We report on 45 Pb, Hf, Nd, and Sr isotope ratios in basalt glasses from the Galápagos Spreading Center (GSC) from 101°W to 83°W, along with related parent and daughter element concentrations. The purpose is to delineate the effect of the Galápagos mantle plume on this NE migrating spreading ridge and the nature of the plume dispersion in the region. Two 1000 km-long Pb-Hf-Nd-Sr isotope mixing gradients symmetrically distributed about 91.5°W are observed along the GSC axis. The gradients are nearly radially distributed about the center of the Galápagos plume, located presumably beneath Fernandina Island (91.5°W, 0.4°S) on the Nazca plate. A simple model computation taking into account spreading rate variation suggests that the along-ridge integrated plume flux is some 15% greater west than east of the 91.5°W point of symmetry. This result is counter-intuitive considering that (1) eastward plate drag is imposed by the moving Nazca plate relative to the plume, and (2) at equal radial distance from the plume center, the GSC axis east of the 91°W FZ is offset 110 km closer to the plume and is systematically some 500 m more elevated as a result of thermal effects. The plume flow toward the east is systematically more diluted than toward the west, probably due to greater entrainment of depleted upper mantle material during the ascent and bending of the plume conduit, such as suggested by Richards and Griffiths  and White et al. . The lack of clear lithosphere damming effects on the isotopic gradients at transform faults suggests that entrainment of depleted upper mantle material has occurred prior to reaching the melting zone underlying the GSC axis. The decoupled Pb-Hf-Nd-Sr isotope patterns observed along the GSC relative to those previously reported over the Galápagos platform on a smaller geographic scale further indicates a non-steady state ascent and dispersion of the Galápagos mantle plume. GSC MORB compositions in Pb, Hf, Nd, and Sr isotope space suggest the presence of two distinct components in the Galápagos mantle plume, a HIMU type and an EM1-like type, most likely representing, respectively, a recycled mix of oceanic crust - lower mantle material and recycled continental-derived material. Only 0.05 to 0.5% of the EM1 component is required if the continental-derived material is terrigenous sediment, and an order of magnitude lower if it is recycled pelagic sediment. The EM1 component in the dispersing plume along the GSC is a factor of 1.5 to 1.75 richer west of 91.5°W than east of it. The possible presence of distinct protolith units in the Galápagos mantle plume could not be ascertained in the absence of any detectable ridge-transform intersection (RTI) thermal effects on the Pb-Hf-Nd-Sr isotope variations along the GSC, and the lack of correlation of the Pb-Hf-Nd-Sr isotope ratios with major elements. If present, the protolith units must be smaller than the scale of RTI thermal effects on the ridge, and may have been eradicated by mixing during the melting, melt segregation, and storage processes taking place beneath the GSC.
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 The Galápagos region is an opportune place to study in time and space the dynamics of interaction of a spreading ridge migrating away from a mantle plume [Hey et al., 1977; Morgan, 1978]. Consequently, in the past 25 years, considerable efforts have been expended in defining the morpho-tectonic, geophysical, and geochemical architecture of the Galápagos volcanic platform, its islands, the Galápagos Spreading Center (GSC), and the Cocos and Carnegie aseismic ridges, the two latter of which are tracing the temporal evolution of this interaction over the Cocos and Nazca plates, respectively (Figure 1). This paper reports on Pb, Hf, Nd, and Sr isotope variations of basaltic glasses along the GSC from 83° to 101°W. The combination of these new data with the extensive Pb, Hf, Nd, and Sr isotopic data base existing for the Galápagos islands [White et al., 1993; Blichert-Toft and White, 2001] and dredged seamount basalts from the Galápagos platform [Harpp and White, 2001] provides a means to explore these goals further. The purpose and focus of this contribution is to better constrain and test proposed models for the nature and degree of heterogeneity of the Galápagos mantle plume and the dynamics of its dispersion and mixing with the ambient depleted upper mantle beneath the lithosphere. The tracer approach followed is much like that of dyes used in laboratory fluid dynamic experiments to follow melt flow and mixing patterns. The limitation of this methodology obviously lies in the two-dimensional character of isotopic tracers used with basalts and the finite nature of the spatial sampling density. Special consideration is given to this problem.
2. Sampling and Results
 The location of the 45 basalts reported on here are shown in Figure 1. The relationships between elevation of the ridge axis, its morpho-tectonic character, fracture zones, rift propagator locations, and the major and compatible and incompatible trace elements of these dredged basalts have been reported in Schilling et al. . Of the 45 samples, 33 are fresh hand-picked glasses from pillow rims or sheet flows, and 12 are fresh rock fragments. The petrology of most of these glasses and phenocrysts has been discussed by Fisk et al. . This sample suite is supplemented by four basalts from the Hess Deep (∼102°W, kindly provided by R. Hekinian). Their major element compositions can be obtained upon request. All the basalts are tholeiitic, with the exception of a nepheline normative glass (TR164 9D-1g), and one rhyodacite flow (DS D-6V and DS D-6M) located near the 95°W rift propagator [Byerly et al., 1976]. The rhyodacites will be treated elsewhere. 87Sr/86Sr ratios and Sr, K, Rb, Cs, and Ba concentrations of the whole-rocks related to the 33 glass rinds reported here have been discussed by Verma and Schilling, , while 143Nd/144Nd ratios of 11 of these whole-rock basalts were published in Verma et al. .
 We present here for the first time Pb and Hf isotope compositions for this sample suite. So far, only 10 Pb isotope analyses have been previously reported for the GSC [White et al., 1987]. All were N-MORB from the 95°W and 85°W rift propagation regions. For the sake of completeness, we also report new Sr and Nd isotope analyses for the same samples with two- to four-fold improved precision relative to previous whole-rock analyses. Pb, Sr, and Nd isotope ratios were obtained from a single sample dissolution followed by ion exchange chromatographic separation as described in Schilling et al. . Hf isotope ratios were acquired from a separate sample attack following the method outlined in Blichert-Toft et al. . Pb isotopes were measured at URI on a VG Micromass 30B single-collector, double-focusing mass spectrometer. Hf isotope ratios were determined by multi-collector inductively-coupled-plasma mass spectrometry at ENS Lyon (MC-ICP-MS VG Plasma 54) [Blichert-Toft et al., 1997]. Nd and Sr isotope ratios were measured at the University of Geneva on a multi-collector Finnigan MAT 262 thermal ionization mass spectrometer with extended geometry and stigmatic focusing, using double Re filaments. Total procedural blanks for Pb, Hf, Nd, and Sr were all negligible. The Pb-Hf-Nd-Sr isotope ratios are listed in Table 1, along with other analytical information on collection modes, precision, mass fraction corrections, and standardizations. Parent and daughter element concentrations listed in Table 2 for Th, U, Pb, Nd, Sm, and Sr were measured by isotope dilution, while Rb, Hf, and Lu concentrations were obtained with external and internal standards, using a high-resolution, inductively-coupled-plasma mass spectrometer (HR-ICP-MS) at URI. Analytical information, including precision and accuracy, of this method is given in Table 2. The sample identification numbers ending with the letter “g” in Tables 1 and 2 refer to basalt glasses.
Table 1. Location, Depth, Pb, Hf, Nd, Sr Isotope Ratios for MORB Samples From the GSC and the Hess Deepa
Pb, Sr, Nd, and Hf chemical separations carried out at URI. The Pb isotopes were measured at URI on a VG Micromass 30B single collector, double focusing, thermal ionization mass spectrometer. The isotope ratios were normalized on the basis of replicate measurements of NBS SRM981, using the values of Todt et al. . The mass discrimination factor averaged 0.81 ± 0.04‰ per mass unit. Measured values ±2s.e. for SRM981 were: 206Pb/204Pb = 16.911 ± 0.004, 207Pb/204Pb = 15.455 ± 0.004, and 208Pb/204Pb = 36.579 ± 0.005. Reported errors in the table are two standard errors on the measured 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb, and take into account the within-run precision and the uncertainty in the mass discrimination correction. The measured blank for Pb was 0.1ng and was insignificant for the sample sizes of 0.4 g. Hf isotopic compositions were measured by MC-ICP-MS (the Lyon VG Plasma-54). 176Hf/177Hf was normalized for mass fractionation relative to 179Hf/177Hf = 0.7325. 176Hf/177Hf of the JMC-475 Hf standard = 0.28216 ± 0.00001. Hf standard was run every second or third sample to monitor machine performance. Uncertainties reported on Hf measured isotope ratios are in-run 2σ/square root of n analytical errors in last decimal place, where n is the number of measured isotopic ratios. The Sr isotope ratios measured in Geneva in static mode are mass fractionation corrected to an 88Sr/86Sr of 8.375209 and normalized to the Eimer and Amend (E&A) standard with 87Sr/86Sr = 0.708000. During the two periods of measurement (respectively of about 13 and 8 months), the E&A standards were 0.708018 ± 0.000006 (2σ from the mean, n = 74) and 0.708088 ± 0.000012 (2σ from the mean, n = 21). The 143Nd/144Nd ratios were measured in static mode and are mass fractionation corrected to a 146Nd/144Nd = 0.721903 and normalized to the La Jolla Nd standard = 0.511835. During the two periods of measurement (of about 10 and 8 months, respectively), the Nd La Jolla standard analyses were very constant, and the general mean was 0.511794 ± 0.000004 (2σ from the mean, n = 100).
Table 2. Parent/Daughter Ratios and Trace Element Concentrations (ppm) for MORB Samples From the GSC and the Hess Deep
Sr, Nd, Sm, Pb, Th, and U concentrations analyzed by isotope dilution ICPMS. Precision for ID-ICPMS analysis ranges from 0.8% (Sr) to 2.7% (U) relative standard deviation (n = 20). The average value of four separate analyses of USGS basalt standards BCR-1, BHVO-1, and BIR-1 analyzed concurrently with the samples from this study are given at the bottom of the table with certified values (Govindraju, 1994 and WF McDonough, pers comm.). Comparisons of analyzed with accepted values are very good. Nb, Ba, La, Rb, Lu, and Hf concentrations were analyzed by internal and external standardization ICPMS. Precision for these elements based on multiple runs of an in-house standard MORB (n = 42) ranges from 1.7% (Lu) to 3.5% (La) relative standard deviation.
BIR-1 (n = 4)
BHVO-1 (n = 4)
BCR-1 (n = 4)
3. Longitudinal GSC Variations
 As expected, the Pb and Hf isotope ratio longitudinal variations along the GSC essentially mimic those of, respectively, 87Sr/86Sr and 143Nd/144Nd previously reported for a smaller subset of whole rock samples (Figure 2a). The accompanying along-ridge variation in elevation, oceanic crust thickness, and mantle Bouguer anomaly (MBA) show similar patterns of approximately the same wavelength (Figure 2b), suggesting a common effect attributed to the presence of the Galápagos hotspot. Noteworthy, the length of the Pb-Hf-Nd-Sr isotopic gradients are more regular and extend conspicuously further than those of incompatible element ratios, such as shown in Figures 3 and 4. Isotope ratios in MORB glasses located close to the Galápagos hotspot are most radiogenic in Pb and Sr, and least radiogenic in Nd and Hf. Two nearly symmetric approximately 1000 km-long gradients are observed about 91.5°W. The longitude of this point of symmetry corresponds to that of Fernandina Island, located 260 km to the south (Figure 1). This island is believed to be the center of the Galápagos hotspot and underlying mantle plume [Graham et al., 1993; White et al., 1993; Kurz and Geist, 1999]. It is evident that the four basalts from the Hess Deep located near the intersection of the GSC with the EPR (∼102°W) do not fit the apparent symmetry about 91.5°W. They are considered to be outliers representing “something else”, but will nevertheless be included here for completeness and potential future importance as more data may become available.
 For convenience and further scrutiny, we will refer to MORB east and west of 91.5°W as the “east group” and “west group,” respectively. This subdivision is not entirely arbitrary. It will become apparent in the following section that these two groups clearly have distinct Pb isotope compositions. For the time being, however, the subdivision is based on the points of intersections of the best-fit lines between these two groups in Figure 2, which vary slightly depending on the Pb, Hf, Nd, or Sr isotope ratios considered. Table 3 lists the equations of these east and west linear best-fit lines, corresponding correlation coefficients (r2), their points of intersection, and Student's t-tests on the absolute values of the east and west slopes. The similarities of the east and west gradients (absolute values of the slopes) reveal a remarkable degree of symmetry for all isotope ratios considered. The east and west pairs of correlation coefficients are also very similar, and are at worst 0.69–0.83 for εHf and at best 0.88–0.91 for 208Pb/204Pb. The points of intersection vary between 92.18°W for 87Sr/86Sr and 90.95°W for 208Pb/204Pb and average 91.51°W, a longitude that is within the range of the location of Fernandina Island, the presumed center of the hotspot [White et al., 1993]. MORB within ±100 km east and west of this median point have essentially indistinguishable Pb-Hf-Nd-Sr isotope ratios.
Table 3. Pb, Hf, Nd, and Sr Isotope Ratio Versus Longitude Best-Fit Lines Through East and West GSC Groups, and Their Point of Intersection
Student's t-tests on the slopes. All of values are less than 2.1 ± 0.4, indicating that the absolute value of the east and west Pb, Hf, Nd, and Sr isotopic gradients are not different at the 95% confidence level.
Errors are based on an iterative method seeking the coordinates of intersections of the error hyperbolae.
92.18 ± 1.20
91.56 ± 1.23
90.97 ± 1.44
90.95 ± 0.35
91.69 ± 1.16
91.73 ± 0.85
 The remarkable degree of along-ridge symmetry about 91.5°W is best revealed by looking at the Pb-Hf-Nd-Sr isotope variation as a function of distance from this point on the GSC (Figure 3). It is evident that ridge-transform intersection (RTI) thermal and damming effects [Vogt and Johnson, 1975; Georgen and Lin, 2003] at the 91°W FZ, 85°W FZ, and the smaller offsets at the 95°W and 93°W rift propagator tips, do not seem to affect the east and west Pb-Hf-Nd-Sr isotope gradients along the GSC in any significant way (Figure 2b). In contrast and relatively speaking, variations in major and trace element concentrations and trace element ratios, such as La/Sm [Schilling et al., 1982] and the parent/daughter ratios reported here (Figure 4), are affected to various extents by such ridge offsets, and likewise is the morphological character of the ridge axis and crust thickness [Christie and Sinton, 1981; Fisk et al., 1982; Schilling et al., 1982; Canales et al., 1997; Detrick et al., 2002]. For example, the enhancement of (La/Sm)n, and conversely of (Lu/Hf)n and (Sm/Nd)n, adjacent to the 91°W FZ clearly suggests smaller degrees of partial melting due to RTI cold edge effects (compare Figure 4 with Figure 2a). The trace element ratio variations reflect both partial melting conditions, melt productivity, segregation and fractionation during magma storage, and mantle heterogeneities along the GSC, whereas Pb-Hf-Nd-Sr isotope ratios seem to reflect merely mantle source heterogeneities and mantle mixing conditions. This important distinction between isotope and trace element ratios suggests that the east and west 1000 km-long GSC mixing gradients about the Galápagos plume center may have already been present below the depth of the melting zone underlying the GSC.
 In stark contrast to the Pb-Hf-Nd-Sr isotope gradient symmetries about 91.5°W, and rather surprisingly, is the observed east-west asymmetry of the GSC ridge axis elevation, whether using the depth of recovery of this sample suite or existing bathymetric compilations (Figure 3). The GSC axis east of the 91°W FZ is systematically about 500 m more elevated than on the west side, at equal distance from the 91.5°W point of symmetry defined by the isotope gradients. This bathymetric asymmetry reflects the fact that the axis of the GSC east of the 91°W FZ is displaced some 110 km to the south relative to the axis of the west rift, and thus underscores the enhanced melt productivity and thermal effect of the Galápagos plume on the ridge. In contrast, the spreading rate increases regularly eastward from 40 to 65 km/m.y. from, respectively, 101°W to 83°W [DeMets et al., 1994], or ±12.5 km/m.y. relative to the 91.5°W point of symmetry. The different symmetries and asymmetries in these various parameters bear importantly on constraining the mode of dispersion of the Galápagos mantle plume and its interaction with the GSC.
 We have previously interpreted these simple isotopic variation patterns along the GSC as reflecting binary mixing and variable dilution between the mantle plume feeding the GSC and the surrounding depleted upper mantle [Schilling et al., 1982; Verma and Schilling, 1982; Verma et al., 1983]. Yet, more recent detailed sampling of the Galápagos islands and seamounts over the Galápagos platform have revealed, on a smaller scale (500 versus 2000 km), a far more complex spatial (and partly temporal) Pb-Hf-Nd-Sr isotopic variation. This horseshoe-like spatial isotopic distribution pattern has been attributed to entrainment of the depleted upper mantle by the eastward bending heterogeneous Galápagos mantle plume composed of two or three components [White et al., 1993; Kurz and Geist, 1999; Blichert-Toft and White, 2001; Harpp and White, 2001]. These two types of sampling (ridge versus islands) and different lines of evidence are difficult to reconcile with a simple and consistent picture revealing the dynamical and thermal dispersion of the Galápagos mantle plume and its interaction with the GSC. Some kind of depth-related decoupling or lack of steady-state condition of the mantle plume and its outward spreading seems to be implied but is difficult to pinpoint. This question will be revisited in the discussion.
4. Pb-Hf-Nd-Sr Isotopic Space Variations
 GSC MORB co-variations in various Pb-Hf-Nd-Sr isotope space representations are shown in Figure 5. Reasonably good positive or negative correlations are readily observed with best-fit linear correlation coefficients r2 in the range of 0.98 to 0.65 (Table 4). This is after excluding the four MORB outliers from the Hess Deep, and for 87Sr/86Sr also the samples DS D6M and TR164 4D-3B, whose 87Sr/86Sr have clearly been enhanced by seawater alteration, as evident in a 87Sr/86Sr versus εNd isotope plot (Figure 5e). No distinction can readily be detected visually between the east and west GSC groups in isotopic space involving Sr, Nd, and Hf isotope ratios, or any of these in combination with the three Pb isotope ratios. This is corroborated by the Student's t-tests on the slopes and intercepts of the linear least square fits through the east and west groups listed in Table 4. On the other hand, the east and west groups are clearly distinct in 206Pb/204Pb versus 208Pb/204Pb space and to a lesser extent also in 206Pb/204Pb versus 207Pb/204Pb space. The best-fit lines through these two populations in Pb-Pb isotope space have statistically distinct intercepts, though not necessarily slopes, as evident by the Student's t-test comparison. In conventional reasoning, such lines would be interpreted as two distinct binary mixing arrays with four end-members. If this were indeed the case, it would require two distinct radiogenic Pb sources in the Galápagos mantle plume, each mixing with two distinct unradiogenic Pb-poor upper mantle domains present east and west of the Galápagos plume.
Table 4. Pb, Hf, Nd, Sr Covariation Best-Fit Lines Through the East and West GSC Groups
Student's t-tests on the slopes and intercepts. The east and west slopes are indistinguishable at the 95% confidence level. The east and west group intercepts are clearly distinct in Pb-Pb and Pb-Sr isotope space at the 95% confidence level where t = 2.1 ± 0.4, and marginally distinct for Nd-Pb and Nd-Hf isotope space. The intercepts are indistinguishable in Nd-Hf and Sr-Nd isotope space. 87Sr/86Sr ratios of sample TR164 4D-3 and DS D-6M were excluded as they clearly have been affected by seawater alteration.
 The lack of distinction in isotopic space, other than simple Pb-Pb isotope space (i.e., Sr, Nd, and Hf), may reflect that binary mixing need not be linear if the contents of the end-members in Sr, Nd, and Hf relative to Pb are not identical, whereas in purely Pb-Pb isotope space it is linear. The east and west distinction is further amplified by the covariation of 207Pb/206Pb versus 208Pb/206Pb and 206Pb/207Pb versus 208Pb/207Pb (Figures 6a and 6b), or the relative 206Pb, 207Pb, and 208Pb variation in a triangular diagram (Figure 7). The triangular diagram represents a good projection of the total Pb isotopic composition, since the 204Pb abundance is only of the order of 1.5% to 2.5%. The east and west groups are completely separated in such Pb isotope representation, and the best-fit lines through the two groups do not converge to typical unradiogenic N-MORB values from either the Atlantic ocean or the EPR [e.g., Kingsley and Schilling, 1998; Schilling et al., 1999; Wendt et al., 1999]. If this is indeed the case, again, two distinct binary mixing scenarios with four end-members would have to be invoked, two of which are radiogenic and two non-radiogenic! Noteworthy, the four MORB outliers from the Hess Deep fall squarely between the two groups in such Pb isotope space representations (Figures 6 and 7). If the Hess subgroup were included in the west group, the best-fit lines would converge near such extreme N-MORB compositions. Two mixing binaries sharing a common N-MORB type end-member and two radiogenic plume-related end-members would then be required. In this case, one could invoke a chronology of mixing within a three-component system, such as for example HIMU, EM1, and DM [Zindler and Hart, 1986]. In such a scenario, EM1 and HIMU would first mix in two distinct proportions to generate the two enriched end-members, which in turn would mix with DM in variable proportions to generate the two converging mixing arrays considered here. The Hess deep samples are clearly outliers unrelated to the mixing gradients observed along the GSC (see Figure 2). The two distinct arrays shown in Figures 6 and 7 need not be considered as two distinct binaries involving four end-members. Under certain conditions they can also be interpreted as pseudo-binary mixing lines within a three component system [Douglass and Schilling, 2000]. In this case, all three components intimately mix in systematic, non-random, variable proportions, in a single stage. There is no particular sequence of mixing, nor is there a need to invoke four end-members. In part due to this relative simplicity, this is our preferred model, which we will discuss and justify further in a subsequent section.
 The co-variations of parent/daughter ratios with their respective Pb-Hf-Nd-Sr isotope ratios are shown in Figure 8. Linear fits on such a type of diagram can be interpreted as either (1) rock errorchrons given an age significance, (2) binary mixing, or (3) a combination of both (such as for example recent mixing between two end-members generated at some time in the past from a common ancestor source). An example of the latter model would be partial melting (or metasomatism), one representing the melt (or fluid), the other the solid residue (restite). For additional inferences to be made, the average parent/daughter ratios integrated over the age of the Earth (4.56 Ga) and corresponding to the Pb-Hf-Nd-Sr isotopic compositions of the GSC glasses are shown on the right-hand ordinate scale in Figure 8, and their range compared with measured values are shown by shaded bands. The following observations can be made:
 1. In all cases there is a rough positive correlation between the parent/daughter ratios and their corresponding Pb-Hf-Nd-Sr isotope ratios (Figure 8). Contrary to correlations purely in Pb-Hf-Nd-Sr isotope space (Figure 2a), the large scatter observed in Figure 8 suggests that, besides mixing, the parent/daughter ratios have recently been affected by varying extents of melting and fractional crystallization along the GSC, as also evident in Figure 4. Pb isotope systematics show the least scatter while Sr isotope systematics the most, the latter probably because Rb/Sr is readily affected by fractional crystallization of plagioclase feldspar.
 2. As expected, no distinction can be ascertained between the GSC east and west groups for Pb-Hf-Nd-Sr isotope systematics, with the exception of 208Pb/206Pb versus 232Th/238U. This suggests that the difference between the 208Pb-rich group (west GSC) and the 208Pb-normal group (east GSC) is not merely the result of a recent fractionation or mixing effect.
 3. In all cases, the range of parent/daughter ratios observed in the MORB glasses greatly exceed the corresponding range of time-integrated ratios deduced from their present-day isotopic compositions. This is true even if one were to correct for partial melting fractionation, using acceptable melting models of spinel to garnet bearing peridotites, such as previously shown [e.g., Schilling et al., 1994; Schilling et al., 1999]. For a degree of partial melting of 10% or greater in producing MORB [e.g., Klein and Langmuir, 1987], the calculated mantle source parent/daughter ratios are not likely to differ by more than 10–20% from the values observed in the melt (i.e., MORB). The observation here of greater percentages of deviation suggests that the parent/daughter ratios of the present MORB have been fractionated at some point during the evolution of their mantle sources.
6. Comparison Between the GSC and Galápagos Platform
 The large Pb-Hf-Nd-Sr isotopic data set from the islands and seamounts from the Galápagos platform is compared with that of the GSC in Figure 9. A number of points are to be noted:
 1. The Galápagos platform spans a larger Pb-Hf-Nd-Sr isotopic space than the GSC. This is particularly so for 206Pb/204Pb, reflecting Floreana's isotopic composition and to a lesser extent that of the western islands dominated by Fernandina and Isabela (Figure 1).
 2. In Pb isotope space, particularly 206Pb/204Pb versus 208Pb/204Pb, only the islands of Wolf, Darwin, two nearby seamounts (PLO2-29 and 30), Pinta, and one young lava from Santa Fe (G86-5) lie on the GSC West Group or its best-fit line extension. From here on, this group will be referred to as the 208Pb-rich group regardless of location. All the other islands and seamounts from the Galápagos platform overlap the GSC east group or its best-fit line extension. They will hereafter be referred to as the 208Pb-normal group.
 3. Thus the 91.5°W boundary on the GSC does not extend over the entire platform, since Pinta and G86-5 from Santa Fe, which belong to the 208Pb-rich group, lie east of 91.5°W, and seamounts and lavas from Fernandina and Isabela islands located west of 91.5° belong to the 208Pb-normal group.
 4. Over the platform, neither the 208Pb-normal nor the 208Pb-rich groups reflect a north-south geographical pattern, as they overlap regardless of their longitudinal positions, with the exception of Floreana and Espanola islands, which exceed the overlap range (Figure 1).
 5. Also, the two Pb isotope groups from the GSC and the platform are not simply related to the so-called Wolf/Darwin lineament (WDL), since Wolf, Darwin, and Pinta islands all belong to the 208Pb-rich group, whereas the group of seamounts (PLO2-26 to 28) located between the east-west GSC boundary belongs to the 208Pb-normal group!
 6. The two Pb-isotope groups clearly do not reflect a systematic age difference, as all the GSC basalts are of zero age, whereas basalts from the islands and seamounts from the 208Pb-rich group range in age from 0.39 to 1.6 Ma [White et al., 1993; Sinton et al., 1996]. The island samples from the 208Pb-normal group range in age from 0 to 3.5 Ma [White et al., 1993], and the dredged seamount samples from the platform, Carnegie ridge, and the Nazca plate (Figure 1), which belong to the 208Pb-normal group, have ages that vary between 0.1 and 11 Ma [Sinton et al., 1996]. Thus no age pattern is discernable between the two Pb isotope groups.
 These six points together indicate a different scale and some yet unspecified kind of decoupling between the spatial distribution of isotopic heterogeneities beneath the Galápagos platform and the GSC.
 How do these four end-member components compare with those inferred from our study of the GSC alone? Since the GSC spans a smaller Hf-Nd-Sr isotope range than the platform, none of these proposed four end-members can be excluded.
 What about Pb isotope space? It first should be noted that the Pb isotope data from the GSC used by White et al.  included only basalts from the Hess Deep and the 95°W and 85°W rift propagators reported by White et al. . These represent 10 samples of essentially N-MORB composition at the low end of the 206Pb/204Pb range, where the distinction between the 208Pb-rich and 208Pb-normal groups begins to blur (e.g., Figures 2a, 5, and 9). Thus this depleted upper mantle end-member (DUM) is consistent with that which can now be inferred from the entire GSC data set reported here (including the Hess Deep). This would call for two binary mixing arrays having a common DUM end-member, such as suggested by one of the two models contemplated in the previous section limited to binary mixing interpretations. The Floreana end-member (FLO) at the high 206Pb/204Pb-end could readily account for the GSC east group (i.e., 208Pb-normal group for the basalt population from Galápagos platform and GSC east of 91.5°W), but need not be that excessive in 206Pb/204Pb. Likewise, the so-called WDL Wolf-Darwin end-member (WD) could account for the GSC west group (i.e., 208Pb-rich group for the basalt population from the Galápagos platform and GSC west of 91.5°W), though its 208Pb/204Pb is slightly too low and its 206Pb/204Pb should extend to somewhat higher Pb isotope values in order to cover all the platform's isotopic data for this group. The only end-member not necessarily required by the GSC data is the so-called plume end-member (PLUME), which appears to have been designed to account for the scatter in 208Pb/204Pb and 207Pb/204Pb below the two major arrays. Decay of U in older island basalts from the platform may contribute to this scatter, as it results in a radiogenic growth vector shifted to higher 206Pb/204Pb at essentially constant 207Pb/204Pb relative to the two GSC MORB arrays.
 The challenge thus remains in using these two sets of spatial and temporal isotopic variations to constrain the Galápagos mantle plume flow, thermal dispersion, and interaction with the GSC.
7. Ridge-Transform Intersection (RTI) Effects
 As previously noted, the 91°W FZ, 85°W FZ, and the smaller offsets at 93°W and 95°W rift propagator tips do not seem to affect significantly the two GSC east and west Pb-Hf-Nd-Sr isotopic mixing gradients. In contrast, major and trace element variations, including trace element ratios (e.g., La/Sm), are affected to variable extents by these RTI thermal effects [Christie and Sinton, 1981; Schilling et al., 1982]. This is further confirmed by the variations of the parent/daughter ratios U/Pb, Th/Pb, Rb/Sr, Sm/Nd, and Lu/Hf reported here (Figure 4). It is generally accepted that such geochemical parameters are susceptible to varying extents to the partial melting and fractional crystallization conditions prevailing along the GSC, as well as to the tectonic segmentation. Pb-Hf-Nd-Sr isotope ratios are not expected to be influenced by partial melting, unless different lithologic units of sufficiently large size with distinct melting properties and isotopic composition are present [Langmuir and Bender, 1984; Sleep, 1984]. If this is the case, isotopic variation would be expected from disequilibrium fractional melting during decompression of either of the following assemblages: (i) the mantle plume assumed to interact with the GSC is composed of a mixture of recycled eclogitic oceanic crust in an harzburgite matrix of distinct isotopic compositions due to different parent/daughter ratios during recycling and aging [e.g., Phipps Morgan, 2000] or (ii) the surrounding upper mantle is veined with pyroxenites [e.g., Hanson, 1977]. In these two scenarios, some correlation between isotope ratios and major element compositions would be expected, as has been observed for example in Hawaii [Hauri, 1996]. This is apparently not the case for the MORB population from the GSC. No correlation can be detected between Pb-Hf-Nd-Sr isotope ratios and major element indicators of degree of partial melting (e.g., Mg#-values, Ca/Al, etc.). This is also the case for basalts from the Galápagos islands [White et al., 1993], suggesting that either no distinct protolith units are present in the Galápagos mantle plume, or if present, these various protoliths have been stretched prior to melting and are small enough for their isotopic signal to be obliterated by equilibrium decompression melting and mixing of melts during their segregation and pooling along the GSC.
 A case against a radial dispersal of the Galápagos mantle plume was made on the basis of La/Sm and Sr and Nd isotope ratio variations along the GSC [Schilling et al., 1982; Verma and Schilling, 1982; Verma et al., 1983]. The constraints were based on a binary mixing model between a homogeneous plume and the surrounding depleted upper mantle. The mass fraction of the plume was assumed to decrease either linearly or in a power-law fashion with radial distance from the center of the plume over Fernandina. Along the GSC, the model predicted the following systematics: (1) a family of curves concave downward, representing the geochemical binary mixing gradients, whose curvatures were dependent on the relative enrichment of the Sm and Sr between the plume and the upper mantle, and (2) a small discontinuity at the 91°W transform fault (TF). The model was rejected because the La/Sm and 87Sr/86Sr gradients about the 91°W FZ were either concave upward for La/Sm or essentially linear for 87Sr/86Sr, and no noticeable discontinuity was observed at the 91°W TZ. The fact that the new Pb, Hf, Nd, and Sr isotope compositions reported here call for an inhomogeneous plume and a mixing model involving at least three components renders this kind of forward modeling test inadequate.
 Surprisingly, Figure 10 shows that there is a good correlation between the Pb, Hf, Nd, and Sr isotope ratios from the GSC and radial distance from the presumed center of the plume located beneath Fernandina. This seems to be the case despite the east and west group distinction in Pb isotope space noted earlier, or the systematic displacement of the GSC about the 91°W TZ along the GSC. This would suggest that a radial dispersion of the Galápagos mantle plume might not be ruled out as readily. On the other hand, the Pb, Hf, Nd, and Sr isotope ratios over the Galápagos platform, as sampled from the island and seamount basalts, clearly show no relation to radial distance from Fernandina (Figure 10), even if age-corrected for absolute plate motion.
8.1. Three-Component Mixing Model
 Another evaluation and testing of the radial mantle plume dispersal flow model will now be considered, assuming a three-component mixing model. In this case, linear isotope arrays in 2-D isotope ratio I versus J representation, such as in Figures 5f and 5g, are considered to be pseudo-binary mixing lines. The three components intimately mix in a single-stage, systematic, non-random fashion. Two special conditions must be met for this to be the case [Douglass and Schilling, 2000], namely: (i) the mass fractions Zi of two of the three end-members in the mixtures forming the linear array must be linearly related, and (ii) the enrichment factor ni of the stable isotope in ratio Ii in component 1 and 2 relative to 3 must be equal to that of the enrichment factor mi of the stable isotope Ji in component 1 and 2 relative to 3. Condition (ii) is always met in Pb-Pb isotope space representation, which is also the only case for which the two distinct GSC east and west pseudo-binary arrays are clearly apparent (Figures 5f, 5g, 6, and 7).
 We now test whether condition (i) is also met and demonstrate that to a first order it is. We have decomposed the Pb isotope variations into a three-component mixing system composed of end-members represented by DM, EM1, and HIMU. These three components presumably would represent a recycled continental-derived component, such as sediments (EM1), the depleted upper mantle (DM), and perhaps old recycled oceanic crust (HIMU) mixed with lower mantle material (possibly component C [Hanan and Graham, 1996]) [e.g., Rehkämper and Hofmann, 1997; Hanan et al., 2000]. The presence of a lower-mantle component, such as C, is required by the high 3He/4He ratios in some Galápagos island basalts [Graham et al., 1993; Kurz and Geist, 1999], as well as by the increase in 3He/4He in GSC MORB from close to 7 times atmospheric values (RA) around 98°W to 8.1 times RA around 91°W [Detrick et al., 2002]. However, since such a component falls within the Pb isotopic space encompassed by HIMU-EM1-DM, it cannot be modeled here. We have calculated the mass fractions Zi of these three end-member components in each MORB from the GSC, using the 206Pb/207Pb and 208Pb/207Pb ratios and the requirement that ΣZi = 1. The closed form method of calculation followed is described in appendix A. The Pb isotope ratios and Pb contents assumed for the three end-members are listed in Table A1 in appendix A. Figure 11 shows that the EM1 component of the mantle plume (Z2) co-varies approximately linearly with the dominant HIMU component of the plume (Z1) in both the east and west groups, with r2 of 0.95 and 0.97, respectively. The west group is systematically richer in the EM1 component than the east group. Likewise, the mass fraction of EM1 co-varies approximately linearly with DM (Z3). Because ΣZi = 1 and the EM1 mass fraction is very small (0.05–0.5%), the DM and HIMU mass fractions co-vary essentially perfectly, since Z2 ≪ Z1 and the closure requirement Σ Zi = 1. This reflects the fact that the Pb content of the sediment component (EM1) and of the HIMU component are significantly greater, by factors of about 300 and 6, respectively, relative to that of the DM component (see Table A1 in appendix A). The minimum 15 ppm Pb content assumed for the sediment component EM1 [Ben Othman et al., 1989; Cousens et al., 1994; Plank and Langmuir, 1998] represents a maximum for the mass fractions Z2 entering the mixtures shown in Figure 11. For example, if one had used the 55 ppm assumed for pelagic sediments in the three-component mixing model proposed by Rehkämper and Hofmann  for modeling Indian ocean MORB, the fraction Z2 would be about an order of magnitude lower. We conclude that condition (i) for the two GSC east and west arrays observed in the Pb-Pb isotope variation diagrams of Figures 6 and 7, and shown to be pseudo-binary mixing lines in the proposed three-component mixing model, is also met to a first order.
Table A1. Isotopic Ratios and Trace Element Compositions in End-Member Components Used in the Three-Component Mixing Modela
 The mass fraction variations of the EM1, HIMU, and DM components with respect to the radial distance from Fernandina are shown in Figure 12. The following observations are made: (1) the mass fractions of both the HIMU and the EM1 plume components Z1 and Z2 decrease regularly with increasing radial distance x due to dilution by the DM component. Conversely, the DM component Z3 increases with x, (2) at a given x, the mass fraction of component HIMU (Z1) and EM1 (Z2) are higher (less diluted by DM) in the GSC west group than in the GSC east group, (3) the difference decreases with increasing x and there is convergence around 1000 km radial distance, where Z1 and Z2 taper out (Figure 11), (4) by difference (i.e., ΣZi = 1), the DM mass fraction (Z3) is more dominant in the east group than in the west group at equal radial distance x, and the two converge around 1000 km distance, where Z3 is approaching 100%, (5) the Zi variations with x appear linear for the east group, but possibly not for the west group, (6) Figure 10 also shows that for a given radial distance x, the ridge axis elevation is systematically 500 m higher over the east than over the west group. At first glance, points 1, 3, and 4 all appear consistent with a radial dispersal flow of the Galápagos mantle plume. However, observations 2, 5, and 6 are inconsistent with a perfectly radial flow pattern. Observation 2 suggests that the dilution of the plume is stronger east of the plume conduit than west of it. This is consistent with the picture observed over the Galápagos platform [White et al., 1993; Blichert-Toft and White, 2001; Harpp and White, 2001] and the preferential entrainment of the DM component by a bending plume [Richards and Griffiths, 1989]. In contrast, observation 6 suggests a thermal enhancement east of the plume center, probably because the GSC east of the 91° FZ is closer to the plume.
 The above noted radially related observations are further complicated by the fact that the spreading rate U along the GSC increases essentially linearly eastward from 40 to 65 mm/yr, from 101°W to 83°W. In the case of a simple ridge-centered plume at steady state, one would expect the full length of isotopic gradients L to be shorter east of 91.5°W than west of it, as shown by Schilling . Following this model modified for the off-ridge Galápagos plume case, the integrated plume flux Q on either side of 91.5°W along the GSC is given by
where y stands for - radial distance y from the 91.5°W point of symmetry on the GSC, H(y) for lithosphere thickness, and U(y) for the full spreading rate as given by U = 52.5 ± 0.0125 y in km/m.y. “plus” for east and “minus” for west of 91.5°W where y = 0 [DeMets et al., 1994].
 The mass fraction ZP (y) of plume-derived material accreting along the GSC axis is given by ZP = k (1 − y/L), by assuming that it varies linearly either east or west of the 91.5°W point of symmetry (Figure 12d) and that ZP is represented by the mass fraction Z1 + Z2, or ZP ≈ Z1 since Z2 ≪ Z1 (Figures 11 and 12). The coefficient k represents the intercept of the best-fit line of ZP (y) versus y shown in Figure 12d for the east (kE) and west (kW) groups.
 Assuming H independent of y, integration between y = 0 to y = L, the length of the linear gradients of ZP (y) versus y either east (LE) or west (LW) of the 91.5°W point of symmetry on the GSC, gives an integrated plume flux: QE = kEH [52.5 LE/2 + 0.0125 /6] for east of 91.5°W, while for west of 91.5°W QW = kWH [52.5 LW/2 − 0.0125 /6]. With the values of L and k given by the best-fit lines for ZP (y) versus y shown and given in Figure 12d, QE = 0.458 km3/yr and QW = 0.525 km3/yr. An along-ridge asymmetric plume flux about 15% greater toward the west than toward the east of 91.5°W is suggested. A higher flux toward the west is surprising and counter-intuitive considering that (1) the plate drag imposed on the plume by the Nazca plate eastward absolute motion is likely to enhance the plume flux in this direction, and (2) at equal radial distance from the plume center, the GSC axis east of the 91° FZ is systematically more elevated, apparently because of its 110 km southward offset toward the plume. We emphasize, however, that the possible east and west plume dispersal flux asymmetry is based purely on the above simple modeling, which ignores the off-ridge plume position, ridge migration, and large fracture zone offsets characterizing the Galápagos.
 Sensitivity tests of the three-component model show that the exact isotopic value arbitrarily chosen for the three end-member components just described do not change the outcome of this model, providing that the three end-members chosen span the GSC MORB data set. This is also true for the relative Pb content enrichments of the end-members EM1 and HIMU relative to DM, within acceptable limits of the presumed nature of these components.
 The validity of the three-component Pb-isotope-based model is further tested by extending it to Hf, Nd, and Sr isotope space representations, using end-member concentrations and isotopic compositions adapted from Andres et al.'s  three-component mixing model involving recycled oceanic crust (OC), sediment (SED), and depleted upper mantle (DM). The three end-member parameter values used are given in Table A1 and the results are illustrated in Figure 13. As required by the test, the GSC basalt data fall within the three end-members prescribed, but for a few exceptions. This is the case despite the fact that the allowed mixing space is far smaller because of the strong curvatures of the limiting binary mixing curves SED-DM and SED-OC (Figure 13). The critical mass fraction ratio of SED/OC obtained in the different Hf, Nd, and Sr versus Pb isotope diagrams are similar and of the order of 1–3% (Figure 13), compared to 1–2% based on the Pb isotope model alone (Figure 14). In Hf-Nd-Sr isotope space, the SED/OC mass fraction ratio ranges from 0.1–2%. A range of 1–3% in the SED/OC ratio is also obtained using the recycled sediment indicator of Ba/Nb against 206Pb/204Pb [e.g., Andres et al., 2002] (Figure 13). The systematically higher content of Ba/Nb in the GSC west group relative to the east group at a given 206Pb/204Pb (Figure 13) and at equal radial distance from 91.5°W along the GSC (Figure 14), is also fully consistent with a relatively higher proportion of the EM1 component in the west group than in the east group.
 It should be noted that the SED/OC mass fraction ratio in Pb-Hf-Nd-Sr isotope space is strongly dependent on the Pb content assumed for SED relative to OC. In view of the large number of parameters involved in the three-component mixing model, we consider the test reasonably conclusive. No attempt was made to tweak the model so as to obtain more comparable SED-OC mass fraction ratios in the various Pb-Hf-Nd-Sr isotopic space representations considered as well as their co-variations with Ba/Nb.
8.2. Source of the EM1 Component?
 An important issue in this three-component mixing model is whether the recycled component is indeed a part of the plume or simply embedded as rafters or schlierens in the upper mantle. Several global kinematic mantle flow models, with very different built-in assumptions, converge at suggesting that a significant upper mantle return flow may be present beneath the Nazca plate, from the Andes subduction zone toward the fast spreading EPR [Chase, 1979; Hager and O'Connell, 1979; Parmentier and Oliver, 1979]. Unless the subducted Nazca plate acts as a dam, it is conceivable that this return flow may entrain some continental-derived material. The continental rafters embedded in this undertow counter current would randomly or progressively be deformed and diluted by the presumed homogeneous, single-component, Galápagos plume-derived material underplating the Nazca plate. If so, one would expect the fraction of continental-derived material to vary progressively down-flow, either randomly, or in an increasing or decreasing fashion westward, depending on the mode of entrainment or delamination taking place. Another possibility would be entrainment by the plume of an EM1 component present in the mantle. It is difficult to envision, however, how this return undertow current or entrainment by the plume would generate the two regular EM1 gradients of opposite sign observed along the GSC about the center of the plume, as well as their asymmetry (Figure 12). EM1 entrainment by the eastward bending plume would be higher east of 91.5°W, as for the DM component, but the opposite is observed (Figure 12). The suggestion that the EM1 component is external to the plume is rejected on these two bases.
8.3. Plume Dispersal Mixing Depth?
 Another important question to consider is how deep the nearly radial plume dispersal flow may be. A shallow dispersion plume flow, molding the base of the rigid lithosphere, is doubtful and ruled out for the following reasons:
 1. No discontinuity in the GSC Pb-Hf-Nd-Sr isotope profiles is observed at the 91°W transform fault offset, as would be expected from a shallow mantle plume flow and lithosphere damming effects [e.g., Vogt and Johnson, 1975; Georgen and Lin, 2003].
 2. The maximum slope of the rigid lithosphere base, from the center of the plume toward the GSC (maximum pressure gradient), where preferential buoyant plume flow may develop, is across the 91°W TZ rather than orthogonal to the GSC strike. Thus from Sleep's  “cascading” effect, one would expect a strong plume-related isotope signal just east of this fracture zone, rather than west of it, such as is observed (Figures 2a and 12d).
 3. Depleted basalts from Genovesa Island with strong DM affinity (radial distance 190 km) are significantly less radiogenic in Pb and Sr (and more radiogenic in Nd and Hf) than GSC MORBs on the same spreading ridge flow line (TR164 7D, radial distance 218 km), as well as GSC MORBs on the same 60° azimuth from the presumed center of the plume beneath Fernandina (i.e., CTW9D-1g, radial distance 284 km). The first observation rules out the possibility that the formation of the low-level Genovesa Island was initiated at the GSC, such as contemplated by Harpp and White . Harpp et al.  have subsequently suggested that Genovesa basalts are recently (<350ka) derived from a DM deep source, as the result of the Galápagos plume-GSC interaction in a near-ridge intraplate dynamic setting. This and our second observation both rule out a shallow radial dispersion of the plume with progressive dilution by the depleted upper mantle.
 We conclude from the GSC isotopic data that the dispersal of the Galápagos mantle plume is not purely radial. Though rather counter-intuitive, the integrated flux of plume material along the GSC appears to be somewhat higher toward the west than toward the east of the 91.5°W point of symmetry. However, the flow to the east is systematically more dilute, which is consistent with greater entrainment of the DM component during the bending of the plume conduit caused by the Nazca plate drag, as suggested by Richards and Griffiths , and supported by White and coworkers' isotopic data over the Galápagos platform [White et al., 1993; Blichert-Toft and White, 2001; Harpp and White, 2001]. The two symmetric mixing gradients along the GSC do not appear to have been generated simply by the spreading of the plume at shallow depth in the upper mantle directly against the base of the rigid lithosphere.
Morgan  suggested that the Wolf-Darwin constructional volcanic lineament (WDL) was formed progressively from the discharge of the Galápagos plume to the GSC along a preferential sublithospheric channel, as the GSC migrated in northeast direction since the time it was ridge centered some 10 Ma [Hey, 1977]. The fact that the maximum Nd-Sr isotopic plume signal along the GSC previously reported seemed to occur in the vicinity of Darwin Island led strong support to this model [Schilling et al., 1982; Verma and Schilling, 1982; Verma et al., 1983]. In order to account for the two symmetric, 1000 km-long isotope gradients along the GSC (Figure 2a), the model assumes that some plume flow and mixing with the depleted upper mantle takes place east and west of this point of discharge. The pros and cons of this model now need to be re-evaluated in the light of the following new information:
9.1. Pb-Hf-Nd-Sr Isotope Profiles Along GSC
 Except for the east and west group distinction in the relative Pb-isotope composition about the GSC point of discharge, the isotope data reported here do not change significantly the constraints previously established. However, the fact that the 91°W FZ, 85°W FZ, and the smaller offsets at 95°W and 93°W rift propagator tips do not seem to create any discontinuities in the east and west Pb-Hf-Nd-Sr isotope gradients along the GSC expected from lithosphere damming effects at shallow upper mantle depth [e.g., Vogt and Johnson, 1975; Georgen and Lin, 2003], does suggest that the presumed sub-axial plume flow cannot be shallow, and most likely not melt-like, as suggested by Vogt and de Boer .
9.2. Age and Pb-Hf-Nd-Sr Isotope Profiles Along the WDL
 Corollaries of the MPS-MRS model require that since the time the NE migrating GSC was located above the plume some 8–10 Ma [Hey, 1977], the age and the plume-derived Pb and Sr isotope signals in the constructional volcanism along the WDL should progressively decrease as the plume-ridge distance increases with time. Radiometric dates and isotopic evidence from the recent sampling of seamounts along the WDL are not consistent with this prediction [Sinton et al., 1996; Harpp and Geist, 2002]. Radiometric ages from these seamounts are young (<1 Ma). The youngest seamounts (0.1 Ma) are located closest to the platform, the oldest (0.8–0.9 Ma) near the GSC (30–40 km), and those with intermediate ages in between (0.3 Ma) [Sinton et al., 1996] WDL. The WDL Pb-Hf-Nd-Sr isotope profiles from these seamounts and Darwin and Wolf islands are also scattered [Harpp and White, 2001; Harpp and Geist, 2002]. Judging from the MPS-MRS mixing model [Schilling et al., 1982], these data clearly do not show the expected progressive decrease in the isotopic compositions of Pb and Sr, (and corresponding increase in Nd and Hf), as the plume-migrating ridge distance increases with time.
 In the study of the lithosphere structure and compensation mechanisms of the Galápagos Archipelago, Feighner and Richards  modeled the WDL as a fault in order to improve the predicted gravity field relative to that observed over the region, and found it consistent with the lack of age progression along the WDL. However, it should be realized that the MPS-MRS model also predicts that the channeled hot plume-derived material accreting at the point of discharge at the GSC, upon plate cooling, should develop a thinner lithosphere than immediately adjacent to it. Thus Morgan's  second track type of hotspot constructional volcanism should also be the locus of an inverted channel (thermal groove) at the base of the lithosphere (rheological boundary layer). As the plume-migrating ridge distance increases with time, this effect decreases for a given constant initial plume-asthenosphere excess temperature. The depth of the inverted channel along the WDL should decrease northwestward from the time the GSC was ridge centered. This effect may cause a zone of weakness in the Nazca plate during subsequent tectonic readjustments caused by plume-related volcanic loading over the Galápagos platform, or changes in plate motion directions [e.g., DeMets et al., 1994]. This in turn may explain in part the recent volcanism along the WDL, perhaps facilitated by normal faulting! A similar and more elaborate model has been recently and independently proposed by Harpp and Geist .
9.3. MPS-MRS Fluid Dynamic Modeling
 The dynamic interaction of mantle plumes with migrating ridges have been investigated in the laboratory and numerically by several workers, starting first with the simpler ridge-centered case (Feighner and Richards , Feighner et al. , Ribe , Ribe and Delattre , Ito et al. [1996, 1997, 1999]). The most complete 3D numerical analyses, which can be directly compared with the geochemical constraints from the GSC, are those of Ribe and DeLattre  and, in particular, Ito et al. . The latter includes thermal diffusion, the viscosity contrast between the plume and the surrounding mantle, as well as the dependence of viscosity on temperature and pressure. The scaling laws for relating the so-called waist width W (i.e., along-ridge geochemical or topographic anomaly-widths observed = 2L) to the volumetric plume flux Q and plume-migrating ridge distance xp, are based on an extension of the effective length scale W0 = (Q/U)1/2 for the case of a stationary ridge-centered gravitational plume investigated experimentally by Feighner and Richards . U is the full spreading rate. A plume buoyancy number defines the relative strength of the gravitational versus plate-driven spreading of the plume-head. The effect of the sloping lithosphere is defined by the so-called non-dimensional up-slope number. A lagrangian passive tracer P is used to trace the plume flow and extent of mixing with the upper mantle. P is unity for 100% plume-derived material and zero for 100% upper mantle-derived material (Figure 2b).
 These two fluid dynamic simulations do not seem to support a narrow channel flow (whose width could perhaps be of the order of the plume stem diameter) as initially envisioned by Morgan . When the GSC was ridge centered some 10 Ma, the predicted shape of the radial spreading of the mantle plume at shallow depth would have been preferentially elongated along the ridge axis. Whereas during the GSC migration away from the plume, the preferential spreading would have to be progressively more and more skewed in the direction of the migrating ridge and accompanied by some small thermal thinning due to plate cooling, if judging from Ribe and Delattre's  numerical experiments. Note that Ito et al.  considered only a northward orthogonal GSC migration, rather than the NE migration direction expected assuming symmetric spreading and the Cocos and Nazca absolute plate motions (as revealed by the aseismic Cocos and Carnegie constructional plume traces in Figure 1). Both studies show that mechanical erosion of the lithosphere by the sloping lithosphere effect is minimal. Because of the relatively small distance (xp ∼ 260 km) of the migrating GSC from the center of the Galápagos plume, a nearly radial dispersion of the plume at shallow depth is anticipated, as also suggested from the isotope variations discussed in the previous section. However, the along-ridge variation of the plume fraction P predicted by Ito et al.'s  dynamic model shown in Figure 2b, does not match the symmetric mixing gradients predicted on the basis of the observed Pb-Hf-Nd-Sr isotopic variations shown in Figure 2a. It also clearly does not match the plume fractions Z1 and Z2 or their sum predicted in our three-component mixing model shown in Figure 12. Ito et al.  suggest that mixing between the plume and ambient upper mantle may not occur in the asthenosphere, but instead takes place deeper in the mantle, possibly by entrainment of depleted mantle as the plume ascends from its source, which seems to be consistent with our observations as discussed in our preferred three-component model.
10. Gravity Current Model of Cooling Mantle Plume Head Versus Bending Plume
 In order to account for the horseshoe-like isotopic anomaly pattern over the Galápagos platform, the cooling, temperature-dependent viscosity, gravity current model of Bercovici  and Bercovici and Lin , has been proposed as an alternative to the bending plume-entrainment model of Richards and Griffiths , Geist , and White et al. . To summarize the main points briefly, as the plume spreads and cools against the lithosphere, upon its own weight the plume develops a mushroom cap-like shape with a dipping frontal lobe at its periphery. The composition of this torus-like lobe is dominated by the isotopic plume-derived signal, whereas the thinner center of the plume head is composed of entrained depleted upper mantle material. The major difference between the gravity current model and the bending plume-entrainment model is primarily thermal. In the gravity current model, the thermal anomaly is at the center of the plume-head and predicts maximum melting of depleted upper mantle material at its center, as also evident from volcanic eruption rate and crust thickness estimates over the Galápagos platform [Feighner and Richards, 1994; Ito et al., 1997; Detrick et al., 2002], or from basalt compositional variations and their modeling [Geist, 1992; White et al., 1993]. The bending plume-entrainment model predicts the opposite melting pattern. Can the gravity current model applied to the 400–500 km scale Galápagos platform be extended in scale and be made consistent with the two symmetric, 1000 km-long geochemical and isotopic gradients observed along the GSC? Thermally it could perhaps be applied, since the maximum crust thickness (Figure 2b) and average degrees of melting along the GSC are found broadly distributed on either side of 91.5°W closer to the center of the plume than further out [e.g., Schilling et al., 1982; Detrick et al., 2002]. However, the observed GSC isotope gradients (Figure 2a) are of opposite signs to those expected in the gravity current model, namely, more radiogenic Pb and Sr in the outer lobe than in the center of the mushroom-shaped like plume head! For this reason we rule out this possibility.
11. Summary and Conclusions
 The nature and scale of the Pb-Hf-Nd-Sr isotopic variations along the GSC are quite different and appear decoupled from those observed on the Galápagos platform. Over the platform, the variations are on a small scale (∼500 km) and complex, whereas along the GSC they are on a large scale (∼2000 km), symmetric, and remarkably simple. This distinction may reflect the nature of the sampling itself and/or the particular modes of mixing that take place in these two very different tectonic settings. The sampling of the mantle from MORB along the GSC is horizontal, essentially uni-dimensional and recent (zero age). Over the platform, sampling is two-dimensional and extends over the last 4–5 Myr. The isotopic tracer variations along the GSC are zoned on a 1000 km scale about the center of the plume. This zoning probably reflects entrainment and mixing of depleted material during the plume ascent through the upper mantle, as suggested by Ito et al. , rather than at shallow depth right against the lithosphere lid. In contrast, over the 500 km large platform, zoning is horseshoe-like with a DM-rich entrained component at its center, apparently caused by the bending plume [White et al., 1993; Harpp and White, 2001]. These two lines of evidence are difficult to combine into a unified quantitative model. They may suggest nonsteady state conditions in the ascent of the Galápagos mantle plume and its spreading beneath the lithosphere. In fact, we have previously suggested that a pulsating plume may have initiated the series of rift propagation observed in the evolution of the GSC [Schilling et al., 1982; Wilson and Hey, 1995].
 Basalts from the Galápagos platform show greater scatter in Pb-Hf-Nd-Sr isotopic space, particularly in the 87Sr/86Sr direction. We have attributed this observation as probably reflecting mixing of melts or crystal/melt mixtures rather than solids, at various stages of magma storage, cooling, and evolution beneath the volcano edifices over the platform [Verma et al., 1983]. It is well recognized that during these emplacement processes and due to petrological effects, Sr bulk crystal/melt partitioning tends toward unity [e.g., Langmuir et al., 1992]. The range of Sr/Pb, Sr/Nd, and Sr/Hf ratios involved in the mixing are increased due to nonlinearity and consequently so is the Pb-Hf-Nd-Sr isotope scatter [Verma et al., 1983]. The more complex magmatic plumbing likely to be present in the old and thicker crust and lithosphere, which has been partly altered by seawater during its formation at the GSC, is also likely to enhance 87Sr/86Sr variation of basalt erupted over the platform.
 On the other hand, consideration of the three-component mixing model for the GSC brings some consistency with observations over the Galápagos platform. Simple modeling taking into consideration the eastward increase in spreading rate along the GSC suggests that the integrated plume flux along the GSC from the 91.5°W point of symmetry is some 15% greater west than east. This is rather counter-intuitive, considering that the Nazca plate drag would enhance plume flow toward the east. Nevertheless, the plume flow toward the east is in a more diluted form at equal radial distance. Close to the plume center, the extent of dilution by the depleted asthenosphere along the GSC tends to be the same immediately east and west of the 91.5°W point of the isotope gradient symmetry (see Figures 2 and 12d). The HIMU + EM1 plume component reaching the GSC attains only a maximum of 26% at this point. In broad terms, these GSC model deductions are qualitatively consistent with the horseshoe-like isotopic pattern observed over the platform and consistent with the bending plume model and the Nazca plate drag effect. The fact that the GSC isotopic gradients are symmetric and not significantly affected by RTI thermal and tectonic damming effects further suggests that the entrainment of depleted asthenosphere by the bending plume must be deep and well below the melting zone present both beneath the GSC and the Galápagos platform.
 The Pb isotope data from the GSC suggest that the Galápagos mantle plume is composed of two distinct components, mildly HIMU- and EM1-like, representing most likely recycled oceanic crust-lower mantle mixed with recycled continental-derived material. Only 0.05 to 0.5% of this EM1 component is required if the continental-derived material is recycled sediment (and an order of magnitude lower if pelagic). The west side of the dispersing Galápagos mantle plume is a factor of 1.5 to 1.75 richer in the EM1 component than the east side. It cannot be ascertained whether the HIMU and EM1 components of the Galápagos plume are present as distinct recycled protolith units. This follows from the fact that no significant thermal RTI effects on the Pb-Hf-Nd-Sr isotope variations along the spreading ridge could be detected, nor could any correlation between the Pb-Hf-Nd-Sr isotope ratios and major elements. If such protolith units are present, they must be smaller than the scale of RTI thermal effects along the GSC, and may have been eradicated by mixing during the melting and melt segregation processes taking place beneath the GSC.
Appendix A:: Three Component Mixing Model for Pb isotope ratios I and J
 Nomenclature for multicomponent mixing:
= Pb isotope ratio I in the mixture (e.g., 206Pb/207Pb)
= Pb isotope ratio J in the mixture (e.g., 208Pb/207Pb)
= Pb isotope ratio I in end-member component, 1, 2, 3, … i (e.g 206Pb/207Pb)
= Pb isotope ratio J in end-member component, 1, 2 or 3, …i (e.g 206Pb/207Pb)
= Pb concentration in the mixture
= Pb concentration in end-member component 1, 2, 3, …i
= Pb enrichment factor in end-member component, 1, 2, 3, . i relative to k, that is ni = Ci/Ck
= mass fraction of end-member component 1, 2, 3, …i in the mixture, Σ Zi = 1
 Mass balance for a multi-component mixture requires:
 For a three component mixure, with n1 = C1/C3, n2 = C2/C3 and n3 = 1 and Z3 = 1 − Z1 − Z2, equations (A1) and (A2) becomes:
 Solving for Z2 in both (A3) and (A4) and equating these two relations and solving for Z1 gives:
Assuming three reasonable end-members, and n1 and n2 as given in Table A1, one can solve for Z1, Z2 and Z3 for each sample analyzed for the Pb isotope ratios 206Pb/207Pb and 208Pb/207Pb.
 Helpful reviews by Karen Harpp, an anonymous reviewer, Associate Editor Catherine Chauvel, and Editor William White are gratefully acknowledged. This work was supported by the National Science Foundation, the Fonds National Suisse de la Research Scientific and the French Institut National des Sciences de l'Univers.