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Does the variation in 3He/4He prove that MORB and OIB come from different reservoirs?

Don L. Anderson

Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125

dla@gps.caltech.edu

The standard model

It is commonly assumed that 3He/4He in mantle-derived materials represents two distinct populations corresponding to two distinct reservoirs. These are the source of mid-ocean ridge basalt (MORB) and that of ocean island basalt (OIB). The former is postulated to be the upper mantle, and the latter the lower mantle [Allègre, 1987; Allegre et al., 1995].

The existence of a few extreme values does not necessarily indicate the presence of more than one distinct population

It is generally believed that the noble gases are the only reliable geochemical indicator of lower mantle involvement in surface volcanism. All other indicators have been traced to the recycling of subducted crust. High 3He/4He is assumed to result from a high abundance of 3He, and this has been used to argue that the lower mantle is undegassed in primordial volatiles. Plumes are thought to carry the high 3He/4He signal from the deep mantle to the surface. However, the assumptions underlying this model require that the deep mantle has a high absolute abundance of He [Kellogg & Wasserburg, 1990]. In this model, the observed low abundance of He in OIB is a paradox.

The MORB reservoir is thought to be homogeneous because some isotopic ratios show less scatter in MORB than in OIB. The common explanation is that MORB are derived from a well-stirred, convecting part of the mantle while OIB are derived from a different, deeper reservoir. Alternatively, the homogeneity of MORB can be explained as a consequence of the sampling process, as explained below [Anderson, 2000a; Anderson, 2000b].

An alternative model

Ridges process large volumes of the mantle and involve large degrees of melting. A consequence of the Central Limit Theorem is that the variance of samples drawn from a heterogeneous population (reservoir) depends inversely on the sampled volume [Anderson, 2000b; Meibom & Anderson, 2003]. The homogeneity of a sample population (e.g., all MORB samples) can thus simply reflect the integration effect of large volume sampling. The presumed homogeneity of MORB source may thus be an illusion.

The standard, two-reservoir model is reinforced by questionable data filtering practices. Samples that are judged to be contaminated by plumes (i.e., OIB-like samples) are often removed from the dataset prior to statistical analysis. Sometimes the definition of plume influence is arbitrary. For example, isotopic ratios which exceed an arbitrary cutoff may be eliminated from the dataset. In this way, the MORB dataset is forced to appear more homogeneous than it really is. This method is commonly applied to 3He/4He. Despite this, various ridges still have different means and variances, and these have been shown to depend on spreading rate and ridge maturity. The variance for many ridge segments increases as spreading rate decreases and, by analogy, the observed high variance of various OIB datasets is thus consistent with slow spreading, small sampled volume, or low degrees of melting or degassing.

Data

There are several recent compilations of 3He/4He for MORB and OIB [Anderson, 2000a; Anderson, 2000b; Graham, 2000]. Some datasets are filtered to remove samples thought to influenced by plumes, and consequently the results vary. Nevertheless, OIB datasets show greater diversity, and exhibit values both higher and lower, than MORB datasets [Farley & Neroda, 1998].

Geochemical variations in a well-sampled system such as a mid-ocean ridge or an oceanic island can be characterized by an average value, or mean, and a measure of dispersion such as the standard deviation or variance. When dealing with isotopic ratios the appropriate measures of central tendency are the median and the geometric mean, since these are invariant to inversion of the ratio. Likewise, when dealing with ratios, the absolute concentrations must be taken into account, in addition to the ratios. That is, the ratios must be weighted appropriately before being combined [Anderson, 2000a].

The Central Limit Theorem and the Law of Large Numbers [Anderson, 2000b; Botz et al., 1999] state that variably sized samples from a heterogeneous population will yield the same mean but will have variances that decrease as n (the number of samples) or V (the volume, of the sampled region) increases. If OIB are small volume samples and MORB are large volume samples from the same reservoir then the variance of OIB will be greater than the variance of MORB. Small samples are thus more likely to have extreme values than samples that blend components from a large volume.

Large-scale averaging yields data with lower variances than small-scale sampling

The scale of heterogeneity

Chemical heterogeneity probably exists at all scales, from the grain scale to the hemisphere scale. Some individual oceanic islands have data variances that are smaller than that of the global spreading ridge system, suggesting that an important scale length in the mantle is tens to hundreds of kilometers. Individual volcanoes at any point in time may not have access to the total suite of heterogeneities. Some scales are large enough that diffusive homogenization does not occur. When taken all together the global OIB dataset defines a distribution that is statistically the same as the MORB dataset. 3He/4He data for individual islands and groups of islands thus support the conclusions reached here.

Conclusion

The statistics of many OIB isotope datasets are identical or similar to those of MORB datasets. Thus, on statistical grounds, the hypothesis that OIB and MORB are drawn from the same population cannot be rejected. The differences in variances of the datasets are consistent with mid-ocean ridges sampling larger volumes than most oceanic islands. This is an extension of the idea that fast spreading ridges sample larger volumes of the mantle than slow spreading ridges and therefore have smaller variances of various geochemical parameters [Allegre et al., 1995]. The ongoing debate about whole-mantle vs. layered-mantle convection and deep slab penetration may have nothing to do with the chemical inhomogeneity of the mantle as sampled by basalts and xenoliths.

References

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