The influence of radiogenic 4He on cosmogenic 3He determinations in volcanic olivine and pyroxene

Earth and Planetary Science Letters 276 (2008) 20–29

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The influence of radiogenic 4He on cosmogenic 3He determinations in volcanic olivine and pyroxene P.-H. Blard ⁎, K.A. Farley Division of Geological and Planetary Sciences, MS 100-23, California Institute of Technology, Pasadena, CA 91125, USA

a r t i c l e

i n f o

Article history: Received 2 May 2008 Received in revised form 29 August 2008 Accepted 2 September 2008 Available online 22 October 2008 Editor: R.W. Carlson Keywords: cosmogenic magmatic radiogenic Helium-3 Helium-4 R-factor

a b s t r a c t Accurate determination of cosmogenic 3He concentrations in olivine and pyroxene phenocrysts requires knowledge of the amount of magmatic 3He also in the sample. The magmatic 3He component is commonly estimated by measuring the magmatic 3He/4He ratio and assuming that all 4He is magmatic. However, this approach yields incorrect results if 4He produced by U and Th decay is also present. Here we propose several strategies to account for the presence of radiogenic 4He. The optimal approach depends on whether the helium closure age (Tc) is similar to the exposure age (Te) of the analyzed phenocrysts. (i) When Tc = Te, which applies to uneroded lava flows, the ratio of cosmogenic 3He to radiogenic 4He is constant and the correction for radiogenic helium is independent of time. We provide a simple expression for a correction factor (R) that can be applied in this case. (ii) In the more common case that Tc N Te, it is necessary to obtain an independent constraint on the closure age to estimate the radiogenic correction. In either case a quantitative estimate of the radiogenic 4He production rate is required. Because of the long stopping distance of α-particles, this production rate depends on the U and Th concentrations of both phenocryst and host, and also on phenocryst grain size. To illustrate the magnitude and uncertainty of the necessary corrections, we compiled U and Th measurements on phenocrysts and whole rock samples of basalts and andesites, supplemented by new measurements on Hawaiian basalts and Altiplano andesites. Our data and models suggest that some published cosmogenic 3He production rate determinations may have underestimated the true production rate by up to 5% because the presence of radiogenic 4He was not recognized. Similarly, a recent study presenting cosmogenic 3He derived erosion rates in N 4 Ma Hawaiian olivines probably overestimates true erosion rates by an order of magnitude or more. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Cosmogenic 3He (3Hec) is a powerful tool for quantifying Earth surface processes. Thanks to its very low ratio of detection limit to production rate, this cosmogenic isotope allows the detection of very young exposure ages (b1 ka, e.g. Kurz and Geist, 1999) in small masses of mineral samples (b100 mg). Moreover, as a result of its nuclear stability, 3He has the potential to record ancient information and document events that occurred millions of years ago (e.g. Blard et al., 2006a). Because the production rate of 3Hec is reasonably-well established in olivine and pyroxene (see review in Balco et al., 2008), the majority of successful 3Hec applications have relied on the use of these phases (e.g. Licciardi et al., 2001). Accurate determination of the 3Hec concentration in olivines and pyroxenes however requires that the concentrations of the non-cosmogenic components of 3He be properly quantified. One of the most important of these is magmatic helium trapped in melt and fluid inclusions during mineral crystallization (Fig. 1). To overcome this issue, Kurz (1986) designed an ⁎ Corresponding author. GPS-Caltech, MC 100-23, 1200 E. California Blvd., Pasadena, CA 91125, USA. Tel.: +1 626 395 6177. E-mail addresses: [email protected], [email protected] (P.-H. Blard). 0012-821X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2008.09.003

efficient strategy that relies on a two-step routine: the initial crushing step permits extraction of gas contained within fluid inclusions (where the magmatic helium is preferentially located) in order to measure the magmatic helium isotope ratio (3He/4He)mag. A second step consists of fusing the sample to extract the remaining helium (4He and 3He). The total 3He extracted by fusion (3Hef) is then corrected for the magmatic 3He component assuming that the 4He extracted by fusion (4Hef) is entirely magmatic: 3

Hec ¼ 3 Hef −4 Hef 




3

 He=4 He

mag

ð1Þ

If the hypothesis that the 4He is entirely magmatic is not valid, use of Eq. (1) will lead to an overestimate of the magmatic correction and an underestimate of the cosmogenic 3He concentration. Importantly, the radioactive decay of U and Th may introduce significant amounts of radiogenic 4He (4He⁎) in mafic phenocrysts, and can thus invalidate Eq. (1) because helium includes radiogenic, magmatic and cosmogenic components. In this study we investigate the influence of the production of radiogenic 4He on the accuracy of cosmogenic 3He determinations. In Section 2, we describe the mechanisms involved in the accumulation

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underestimation of 3He production rates by ∼5% (e.g. Ackert et al., 2003). We also propose a reevaluation of a study that neglected the influence of 4He⁎ in the determination of 3Hec-derived erosion rates from ∼ 4.5 Ma old olivines in Hawaii (Gayer et al., 2008). 2. The production of 4He⁎ in mafic phenocrysts

Fig. 1. The different sources of helium in a mafic phenocryst (olivine or pyroxene) exposed to cosmic-rays. Nucleogenic production of 3He is not shown.

of 4He⁎ along with a review of the abundances of U and Th in mafic phenocrysts and in their surroundings. Section 3 details several strategies to quantify the presence of radiogenic 4He so as to obtain accurate corrections for the non-cosmogenic 3He component. The last section discusses the implications of this correction for several previous studies that have neglected the production of radiogenic 4 He. We show that neglecting this component may have led to

4 He⁎ is produced in olivine and pyroxene by in situ decay of U and Th. In addition, because the ejection distance of α-particles is about 20 μm in these minerals (Ziegler, 1977), some radiogenic 4He produced in the host lava may also be implanted into the phenocrysts (Lal, 1989). Similarly, a fraction of the in situ 4He⁎ may be ejected from the phenocryst. Consequently, an accurate estimate of the 4He⁎ production rate (P4) in olivine and pyroxene phenocrysts must take into account both mechanisms: ejection and implantation. P4 (at. g− 1 a− 1) can be calculated following the approach proposed by Farley et al. (2006) that combines the mathematical expression for α-ejection from a sphere (Farley et al., 1996) with the formula for α-implantation into a sphere (Dunai and Wijbrans, 2000):

h i P4 ¼ I4  1−1:5  ðS=DÞ þ 0:5  ðS=DÞ3 þ M4 h i  1:5  ðS=DÞ−0:5  ðS=DÞ3

ð2Þ

where I4 (at. g− 1 a− 1) and M4 (at. g− 1 a− 1) are the 4He⁎ production rates within the mineral of interest and within the surrounding lava,

Fig. 2. Histogram of a) U and b) Th concentrations in andesites and basalts. Dataset and reference list are available online at http://www.earthchem.org/earthchemWeb/search.jsp.

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respectively. S (μm) is the stopping distance of the α-nuclei (∼20 μm) and D (μm) is the crystal diameter. Eq. (2) is valid for minerals having spherical geometry. Therefore, in the case of non spherical phenocrysts, it is necessary to determine the shape and size of the grains, so that an equivalent sphere diameter can be calculated (Farley and Stockli, 2002). At secular equilibrium (e.g. Wolf et al., 1998): I4 ðor M4 Þ ¼ 8 

h

238

i h i h i U  λ238 þ 7  235 U þ λ235 þ 6  232 Th ð3Þ

 λ232

where I4 is the in situ production rate, M4 the lava production rate, [238U], [235U] and [232Th] are the concentrations of these isotopes measured within the phenocrysts, for I4, and within the lava, for M4. The relative proportion of in situ and implanted production of 4He⁎ is determined by the size of the phenocrysts and by the relative U and Th concentrations in phenocrysts and host, i.e., the effective mineral/melt partition coefficients for these elements. The abundance and location of uranium and thorium in the minerals and in the host lava are clearly

the main parameters controlling the production rate of 4He⁎ in the phenocrysts. Here we provide a review of U and Th concentrations in basalts and andesites lavas, using the dataset available at http://www. earthchem.org/earthchemWeb/search.jsp. The observed concentrations in basalts and andesites range between 0.002 and 400 ppm for U and between 0.005 and 445 ppm for Th, with respective mean of 2.3 and 6.1 (Fig. 2). Although these incompatible elements are theoretically enriched during magma differentiation, there is no clear relationship between the U–Th concentrations and the degree of differentiation. Some basalts can indeed be richer in U and Th than andesites, suggesting that crustal assimilation can significantly control the abundance of U and Th in mafic and intermediate lavas. Moreover, the large range (5 orders of magnitude) in reported concentrations underscores the importance of determining the U and Th abundances of lavas studied for cosmogenic 3He. Importantly, the U and Th concentrations in mafic phenocrysts are mainly determined by the effective phenocryst-lava partition coefficient for these elements. Table 1 and Fig. 3 present published partition

Table 1 Review of phenocryst-lava partition coefficient reported for U and Th in mafic and intermediate lavas Rock type

Mineral

Andesite Andesite Andesite Andesite Andesite Andesite Andesite Andesite Andesite–basalt Andesite Mugearite Mugearite Calco–alkaline andesite Basalt–andesite Basalt–andesite Basalt–andesite Basalt–andesite Basalt–andesite Basalt–andesite Basalt–andesite Basalt–andesite–dacite Basalt–andesite–dacite Basalt Basalt Basalt Hawaiian basalt Basalt–hawaite Basalt–hawaite Basalt–hawaite Bentonite–trachyte Leucitite, Gaussberg, Antarctica Leucitite, Gaussberg, Antarctica Trachybasalts, Mt Etna Trachybasalts, Mt Etna Trachyte–basalt Trachyte–basalt Alkali basalt, New Zealand Latite Latite Bentonite–trachyte Bentonite–trachyte Trachyte Trachyte Trachyte Trachyte–phonolite Porphyric trachyte Alkali basalt Basalt–andesite Basalt Basalt

Clinopyroxene Low calcium pyroxene Clinopyroxene Low calcium pyroxene Olivine Olivine Olivine Olivine Olivine Clinopyroxene Clinopyroxene Olivine Olivine Clinopyroxene Clinopyroxene Low calcium pyroxene Olivine Olivine Olivine Olivine Low calcium pyroxene Olivine Clinopyroxene Low calcium pyroxene Low calcium pyroxene Olivine Clinopyroxene Clinopyroxene Olivine Clinopyroxene Olivine Clinopyroxene Olivine Clinopyroxene Clinopyroxene Olivine Olivine Clinopyroxene Olivine Clinopyroxene Olivine Clinopyroxene Clinopyroxene Clinopyroxene Clinopyroxene Low calcium pyroxene Clinopyroxene Olivine Low calcium pyroxene Olivine

Dphenocryst-lava (U)

2σ

Dphenocryst-lava (Th) 0.10 0.14 0.10 0.13 0.02

0.06 0.01 0.01 0.04 0.112 0.03 0.01 0.04 0.019

0.41 0.05 0.02 0.09

0.0012 0.02 0.063 0.080 0.02 0.01 0.003 0.15 0.01 0.02 0.03 0.11 0.11 0.03 0.03 0.01 From 1.8E-05 to 7.9E-03 3.98E −05 7.80E −06

2σ

0.06 0.09

0.02

0.003

0.001

0.29

0.07

0.008 0.008

0.11

0.07 0.07

5.02E − 06 3.11E −06

0.03 0.144 0.05 0.01 0.015 0.03 0.029 0.01 0.014 0.031 0.02 0.02 0.045 1.72 0.04 0.01 0.01 0.02 0.02 0.03 0.01 0.02 0.0002 0.01 0.060 0.090 0.03

0.005 0.006 0.01

0.001 0.17

0.12

0.06 0.01 0.15 0.04 0.02 0.01 2.25E −05 6.20E −06

0.013

0.005 0.010

0.009

0.004 1.45

0.01

0.10

9.62E − 06 5.37E −06

Measurement

Reference

Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Whole phenocryst Experimental Spot measurement Spot measurement Spot measurement

Bacon and Druitt (1988) Bacon and Druitt (1988) Luhr and Carmichael (1980) Luhr and Carmichael (1980) Luhr and Carmichael (1980) Dunn and Sen (1994) Larsen (1979) Lemarchand et al. (1987) Villemant et al. (1981) This study Lemarchand et al. (1987) Lemarchand et al. (1987) Villemant (1988) Dostal et al. (1983) Larsen (1979) Dunn and Sen (1994) Larsen (1979) Dunn and Sen (1994) Villemant (1988) Lemarchand et al. (1987) Okamoto (1979) Mahood and Hildreth (1983) Villemant et al. (1981) Matsui et al. (1977) Onuma et al. (1968) This study Lemarchand et al. (1987) Lemarchand et al. (1987) Lemarchand et al. (1987) Lemarchand et al. (1987) Foley and Jenner (2004) Foley and Jenner (2004) Blard et al. (2005) Blard et al. (2005) Villemant (1988) Villemant (1988) Huang et al. (1997) Villemant (1988) Villemant (1988) Lemarchand et al. (1987) Lemarchand et al. (1987) Mahood and Stimac (1990) Mahood and Stimac (1990) Villemant (1988) Villemant (1988) Luhr et al. (1984) Zack and Brumm (1998) Kennedy et al. (1993) Beattie (1993) Beattie (1993)

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production of 4He and thus overestimation of the magmatic 3He correction (see Section 4.2). It appears that the natural range of U and Th concentrations in the lava and in the phenocrysts may induce variations in the 4He production rate that vary by several orders of magnitude among samples from various natural settings. There are two possible approaches to determining P4. The first involves measurement of U and Th in phenocrysts and host, as well as measurement of phenocryst size and shape distribution for making a correction for the long stopping distance of radiogenic 4He. An alternative approach that obviates the need to consider the implanted (and ejected) component relies on a removal (by abrasion or chemicaletching) of at least 20 μm of the outer portion of the phenocrysts, prior to the analyses of their helium content (Min et al., 2006; Aciego et al., 2007; Blackburn et al., 2007; Gayer et al., 2008). In this case all geometric corrections become unnecessary and the production rate of radiogenic 4He equals the in situ production of 4He⁎. In the case of young (b100 ka) lava flows, the assumption of secular equilibrium may not be valid, so disequilibrium must be considered when calculating P4 (Farley et al., 2002; Aciego et al., 2007). A slight fractionation of the 230Th/238U ratio from secular equilibrium may occur during crystallisation of olivines and pyroxenes (Wood et al., 1999; Aciego et al., 2007). However even for b200 ka lavas and using the maximum fractionation reported for pyroxenes and olivines (Wood et al., 1999; Aciego et al., 2007) the resulting shift in P4 differs from the value obtained under the secular equilibrium assumption by less than 5% (Farley et al., 2002). 3. Strategies to deal with the effect of 4He⁎ on the magmatic 3 He correction

Fig. 3. Histogram of phenocryst-lava U and Th partition coefficients for olivine and pyroxene in basalts and andesites. References are given in Table 1.

coefficients from different lavas as well as new data obtained from olivines and pyroxenes from Bolivian andesites and from Hawaiian basalts. These new data were determined by measuring U and Th in ∼ 5 separated phenocrysts and their host lava by isotope dilution, following the procedure developed for (U–Th)/He dating (Farley, 2002). Samples were spiked with a solution enriched in 230Th and 235U before being completely dissolved in a 2:1 mixture of concentrated HF and HNO3. The 232Th/230Th and 238U/235U ratios were then measured by ICPMS. Partition coefficients obtained from microprobe analyses or experimental equilibration (Beattie, 1993; Kennedy et al., 1993) are lower by 2 to 4 orders of magnitudes than those obtained by analyzing whole natural phenocrysts (which range between 10− 3 and 4 × 10− 1 for U and between 2 × 10− 4 and 1.7 for Th) (Table 1 and Fig. 3). It is probable that this discrepancy is explained by the presence of U and Th-rich melt inclusions in the analyzed olivines and pyroxenes. The presence of micromineral inclusions, such as britholite and chevkinite (Min et al., 2006), may also contribute to these high apparent partition coefficients for U and Th. Whatever their nature, these inclusions contribute to the production of 4He⁎ in the phenocrysts, and thus the relevant partition coefficients are those obtained from whole natural phenocrysts. Arbitrary use of the lowest partition coefficients (about 10− 5 for U and Th) may lead to significant underestimation of the

The presence of non-negligible amounts of 4He⁎ in mafic phenocrysts results in a mixture that can be impossible to deconvolve isotopically: helium originates from three independent sources (cosmogenic 3He, radiogenic 4He and magmatic 4He and 3He) but is represented by only two isotopes (3He and 4He) (Fig. 1). It is thus necessary to consider alternative strategies, for example by using relationships that may exist between cosmogenic 3He and radiogenic 4 He. For this purpose, it is useful to investigate the budget of both helium isotopes: In a phenocryst sample that has been exposed to cosmic rays, 3He originates from (i) cosmogenic production (this component includes both the spallation and the thermal-neutron production (Dunai et al., 2007)), (ii) nucleogenic production (Andrews and Kay, 1982) and (iii) inherited magmatic gas. This budget can be written (Farley et al., 2006): 3

Z Hetotal ¼

Te 0

Z P3  dt þ

Tc 0

Pn  dt þ 3 Hemag

ð4Þ

where P3 (at. g− 1 a− 1) is the local cosmogenic 3He production rate, Te (a) the exposure age, Pn (at. g− 1 a− 1) the nucleogenic production rate of 3 He and Tc (a) is the closure age of the sample. 3Hemag (at. g− 1) is the magmatic component. Cosmogenic 4He produced at the Earth's surface is negligible compared to the other component, so the budget of 4He only needs to integrate (i) the radiogenic production and (ii) the inherited magmatic component: 4

Z Hetotal ¼

0

Tc

P4  dt þ 4 Hemag

ð5Þ

where P4 (at. g− 1 a− 1) is the production rate of radiogenic 4He⁎, Tc (a) the closure age of the sample and 4Hemag (at. g− 1) is the magmatic component. The strategy for dealing with the presence of 4He⁎ is determined by the age of helium closure of the analyzed phenocrysts. Any exposed

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sample can be assigned to one of two distinct cases: (i) the helium closure age is similar to the exposure age (case 1: Tc = Te), or (ii) the closure age is older than the exposure age (case 2: Tc N Te). 3.1. Case 1: the closure and exposure ages are similar; Tc = Te (e.g., an uneroded lava flow)

Uneroded and unshielded flows (ensuring the condition Te = Tc) are generally younger than ∼1 Ma, so nucleogenic production of 3He (Andrews and Kay, 1982) can usually be neglected (i.e., when Te = Tc, R Tc then 0 Pn  dtV3 Hetotal ). Consequently Eq. (4) can be simplified: 3

Hetotal ¼ 3 Hec þ 3 Hemag 3

3.1.1. Theory Although it is rare in nature, the condition Tc =Te applies to the important case of uneroded-unburied lava flows, which are essential for calibration of 3Hec production rates. Given the diffusivity of helium in olivines and pyroxenes (Trull and Kurz, 1993; Shuster et al., 2004), these phenocrysts reach the helium closure temperature synchronously with lava eruption (Aciego et al., 2007). As a result, radiogenic 4He and cosmogenic 3He start accumulating at the same time. Then: 4

P4mean 3 He⁎ ¼  Hec P3mean

ð6Þ

where P4mean (at. g− 1 a− 1) and P3mean (at. g− 1 a− 1) are the timeintegrated
(over Te) production rates of radiogenic 4He and cosmo R Te R Te genic 3He P4mean ¼ T1e  0 P4  dt and P3mean ¼ T1e  0 P3  dt .

ð7Þ 3

4

4

Then, because Hemag = ( He/ He)mag × Hemag: ! 3
 He 3 Hetotal ¼ 3 Hec þ 4 Hetotal −4 He⁎  4 He mag Combining Eqs. (6) and (8) yields: 0 ! 3 P4mean He 3 3 Hetotal ¼ Hec  @1−  4 P3mean He

mag

1 A þ 4 Hetotal 

ð8Þ

3 4

! He He

ð9Þ

mag

This equation permits defining a factor following Blard and Pik (2008): ! 3 P4mean He R ¼ 1−  4 ð10Þ P3mean He mag

In this case the cosmogenic 3He concentration of a sample can be calculated by this simple relationship, assuming that

Fig. 4. Calculation of the R-factor (Eq. (10)) as a function of phenocryst size and the U and Th concentrations a) at sea level and N 50° latitude, b) at 4000 m and N 50° latitude. This simulation shows that (i) the value of R is strongly dependent on the altitude of the lava flow and that (ii) R is all the more sensitive to the grain size as the phenocryst diameter becomes smaller. The R-factor (see definition in Section 3.1) is computed here with a Th/U ratio of 3, a lava-phenocryst partition coefficient of 0.05 and a 3He/4He magmatic ratio of 8 Ra. α-implantation is modeled using Eq. (2). The equations of (Stone, 2000) were used to scale the sea level 3Hec production rate of 128 at. g− 1 a− 1 (Blard et al., 2006b).

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3 Hetotal = 3Hef and 4Hetotal = 4Hef (the subscript f meaning “extracted by fusion”):

3 3

Hec ¼

Hef −4 Hef 




3

 He=4 He

mag

ð11Þ

R

The strength of this approach resides in its capacity to provide a complete assessment of the radiogenic 4He correction, without requiring any independent constraint on the eruption age of the flow (Tc = Te in this case). Indeed, the calculation of R only requires as inputs the local time-integrated production rate P3mean, the production rate of 4He⁎, P4mean, and the magmatic 3He/4He ratio. When R ∼ 1, the radiogenic correction is negligible and the magmatic correction simplifies to Eq. (1). This circumstance applies when the radiogenic 4 He production is
negligible compared to the cosmogenic 3He  production, i.e.

P4 P3



3 4

He ≪1. He mag

However we have performed sensi-

tivity tests showing that this extreme situation is rarely observed in nature (see Section 3.1.3). Instead, R is generally b1. The lower R is, the higher is the correction arising from radiogenic 4He. 3.1.2. Case of uneroded lava flows independently dated This case is generally encountered for lava flows that are used for the purpose of production rate calibration. In this case the eruption age (Te) is known, e.g., by a radiometric dating technique. Here the relationship P3mean = 3Hec/Te can be used to modify Eq. (9), yielding: 3

P3mean ¼

Hef −4 Hef  Te


3 4



He He mag

3

þ P4mean 

4

! He He

ð12Þ

mag

This simple expression allows estimation of the local integrated production rate of 3He, P3mean, for lava flows whose sampled surface is negligibly eroded. 3.1.3. The range of R-factors for terrestrial lava flows It should be highlighted that, contrary to a common view (e.g. Sims et al., 2007), the relative radiogenic 4He correction does not increase with the eruption age of an uneroded lava. Instead the 3Hec/4He⁎ ratio is invariant with time (once P3 is corrected for time-integrated geomagnetic variations and P4 has reached secular equilibrium), and therefore R is only controlled by the spatial position of the sample (which determines P3), and by the U and Th concentrations and the size of the phenocrysts (which determine P4). We performed several sensitivity tests (Figs. 4 and 5) to explore the range of R values for different natural configurations that can be observed for lava flows on Earth. For this we assessed the influence of the flow location, the U–Th concentrations, the phenocryst-lava partition coefficient, and the grain size. These calculations show that, at sea level (Fig. 4 a) the R-factor may range from negative values (for b150 μm phenocryst diameter and Ulava N 6 ppm, Thlava N 18 ppm) to N0.8 (for N200 μm phenocrysts diameter and Ulava b 1, Thlava b 3 ppm), assuming an effective phenocryst-lava partition coefficient of 0.05. This shows how significant the correction arising from radiogenic 4He can be at low elevation, this being larger for high U and Th concentrations and small phenocrysts, whatever the age of the flow. In contrast, at 4000 m (Fig. 4b), the R-factor remains close to 1 (N0.90), even in lavas having high U and Th concentrations (Ulava N 8 ppm, Thlava N 24 ppm) and small phenocrysts (b200 μm diameter). At such elevation, the 3Hec production rate is high (∼17 times the sea level production at 50° latitude) and the radiogenic correction thus remains negligible. The sensitivity of R to the phenocryst-lava partition coefficient is also shown in Fig. 5 (a and b). These results show that for phenocrysts of 300 μm diameter, R may range between 0.2 and N0.9 at sea level, and between 0.95 and 0.99 at 4000 m for Dphenocryst-lava values of 10− 1

Fig. 5. Calculation of the R-factor (Eq. (10)) as a function of the U and Th concentration and the phenocryst-lava partition coefficient for U and Th a) at sea level and N 50° latitude, b) at 4000 m and N 50° latitude. The R-factor is computed here with a Th/U ratio of 3, a phenocryst diameter of 300 μm and a 3He/4He magmatic ratio of 8 Ra. α-implantation is modeled using Eq. (4). The equations of (Stone, 2000) were used to scale the sea level 3Hec production rate of 128 at. g− 1 a− 1 (Blard et al., 2006b).

to 10− 5. The R value is increasingly sensitive to the U and Th concentrations as the partition coefficient (Dphenocryst-lava) increases. Moreover, when Dphenocryst-lava is below ∼ 10− 3 (for phenocrysts of 300 μm diameter), R becomes insensitive to Dphenocryst-lava. This radiogenic correction then mainly depends on the U and Th concentration of the lava, due to the implanted 4He component. Given the range of U and Th concentrations and partition coefficients reported for andesites and basalts (Figs. 2 and 3), the model shown in Fig. 5 highlights that plausible values of the R-factor may span a large range. All these results highlight that the correction arising from radiogenic 4He in many cases cannot be neglected. Except when R is very close to 1, accurate determination of 3Hec cannot be accomplished without a determination of the R-factor specific to the analyzed sample. This requires accurate determinations of the U and Th concentrations in the lava as well as in the phenocrysts, and the magmatic 3He/4He ratio. 3.1.4. Uncertainty of the R-factor radiogenic correction The uncertainty associated with the R-factor correction is directly dependent on the precision of the radiogenic 4He production rate,

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P4mean. When the correction is significant (R ≪ 1), special attention must thus be paid to determine the size and geometry of the phenocrysts, as well as the distribution of U and Th in the grain boundaries. Additionally, the suppression of the implanted 4He⁎ component by mechanical abrasion of the outer part of the grains may be a profitable strategy to improve the precision of the radiogenic correction. The accuracy of R is also dependent on the value of the (3He/4He)mag ratio (see Eq. (10)). This ratio is generally determined by vacuum crushing of the phenocrysts (e.g. Kurz, 1986). However, the magnitude of this value may be very sensitive to the addition of a few percent of cosmogenic 3He extracted during the crushing (e.g. Hilton et al., 1993; Yokochi et al., 2005). It should be noted that the magnitude of this undesirable release of cosmogenic 3He seems to depend on the crushing conditions and the used analytical apparatus (Blard et al., 2008). Leakage of cosmogenic helium during crushing may lead to overestimation of the magmatic ratio, and thus underestimation of the R-factor. To avoid this possible bias, the magmatic ratio can be obtained by crushing shielded phenocrysts belonging to the same lava flow (Kurz et al., 2004). If no shielded sample is available, the issues related to a possible crushing-induced 3 Hec loss could be overcome with an alternative strategy analyzing several replicates of the same exposed sample to draw isochrons in the (3He/4He)f vs (1/4He)f space or in the 3Hef vs 4Hef space (e.g. Blard and Pik, 2008). This technique allows a graphical determination of the magmatic ratio that avoids any potential bias arising from the crushing step.

3.2. Case 2: the closure age is higher than the exposure age, Tc N Te 3.2.1. Theory In the case of a surface that has been subjected to erosion or shielding, the effective exposure age Te (i.e. calculated assuming zero erosion) is necessarily lower than the closure age Tc. In this case, without any independent estimate of the erosion rates, it is not possible to derive a simple relationship between 3Hec and 4He⁎. So in this case the cosmogenic 3He concentration must be calculated using the following equation (from Eqs. (4) and (5)): 3

3

Hec ¼ Hef −

Z 0

Tc

 Z Pn  dt− 4 Hef −

0

Tc

 P4  dt 

3 4

! He He

ð13Þ

mag

This calculation requires an independent determination of the closure age Tc. For lavas this constraint can be obtained by dating lava emplacement, for example by radiochronometric techniques (e.g. K/Ar, (U–Th)/4He⁎). If the radiogenic production rate P4 is not determined accurately, the magmatic 3He correction will be biased, the error being larger as Tc increases (see Section 3.2.2). Alternatively, the concentration of magmatic helium can be obtained by prolonged vacuum crushing of a phenocryst aliquot (Scarsi, 2000). Once the magmatic 4He is totally removed, then the subsequent fusion of the sample should extract only the remaining R Tc radiogenic 4He⁎ (4 Hef ¼ 0 P4 :dt) and the magmatic 3He correction would be null. However, it should be kept in mind that a fraction of the matrix-sited 4He⁎ can be extracted after several minutes of vacuum

Fig. 6. Bias (Δ3Hec/3Hec) in the calculated 3Hec cosmogenic concentration under the hypothesis that radiogenic 4He⁎ is neglected to calculate the magmatic 3He. This modelling was obtained from Eq. (14), assuming a U and Th lava concentration of 1 ppm and 3 ppm, respectively, a magmatic ratio of 8 Ra and a sea level high latitude production rate of 128 at. g− 1 a− 1 (Blard et al., 2006b) scaled with the factors of (Stone, 2000). The bias shown in a) and b) consider the implantation and ejection of 4He⁎ in 300 μm phenocrysts at sea level and at 4000 m, respectively. c) and d) only consider in situ production of 4He. Δ3Hec/3Hec can be N 100% for phenocrysts in which magmatic 3He is significant.

P.-H. Blard, K.A. Farley / Earth and Planetary Science Letters 276 (2008) 20–29

phenocryst-lava partition coefficient is low (Dphenocryst-lava b 10− 2). Estimation of the implanted 4He⁎ component may be a major source of uncertainty if the geometry and size of the phenocrysts is difficult to establish. Thus, the strategy of eliminating the implanted 4He⁎ by mechanical removal of the outermost 20 μm (e.g. Aciego et al., 2007) is especially appropriate when Dphenocryst-lava b 10− 2. Moreover, if the Tc/Te ratio is b10 for phenocrysts with U concentrations b10 ppb (and Thb 30 ppb), then the bias arising from the radiogenic correction remains negligible (b1%) (Fig. 6 c,d). This reinforces the advantages of a systematic removal of the external part of the phenocrysts.

crushing (Scarsi, 2000), leading to an overestimate of the magmatic component. Hence, although the preliminary step of vacuum crushing may bring some useful information, this technique should be used with caution. Another possibility (proposed by Williams et al., 2005) would be to select small microphenocrysts (diameter b200 μm). These small mineral grains are generally so poor in magmatic helium that all the 4 He extracted by fusion is radiogenic and the magmatic 3He correction is negligible. 3.2.2. The importance of the radiogenic correction when Tc N Te When Tc N Te, 4He⁎/3Hec is no longer time independent but increases with the ratio Tc/Te. In this case, neglecting the radiogenic 4 He production (or even using the no-longer valid relationship Te = Tc) may lead to significant overestimation of the magmatic correction, and thus to underestimation of the actual 3Hec concentration. To provide a quantitative estimate of the importance of this radiogenic correction, we modeled the Δ3Hec/3Hec excess corresponding to the relative error that would be made if 3Hec were calculated neglecting the radiogenic correction (Aciego et al., 2007). This systematic error can be calculated from: Δ3 Hec 3

Hec

¼

P4mean  P3mean

3 4

! He He

 mag

Tc Te

27

4. Discussion: implication for previous studies 4.1. Revision of published 3He production rates (by calculating the R-factor) The majority of published 3Hec production rates were determined empirically from basaltic lava flows. These flows are well suited for this purpose because their emplacement can be independently dated by radiochronometric techniques, and the presence of surficial geomorphic features (e.g., ropy texture) can document limited erosion. The lava flows used in production rate calibration studies generally fulfill the criteria corresponding to case 1: closure age and exposure age are equal (Tc = Te). Thus it is possible to calculate R-factors for these flows. With the exception of two studies (Dunai and Wijbrans, 2000; Blard et al., 2006b), the influence of radiogenic 4He has been neglected in previous calibration work (Cerling and Craig, 1994; Licciardi et al., 1999, 2006). Here we assess whether the hypothesis of negligible 4He⁎ is justified in these studies. For this purpose we calculated the R-factors and use these criteria to estimate the magnitude of the radiogenic correction in these calibration studies (Table 2). Unfortunately some key-studies (Cerling and Craig, 1994;

ð14Þ

Fig. 6 a, b shows the magnitude of this bias both for samples exposed to cosmic-rays at sea level and at 4000 m, for a typical range of U and Th concentrations. This model assumes a phenocryst diameter of 500 μm for the calculation of P4. We also modeled the Δ3Hec bias neglecting the implanted 4He⁎ (Fig. 6 c,d). The difference between these models highlights that the implanted component becomes important when the

Table 2 R-factors of lava flows used for 3Hec production rate calibrations Reference

Location-flow name

Cerling and Craig (1994)

Tabernacle Hill Bonneville Flood deposit Yapoah Crater South Belknap Clear Lake Lava Butte Cerro Volcano Cerro Volcano Rio Pinturas Lambahraun Leitahraun Burfellshraun Dingvallahraun Tahiche Atalaya de Femes Montanarroja Simeto Nave Solichiatta Mauna Loa ML1 Mauna Loa ML5 Mauna Kea MK4

Licciardi et al. (1999)

Ackert et al. (2003)

Licciardi et al. (2006)

Dunai and Wijbrans (2000)

Blard et al. (2006b)

a

Age (yr)

1σ

14400 14500

100 100

2453 2800 2880 7130 108700 108700 67800 4040 5210 8060 10330 152000 281000 1346000 41000 33000 6000 8284 1524 149000

780 17 69 130 2800 2800 3000 250 110 120 80 13000 10000 5000 3000 2000 1000 80 50 23000

Scaling factor (Dunai, 2001 and Stone, 2000)a

Depth-snow correction

Ulava (ppm)b

2.8 2.9

0.96 0.96

0.5 0.5

3.4 3.2 2.0 2.8 1.6 1.4 2.2 1.5 1.3 1.0 1.1 0.93 0.77 0.79 1.00 1.64 1.18 0.64 1.19 1.43

0.96 0.97 0.95 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.99 0.97 0.97 0.97 0.93 0.89 0.95 0.97 0.97 0.88

2 2 2 2 1.4 1.4 1.4 0.5 0.5 0.5 0.5 0.9 0.5 0.7 2.013 4.14 3.96 0.18 0.18 0.21

Thlava (ppm)b 1.8 1.8 5 5 5 5 6.6 6.6 6.6 1.5 1.5 1.5 1.5 3.1 1.7 2.8 8.793 15.28 14.78 0.49 0.53 0.62

Partition coefficientc

Phenocryst diameter (μm)d

(3He/4He)mag (Ra)e

P4 (at g− 1 a−1)

R− factor

0.05 0.05

750 750

6.1 12.5

2.6E + 05 2.6E + 05

0.99 0.99

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.025 0.025 0.025 0.07 0.07 0.07 0.01 0.01 0.01

750 750 750 375 750 750 750 633 428 750 589 300 300 300 500 500 500 800 800 800

7.5 8.5 7.9 8.3 7.6 7.6 7.6 13.4 14.4 13.2 13.8 6.48 6.45 6.79 6.2 5.6 6.6 8.7 8.3 8.2

9.8E + 05 9.8E + 05 9.8E + 05 1.4E +06 8.5E + 05 8.5E + 05 8.5E + 05 2.6E + 05 3.2E + 05 2.4E + 05 2.7E + 05 6.5E + 05 3.6E + 05 5.4E + 05 1.7E +06 3.2E + 06 3.0E + 06 4.5E + 04 4.7E + 04 5.4E + 04

0.98 0.97 0.96 0.95 0.95 0.95 0.97 0.97 0.96 0.97 0.96 0.95 0.97 0.95 0.88 0.87 0.81 0.99 1.00 1.00

Scaling factors are calculated combining the paleomagnetic correction of Dunai (2001) and the spatial correction of Stone (2000). Used U and Th concentrations are from Peate (Personal communication, 2007) and Vigier et al. (2006) for the lava flows studied by Cerling and Craig (1994) and Licciardi et al. (2006), respectively. For the study of Licciardi et al. (1999) we used average U and Th concentrations reported for basalts (see database at http://www.earthchem.org/earthchemWeb/ search.jsp). For Dunai and Wijbrans (2000), Ackert et al. (2003) and Blard et al. (2006b) we used the U and Th concentrations measured by these authors in the corresponding lavas. c Used partition coefficient for Cerling and Craig (1994), Licciardi et al. (1999), Ackert et al. (2003) and Licciardi et al. (2006) are mean values from Table 1. For Dunai and Wijbrans (2000) and Blard et al. (2006b) we used the values determined by these authors. d For the studies of Cerling and Craig (1994) and Licciardi et al. (1999), phenocrysts diameter are assumed to be 750 μm (Licciardi, Personnal communication, 2008). For the studies of Dunai and Wijbrans (2000), Ackert et al. (2003), Licciardi et al. (2006) and Blard et al. (2006b), grain sizes were determined by the authors. e Ra = 1.384 × 10− 6 is the 3He/4He ratio of air. All these magmatic values were determined by vacuum crushing. b

28

P.-H. Blard, K.A. Farley / Earth and Planetary Science Letters 276 (2008) 20–29

Licciardi et al., 1999; Ackert et al., 2003; Licciardi et al., 2006) do not provide all the necessary data for precise determination of P4, such as U and Th concentrations in the lavas and phenocrysts, as well as the mineral diameters. Instead, we used estimates from the literature by selecting reasonable values for each site (see Table 2 caption). When no information is provided about the phenocryst diameter, we assume that the analyzed grain size is the same as the original grain size in the rock. Therefore, our approach does not provide a precise revision of previously published production rates. Rather, by providing a quantitative estimate of the radiogenic correction through the R-factor, our study examines if the accuracy of previous P3 determinations could be improved by additional U and Th measurements. Our calculations (Table 2) show that the North-American basaltic flows used in the study of Cerling and Craig (1994) are characterized by R-factors ranging between 0.98 and 1. Thus, if the order of magnitude of the partition coefficients that we used here are correct, the correction associated with the R-factor would be b2%. Given the uncertainty associated with these measurements, ignoring the influence of 4He⁎ on these 3Hec determinations can thus be considered reasonable. The Patagonian, North-American and Iceland lava flows used in the calibration studies of Ackert et al. (2003), Licciardi et al. (1999) and Licciardi et al. (2006) have R-factors ranging between 0.95 and 0.97 (Table 2). Inclusion of the radiogenic 4He correction would thus raise the production rates published in Ackert et al. (2003), Licciardi et al. (1999) and Licciardi et al. (2006) by 3 to 5%. This revision should however be performed on the basis of new measurements designed specifically for the purpose. 4.2. Determining modern erosion rates in Hawaii using ∼ 4.5 Ma old olivines: a reevaluation of the conclusions of Gayer et al. (2008)

Fig. 7. Influence of the U and Th phenocryst-lava partition coefficient on the 3Hec estimate from Kauai olivines (Gayer et al., 2008). 3Hef is the total 3He extracted by fusing these samples. Δ3Hem/3Hef is the magmatic 3He overcorrection arising from the assumption that radiogenic 4He is negligible.

considered with caution. To test the spatial variability of erosion rates in Kauai, we suggest that a rigorous reevaluation would require measuring U and Th on each individual olivine aliquot processed for 3 Hec. 5. Conclusion

In a recently published article Gayer et al. (2008) derive erosion rates from 3Hec measured in olivines from rivers of a watershed on the island of Kauai. Their results yield a basin-wide average erosion rate of 0.056 mm a− 1 and a high variability of smaller-basin erosion rates, ranging from b 0.1 to 4 mm a− 1. Gayer et al. (2008) came to these conclusions using Eq. (1) to estimate the magmatic 3He correction. They argued that the 4He⁎ build-up can be neglected in these ∼ 4.5 Ma old olivines (McDougall, 1979). This assumption relies on the use of partition coefficients of 2 × 10− 5 and 5 × 10− 5 for U and Th (Beattie, 1993; Kennedy et al., 1993) and U and Th of 0.3 and 1 ppm in the host lava. However, these partition coefficients are obtained from ion microprobe spot measurements in phenocrysts. They lie between 2 and 5 orders of magnitude below the range of published values obtained on bulk phenocrysts (Table 1 and Fig. 3). Moreover, the low partition coefficients used by Gayer et al. (2008) are not compatible with the values (ranging between 0.03 and 0.1 for U and Th) measured on Kauai olivines in the present study. Consequently, we propose that the 3Hem corrections performed by Gayer et al. (2008) are probably overestimated, which led these authors to overestimate the 3Hec-derived erosion rates. To assess the magnitude of this bias, we calculated the relative magmatic 3He overestimate (Δ3Hem/3Hef) arising from the assumption that radiogenic 4He is negligible (Fig. 7). This calculation shows that the proportion of the total 3He due to improper 4He⁎ consideration may range between a few percent up to 100%. This variability is due to the large span of the 4He concentrations observed in these samples. This implies that the cosmogenic 3He concentrations proposed by Gayer et al. (2008) should be revised upward by from a few percent to two orders of magnitude and the actual erosion rates for this western watershed of Kauai might be far lower than 0.056 mm a− 1. Moreover it cannot be excluded that the inter-basin variability observed by (Gayer et al., 2008) is an artifact due to improper 4He⁎ correction. Indeed, it is possible that the observed 3Hec interaliquot variability arises simply from inter-sample [U] and [Th] variability. We thus propose that the main conclusions of Gayer et al. (2008) should be

The proposed strategies for eliminating the influence of radiogenic 4He on cosmogenic 3 He measurements depend on the relationship between the closure age (Tc) and the exposure age (Te) of the sample. • If Te = Tc (e.g., uneroded lava flows), then a proportional relationship exists between cosmogenic 3He and radiogenic 4He. This remarkable property can be exploited to perform the correction through the calculation of the R-factor (see Eq. (10)), without any independent constraint on the closure age Tc. The calculation of R requires that the radiogenic production rate P4 and the local 3Hec production rate are known, as well as the magmatic 3He/4He ratio. • If Te N Tc, then an independent measurement of the closure age is necessary to estimate the respective proportions of radiogenic and magmatic 4He in the studied phenocrysts. We modeled the magnitude of this radiogenic 4He correction using the U and Th concentration data reported for basalts and andesites. These calculations allowed us to establish that this correction is rarely negligible under many natural configurations. However the influence of radiogenic 4He on the accuracy of the magmatic 3He correction has been neglected in several studies during the last 20 years. Our calculations suggest that several published 3Hec production rate (Ackert et al., 2003; Licciardi et al., 2006) might have been underestimated by a few %. A careful revision of these published rates should however be done on the basis of additional determination of the U and Th concentrations in the considered phenocrysts and lava. Similarly, the radiogenic 4He component almost certainly had a substantial effect in the recent study of Gayer et al. (2008). This implies that the 3 Hec-derived erosion rates proposed by these authors are possibly overestimated by between a few % and perhaps 2 orders of magnitude (depending on the U and Th concentration of the analyzed samples). Additional U and Th measurements are required to improve the accuracy of the determination of these Hawaiian erosion rates.

P.-H. Blard, K.A. Farley / Earth and Planetary Science Letters 276 (2008) 20–29

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