Helium and Argon Isotopic Studies of Fossil Material and the Theoretical Evolution of He and Ar in Earth ’ s Atmosphere through Time

We analyzed the elemental concentrations and the isotopic compositions of helium and argon in Cambrian to Jurrassic aged Gastropod, Ammonite and Trilobite fossils in order to examine variation in these gases through time. Fossil samples yielded He and Ar isotopic ratios close to the present day atmospheric values, but also indicated some addition of a radiogenic component. We compared the results to theoretical values calculated from a mathematical model of Earth’s atmosphere assuming mantle degassing. Results from our mathmatical models showed that the Ar/Ar ratio of Earth’s atmosphere increased rapidly after the formation of the Earth, but has been almost identical to the present day value for the last 1 Ga. For atmospheric helium, model results were consistent with present day atmospheric values, assuming complete helium degassing from the continental crust into the atmosphere. The model suggests that the atmospheric He/He ratio has remained relatively constant for the last 0.1 Ga. Given the similarity between present day and ancient He and Ar isotopic ratios, we conclude that the corresponding ratios measured in ancient fossil material may partially reflect composition of the ancient atmosphere and are not necessarily due to contamination by the present day atmosphere.


Introduction
The Earth's atmosphere is believed to be secondary in origin, having been produced by degassing from the Earth's interior.This understanding is evident from the lower atmospheric abundances of noble gases relative to the abundances of active gases with similar mass numbers [1].Noble gas isotopes are often used to trace the degassing history of the Earth's mantle, and various models have been proposed based on their abundances and isotopic ratios (e.g.[2]).We previously proposed a model for noble gas transfer from Earth's interior [3,4] based on the finding that the lower mantle has experienced an extensive degassing history [5].
Most mantle degassing models calculate the hypothetical isotopic trajectories for noble gases in the mantle (e.g.[6]), but few have addressed the isotopic evolution of atmospheric helium and argon through Earth's history.Noble gas models, including the one described here, assume that the Earth began its existence with the planetary helium isotopic ratio ( 3 He/ 4 He = ~10 -4 ), which differs from the 3 He/ 4 He ratio of the present mantle (~10 -5 ) by an order of magnitude, and from that of the present at-mosphere (1.4  10 -6 ) by two orders of magnitude.If ancient terrestrial samples show 3 He/ 4 He and 40 Ar/ 36 Ar ratios similar to modern atmospheric ratios, it is very likely that this finding is attributed to present day atmospheric contamination.This interpretation assumes that ancient He and Ar isotopic ratios were markedly different than present day values.In the absence of viable gas inclusions from which pristine He and Ar isotopic values could be measured, the precise value of these isotopic ratios in the ancient atmosphere remains unknown.
This report examines the potential use of fossil material as a record for atmospheric He and Ar evolution through time.We begin with the hypothesis that fossil material may contain ancient gas signatures within their internal void spaces.To test this hypothesis, we measured the He and Ar isotopic ratios of crushed samples of varying age and compared our results to those estimated from a model of atmospheric He and Ar isotopic evolution through time.ite, and Trilobite fossils of Cambrian to Jurassic age.Samples were obtained through commercial sample collections.Sample names, weights and the localities are given in Table 1.Samples weighed between 5 to 38 g, and had an average size of about 3 × 5 cm.To capture noble gases potentially encapsulated in the internal void space of these samples, we crushed the samples under vacuum using a closed system crushing device specifically built in our laboratory to process large tektite samples [7].The sample chamber of the crushing device is a stainless steel cylinder with a diameter of 10 cm and a height of 10 cm.An airtight piston is inserted into the chamber by turning a handle that slowly crushes the sample.This device makes it possible to reduce a large sample into fine scale fragments (Figure 1), extract noble gases and analyze them within a closed system.
The crusher directly connects to a purification system and a VG5400 noble gas mass spectrometer.The purification system consists of two Ti-Zr getters held at 700˚C, and a cryogenic cold trap which separates He and Ar fractions.Further details concerning the purification system and the noble gas measurements can be found in Matsuda et al. [8,9].Elemental concentrations and isotopic ratios for He and Ar were corrected to procedural blanks analyzed before each sample measurement.The measured concentrations of procedural cold blanks for 4 He (and 3 He) were effectively zero, and those for 36 Ar were 0.6 to 4.2 × 10 -11 cm 3 STP.The noble gas concentrations of the samples were normalized to the original sample weights.The uncertainty for the noble gas concentration was about 10%.Helium isotopic ratios were calibrated using the HESJ internal He Standard [10] and Ar isotopic ratios were calibrated using a pipetted air (atmospheric values).

Results
The results for sample He and Ar concentrations and isotopic ratios are given in Table 1.
We plotted the 4 He and 40 Ar concentrations in Figure 2 along with theoretical and atmospheric envelopes for 40 Ar and 4 He values.The theoretical 40 Ar- 4 He space was constructed according to assumptions and calculations described below.The 4 He isotope is produced by radiogenic decay of 238 U, 235 U and 232 Th.The 40 Ar isotope forms from 40 K (electron capture).The amounts of radiogenic 4 The K/U ratio for the upper continental crust is 10,000, and is assumed to be the same for the Archean bulk crust [11].As the mantle K/U ratio is estimated to be 12,700 [12], the elemental fractionation between K and U is similar under different conditions.Thus we get the following equation by eliminating time t and using K/U = 10,000 from the two Equations ( 2) and (3), The new expression for 4 He does not depend on time, and is represented by the upper line plotted in Figure 2.
Assuming closed systems for radiogenic 4 He and 40 Ar for the crust (and the whole Earth), the encapsulated 4 He and 40 Ar contents should lie on this line.Present day atmospheric compositions would be located below this line reflecting He loss from the atmosphere to space.The data points of fossils in this study are situated between the upper line and the present day atmospheric line below (Figure 2).We interpret the position of the empirical data (between the upper and lower 4 He-40 Ar envelopes) as evidence that the He and Ar contents of the fossil samples reflect ancient atmospheric compositions, assuming some degree of 4 He loss from the ancient atmosphere.
All samples gave reasonable He and Ar isotopic ratios except for the Gastropod sample, which yielded only a trivial amount of 3 He.The 3 He/ 4 He ratio of this sample could therefore be given only as an upper limit.Measured values for the stable Ar isotopes ( 38 Ar/ 36 Ar ratio) varied relative to the expected value of 0.188 (Table 1).We interpret variation relative to the 38 Ar/ 36 Ar constant as a mass fractionation effect that occurred during the trapping stage of the gas at the void space in fossil material.We corrected for the mass fractionation effect by calculating a 40 Ar/ 36 Ar corrected ratio based on the 38 Ar/ 36 Ar ratio in Table 1.The obtained values are close to the present day 40 Ar/ 36 Ar ratio of the atmosphere (295.5) with some variation.Certain higher values are interpreted to reflect the addition of radiogenic 40 Ar.
Similarly, the measured 3 He/ 4 He ratios are lower than the present day atmospheric value due to the addition of radiogenic 4 He.The crushing apparatus and procedures used here were intended to exclude radiogenic material issuing from solid parts of the fossil but previous studies using the same technique have demonstrated that some inclusion of a radiogenic component in inevitable (e.g.[13]).The effect of the addition of radiogenic component is larger for He than for Ar.At any rate, considering that He isotopic ratios generally change in orders, the measured 3 He/ 4 He ratios were close to the present day atmospheric value with some addition of a radiogenic component.Ancient terrestrial samples often exhibit He and Ar isotopic ratios similar to those of the present day atmosphere, which are generally interpreted to reflect the present day atmospheric contamination.Although this interpretation fits the criterion of simplicity, it assumes that ancient atmospheric He and Ar isotopic ratios were markedly different than present day values.Below, we will assess this assumption through mathematical modeling of atmospheric He and Ar through time.

Mathematical Modeling of He and Ar
Isotopic Ratios in the Atmosphere

Model Assumptions and Construction
The model used here is based on our previously pub-lished work concerning He and Ar dynamics in the mantle [3,4].The model assumes that the Earth was initially uniform in composition but was subsequently divided into three separate reservoirs: the degassed or depleted mantle (Mid-Oceanic Ridge Basalt; MORB source), the less-depleted mantle (Oceanic Island Basalt; OIB source), and the surface reservoir (crust and atmosphere).Individual elements are exchanged through mass flow between reservoirs, and velocities decrease exponentially as a function of time.We treated the decrement factor as a variable parameter, and used the steady-state flow model proposed by Porcelli and Wasserburg [14,15].Mass flow from the depleted and less-depleted mantle reservoirs to the surface reservoir (M Dout and M Lout , respectively) decreases as a function of time t with the decrement factors D  and L  , respectively, as follows: Only solid elements were assumed to be recycled into the mantle with an extraction factor, r.Noble gases were not recycled in the mantle because of the subduction barrier for noble gases [16,17].Continental crust was assumed to be produced at a constant rate throughout the Earth's history, and radioactive elements such as U, Th, and K were transferred from the depleted reservoir to the continental crust with an extraction factor, x.

Atmospheric Argon Isotopic Ratios
The total amounts of 36 Ar and 40 Ar in the atmosphere at time t are described by the following equations: where C is the concentration of species represented by the associated superscript, and the subscripts A, D, and L represent the atmosphere, depleted mantle, and less-depleted mantle reservoirs, respectively.From these equations we can calculate 36 Ar and 40 Ar concentrations and the 40 Ar/ 36 Ar ratio of the atmosphere through time.The results are shown in Figure 3.The observed 40 Ar/ 36 Ar ratio for the present day atmosphere is identical to the calculated model value due to its use as a boundary condition input to the model.The two lines in Figure 3 are derived from present-day concentrations of 40 K in the continental crust and in the depleted mantle, corresponding to the upper and lower limits for this parameter [4].As seen in Figure 3(a), 36 Ar abundance rapidly increases during the first 1 billion years and is almost constant thereafter.The increase in 40 Ar abundance through time is more steady due to the addition of radiogenic 40 Ar from 40 K.The 40 Ar/ 36 Ar ratio in the atmosphere increased very rapidly since the formation of the Earth and has been almost constant for the last 1 billion years (within 4% of the present day atmospheric value).

Atmospheric Helium Isotopic Ratio
Calculating the atmospheric He isotope ratio through time requires compensation for He escape into space.To incorporate these conditions, we added an escape term in the form of a simple first-order rate equation.The total amounts of 3 He and 4 He in the atmosphere at time t are described by the following equations:

He
He , where k 1 and k 2 are the escape coefficients for 3 He and 4 He, respectively.In addition to Jeans thermal escape, non-thermal escape may occur due to the photoionization of He and the interaction of He with the magnetic field [22].Ozima and Podosek [23] summarized the major fluxes of the total escape for 3 He and 4 He as 10.1 atoms cm -1 •s -1 and 3.06  10 -6 atoms cm -1 •s -1 , respectively.The values for k 1 and k 2 were calculated from these fluxes as 1.20  10 -6 year -1 and 8.64  10 -7 year -1 , respectively.Note that these values were independently obtained from the present atmospheric helium budget.As the nonthermal escape flux is considerably larger than that of the thermal escape (especially for 4 He) and does not depend on the temperature of the Earth, we assumed that k 1 and k 2 are constant through the time.
Using the above values, we obtain the results shown in Figure 4.Both 3 He and 4 He abundance rapidly increased during the first several million years and then decreased 0 1×10   slowly due to thermal and non-thermal escape.The escape term describes a relatively efficient process for He, and a less efficient process for the more refractory Ar (Figures 3(a) and (b)).The calculated present day atmospheric 3 He value is in good agreement with the observed atmospheric 3 He abundance (Figure 4(a)).The calculated present day atmospheric 4 He value however is about an order of magnitude lower than the corresponding observed 4 He value (Figure 4(b)).Our k 1 /k 2 ratio is 1.39, which is slightly higher than the simple mass square root ratio ((4/3) 1/2 = 1.15).In the current model, the only way to reconcile the calculated and observed present day atmospheric 4 He values, would be to lower k 2 by an order of magnitude.Given that helium escape from the atmosphere is not isotope-specific, both k 1 and k 2 must be treated the same and thus cannot be used to resolve discrepancies in observed and calculated 4 He values.
In previous models (i.e.[3,4]), we assumed that noble gases transported into the continental crust remained there.However, helium is a relatively labile and tiny element and may degas from the continental crust into the atmosphere during weathering etc.We accounted for these degassing mechanisms in the present model as follows: where the subscript cc represents continental crust.We assume that all the helium in the continental crust degasses to the atmosphere.Under these conditions, we obtain the results shown in  4 He ratio at 0.1 Ga is only 10% -12% higher than the present day value.

Comparison of Measured Fossil He and Ar Values with Model He and Ar Trajectories
The Ar and He isotopic ratios obtained from fossil material were fairly consistent with present day atmospheric values although there is some addition of radiogenic component.We plotted the isotopic ratios versus age  Copyright © 2012 SciRes.IJG along with isotopic trajectories from the mathematical models in Figure 6.The age is given as "B.P." (present day at time zero) and represented on a logarithmic scale.
For Ar, we plotted 40 Ar/ 36 Ar corrected ratios after making the correction for the mass fractionation effect.Figure 6 clearly indicates that Ar and He isotopic ratios have been nearly constant for the last 1 and 0.1 billion years, respectively.The ages of fossils analyzed in this study fell between 10 8 and 10 9 years, a range consistent with the range of their known stratigraphic ages.Considering that the isotopic ratios are represented on a linear scale, the measured 40 Ar/ 36 Ar ratios in fossils were the values slightly higher than those given by the mathematical model.We attribute the variation relative to the model trajectory to a radiogenic component within the fossil material (Figure 6(a)).Similarly, a plot of fossil 3 He/ 4 He ratios versus age relative to the predicted isotopic trajectory (model) indicates the addition of radiogenic 4 He.We interpret the similarity of these ratios to the present day atmosphere that the measured isotopic ratios are not simply the result of sample contamination by the present day atmosphere.Our models suggest that 40 Ar/ 36 Ar and 3 He/ 4 He ratios in the ages of fossils also indicate the similar values to the present day atmosphere.The relatively high 40 Ar/ 36 Ar ratios and low 3 He/ 4 He ratios measured from fossil material are likely to reflect the addition of radiogenic component from gas-mineral exchange within the fossil matrix to the trapped ancient atmosphere.

Conclusion
We measured elemental abundances and isotopic ratios of He and Ar in fossil material of varying age, using a large, closed system crushing apparatus.The elemental abundances of radiogenic component of He and Ar are between the present day atmospheric value and those estimated from the radiogenic decay product from the continental crust.The measured 3 H/ 4 He ratios were lower than the corresponding present day atmospheric value, whereas measured 40 Ar/ 36 Ar ratios were higher than the present day atmospheric value.These isotopic ratios in fossils therefore indicate the addition of a radiogenic component to He and Ar contents that are similar to present day atmospheric values.These results may indicate that the fossil's void space has exchanged gas with the present atmosphere.However, results from a mathematiccal model of atmospheric He and Ar isotopic ratios through time offer an additional explanation.The model results specifically suggest that He and Ar isotopic ratios have been nearly constant for the last 0.1 and 1 billion years, respectively.It is therefore possible that the fossils retained ancient atmospheric signatures in their void space, along with a radiogenic component incorporated from solids and released during the crushing procedure.

Figure 1 .
Figure 1.A trilobite sample before and after the crushing.The sample was an Asaphitscus wheeleri specimen from the Middle Cambrian period.

Figure 2 .
Figure 2. The measured 4 He and 40 Ar contents of crushed fossil samples shown in 4 He-40 Ar space.The line labeled "present day atmosphere" shows present day atmospheric ratios for 4 He and 40 Ar.The upper line gives these ratios calculated from K/U=10,000 and Th/U = 3.8 (see text).where bracketed terms refer to absolute amounts of the individual nuclide, t is time, and   ,  and e  are decay constants for 238 U, 235 U, 232 Th, and 40 K (electron capture), respectively.The upper continental crust and Archean bulk crust have a Th/U ratio of about 3.8 [11].The amount of [ 4 He] rad can thus be represented only by [ 238 U] as  4 2 238 rad He 8 5.1 10 23 U t

Figure 3 .
Figure 3.Time versus (a) 36 Ar abundance (atoms); (b) 40 Ar abundance (atoms); and (c) 40 Ar/ 36 Ar ratio in the atmosphere.The two lines correspond to the upper and lower limits derived from the present day concentration of 40 K in the continental crust and in the depleted mantle (for details, see [4]).The closed circle represents the observed present day atmospheric values.

Figure 4 .
Figure 4. Time versus (a) 3 He abundance (atoms) and (b) 4 He abundance (atoms) in the atmosphere, with no helium degassing from the continental crust.The two lines correspond to the upper and lower limits derived from the present day concentration of 40 K in the continental crust and in the depleted mantle (for details, see [4]).The closed circle represents the observed present day atmospheric values.

Figure 5 . 3 He/ 4
Values for 3 He (Figure 5(a)) calculated from this crust degassing model are almost the same as those of the previous model (shown in Figure 4(a)), indicating that the amount of 3 He in the continental crust is negligible relative to 3 He contents of the atmosphere.Values for 4 He calculated in the crust-degassing model (Figure 5(b)) however are markedly different from the non-degassing scenario shown in Figure 4(b).This suggests that the radiogenic 4 He produced from U and Th in the continenttal crust is relatively large.The calculated value for present day atmospheric 4 He (Figure 5(b)) is about an order of magnitude higher than that of the non-degassing scenario shown in Figure 4(b), and is close to the observed present day atmospheric value.The corresponding He ratio calculated in the crust-degassing model is also consistent with observed atmospheric values (Figure 5(c)).This ratio decreases rapidly during the first several million years of Earth history, then changes slowly, and shows little change over the last 0.1 billion years.The 3 He/

Figure 5 .
Figure 5.Time versus (a) 3 He abundance (atoms); (b) 4 He abundance (atoms); and (c) 3 He/ 4 He ratio in the atmosphere, assuming complete helium degassing from the continental crust to the atmosphere.The two lines correspond to the upper and lower limits derived from the present day concentration of 40 K in the continental crust and in the depleted mantle (for details, see [4]).The closed circle represents the observed present day atmospheric values.

Figure 6 .
Figure 6.Comparison of (a) 40 Ar/ 36 Ar ratios (corrected for the mass fractionation effect) and (b) 3 He/ 4 He ratios measured from fossil material with corresponding trajectories of Ar and He isotopic evolution through time from mathematical models.The two trajectories correspond to the upper and lower limits derived from the present day concentration of 40 K in the continental crust and in the depleted mantle (see the captions of Figures 4 and 5).Here, age is represented on a logarithmic scale in years before present (B.P.).
He and 40 Ar ([ 4 He] rad and [ 40 Ar] rad ) are written as follows: