The contemporary degassing rate of 40Ar from the solid Earth (original) (raw)

Abstract

Knowledge of the outgassing history of radiogenic 40Ar, derived over geologic time from the radioactive decay of 40K, contributes to our understanding of the geodynamic history of the planet and the origin of volatiles on Earth's surface. The 40Ar inventory of the atmosphere equals total 40Ar outgassing during Earth history. Here, we report the current rate of 40Ar outgassing, accessed by measuring the Ar isotope composition of trapped gases in samples of the Vostok and Dome C deep ice cores dating back to almost 800 ka. The modern outgassing rate (1.1 ± 0.1 × 108 mol/yr) is in the range of values expected by summing outgassing from the continental crust and the upper mantle, as estimated from simple calculations and models. The measured outgassing rate is also of interest because it allows dating of air trapped in ancient ice core samples of unknown age, although uncertainties are large (±180 kyr for a single sample or ±11% of the calculated age, whichever is greater).

Keywords: geochronology, ice cores, geodynamics, noble gases

The elemental abundance and isotopic composition of noble gases in the atmosphere inform us about Earth's composition, the history of the ocean and atmosphere, and the present and past geodynamics of the planet. The atmospheric abundance of 40Ar reflects the balance between production by radioactive decay of 40K in the crust, upper mantle, and lower mantle, and outgassing to the atmosphere. It is well recognized that the atmospheric inventory comprises approximately half of the total 40Ar produced by potassium decay over Earth history, assuming the canonical value of 240 ppm for the K content of the bulk silicate Earth (1). The most parsimonious explanation for the remainder is that there is a large reservoir containing undegassed Ar, which is presumably the lower mantle (1). However, extensive seismic evidence has shown that oceanic plates subduct into the lower mantle while plumes rise from the core-mantle boundary to produce volcanism at the surface (e.g., refs. 2 and 3). Because of such observations, it is problematic to maintain that the lower mantle is undegassed. A number of recent papers have attempted to explain the limited atmospheric 40Ar inventory in the face of whole mantle convection. As one example, Davies (4) and Lassiter (5) have proposed that the bulk silicate Earth K concentration is ≈150 ppm rather than 240.

In this article, we present and explore another constraint on the planetary 40Ar balance: the contemporary degassing rate of 40Ar. We determine this rate by measuring the paleoatmospheric 40Ar/38Ar ratio of fossil air from ice core samples. Critical to this effort are the Vostok and especially EPICA Dome C cores (6), which allow us to access air as old as ≈779 ka. We compare the observed outgassing rate with the contributions to this term from outgassing of the continental crust and various degassing modes of the upper mantle. It is possible to account for the present rate of 40Ar increase with our estimates of degassing rates by the continental crust and midocean ridge volcanism, although the uncertainties are large.

The paleoatmospheric 40Ar/36Ar ratio has previously been examined by measuring the isotopic composition of Ar retained in the Devonian Rhynie Chert (7). Rhynie Chert Ar has a 40Ar/36Ar ratio of 291.0, when the modern ratio is taken as 295.5. The Rhynie Chert data correspond to a 40Ar outgassing rate of 0.66 × 108 mol/yr, and a rate of increase in the atmospheric 40Ar/36Ar ratio (or 40Ar/38Ar ratio) of 0.040 ‰/Ma. These numbers are problematic because of the possibility that the samples have been contaminated with atmospheric Ar subsequent to their formation (which makes the rate of 0.04 ‰/Ma a lower limit). If one accepts the Rhynie data, determining the 40Ar rise rate for the more recent past is still useful because the rate may have varied since the deposition of the Rhynie Chert.

Measuring the paleoatmospheric 40Ar/38Ar ratio in ice core samples is complicated by gravitational fractionation in the firn (8, 9), the snowpack overlying the zone of ice where air is trapped in isolated bubbles. At Vostok and Dome C, the firn layer is ≈100 m thick, and gravitational fractionation enriches heavy isotopes relative to light isotopes by ≈0.5 ‰/mass unit. The corresponding enrichments for 40Ar/38Ar and 40Ar/36Ar are 1 and 2‰, respectively, factors of 20–40 higher than the change in the paleoatmospheric ratios we need to measure. To address this challenge we note that gravitational enrichments scale exactly with mass differences, and we assume that the atmospheric 38Ar/36Ar ratio has remained constant throughout the measurement period. We then calculate the paleoatmospheric 40Ar/38Ar ratio, relative to the modern atmosphere, as:

1.002 is the precise ratio of the mass difference between 40Ar and 38Ar, and 38Ar and 36Ar. Isotope ratios are reported in the standard δ notation, with 40/38, 40/36, and 38/36 indicating the isotope abundances that are being compared. In practice, the mass spectrometer reference is pure Ar, and the paleoatmospheric ratio is calculated after subtracting the δ values measured for air relative to this reference. We refer to the paleoatmospheric value in terms of δ40/38Ar, because this term is closest to the measured property, but the paleoatmospheric δ40/36Ar value would be identical.

Although some deep ice cores are well dated to their base, this is not the case for other glacial ice. In Greenland, the GISP2 and GRIP cores have disturbed glacial ice at their base, underlain by dirty ice that may date to the origin of the Greenland Ice Sheet (10). There is also ice of unknown age at Vostok (11) and Siple Dome (West Antarctica) beneath the well ordered strata. In the Dry Valleys region of Antarctica, glacial ice underlying englacial debris may have a very old age. Having determined the rate of change of the 40Ar/38Ar ratio of air, we have a tool for dating these samples by measuring the Ar isotope composition of their trapped gases.

We assume that the outgassing rate has been constant during recent Earth history. Constancy is likely for mantle degassing associated with the widely dispersed processes at midocean ridges. Most degassing is from the continental crust, however, and here rates may vary as weathering rates change and major tectonic events wax and wane. Therefore, our assumption of constant outgassing is provisional, and can hopefully be refined if old ice samples are recovered with datable ash layers.

In this article, we describe the analytical method used to measure 40Ar/38Ar in ice core samples and present results describing the atmospheric increase, and we discuss the implications of the data for simple Earth outgassing models.

Results

We have analyzed a total of 15 Holocene ice samples from 4 ice cores, 9 samples dating to ≈100 and 400 ka from the Vostok ice core, and 7 samples dating to ≈800 ka from the EPICA Dome C ice core. Data are summarized in Table 1, and the paleoatmospheric δ40/38Ar ratio is plotted vs. age in Fig. 1. The best estimate of precision comes from the analysis of trapped air in a variety of ice core samples dated to ≤5 ka: ±0.012‰ (1 σ).

Table 1.

Isotopic composition of Ar in ice core trapped gases

Fig. 1.

Paleoatmospheric δ40/38Ar ratio plotted versus age.

Paleoatmopsheric δ40/38Ar, calculated according to Eq. 1 and written as δ40/38Ar − δ38/36Ar, is plotted vs. age in Fig. 1. A regression line gives the best fit to the data and corresponds to a rate of change in the δ40/38Ar of 0.066 ± 0.007 ‰/Ma (1 σ confidence limits). This rate corresponds to a 40Ar outgassing rate of 1.1 ± 0.1 × 108 mol/yr. The uncertainty is the uncertainty in the regression associated with scatter in the data. The data are consistent with a constant rate of change during the study period, but given the large uncertainty and low resolution, we can only say that there is no evidence for variability. Here, we assume that the rate has been constant for the recent geologic past. With this assumption, we can date trapped gases in old ice. For a single sample, given a reproducibility of ± 0.012 ‰ and an uncertainty in the rate of change of 11%, the age uncertainty would be ± 180 ka or 11% of the age, whichever is greater. With this uncertainty, δ40/38Ar dating is not useful for well ordered sections of deep ice cores, but can be used to date old ice samples of unknown age as discussed above.

Discussion

The 40Ar Outgassing Rate and the Atmospheric 40Ar Mass Balance.

Following the literature we regard atmospheric 40Ar as coming from radioactive decay of 40K in three realms: the continental crust, the upper mantle at midocean ridges, and other sources (such as mantle plumes). By using data in Table 2, we calculate outgassing rates of these realms and compare them with global outgassing assessed using our data, 1.1 × 108 mol/yr (Table 2).

Table 2.

Estimates of 40Ar outgassing rates from the solid Earth by various processes

Outgassing from Midocean Ridge Spreading Centers and Other Mantle Sources.

We estimate the radiogenic 40Ar outgassing rate from the upper mantle, starting with the midocean ridges. We base our calculation on estimates of the 3He degassing rate, the 4He/3He ratio of the upper mantle, and the 4He/40Ar ratio of the upper mantle:

The subscript “UM” refers to the upper mantle and F = flux.

For the 3He flux from the upper mantle (F3He-UM) we adopt a value of 422 mol/yr, based on mantle trace element studies of Saal et al. (12) (Table 2) and a recent analysis of the oceanic 3He distribution in the context of ocean circulation models.¶ Parenthetically, this flux is considerably less than the “canonical” value of 103 mol/yr (13), derived from a zero-order model of ocean mixing. (4He/3He)UM, the 4He/3He ratio of the upper mantle, is 9.1 × 104. 4He/40Ar ratios in basalt glasses from the upper mantle are enriched relative to parent magmas during vesiculation, because 4He is more soluble in the melt (14, 15). Four studies give estimates of (4He/3He)UM independent of vesiculation. Studies of well gases derived from the mantle give ratios between 0.5 and 3.4, with a mean of 1.9 (16, 17). Winckler et al. (18) measured 4He/40Ar in Red Sea brines ranging from 1.5 to 2.7, with a mean of 2.1. Moreira et al. (19) measured ratios in “popping rocks” from the Mid-Atlantic Ridge lying between 1.4 and 1.7, and averaging 1.5. We adopt the median of these estimates (1.9), and calculate an upper mantle outgassing rate of 40Ar at midocean ridges of 0.20 × 108 mol/yr. Stuart and Turner (20) measured the 4He/40Ar ratios between 3.4 and 36.4 in fluid inclusions from hydrothermal vent sulfide deposits, interpreting the lower values as representing ratios in the upper mantle. Adding these values to the average would decrease the calculated 40Ar outgassing rate of the upper mantle by ≈30%.

We estimate that the crustal production rate in back arc basins is 5% of the midocean ridge rate. If the other terms are the same as at midocean ridges, the corresponding mantle 40Ar flux associated with subduction zones is then only 0.01 × 108 mol/yr.

The mantle 40Ar loss through extensional basins, estimated based on a mantle 3He flux of 8.4–84 mol/yr (21) is also very small, up to only 0.04 × 108 mol/yr.

Finally, we estimate lower mantle degassing by calculating 40Ar degassing from hotspot volcanism. Intraplate volcanic fluxes have been estimated to lie between ≈1% (22) and 12% (23) of the midocean ridge rate (the highest estimate includes seamounts38) and to have a 3He/4He ratio of 20 times atmospheric (24). Assuming that hotspots are the result of mixing of midocean ridge basalt (MORB) source material and a small amount of material with a 3He/4He ratio of 50 _R_a and a 3He concentration that is 10 times greater than MORB (25, 26), then a simple mass balance calculation indicates that hotspot sources have an average 3He concentration that is ≈2.5 times greater than MORB, and a similar 4He concentration. If both components have the same 4He/40Ar ratio, the 40Ar concentrations are also similar. The maximum contribution of 40Ar from the hotspot source is simply equal to 12% of the contribution from ridges, the number corresponding to the relative proportion of volcanism. The corresponding hotspot outgassing rate is 0.024 × 108 mol/yr.

We thus estimate mantle degassing of 40Ar as 0.27 × 108 mol/yr, ≈25% of the global value estimated from the ice core data.

Outgassing from the Continental Crust: Estimates from Box Models.

We calculate outgassing rates from the continental crust in four ways based on simple assumptions, together with independently estimated terms in the literature (Table 2). We assume that 40Ar degassing is proportional to the 40Ar content of the continental crust. The 40Ar mass balance of the continental crust is then:

_k_1 is the first-order degassing rate constant, λ40K is the 40K decay constant, and _M_crust is the mass of the crust. We note that [40Ar]crust and _M_crust are both time-dependent terms.

According to Armstrong (27), the mass of the continental crust grew to its present value early in Earth history, and has remained roughly constant since. We assume that the mass of the crust increased linearly from zero at 4.4 Ga to its present magnitude at 3.6 Ga. We adopt values for the mass and composition of the continental crust listed in Table 2, and an average 40Ar/K age of 1.12 Ga (Table 2). The degassing rate constant is then adjusted by using a simple finite-difference model to give our chosen value for the average crustal 40Ar/K age. The current degassing rate, given by the product of _k_1 and the 40Ar inventory, is 2.24 × 108 mol/yr. Alternatively, we assume that degassing has been first-order with respect to the Ar concentration and radiogenic heat production. In this case the crustal 40Ar mass balance is described by:

The calculated degassing rate is then higher earlier in Earth history, and lower today: 1.68 × 108 mol/yr.

We repeat this calculation according to Taylor and McLennan (28), who argue that the crust has increased in mass throughout geologic time. We assume that crustal mass began to grow from zero at 3.8 Ga, rising linearly to 20% of the current mass at 3.2 Ga, 80% of the current mass at 2.5 Ga, and then to 100% today. Other terms remain as in the Armstrong calculation. We then estimate that the current outgassing rate is 1.62 × 108 mol/yr if outgassing is first-order with respect to the crustal 40Ar inventory, and 1.28 × 108 mol/yr if it also scales linearly with heat production.

We also estimate modern 40Ar outgassing with very simple models applied to the continental crust as envisioned by Allegre et al. (1) and Coltice et al. (29). According to these articles, the crust has an age of either 2.0 Ga (1) or 2.7 Ga (29), and has retained half its argon. In each case, we assume that the crust formed instantaneously at a time corresponding to its age, and that 40Ar loss is first-order with respect to concentration. We next calculate the rate constant that gives the assumed values of crustal age and 40Ar retention. Given retention, age, and the rate constant, we then calculate the present day outgassing rate. The results are 0.86 × 108 and 1.01 × 108 mol/yr for crustal ages of 2.0 and 2.7 Ga, respectively. Finally, we repeat this calculation after invoking the assumption that the 40Ar loss constant scales with the product of heat production and concentration, and get current loss rates of 0.73 and 0.79 × 108 mol/yr for crustal ages of 2.0 and 2.7 Ga, respectively. Fluxes calculated in this way are low because the crust lacks the memory of earlier times when 40Ar production was faster.

Outgassing from the Continental Crust: Estimates Based on Observed Fluxes for the Various Pathways.

As an alternative to these box models, we consider the individual pathways by which crustal 40Ar is lost to the atmosphere, and estimate the loss rates associated with each.

Argon can be degassed during the chemical breakdown of K-bearing mineral phases. The total amount of K released can be calculated from the total riverine flux of dissolved K to the ocean. This flux is divided here into K derived from older crystalline rocks and younger sediments, with the K-Ar ages and proportions shown in Table 2. We assume that all of the Ar associated with dissolved K in rivers has been outgassed to the atmosphere. By using results in Table 2, we calculate that chemical weathering leads to an outgassing flux of 0.39 × 108 moles of 40Ar per year. As seen in Table 2, this is the largest calculated continental Ar flux. It is difficult to estimate the uncertainties associated with each parameter used, although the most poorly constrained is likely to be the 40Ar/K ratio of weathered minerals.

“Mechanical weathering,” as used here, includes all of the K associated with the suspended load of rivers carried to the oceans. We assume that all of the 40Ar originally associated with this K is released, either during the chemical transformation of crystalline rocks to K-bearing solid phase products of weathering, or during deposition and diagenesis. Sedimentation is largely cannibalistic (30), so that the average K-Ar age of the crustal sedimentary mass has been adopted for the source material. The largest uncertainties are likely to be the initial K-Ar age of sediments and the extent to which they are degassed. The calculated 40Ar degassing rate caused by mechanical weathering, 0.06 × 108 mol/yr, is a relatively minor crustal flux.

The entire sedimentary mass may also lose 40Ar diffusively from K-bearing phases. Based on discrepancies between stratigraphic ages and measured K-Ar ages, Lerman et al. (31) calculated that the associated 40Ar loss is 0.05–0.13 × 108 mol/yr.

We estimate degassing associated with metamorphism by assuming that the average K-Ar basement age reflects 40Ar loss according to a first-order rate constant. The amount of 40Ar released is based on the average K-Ar age and K concentration of basement rocks. Our estimate for the resulting flux is 0.3 × 108 mol/yr. The two largest uncertainties are the actual rate of material being metamorphosed over recent time scales and the actual K-Ar age of the material being metamorphosed. Regarding the former, a similar rate is obtained by assuming that in active areas the temperature increases by ≈10°C/Ma (32), and dividing by a typical geotherm of ≈10°/km to determine the rate at which material is heated above the feldspar closure temperature of ≈250°C over an area the size of Tibet, the area where most of active metamorphism is currently occurring (P. England, personal communication).

Overall, the calculations indicate that metamorphism and chemical weathering are the main pathways for degassing of the continental crust. The degassing rate associated with all of the crustal processes described above, 0.80–0.88 × 108 mol 40Ar per year, is similar to the rate obtained from the ice core data of 1.1 × 108 mol/yr. Also similar are degassing rates calculated above from simple models (0.7–2.2 × 108 mol/yr). Our calculations thus support the general understanding that crustal degassing is the major source of 40Ar to the atmosphere.

Summary and Conclusions.

We have measured the rate of increase in the 40Ar/38Ar ratio of air by measuring the triple isotope composition of Ar in ice-core-trapped gases going back to ≈779 ka B.P. The results imply a contemporary rate of increase in the 40Ar/38Ar ratio of 0.066 ± 0.007 ‰/Myr, and a 40Ar outgassing rate of 1.1 ± 0.1 × 108 mol/yr. With this rate, it is possible to date trapped gases in old ice of unknown age, with an uncertainty of approximately ±180 kyr (1σ) or ±11% (whichever is greater) for a single sample.

The observed atmospheric 40Ar increase (1.1 × 108 mol/yr) is similar to the summed outgassing rates estimated for the continental crust (0.80–0.88 × 108 mol/yr) and the upper mantle (0.27 × 108 mol/yr). The close agreement is fortuitous, but the similarity of rates validates the current understanding of 40Ar outgassing as outlined above.

Materials and Methods

We measured the isotopic composition of Ar in air by using a modified version of the method of Severinghaus et al. (33). To extract and purify Ar from trapped air, we placed 200- to 500-g samples of ice in glass flasks sealed with Viton O-rings, cooled the flasks to −30°C, and pumped to vacuum. We melted the ice, equilibrated water and head space, and drained the water as described by Emerson et al. (34). We then removed residual water and CO2 by freezing with liquid N2, and transferred the noncondensible gases (essentially O2, N2, and Ar) onto a mole sieve U-trap at liquid N2 temperature. We then warmed the trap and expanded the gas into a Pyrex and quartz loop containing SAES ST 101 getter material on one side of the loop. Heating the getter to 900°C led to convection of the gases through the loop, as well as to the absorption of all compounds other than the noble gases. The purified noble gases were then transferred into a stainless steel tube immersed in liquid He.

We measured δ40/38Ar and δ38/36Ar by using a standard Finnigan MAT 252 isotope ratio mass spectrometer with collectors configured for the simultaneous measurement of masses 36, 38, and 40. To maximize the sensitivity of the instrument to relatively small Ar samples, we bypassed the instrument's inlet system by attaching the sample side capillary inlet to a cross, with the sample tube connected to another port of the cross. The reference side inlet was customized such that the reference ion current could be set at a value identical to that on the sample side, and then a volume containing reference gas could be isolated that was identical to the volume containing the sample gas. The ion currents were balanced to approximately ±0.2%, and this balance was maintained while ion current ratios were measured. Each sample was analyzed for ≈2 h, leading to high precision even for ratios involving 38Ar (0.063% natural abundance).

Ar purified from trapped gases of ≈200- and ≈500-g samples was frozen into stainless steel tubes of nominal volumes 3 scc and 12 scc, respectively, to provide appropriate pressures in the dual inlet system during the analyses. Zero enrichments (the artefactual isotopic difference measured when the identical gas is admitted to the mass spectrometer on both sample and standard sides) were slightly different for the two tube sizes. As well, values of δ40/38Ar − 1.002 × δ38/36Ar were lower, by 0.028‰, for small air samples (nominally, 0.2 scc air, corresponding to a 200-g ice sample) than for large air samples (0.5 scc, corresponding to 500 g of ice). We observed no such difference, however, in the Ar isotopic composition of contemporary ice (age <5 ka). When we calculated δ40/38Ar − 1.002 × δ38/36Ar for these contemporary ice samples by using the average of all zero enrichment measurements and all air measurements, we obtained essentially identical results for large and small tubes: this term was higher for small tubes by 0.005 ± 0.007‰ (standard error of the difference). Therefore, we normalized Ar isotopic compositions of all our ice core samples against our average measured value for ice core trapped gases. This approach is nearly equivalent to comparing the composition of Ar in old ice samples with the composition of contemporary samples collected from the same mass of ice core.

The standard deviation of δ40/38Ar − 1.002 × δ38/36Ar for the contemporary ice core samples (age, ≤5 ka) is ±0.012‰ (n = 12). There was insufficient ice to carry out duplicate analyses on older samples.

Acknowledgments.

M.L.B. was stimulated to pursue this research by a talk given by K. K. Turekian many years ago. We thank J. L. Sarmiento and D. Bianchi for discussions about the hydrothermal 3He in seawater and P. England for discussions about metamorphic degassing of the continental crust. D. Marchant, Boston University, provided an ice sample from Mullins Valley, Antarctica. This work was supported by a grant from the Office of Polar Programs, National Science Foundation.

Footnotes

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

¶

Bianchi D, Sarmiento JL, Gnanadesikan A, Schlosser P (2008) Constraining the upwelling branch of the meridional overturning circulation with helium-3 numerical simulations. 2008 Ocean Sciences Meeting, March 2–7, 2008, Orlando, FL (abstr.).

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