pb isotope ratios evolve further during the third stage to form the mixing end-members of the HSDP-2 arrays. Three example evolutions are plotted: for the radiogenic end-member (model 1), the unradiogenic end-member of the Kea-hi8 array (model 2) and of the Kea-lo8 array (model 3). In all three evolutions, the last Th/U and U/Pb fractionation occurred at ∼1 Ga.
 The observed differences in 208Pb/204Pb ratio for the lower end-members can be accounted for by small variations in κ during the third stage. Assuming no common initial isotopic composition (Figure 8), this difference can be produced by κ3 = 4.1 (model 2) to κ3 = 4.3 (model 3), for example. With a common initial Pb isotopic composition for the two end-members (for example, 206Pb/204Pb = 16.5, 207Pb/204Pb = 15.33 and 208Pb/204Pb = 36.0) one billion years ago and a μ value of 10.8 (not shown), the differences in present-day 208Pb/204Pb and 206Pb/204Pb ratios can be generated with κ values ranging from 3.4 to 3.9 (i.e., a 15% difference). No matter how we choose the evolution for the unradiogenic end-members, the Th/U fractionation required is not large. Further, for the example evolutions shown, μ2 is relatively low (∼8 to 9), while μ3 values are elevated, ranging between 10.5 and 14.4.
 The Pb isotope evolutions are further explored using Monte Carlo simulations. Only those models that resulted in suitable compositions for the HSDP-2 end-members were selected (Figures 9a and 9b) (see Appendix C and Eisele et al.  for details). Although the two-stage model with variable initial composition has several degrees of freedom, and none of the parameters (age, μ, κ) can be tightly constrained, such an approach provides bounds on possible timing of differentiation and ranges of μ and κ for the end-members (Figures 9 and 15).
 The results indicate that for the radiogenic end-member of the three Mauna Kea arrays, an increase in U/Pb ratio with time is necessary. For an early differentiation at 3 Ga, μ2 is lower than 8.8 (Figure 9d), while μ3 could range from 9.6 to 11 (Figure 9f). If differentiation occurred at 2 Ga, μ3 is moderately high, between 9.9 and 12.5. For a differentiation age of 1 Ga, μ3 could be more extreme, ranging from 10 to 16. Such a range would be consistent with measured μ values of 10 to 33 [Huang and Frey, 2003]. Finally, there are no possible solutions for t2 ages younger than 0.2 Ga (Figures 9d and 9f).
 For the unradiogenic end-members, early differentiation (3.5 to 2 Ga) could only have occurred with a limited range of μ3, lying between 8.7 and 11.4 (Figure 9e). On the other hand, a relatively recent differentiation age of ∼1 Ga would allow for a large range in μ3 from 8.1 to 16. Consequently, even materials with drastically different U/Pb ratios can explain the composition of the unradiogenic end-members if differentiation occurred relatively recently. Such materials would have a restricted range in 207Pb/204Pb ratios and would still have distinct 208Pb/204Pb ratios, as observed (Figures 9a and 9b).
 Considering all the end-members together, it appears that for early differentiation ages (between ∼3.5 and 2 Ga), both μ3 and κ3 must be relatively homogeneous. In this case, not much can be said about the specific origins of the individual Kea end-members at all. Alternatively, if differentiation took place more recently, between 2 and 0.5 Ga, the common radiogenic end-member requires an elevated μ value, whereas a large range in both μ3 and κ3 values for the lower end-members would be possible.
 In summary, the geometry observed for the HSDP-2 end-members in Pb isotope space may be explained by differentiation less than 1.5 Gyr ago. For example, if we allow for a variation of μ2 = 8.7 to 9.3, μ3 = 10 to 16, and κ2 = κ3 = 3.5 to 4.3, then t2 can only range between 0.02 and 1.4 Ga. This illustrates that a relatively recent differentiation age of about 1.5 Ga or younger — provided some variation in μ and κ for all end-members is allowed — appears more likely, and would produce the geometry observed in Pb isotope space for the Mauna Kea end-members. In this case, the composition of the radiogenic end-member would hint at relatively young material having elevated μ values. This inference would be consistent with the presence of “young HIMU” material in the Mauna Kea source, as suggested by Thirlwall .
5. Significance of the Mauna Kea Pb Array End-Members
5.1. Common Radiogenic End-Member
Thirlwall  has argued that the Mauna Kea source contains “young HIMU mantle.” From our Monte Carlo modeling, it also appears that the common radiogenic end-member may have differentiated less than 1.5 Ga and had elevated μ values (μ3 = 10 − 20). Such “high-μ” signatures have mostly been explained by invoking Pb loss in the source through hydrothermal alteration of the oceanic crust [Chauvel et al., 1992, 1995; Peucker-Ehrenbrink et al., 1994; Woodhead, 1996]. The Pb isotope evolution model presented above suggests that the common radiogenic end-member is older than 0.2 Ga. Such an age is too old to be consistent with derivation of this end-member from the oceanic crust underlying Hawaii, which is about 100 Myr old [Eiler et al., 1996]. This inference reinforces the conclusion of Abouchami et al. [2000a] that the Pacific lithosphere was not involved in the generation of Mauna Kea lavas, based upon the lack of Pb isotopic overlap between East Pacific Rise MORB [Galer et al., 1999] and HSDP-1 lavas.
 Thus, it seems plausible that the common end-member of the three Pb isotope arrays represents recycled oceanic crust which may be younger than 1.5 Ga. Such a model is supported by isotopic (Hf, Pb and Os) and trace element compositions of Mauna Kea lavas, which can also be interpreted in terms of recycled oceanic lithosphere in the source [e.g., Hofmann and Jochum, 1996].
5.2. Unradiogenic End-Members
 It appears that three unradiogenic end-members with distinct 208Pb/204Pb ratios were involved at different stages in the eruptive history of Mauna Kea (Figure 7a). These three end-members do not show any resolvable differences in their 207Pb/204Pb ratios (Figure 5b).
 In the Pb isotope evolution model, the unradiogenic end-member(s) would lie close to a 3.7 Ga isochron in 207Pb/204Pb-206Pb/204Pb space. Thus, the three unradiogenic end-members would be consistent with a single-stage closed system U-Pb evolution over 3.7 Ga. The single-stage μ and κ values for this evolution in the Monte Carlo simulations correspond to the μ2 (8.9 to 9.2) and κ2 (3.6 to 3.9) values at t2 = 0 (see Figures 9 and 15). For a younger differentiation event, the Pb isotope evolution model suggests that there were no large fractionations of U/Pb and Th/U prior to 2 Ga. From 2 Ga toward the present, however, κ and μ values could have been more variable. In principle, all these scenarios are possible, and different types of material could have such characteristics, including 2 Gyr-old recycled lower oceanic crust, as has been previously suggested for the Mauna Kea source on the basis of trace element and Os isotopic evidence [Hofmann and Jochum, 1996; Lassiter and Hauri, 1998]. However, very few constraints can be put on the origin of the unradiogenic end-members based upon their Pb isotope characteristics alone.
6. Correlations With Other Isotope Systems
 Correlations with other isotopic systems may help understanding the nature of the Mauna Kea source. Neodymium, Sr [Bryce and DePaolo, 2000] and Hf isotopes [Blichert-Toft et al., 2003] overall show restricted variations in HSDP-2 lavas. As mentioned previously, the 208Pb*/206Pb* ratio can be used to distinguish the different Pb isotope arrays identified here. There appear to be some covariations between the 208Pb*/206Pb* ratios and other radiogenic isotope tracers in the HSDP-2 lavas. There is a broad negative correlation between 208Pb*/206Pb* ratio and εNd or εHf values; however, there do not appear to be gross differences in the Nd, Sr, or Hf isotopic compositions of any of the Pb isotope end-members identified.
 Some constraints can be derived from the relationships between Pb isotopes and 3He/4He ratios [Althaus et al., 2003; M. D. Kurz et al., Rapid helium isotopic variability in Mauna Kea shield lavas from the Hawaii Scientific Drilling Project, submitted to Geochemistry Geophysics Geosystems, 2003 (hereinafter referred to as Kurz et al., submitted manuscript, 2003)]. Although there is no simple covariation between 3He/4He and 206Pb/204Pb ratios, radiogenic 208Pb*/206Pb* ratios correlate well with 3He/4He ratios (Figure 10). The average 208Pb*/206Pb* ratio increases in the order: Kea-lo8 (0.933 ± 3) < Kea-mid8 (0.939 ± 5) < Kea-hi8 (0.949 ± 9) (Figure 4b), while 3He/4He ratios for these samples increase in the same order from 7 to 24 times atmospheric values (R/Ra). By comparison, the 208Pb*/206Pb* ratios of the samples lie between estimates for average MORB (208Pb*/206Pb* ∼0.92) and primitive mantle (208Pb*/206Pb* ∼0.96) [Galer and O'Nions, 1985]. The high 3He/4He and 208Pb*/206Pb* ratios in the Kea-hi8 array samples indicates a contribution from relatively undegassed and possibly undepleted mantle material.
 The correlation between He and Pb isotopes is not only a characteristic of the HSDP-2 samples. HSDP-1 samples [Kurz et al., 1996; Abouchami et al., 2000a; Lassiter et al., 1996; Lassiter and Hauri, 1998; Althaus et al., 2003] lie on the lower extension of the array formed by HSDP-2 in He-Pb isotope space (Figure 10). Loihi samples form the upper extension of the HSDP correlation, emphasizing the similarities between Kea-hi8 array lavas and those of Loihi (Abouchami et al., manuscript in preparation, 2003). The correlation between 208Pb*/206Pb* ratios and 3He/4He ratios (Figure 10) is similar to the correlation between He and Pb isotopes found in Hawaiian lavas by Eiler et al. . Overall, the correlation clearly shows that there is some coupling of He and Pb isotopic compositions. However, with all the complexities in the isotope and trace element composition of Hawaiian volcanism, it is not possible to explain the covariation of He and Pb isotope ratios by a single binary mixing process or to equate the mixing components with reservoirs such as “depleted upper mantle” or “primitive mantle.”
 In this study, depths between samples range between 10 and 150 m, with a mean of 60 m. Using the HSDP-2 age model of D. J. DePaolo et al. (Lifetimes, lava accumulation, and geochemical patterns of Hawaiian volcanoes: Inferences from HSDP data and plume models, submitted to Geochemistry Geophysics Geosystems) (hereinafter referred to as DePaolo et al., submitted manuscript, 2003), a depth interval of 60 m corresponds to a time interval of ∼3 kyr. The shifts in 206Pb/204Pb ratio of ∼0.2 at ∼1400 mbsl and ∼2600 mbsl (Figure 4), occur over several thousand years and are therefore less dramatic than those documented in Kilauea [Pietruszka and Garcia, 1999]. The rapid 206Pb/204Pb fluctuations in the HSDP-2 core (Figures 4a and 4c) show that (1) homogenization in any long-lived magma chamber, or in a deep molten zone, under Mauna Kea did not occur throughout the 320 kyr record, and (2) residence times of Pb in a magma chamber must be sufficiently short to preserve rapid isotopic fluctuations in the erupted lavas.
 The 208Pb*/206Pb* ratios also fluctuate rapidly throughout the HSDP-2 core. High 208Pb*/206Pb* ratios are associated with high 3He/4He ratios (Kurz et al., submitted manuscript, 2003), especially in the chemically distinct zones at 1900–2200 mbsl and 2300–2500 mbsl, and also as short-period “spikes” at ∼800, 1400 and 3000 mbsl (Figure 11). These isotopic fluctuations are associated with changes in major element composition of the lavas, as illustrated by the anti-correlation between Pb isotopes and the SiO2 content in glasses [Sherman et al., 2000]. The zones that are distinguished isotopically by high 208Pb*/206Pb* ratios and 3He/4He ratios display low SiO2 content in glasses (∼48 and 50 wt.%) (Figure 11). Even relatively short-period “spikes” in 208Pb*/206Pb* ratios, 3He/4He ratios and SiO2 content of the lavas (for example, at ∼800, 1400 and 3000 mbsl) are correlated. These observations indicate that chromatographic processes have not separated compatible (major) elements from incompatible elements such as Pb or He. Consequently, chromatographic magma infiltration mechanisms, first invoked by Navon and Stolper  and developed further by McKenzie and O'Nions , DePaolo , and Hauri , are not borne out by the chemostratigraphy observed. The covariations of He isotopes with other isotope tracers also indicate a coupling of gaseous and solid phases in the Mauna Kea source.
7.2. Time Series Analysis
 We performed a time series analysis of the Pb isotope stratigraphy in HSDP-2 with a similar approach as that used for HSDP-1 by Abouchami et al. [2000a]. Depths in the HSDP-2 drill core were converted into ages using the provisional age model of DePaolo et al. (submitted manuscript, 2003). The HSDP-2 data set comprises sixty-four samples spanning an age range of 320 kyr, and therefore the average Nyquist frequency fc of the time series is 0.10 kyr−1, corresponding to a period of 10 kyr. In principle, if the data were evenly spaced in time, no reliable information could be obtained for frequencies above fc. However, since the data are spaced from 58 to 1 kyr apart, some information is potentially present at higher frequencies.
 As in the previous analysis, we use a Lomb periodogram approach [Press et al., 1992], which has two advantages over other time series methods. First, the Lomb periodogram allows handling of data that are unevenly spaced in time without the need for interpolation onto an even-spaced grid; second, the statistical significance of any peak can be easily related to the respective spectral powers of the peaks. The “significance” of a peak at a given frequency, as used here, is 1 − Pn, where Pn is the null hypothesis probability that the peak arose from random noise in the data set (see Press et al.  for details). To check further that the spectra are “real” and do not contain artifacts due to the uneven data spacing, we also obtained power spectra on time series consisting of the same “ages” but with the Pb isotope data randomly “shuffled” [cf. Galer, 1996]. These spectra exhibited no significant peaks.
 The power spectra of the 206Pb/204Pb and 208Pb*/206Pb* time series, together with significance levels of the peaks, are plotted in Figure 12. The most important observations are, first, that in both spectra there are peaks with a high significance level, and second, the frequencies of these peaks differ between the two spectra. In the 206Pb/204Pb spectrum, the most prominent peak has a relatively short period of 10.0 kyr and a significance level of 99%, while for the 208Pb*/206Pb* spectrum, the highest-significance peak (99%) is located at 109 kyr (Figure 12). Further peaks with significance of 60% or above are found at 88 kyr, 10.4 kyr and 6.7 kyr in the 206Pb/204Pb spectrum, and at ∼1710 kyr and 9.8 kyr in the 208Pb*/206Pb* spectrum. The ∼1710 kyr peak is clearly irrelevant given the 320-kyr span of our record.
 The spectral peaks are also present if the analysis is done for all available HSDP-2 Pb isotope data, combining data from this study and those of Blichert-Toft et al. . For this reason, we are reasonably confident that the Pb isotope power spectra shown in Figure 12 are representative for the HSDP-2 core. A ∼48 kyr peak with 99.5% confidence was found by Blichert-Toft et al.  in their HSDP-2 207Pb/204Pb data (as well as εHf) using virtually the same periodogram approach as in this study, but with a data set preprocessed with a Gaussian filter. We are, however, unable to confirm the presence of such a peak in our 207Pb/204Pb spectrum. We also differ in our assessment of the 10 kyr peak, which we consider to be highly significant, in contrast with the analysis of Blichert-Toft et al. .
 The HSDP-2 spectra contrast with those obtained for HSDP-1, where peaks with significance above 60% were found in the 206Pb/204Pb spectrum at periods of 187 kyr and 49 kyr, and only a weak peak (significance of 32%) at 9.5 kyr [Abouchami et al., 2000a]. These differences between the HSDP-1 and HSDP-2 spectra may reflect inadequacies in the current age-depth models of one (or both) drill hole(s) or, alternatively, the 206Pb/204Pb spectrum 10 kyr-periodicity in HSDP-2 may be more predominant in the deeper parts of the section not sampled by the HSDP-1 pilot hole.
 Overall, the HSDP-2 spectra suggest that the gross fluctuations in 206Pb/204Pb and 208Pb*/206Pb* ratios reflect different features of the mantle source occurring on different characteristic length scales. Such an inference is consistent with the observation that 208Pb*/206Pb* ratios can be used as a parameter to delineate the three Pb isotope arrays found in the HSDP-2 section (see Figures 4 and 11), while 206Pb/204Pb ratios do not, but instead reflect the changing proportions of mixing end-members within a particular Pb isotope array (Figure 2). Further, the fact that the mixing proportions of the end-members vary rapidly with a 10 kyr period, as shown by the 206Pb/204Pb spectrum, implies that 206Pb/204Pb ratios provide little insight into the large-scale chemical structure of the Hawaiian mantle plume beneath Mauna Kea. Rather, these variations occur on timescales characteristic of the melting and magma extraction process. In contrast, the longer-term change from one Pb isotope array to another, as recorded by 208Pb*/206Pb*, probably reflects the transition between different chemical “zones” in the Hawaiian plume.
8. Models for the Hawaiian Plume
 One of the aims of the HSDP is to integrate the geochemical information into a geophysical model of mantle upwelling and melting in the Hawaiian plume [DePaolo and Stolper, 1996]. Recently, DePaolo et al.  modeled the chemical structure of the Hawaiian plume on the basis of the spatial distribution of Nd and He isotopes in Hawaiian volcanoes.
 In the following, we evaluate the length-scale and distribution of Pb isotope heterogeneities within the plume conduit as recorded in HSDP-2. This is possible because a particular Pb isotope array dominates the HSDP-2 record over a given time interval (Figures 13a and 13b), and the transition between arrays is a boundary marker for material upwelling in the plume. Although the Kea-hi8 and Kea-mid8 arrays are not strictly confined to a particular depth interval (Figure 4), they dominate over time intervals ranging from 30 to 190 kyr (Figure 13a) as inferred from the HSDP-2 age model [DePaolo and Stolper, 1996; DePaolo et al., submitted manuscript, 2003].
 The time interval corresponding to a particular Pb isotope array can be converted into a length scale in the plume source provided the upwelling velocity structure is known. In particular, assumptions have to be made concerning: (1) the position of the volcano relative to the plume center, (2) the radius of the mantle plume, and (3) the velocity structure within the plume conduit. In order to determine the location of Mauna Kea relative to the plume center, we used an approach similar to that of DePaolo et al. . Figure 13c shows the radial distance from Mauna Kea volcano to the (hypothetical) plume center as a function of time. It can be seen that this distance varies from ∼20 km, about 550 kyr ago, to ∼60 km at present.
 Constraints on the radius and radial velocity structure of the plume come from geophysical models [Hauri et al., 1994; DePaolo and Stolper, 1996; Ribe and Christensen, 1999]. Two different flow models were used: first, a simple pipe flow velocity model, and second, a parameterization of the Hauri et al.  variable viscosity-entrainment model (Figure 13d). The length scales of the plume source materials were calculated by integrating the mantle upwelling velocities over a given time interval. Details of the calculations are described in Appendix D.
 The results indicate that the minimum lengths of the mantle source materials sampled by the HSDP-2 Pb isotope arrays ranged between 21 and 86 km (Figure 13e). It is important to stress that these length scales were integrated over the flow path beneath the location of HSDP-2 and do not solely represent the vertical extent of heterogeneities in the plume (see Appendix D). If the flow model used is correct, then the calculated vertical lengths of these “streaks” in the plume are minimum values because the volcano samples a given streak for a limited time only, namely until the lithosphere has moved the volcano to sample another streak.
 Our results differ fundamentally from those obtained by Blichert-Toft et al. , partly due to the different flow model (“piston flow”) and approach they used to calculate the length scale of heterogeneities in the plume. In their model, the main importance is attached to vertical heterogeneities in the plume, neglecting horizontal changes in composition across the plume section.
 Assuming a radius of 40 km for the Hawaiian plume [Hauri et al., 1994] and a pipe flow upwelling velocity structure, the location of the material sampled by HSDP-2 can be inferred further back in time as well (Figure 13f). This was done by “turning time backwards” and back-calculating the position of the material at past times in the plume conduit.Figure 13f shows snapshots of the location of the HSDP-2 material 0.55, 1.5, 2.5 and 3.5 Myr ago. The lines shown in Figure 13f can be regarded as a front of passive tracers in the mantle plume moved backwards in time. The Kea-hi8 and Kea-mid8 source materials are located in the more central portions of the plume, while the Kea-lo8 material is located in the peripheral part. The velocity structure in the upwelling mantle is such that the material in the plume center will move faster (see Figure 13d). The central portions could have risen from the deep mantle in 3.5 Ma (Figure 13f), while material from the periphery may only have risen from depths equivalent to the middle or upper mantle in the same time interval. In this way, completely unrelated types of mantle material may be juxtaposed horizontally.
 This procedure assumes that the vertical “streaks” can be extrapolated back in time well beyond the “observable” 550 ka. In addition, it is assumed that there is no horizontal stratification within the plume. These assumptions appear justified in view of plume structure modeled by Farnetani et al. , although the resolution of this model within the plume stem is marginal. Some confirmation of our view of the plume structure is provided by the overall Pb isotope similarity between present-day Kilauea lavas and ∼400 to 550 kyr-old HSDP-2 lavas belonging to the Kea-mid8 array [Abouchami et al., 2000b; Abouchami et al., manuscript in preparation, 2003], which suggests considerable continuity of source materials vertically within the plume stem.
 An important outcome of the HSDP-1 pilot project was the development of the concentrically zoned plume model for Hawaii [Hauri et al., 1996; Kurz et al., 1996; Lassiter et al., 1996]. The new HSDP-2 data presented here provide support for such a model only to the extent that significant Pb isotope differences exist between the center and periphery of the plume sampled by Mauna Kea (see Figure 13b). In fact, there is evidence against a concentric zonation of the Hawaiian plume as a whole. Although Mauna Kea and Mauna Loa lie almost equidistant from the proposed present-day center of the plume (Figure 13b), the isotopic compositions of lavas from these two volcanoes do not overlap one another [Abouchami et al., 2000a, 2000b], implying substantial axial asymmetry in the Hawaiian plume.
 Two main questions remain: where do the Pb isotope end-members sampled by Mauna Kea originate from, and where do they become incorporated into the plume? Two possible solutions are: (1) these materials represent heterogeneities in the “feeding zone” of a mantle plume at the D″ layer [e.g., Farnetani et al., 2002]; (2) the isotope heterogeneities are derived from thermally entrained material into the plume during its ascent [e.g., Hauri et al., 1994]. In the former case, the Pb isotope end-members would represent heterogeneities from the lowermost mantle that were incorporated in the plume stem, deformed in a laminar flow field and ejected at the top, as shown in the simulations of Farnetani et al. . These end-members may then represent horizontal or vertical heterogeneity of less than a few hundred kilometers in the lower mantle. If there was substantial entrainment into the plume [Hauri et al., 1994], and if this entrained material was also incorporated into the central part of the plume where melting occurs, then one or several of the end-members may represent material entrained at different depths. However, the repetition of the Kea-mid8 array material in the section of the mantle plume is difficult to reconcile with the entrainment model, and only the Kea-lo8 array might represent entrained material.
 Lead isotopes in HSDP-2 Mauna Kea lavas reveal the presence of three distinct Pb isotope arrays that we interpret to reflect mixing of a common end-member with three independent end-member materials contained in the Hawaiian plume. The common end-member has a signature consistent with relatively young (<1.5 Ga) mantle material with elevated μ values. We interpret these high μ characteristics as an indication of recycled oceanic crust in the Mauna Kea source.
 The HSDP-2 lavas record the displacement of Mauna Kea away from the Hawaiian plume center and sample heterogeneities derived from initially more central and later more peripheral parts of the Hawaiian plume. The minimum lengths of the major Pb isotope heterogeneities in the plume source, represented by the arrays, are on the order of at least several tens of kilometers. The Pb isotope end-members are likely to record relatively small-scale heterogeneities in the plume derived from the D″-layer in the lower mantle and possibly also material entrained during the rise to the surface.
Appendix A:: Analytical Methods
 The analytical methods followed the procedures outlined by Abouchami et al. [2000a]. Rock chips (∼100–200 mg) were used for Pb isotope analysis. To remove contaminants and render the basalts as clean as possible, the rock chips were thoroughly cleaned in milli-Q H2O, leached with hot 6N HCl for one hour, and then rinsed with water prior to dissolution. Following dissolution, lead was separated by anion exchange in mixed HBr-HNO3 media. Pb isotopic compositions were measured on a Finnigan MAT 261 mass spectrometer operating in static multicollector mode, and corrected for instrumental mass bias using a triple-spike technique [Galer, 1999]. The NIST SRM-981 standard yielded 206Pb/204Pb = 16.9409 ± 19, 207Pb/204Pb = 15.4976 ± 24 and 208Pb/204Pb = 36.7262 ± 86 (2σ) based on 60 runs (10 ng loads) over a 10 month period. These values are within error of those reported by Abouchami et al. [2000a] for HSDP-1 (206Pb/204Pb = 16.9405 ± 15, 207Pb/204Pb = 15.4963 ± 16 and 208Pb/204Pb = 36.7219 ± 44). Procedural Pb blanks analyzed alongside the samples varied between 5 and 65 pg and are comparable to those obtained during analysis of HSDP-1 samples (15 to 50 pg).
Appendix B:: Reproducibility of Pb Isotope Ratios
 The 2σ deviations of fourteen HSDP-2 sample duplicates from their respective means is 0.0019 (100 ppm) for 206Pb/204Pb, 0.0020 (130 ppm) for 207Pb/204Pb and 0.0060 (160 ppm) for 208Pb/204Pb (Figure 1; Table 1). Six of the replicate analyses were re-runs of the same dissolution and eight were duplicate dissolutions of rock chips. This external reproducibility for the samples is slightly better than the long-term reproducibility of the NIST SRM-981 standard (see Appendix A), indicating that the main source of error is the precision of the mass-spectrometric measurement and not variation in either blank contribution or the leaching procedure used. Whether or not the absolute Pb isotope ratios of HSDP-2 samples measured here, and in particular the 207Pb/204Pb ratios (see Figures 2 and 3), represent the true isotopic compositions of the lavas erupted is more open to question. It is possible, for example, that the degree of residual contamination left after the leaching procedure might be similar for duplicate analyses, though this possibility is rather remote.
 Deviations between the Pb isotope ratios of HSDP-1 samples measured in this study and those reported by Abouchami et al. [2000a] are more variable and larger, in some cases, than those on duplicate HSDP-2 samples (see Figures 1 and 3). In the case of the HSDP-1 duplicates, the deviations range from 20 ppm in 206Pb/204Pb to as much as 530 ppm in 208Pb/204Pb (see Figure 1; Table 1). Samples R160 and R166 re-measured in this study yield higher Pb isotope ratios, but these are still within analytical error of those reported by Abouchami et al. [2000a]. However, lower Pb isotope ratios are found for samples R212, R229, R243, R286 and R395, which lie significantly outside the reproducibility of the NIST SRM-981 standard or that of HSDP-2 duplicates. In the case of sample R229, the values of Abouchami et al. [2000a] are consistent with those of Thirlwall , and both values are higher than those reported here.
 The offset between the HSDP-1 array and the HSDP-2 Kea-lo8 array is similar to the offset found between some HSDP-1 samples reported by Abouchami et al. [2000a] and those reanalyzed in this study (Figure 3). This might potentially arise from an interoperator bias or variable degrees of sample contamination. An interoperator bias could theoretically be produced by different blank contributions, a different leaching procedure, or some unknown mass spectrometer bias (e.g., isobaric interferences). However, neither the blank levels, nor the leaching procedure, nor the measured isotope ratios of the NIST SRM-981 standard (see Appendix A) changed appreciably between the time periods of analysis of the HSDP-1 and HSDP-2 samples. Five out of seven of the HSDP-1 duplicates show an offset (Figure 2). Moreover, the offset observed for HSDP-1 duplicates is parallel to the offset between leached and unleached rock powder analyzed for HSDP-1 sample R466 [Abouchami et al., 2000a] (see Figure 2). We therefore believe that the offset is caused by variable degree of contamination of the samples rather than by interoperator bias or other causes.
 In order to test this hypothesis, we performed a leaching experiment on sample R-365, the most radiogenic sample reported by Abouchami et al. [2000a]. Unleached and leached samples were analyzed. Leaching was performed in hot 2N HCl and hot 6N HCl for one and two hours prior to dissolution (see Table 1; Figures 14c and 14d). We also analyzed the HSDP-2 borehole mud and the mud from the right slag pond, since these represent potential contaminants of the lavas.
Figure 14 shows the Pb isotope relationships between HSDP-2 mud, the leaching results on sample R365 as well as those obtained on sample R466 [Abouchami et al., 2000a]. Also shown are other potential contaminants, which include seawater Pb, represented by the field of Pacific Fe-Mn nodules [Abouchami and Galer, 1998], and eolian dusts blown into the Pacific from Asia [Jones et al., 2000; W. Abouchami, unpublished data, 1999]. It has been shown that eolian dust is a significant source of strontium in Hawaiian soils [cf. Kennedy et al., 1998], and Abouchami et al. [2000a] recently suggested that the carbonate fraction of Asian dust might be the source of the radiogenic Pb contaminant found in HSDP-1 lavas. This inference is supported by the leaching experiment presented here, which shows that the acetic acid leach of Asian loess lies at the radiogenic extension of the Pb isotope array defined by the leaching results on sample R365 (Figures 14a and 14b).
 A mass fractionation line passing through sample R365 is also plotted in Figure 14. As can be seen, the mass fractionation line and the mixing line joining the carbonate fraction of eolian dust and R365 are parallel to one another and almost indistinguishable. Hence, it is difficult a priori to distinguish whether contamination or mass fractionation is responsible for the trend observed. However, the fact that the sample of R365 leached for two hours in 6N HCl has a higher 207Pb/204Pb ratio than the one leached for one hour, but similar to that measured after leaching with 2N HCl suggests that the degree of contamination may vary from one aliquot of this sample to the next. Thus, the residual Pb isotope scatter observed in HSDP lavas, and the variation in 207Pb/204Pb ratios overall are both most probably related to variable contamination of the lavas. However, the observed offset between HSDP-1 and HSDP-2 samples does not obliterate the differences between the three groups of samples found in HSDP-2.
 The fact that large deviations between duplicate analysis are not observed for HSDP-2 samples that were erupted in the submarine part of the section (Figure 1; Table 1) leads us to suggest that Pb contamination is most problematic for samples erupted subaerially. This suggestion is supported by the well-defined linear Pb isotope arrays found in MORB glasses [Galer et al., 1999].
 In summary, Pb contamination of subaerial samples is a serious issue, and there is no guarantee that strong leaching will completely remove it in a reproducible way. Such problems were already encountered for HSDP-1 samples from Mauna Loa [Abouchami et al., 2000a] and may represent one of the ultimate limitations on high-precision Pb isotope measurements of basaltic rocks.
Appendix C:: Monte Carlo Simulations of a Pb Isotope Evolution Model
 In order to evaluate quantitatively the possible ranges in U/Pb and Th/U ratios in the Mauna Kea source, we used a multistage Pb isotope evolution model. Lead isotope models having more than one evolutionary stage have many degrees of freedom, resulting in many unknown or ill-constrained parameters. Such models are best evaluated using Monte Carlo simulations. Such an approach was previously applied to the EM-1 Pb isotope signature present in Pitcairn hot spot lavas, and is further explained by Eisele et al. .
 In principle, Pb isotope compositions of oceanic volcanics can be modeled using two or more evolutionary stages. Models with a limited number of evolutionary stages (two or three) assume episodic changes in U/Pb and Th/Pb ratios at given times and can mimic stepwise differentiation processes quite well. Here, we chose to model the Pb isotopic evolution of Mauna Kea lavas using two abrupt changes in parent-daughter ratios. In addition, this two-stage model is allowed to have a variable initial starting isotopic composition. Such a model can be described in terms of
where (206Pb/204Pb)I is the initial isotopic composition at t1 (fixed here at 3.7 Ga), which is allowed to vary by the range ±n. The parameter μi is the (present-day) 238U/204Pb ratio during stage i, ages t1 and t2 mark the start of the second and third stages, respectively, and λ is the decay constant of 238U. The corresponding isotopic evolutions of 207Pb/204Pb and 208Pb/204Pb can be calculated in an analogous manner. We realize that the evolution parameters in such a two-stage model can only provide estimates for those in any particular time interval for more complex models.
 The aims of the modeling are, first, to find estimates of the U/Pb and Th/U elemental fractionations in the Mauna Kea source for the various end-members, and second, to estimate the corresponding differentiation times. A two-stage model with a variable initial isotopic composition was chosen because the terrestrial Pb isotope evolution is very uncertain in the interval between the formation of the solar system (∼4.56 Ga) and the beginning of the geologic record (∼3.8 Ga). During this interval, complications arise, in particular, from uncertainties about the age of the Earth, the duration of terrestrial accretion, and the processes responsible for Th-U-Pb fractionation [Galer and Goldstein, 1996]. Therefore, instead of using a fixed age, μ and κ for the first stage, we defined a range of Pb isotopic compositions at the start of the geological record at 3.7 Ga (t1), and used this as the starting point for the second stage. In this model, this range of Pb isotopic compositions at t1 is constrained by the measured range in Pb isotopic compositions of galenas from Isua, West Greenland [Appel et al., 1978; Richards and Appel, 1987; Frei and Rosing, 2001]. Such compositions are consistent with models of terrestrial Pb isotope evolution [Stacey and Kramers, 1975; Galer and Goldstein, 1996; Kramers and Tolstikhin, 1997]. We therefore defined a generous “box” in Pb isotope space encompassing possible compositions at 3.7 Ga. For this “Archean box,” we use 206Pb/204Pb ratios varying randomly between 11.151 and 11.434, 207Pb/204Pb from 12.998 to 13.345, and 208Pb/204Pb from 30.978 to 31.424 (see Figure 8). The Pb isotope evolution parameters for the second and third stage were allowed to vary freely within broad limits (μ between 4 and 20, κ between 2 and 5, t2 between 0.01 and 3.69 Ga).
 From the Monte Carlo simulations, models with present-day Pb isotopic compositions that lay on the extensions of the observed Mauna Kea HSDP-2 Pb isotope arrays (Figures 7a and 7b) were filtered out from a large number of “unsuccessful” trials. These “successful” trials were then used to estimate the Pb isotope evolution of the Mauna Kea end-member source materials.
Figures 9 and 15 show ∼3000 models for the end-members at the lower extension of the Pb isotope arrays, together with ∼600 models for the upper end-member. The evolution parameters (μ2, μ3, κ2, κ3 and t2) of these models were used to constrain the permissible elemental fractionations in the Mauna Kea source, as well as corresponding timing of these fractionations. The possible μ-values during the evolution of the Mauna Kea source materials are shown in Figure 9, and three example evolutions are shown in Figure 8. The interdependence between the various Pb isotope evolution parameters is illustrated in Figure 15.
Appendix D:: Calculation of Length Scales in the Mantle Source
 In order to determine the position of Mauna Kea relative to a hypothetical plume center, we adopt the approach used by DePaolo et al. . Figure 13b illustrates the path of movement of the Mauna Kea summit relative to the plume, as recorded in the HSDP-2 drill core. The x and y-coordinates of the volcano summit can be calculated as a function of time as
where x0 = −12330 m and y0 = 54200 m is the present-day position of Mauna Kea relative to the plume center. The plume center is chosen as the origin at (0∣0). The angle of plate motion is α = 30°. The plate velocity is w = 9 cm/yr, and t is age. The radial distance from the plume center can be calculated as function of time using
 The upwelling velocity structure in the mantle plume is described using two models: (1) a pipe flow model, which has constant viscosity and a parabolic velocity structure, approaching zero at the outer boundary, and (2) using an approximation to the model of Hauri et al.  which is a model having temperature-dependent viscosity (see Figure 13d).
 The flow velocity through a pipe as function of the radius r is given by
[Kuchling, 1995], where Δp is the pressure gradient in the pipe, μ is the viscosity and R is the radius of the pipe. This equation can be scaled to the maximum velocity at the center of the pipe vmax. When vmax is known, the pressure gradient becomes
 For the Hawaiian plume, we scaled this equation to fit the model of Hauri et al.  for a distance between ∼15 to 40 km radial distance from the plume center (see Figure 13d), using vmax = 1 m/yr and R = 40 km. For the Mauna Kea source sampled by HSDP-2, the radial distance from the plume center will be a function of time (equation (2)) and, consequently, the upwelling velocity in the mantle source will be a function of distance and time as follows
The length of a specific Pb isotope array in the Mauna Kea mantle source can then be calculated by integrating over a given time-interval
The integral was solved for the time-intervals of the three HSDP-2 Pb isotope arrays to yield the length scales of the material in the mantle source (Figure 13e). The calculated length is a minimum, because the volcano moves over the plume, so that each Pb isotope array is only sampled for a limited time.
 For a velocity structure in the mantle source assuming temperature-dependent viscosity, we use an approximation to the model of Hauri et al.  (see Figure 13d), which can be described by the parameterization
For estimating the lengths of mantle source materials using equation (8), we use linear interpolation
Finally, to determine the position of the HSDP-2 material in the past (Figure 13f), the depth in the mantle source is calculated using
where z is depth, v(d(t)) is the mantle upwelling velocity, t is the age of a lava in the HSDP-2 core and T is the age at which the material was at depth z in the mantle.
 We thank Tilmann Althaus, Mark Kurz, Mike Garcia for sharing their data with us, and Sieglinde Bederke-Raczek for her help in the laboratory. Reviewers Bruce Nelson and Allen Dodson, and editors Bill White and Don DePaolo are thanked for their comments. This study would not have been possible without the concerted efforts of Don DePaolo, Ed Stolper, Don Thomas and the rest of the HSDP-2 drilling team.