Criterios epistémicos de Kurt Lewin

We now describe a methodology by which our degassing model may be used in combination with measured data to reconstruct initial magmatic noble gas concentrations. For a given set

on the characteristic degassing timescale. When radiogenic noble gases are used, the slope of the degassing path for a sample is defined by the initial composition of the mantle produc- tion ratios and the measured final composition. The fractional extent of volatile loss,x/x0 , can then be found from Equation 3.4, and the initial volatile contentx0 from a measured concentrationx. The extent of volatile loss for any other species y is related to speciesx by rearranging Equation 3.4:

y/y0 = (x/x0)α

′

x,y _(3.7)

Once the characteristic degassing timescale and extent of volatile loss for one species (for ex- ample He as shown in Figure 3.3) is obtained for a sample,θ values and, hence, any initial ratios and concentrations for any other volatile species can be calculated from Equations 3.4 and 3.7.

In the following applications to published data we will make one additional assumption, that upon quenching, nearly all the noble gases are transferred to vesicles during a final closed-system vesiculation step. Such an assumption is justified by the fact that noble gas elemental ratios measured by crushing and by fusion are not systematically offset (Figure 3.1a), and similar assumptions have been previously used (e.g. Burnard, 1999; Marty and Tolstikhin, 1998; Marty and Zimmerman, 1999).

3.4.2 Reconstructed initial volatile contents

We now apply this methodology to predict the initial nonradiogenic noble gas concentrations to 33 of the samples shown in Figure 3.1b. Fitting a degassing path taking advantage of the known mantle production ratios requires4_He*-21_Ne*-40_{Ar* data for the sample, which can} be computed with reasonable accuracy even for samples with only modest radiogenic excesses over atmospheric contamination (e.g. Graham, 2002; see supplemental material). Initial3_He concentrations can then be reconstructed for any sample with a measured 3_{He concentration,} however, reconstructing the nonradiogenic heavy noble gas concentrations requires correcting the measured concentrations for atmospheric contamination, which is especially difficult for

Figure 3.5: Predicted initial3_{He and}22_{Ne contents of samples shown in Figure 3.1b (black dots). Mea-}

sured values are red dots, and dashed lines represent degassing paths. The grey bars show the3_{He con-}

tent of an average primary MORB magma derived from the oceanic 3_{He flux of 527±102 mol} 3_He/year

(Bianchi et al., 2010), a crustal production rate of 21 km3_{/year (Crisp, 1984), and}3_He/22_{Ne of 6 (Tucker}

et al. 2014). The overlap of the middle of our reconstructed values with the independent estimates demon- strates that our degassing model yields reasonable values for initial He and Ne contents in MORBs.

Ar and Xe.

Using the noble gas solubilities and diffusivities listed in Table 3.1, we find initial 3_He and 22_{Ne concentrations that range over approximately two orders of magnitude (Figure} 3.5). The median initial magmatic3_{He is 2.1}+2.7

−1.1 ×10−10 ccSTP/g and median initial 22Ne is 2.9+2₋₁._.3₆ ×10−11 (uncertainties represent the central 68.2% confidence intervals). The re- constructed initial 3_{He and} 22_{Ne broadly form an array indicating that the initial magmatic} 3_He/22_{Ne ratios are less variable than the initial noble gas contents; reconstructed}3_He/22_Ne varies by a factor of ~2 among these samples.

For comparison, average undegassed magmatic noble gas contents can also be predicted independently of MORB measurements. Using the mantle 3_{He flux of 527±102 mol/year} (Bianchi et al., 2010), crustal production rate of 21 km3_{/year (Crisp 1984) and}3_He/22_{Ne of 6} (Tucker and Mukhopadhyay, 2014), an average initial magma has 2.1±0.4×10−10 ccSTP/g

Figure 3.6: Histograms of median3_{He and}22_{Ne concentrations of 33 samples in 10}7_{trials. 57% of tri-}

als could not fit all samples and are not included. Parameter ranges used arekHe from 56-64×10−5cc-

STP/g/bar; kNe from 19-38;kAr from 2.3-9.9; log10 DHefrom -8.7 to -8.2 m2/s; log10 DNe from -9.4 to

-8.6; log10 DNe from -11.5 to -9.2. The discontinuous nature of the histograms results from the discrete

parameter ranges used. The overall median and 68.3% ranges are shown, and are centered near the values found in Figure 3.5.

3.5 and overlap the median reconstructed compositions of the 33 samples.

While the solubility and diffusivity values used were chosen because they are generally intermediate to the experimental values, there is considerable uncertainty in some of these values (section 3.3.4; Figure 3.4). To examine the effect of changing our assumed solubility and diffusivity values, we performed a Monte Carlo simulation with 107 _{trials varying the} solubility and diffusivity values. For individual samples, the median initial3_{He and}22_{Ne con-} centrations varied by only a factor of 3 (68.2% range) despite the wide ranges in parameters used. The median value for all 33 samples and 68.2% confidence intervals for the initial 3_He and 22_{Ne concentrations are2.2}+2.4

−0.6×10−10 and 2.9 +3.0

−0.9×10−11ccSTP/g (Figure 3.6), quite similar to the values found using the standard set of parameters (Table 3.1).

The correspondence between our estimates based on reconstructing initial magmatic volatile contents and the independent estimate based on the oceanic He flux is a heartening indication that our simple degassing model has the capacity to produce reasonable estimates of reconstructed initial magmatic volatile contents. Furthermore, we have not made any as- sumptions about initial concentrations or elemental ratios. And although these samples were not chosen as representative of global MORB, they span wide geographic and geochemical

ranges. Acknowledging the very large range in initial concentrations between the samples, and the potential bias that the best data often come from volatile-rich samples, this proce- dure must be applied to many more samples with high precision He, Ne, and Ar data to con- firm the robustness of our median initial magmatic noble gas concentrations.

3.4.3 A range in reconstructed initial elemental ratios

Our range in initial magmatic3_He/22_{Ne ratios contradicts a conclusion from other disequilib-} rium models that the variety of measured elemental ratios in MORBs (Paonita and Martelli, 2007), as well as OIBs (Weston et al., 2015), could be explained by disequilibrium degassing of a uniform initial composition. However, neither of those models considered the strict con- straints placed on the degassing path by the4_He*/21_{Ne* ratio. Any process that fraction-} ates He from Ne, such as equilibrium or disequilibrium degassing, or helium loss, affects the 3_He/22_{Ne and} 4_He*/21_{Ne* ratios by the same relative amounts as long as there is no or mini-} mal isotopic fractionation. Therefore, initial mantle source3_He/22_{Ne ratios can be computed} solely from the measured (air contamination-corrected) 3_He/22_{Ne and}4_He*/21_{Ne* ratios} (Tucker and Mukhopadhyay, 2014):

(₃

He/22Ne)_mantle =(3He/22Ne)_measured×(4_He∗_/21_Ne∗)

mantle/

(₄

He∗/21Ne∗)_measured (3.8)

where4_He*/21_Ne*

mantle is the production ratio—a relationship which is being implicitly ex-

ploited in our degassing model.

The coupled relationship between3_He/22_{Ne and} 4_He*/21_{Ne* can also be demonstrated} graphically (Figure 3.7) where the mantle source 3_He/22_{Ne for a sample can be found by ex-} trapolating a He/Ne fractionation line to the mantle 4_He*/21_{Ne* production ratio. This fig-} ure demonstrates, similar to previous results (Honda and McDougall, 1998; Moreira et al., 2001; Graham, 2002; Tucker and Mukhopadhyay, 2014), that in general the mantle source of MORBs generally has higher 3_He/22_{Ne than that of OIBs, but significant heterogeneity even}

Figure 3.7: Measured4_He*/21_{Ne* vs}3_He/22_{Ne (filled symbols;}22_{Ne is corrected for atmospheric contam-}

ination) and reconstructed mantle values (open symbols) for various OIBs (red) and MORBs (blue). Man- tle source values are reconstructed only by assuming the extent of 3_He/22_{Ne fractionation from the source}

ratio is equivalent to the extent of 4_He*/21_{Ne* fractionation from the mantle production ratio. The com-}

positions must follow the dashed lines during any fractionation process. This figure clearly demonstrates that significant mantle source 3_He/22_{Ne heterogeneity exists between MORBs and OIBs (indicated by the}

arrows), as well as within both groups, contrary to the conclusions of Paonita and Maretlli (2007) and We- ston et al. (2015) that the mantle has uniform noble gas elemental ratios. MORB data from Tucker et al. (2012); OIB data from Jackson et al. (2009), Kurz et al. (2009); Mukhopadhyay (2012).

We argue that just because a degassing model can fit a subset of observed data with a uni- form initial3_He/22_{Ne ratio, one cannot conclude that the mantle ratio is indeed uniform. For} example, the model of Gonnermann and Mukhopadhyay (2007) also assumed a constant man- tle 3_He/22_{Ne ratio only to minimize the number of model parameters, but acknowledged that} the mantle ratio could be heterogeneous.