Evolution of helium and argon isotopes in a convecting mantle

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Abstract

Outgassing of helium and argon and the isotope ratio distribution of helium isotopes in basalts are some of the most important geochemical constraints on mantle structure and evolution, but their interpretation in terms of mantle processes is ambiguous and controversial. Here, the evolution of these isotopes and their radiogenic parent isotopes of U, Th and K are studied using a numerical model of mantle convection that combines a treatment of major and trace element melting-induced differentiation and evolution with a self-consistent mantle convection-plate tectonics treatment. Both olivine and pyroxene-garnet system phase transformations are included, with density profiles of the different components following established data up to 720 km depth, but varied in the deeper mantle to reflect present uncertainties. Cases are presented that focus on the influence of two uncertain physical parameters: the density of subducted eclogite in the deep mantle, and the partition coefficient for helium. Results indicate that the system self-consistently evolves regions with the observed range of 3He/4He, but the exact distribution depends strongly on physical parameters. Furthermore, the distribution depends on sampling method, with the distribution in erupted material often being different from mantle-averaged distributions. Some parameter combinations simultaneously lead to MORB-like distributions of 3He/4He ratios in erupted material, and ∼50% outgassing of radiogenic 40Ar consistent with geochemical constraints. MORB-like 3He/4He histograms are produced in erupted material either when the shallow mantle has a high proportion of residue that evolves MORB-like 3He/4He due to the high incompatibility of He, or when sufficient recycled crust mixes back into the shallow mantle to suitably reduce its 3He/4He. Outgassing is also studied for Venus and Mars-like models, both of which are found to outgas substantially despite their lack of plate tectonics. The 25% outgassing of Venus proposed by [W.M. Kuala. Icarus, 139(1) (1999) 32] is plausible if Venus’ mantle viscosity is high or melt does not efficiently degass. It is estimated that Mars has lost ∼90% of its outgassed Ar to space, consistent with other estimates.

Introduction

The noble gases represent excellent natural tracers for sources and migration of volatiles in the Earth’s crust, mantle and atmo-hydrosphere. The state of noble gases within Earth’s mantle can be studied by analyzing mantle derived materials, such as volcanic rocks, volcanic gases, and mantle xenoliths, which trapped mantle noble gases. During the past decades, noble gas information has been obtained from mid-ocean ridge basalts and ocean island basalts. Although there has been some progress in this field, noble gas isotopes are still the most difficult and weakest area in isotope geochemistry, mainly because of the difficulties in obtaining useful data with high precision.

Observational data from noble gas isotopes impose strong constraints on mantle convection models. According to meteoritic measurements, primordial values of 3He/4He are in the range of 1.4–3.0 ×10−4, or about 100–200 Ra Jeffrey and Anders, 1970, Craig and Lupton, 1981, where Ra (the atmospheric value of 3He/4He) is 1.38×10−6 (Kurz et al., 1983). Over the history of the Earth, the ratio has decreased over time due to radiogenic ingrowth of 4He from U and Th decay. Elemental fractionation between He and U, Th upon melting and outgassing to the atmosphere also have first-order effects on isotope ratio distributions. Thus the present-day distribution of He isotope ratios reflects a combination of ingrowth, fractionation and outgassing.

Histograms of these distributions for mid-ocean ridge basalts (MORBs) and ocean island basalts (OIBs) (Fig. 1) show clear differences. MORBs have a relatively constant 3He/4He ratio with a mean value of 1.16×10−5, which is a factor of 8.4 higher than the atmospheric value Kurz et al., 1983, Allègre et al., 1995. The range of 3He/4He ratios between 7 and 9 is thus taken as characteristic of the depleted upper mantle. Prominent exceptions are the higher values in the vicinity of Iceland (52°–71°N) and the Easter micro-plate, which are attributed to the involvement of a plume-derived component.

OIB 3He/4He ratios are, in contrast, extremely heterogeneous, extending to both higher and lower values than MORB, although the prominent histogram peak at the MORB value suggests that the depleted upper mantle plays an important role in OIB helium budget. The relationship between 3He/4He and 3He (Fig. 1(B)) indicates very weak, if any, correlation between the 3He/4He ratio and the concentration of 3He. Basalts from the Loihi Seamount are amongst those with the highest ratios, with 3He/4He = 3.34×10−5, or about 35 Ra (Kurz et al., 1983). The source of these basalts with high 3He/4He is still controversial, and is one focus of this paper.

Another inert gas of interest is argon. There is almost virtually no primordial 40Ar in the Earth (Ozima and Kudo, 1972), it being entirely produced by the decay of 40K. 40Ar in Earth’s atmosphere represents the amount of argon degassed from the Earth’s interior, because argon does not escape to the space due to its heavy atomic mass. The atmospheric 40Ar budget implies that approximately half of all 40Ar produced within Earth since its formation is retained within the solid Earth (Allègre et al., 1996), although this figure is rather uncertain, mainly because the amount of 40K in the mantle is uncertain; for example, estimates of K/U range from a widely-accepted value of 12,700 (Jochum et al., 1983) to as low as 2800(Stacey, 1992). Another more problematic constraint is that the inferred concentration of argon in the MORB source is much lower than what would be expected if the 40Ar remaining in the mantle were evenly distributed (Turner, 1989), which has been interpreted to mean that the additional, ‘missing’ 40Ar must be ‘hidden’ somewhere in the lower mantle (Allègre et al., 1996), although this difficulty could be resolved if the amount of 40K in the mantle were lower than commonly estimated Albarède, 1998, Davies, 1999. This, as well as two other major noble gas paradoxes, could be reconciled if the estimate of 40Ar in the shallow mantle, which comes from measured short-term 3He fluxes into the oceans, were too low by a factor of 3.5(Ballentine et al., 2002). Argon isotope ratios do not receive a lot of interest but are here summarized for completeness: The present isotope ratio for the atmosphere is 40Ar/36Ar = 295.5. The value for MORB 40Ar/36Ar ranges from slightly above the atmospheric value to 40,000 Allègre et al., 1983, Farley and Neroda, 1998. At the other extreme, a sample from the Loihi Seamount has 40Ar/36Ar=400–4000 (Hiyagon et al., 1992). However, the differences in 40Ar/36Ar between MORB and OIB have been dimishing, e.g., 40Ar/36Ar ratios in Samonan xenoliths range from 300 to 15,000 (Burnard et al., 1998). All OIB have gone through source outgassing and contamination before eruption so it is difficult to infer argon isotope ratios in the source region.

In summary, helium and argon data impose severe constraints on models of mantle structure and evolution, which must be able to answer questions such as: Where exactly is the high 3He/4He material? Can the required isotope ratio distributions be generated by recycling, or is primordial material necessary? If there is a primitive helium or argon “reservoir”, how can it survive for billions of years in the presence of efficient mantle mixing? To satisfy both helium and argon constraints, a mantle convection model must be able to generate a 3He/4He distribution that is Earth-like, and to outgas about 50% of its 40Ar.

The Venusian atmospheric abundance of 40Ar, 3.3(±1.1)×10−9 of planet mass (von Zahn et al., 1983), indicates that only 24(±10)% (Kaula, 1999) of the radiogenic argon has escaped from the mantle (assuming K/U of 7220(±1220), which is the average of Venera samples, with a primordial U mantle abundance of 21(±3) ppb, which is the same as Earth’s), which contrasts with 52(±9)% for Earth (Allègre et al., 1996). This reduced outgassing efficiency has been attributed to the generally-assumed dryness of Venus’ upper mantle and crust, which would result in higher viscosity (other things being equal), or to the rigid lid convection mode of Venus, which may result in lower rate of surface volcanism and outgassing than Earth’s plate tectonics convection.

Mars’ volatile system is much more complex than Earth’s or Venus’. Taking 36Ar=2.71×10−13 kg/kg-planet (Pepin, 1991), 40Ar/36Ar=3.01×103 (Sasaki and Tajika, 1994), it is estimated that the 40Ar concentration in the Martian atmosphere is about 0.65 ppb. Taking a terrestrial potassium concentration, and assuming that the loss of radiogenic 40Ar from the Martian atmosphere is negligible (Turcotte and Schubert, 1988), it is estimated that only about 3% 40Ar degassed from the interior of the Martian mantle during the past 4.6 billions years, which is surprisingly low. However, Martian atmospheric volatiles are capable of being lost to space by thermal or non-thermal mechanisms. The noble gases Ar and He can be lost to space because of the impact of O+ ions and the solar wind (Jakosky and Jones, 1997). The isotopic data for Ar, C, and H all require the loss of at least half, and more likely, 90%, of the initial inventory of each gas (Jakosky and Jones, 1997). Hutchins and Jakosky (1996) estimated that 85–95% of the 36Ar and 70–88% of the 40Ar has been lost from the atmosphere of Mars. If the fraction of 40Ar that has been lost is assumed to be 90%, the outgassed fraction is increased to about 30–40%.

There is no consensus on how the Earth’s mantle obtained material with a high 3He/4He ratio, as sampled, for example, at Hawaii. However, the most common interpretation is that this component comes from an undegassed, ‘primitive’ source, because noble gases are highly incompatible and volatile, and are thus expected to enter any melt and be heavily outgassed prior to or during eruption Allègre et al., 1983, Farley et al., 1992, Porcelli and Wasserburg, 1995 (note that outgassing requires CO2 bubbling, which occurs at depths less than 60 km). The need to keep this hypothesized undegassed, high 3He/4He material intact for billions of years has been used as evidence for a layered mantle, conflicting with various types of geophysical evidence (e.g., reviewed in Tackley, 2000a). One problem with the primitive helium reservoir hypothesis is the question of how such a reservoir could survive for the whole history of the Earth in the face of mantle stirring if, as geophysical evidence implies, convection is basically mantle-wide.

Another possible interpretation of “primordial” helium is that it comes from the core (Porcelli and Halliday, 1992). However, measurements of noble gas partitioning between silicate melt and iron melt under pressures up to 100 kilobars indicate that the partition coefficients are much less than unity and that they decrease systematically with increasing pressure (Matsuda et al., 1993). These results suggest that Earth’s core contains only negligible amounts of noble gases if core separation took place under equilibrium conditions at high pressure.

Anderson (1993) suggested that a large amount of 3He could be delivered to the Earth’s surface by cosmic dust, and then recycled to the mantle. Although Anderson’s hypothesis has great theoretical appeal, more observations and detailed study of the whole process are needed to fully support it.

Recently it has been argued that high 3He/4He could be associated with recycled depleted lithosphere Anderson, 1998, Coltice and Ricard, 1999, Coltice and Ricard, 2002, Ferrachat and Ricard, 2001. The latter three studies showed that high 3He/4He is preserved if residuum can be stored for substantial time periods while the rest of the mantle becomes substantially outgassed. Tackley and Xie (2002) presented two preliminary thermo-chemical convection models that provide some insight into such processes, finding that high 3He/4He can be generated by recycling residue if He is more compatible than U and Th (e.g. Graham et al., 1990), so that He ratios are frozen in the residuum at the time of melting. However, if was found that the resulting high 3He/4He residue tends to aggregate near the top (due to its buoyancy) where it should be sampled by mid-ocean ridge volcanism. It was also found that if primitive material exists as a dense basal layer, it must be much denser than subducted crust in order that its primitive (e.g., high 3He) signature is not swamped by rapid 4He ingrowth in the U-enriched, He-degassed recycled crust. This line of investigation is further pursued here.

Extreme compositional heterogeneity of the mantle, reminiscent of the “marble cake” proposal of (Allègre and Turcotte, 1986), is a common theme in recent attempts to explain mantle geochemistry. In the marble cake of (Coltice and Ricard, 2002), strips of former oceanic lithosphere carry the high 3He/4He component and radial stratification is proposed to account for different MORB and OIB signatures. In contrast, Meibom et al., 2003, Meibom and Anderson, 2003 proposed that the difference between MORB and OIB is not related to different source regions but is entirely due to different statistical sampling of a highly heterogeneous source region, the Statistical Upper Mantle Assemblage. If this is correct, then the use of He isotopic signature as a fingerprint of plume components is not justified. Helffrich (2002) focused on the role of strips of subducted oceanic crust and supporting seismological observations of mantle heterogeneity.

Several other previous numerical modeling studies have given important insight into relevant issues, including the ability (or otherwise) of primitive material to survive over geological time, the possibility of layered convection due to mantle phase transitions, and the evolution of noble gases in a convecting system.

The evolution of noble gases in a mantle that included outgassing and radiogenic ingrowth but not major-element differentiation was investigated by Van Keken and Ballentine, 1998, Van Keken and Ballentine, 1999. These studies investigated various proposed mechanisms for maintaining a relatively undegassed lower mantle over billions of years, finding that neither high deep-mantle viscosity, a strongly endothermic phase transition at 660 km depth, or temperature-dependent viscosity, are capable of causing a relatively undegassed deep mantle, in contrast to earlier modeling at lower convective vigor (Gurnis and Davies, 1986). They did find that the observed total amount of 40Ar outgassing is consistent with whole-mantle convection over geological history: a layered mantle is not required. While the issue of ‘primitive’ signatures was not resolved, the compositional heterogeneity considered was purely passive, i.e., was not associated with buoyancy variations.

The helium ratio evolution caused by subduction of differentiated oceanic plates was studied by Ferrachat and Ricard (2001), who tracked the evolution of oceanic crust and residue and showed that if oceanic crust segregates at the CMB, a large region of recycled oceanic lithosphere with high 3He/4He can form above it. However, in their model compositional variations were also purely passive, not influencing the flow.

The present paper investigates the possibility that active (buoyant) compositional variations caused by crustal production may play an important role in the evolution of noble gas isotopes and the generation and maintenance of distinct reservoirs. A recent modeling study by Samuel and Farnetani (2003) focused on whether the deep layer proposed by Kellogg et al. (1999) could supply the high 3He/4He component. Here the alternative possibility that He ratios can be generated from a homogeneous start condition (i.e., with no layering) is considered.

An important influence in mantle convection models is the endothermic spinel to perovskite + magnesiowustite phase transition at around 660 km depth, which may cause some partial layering of the convection, and possibly a filtering of chemical anomalies (Weinstein, 1992). However, published models have assumed that the mantle is made of 100% olivine and its high pressure phases, whereas it is well known that the garnet-pyroxene system accounts for at least 40% of the mantle. Phase changes in the latter system occur over a wider depth range, and the equivalent ‘660’ transition was thought to have a neutral or even positive Clapeyron slope, leading to the expectation that it would dilute or even act against the dynamical effect of the endothermic olivine-spinel transition (Weidner and Wang, 1998). Furthermore, when compositional effects are considered, subducted oceanic crust is likely to be buoyant in the depth range 660–720 km Ringwood, 1990, Ono et al., 2001. Thus, it seems important to take this into account when performing models that include compositional variations associated with oceanic crust and lithosphere. The presented models include these.

Section snippets

Physical model

A two-dimensional (2D) cylindrical geometry is assumed Tackley and Xie, 2002, Tackley and Xie, 2003 with the core size scaled to give the same ratio of CMB surface area to outer surface area as in spherical geometry (Van Keken, 2001). The infinite Prandtl number and compressible anelastic approximations are made (Tackley, 1996a). The equations, nondimensionalized to the mantle depth (D), thermal diffusion time-scale (D2/κ, where κ = thermal diffusivity) and super-adiabatic drop, ΔTsa, are those

Cases

Five Earth-like cases are presented here: a reference case, in which the partition coefficient for He is the same as that for U and Th and the crustal component is dense at the CMB, two cases with different He partition coefficients (10 times more compatible and 10 times less compatible), and two cases with differing compositional buoyancy in the deep mantle (crust is either equal in density to the other component or less dense, as in Fig. 2). Compositional density variations down to 720 km are

Outgassing on Mars and Venus

It seems that Kaula (1999)’s estimate of 24(±10)% radiogenic argon outgassing on Venus is dynamically reasonable, and may be matched either by Venus having a much higher mantle viscosity than Earth, i.e., of the order of 1023 Pa s, or by incomplete (e.g., ∼50%) eruption (outgassing) of produced melt. For Mars, a comparison between model and observations is much more difficult, but it appears difficult to avoid ∼30–40% outgassing, implying that Mars must have lost most of its atmospheric noble

Acknowledgements

This research was supported by Los Alamos National Laboratory, the David and Lucile Packard Foundation, NSF grant EAR0207741 and NASA grant NAG 5-3956. Reviews by P.E. van Keken, N. Coltice and two anonymous reviewers were very helpful in improving this manuscript, as were comments by Francis Albarède.

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