SUPPLEMENTARY DOCUMENT

Session 1,  25/9/00
25/9/00 Run Table:  
	206, 206.1, 207, 208, 238, 248, 254, 270

25/09/00 PRAWN output
#, 7/6, ±, 8/6, ±, UO/U, ±, Pb/UO, ±, ThO/UO, ±, UO2/UO, ±, Pb/UO2, ±, BG, Pb cps, t1, Time, SL13 cps, CAL AS3.  

First Reduction
First, the U ppm was calculated using the comparative cps UO for SL13 and the unknowns.  Then the fractions and amounts of common 206 per analysis, which indicated that most analyses had indistinguishable small amounts of common Pb that could be averaged as a ‘surface blank’.  A program was written to reduce the data ratioed to UO2 and equating the mean observed Pb/UO2 for AS3 to 1099 Ma.  The latter gave a starting calibration which was adjusted later when the extent of Pb loss within AS3 was assessed and allowed for.   

Second Reduction method
	The same Prawned data was formatted for the usual reduction programs by inserting a dummy 4/6 and UO/Zr (and their errors) into the necessary columns, and Pb/UO2, ± into cols 11, 12.  The usual programs then interpret Pb/UO2 in c11 as Pb/UO.  

207/206 ages
	For GA842 corrected for common Pb by the mean surface blank, the 207/206 ages agreed to within error at 374.3 ± 7.7 Ma.  Two ages at 560 and 600 Ma signify inheritance and were excluded.  Similar agreement was found for GA838, at 359.4 ± 6.0 Ma, and for AS3 at 1084.1 ± 2.5 Ma.  The latter appears to be lower than 1099 Ma.  

Discrimination slopes

The discrimination plots for lnPb/UO vs. lnUO/U are disturbed by Pb loss, as evident both visually and by their high Mswd.  Nevertheless, regression of the AS3 and combined UNKs data give reasonable definition of slope at 0.73 ± .16 and 0.65 ± .10.  (Four analyses were deleted from the latter: one young and one old outlier at 141 Ma and 508 Ma, one at 332 Ma having the highest errors, and one at 334 Ma having the lowest errors and giving the largest residual in the regression.).  The Pb/UO data were reduced using 0.7 ± .1 for the slope.  
Compared with lnPb/UO, ln Pb/UO2 is poorly correlated with lnUO/U and its slope is significantly less, consistent with the view that Pb/UO2 is not sensitive to variable discrimination.  

The correlation between UO2/UO and UO/U is very high and gives a mean slope of 0.57 ± .03.  The attached Appendix on inter-ratio correlations shows that these parameters give an expected slope of ~0.1 for lnPb/UO2 vs lnUO/U, which is consistent with the observed slopes and used here to reduce the Pb/UO2 data.  

Common Pb correction for 29/05 session
	Common Pb was estimated using both the 207- and 208- methods, and the results compared.  The 207-method gave smaller errors, the common Pb estimates were less dispersed, and for most analyses, it was not detectable in both AS3 and the Devonian zircons.  

Calibration to AS3
	25/09/00 session was first calibrated roughly using the mean of two SL13 analyses.  Then the AS3 6/38 ages by each reduction program were put through Mix, and the undisturbed oldest group was normalised to 1099 Ma.  
	Based on the calculated errors, the oldest group for each had only ca. 20% of the ages.  The first question was whether this oldest group was indeed the undisturbed magmatic age, or might it be the result of patches of unsupported radiogenic Pb?  On the interpretation of undisturbed magmatic areas, the adjustment factors calculated for the two methods were 0.9655 ± .0025 and .9288 ± .0027, and the Devonian ages calculated by the two procedures from the 25/09 session were in very close agreement.  
	The second question is whether the calculated errors alone correctly estimate the actual errors in SHRIMP analysis.  This is discussed below.  The decision was made to add an extra 0.5% error (in quadrature) to each age to allow for the possibility of unknown errors.  

Session 2, 23/11/00
23/11/00 Run Table 
204 Zr2O2, 204 Pb, 204.1BG, 206, 207, 208dummy, 254, 254dummy, 270UO2.
	For KD data reduction, the real 254 can be read as 238U, the real 270 as 254UO, and 204Zr2O2 can be read as Zr2O.  This allows existing pgms to be used w/o rewrite.  

PRAWN output 23/11/00
#, 4/6, ±, 7/6, ±, 8/6, ±, UO2/UO, ±, Pb/UO2, ±, Zr/UO, ±, Pb/UO2, ±, dumTh/UO2, ±, 204, BG, tot 206, Pb cps, t1, Time.

Slopes for lnPb/UO2 vs lnUO2/UO 
	These are poorly defined for both UNKs and AS3, at 0.26 ± .13 and 0.68 ± .15 respectively, influenced by variable Pb loss.  The mean value at 0.47 ± .21 (se) was used.  The theoretical value based on previously measured correlations is 0.13 ± .15 (see below) from the first analytical session.  
Common Pb
	Comparison of 4-red and 7-red ppm co suggests 4-red is the better – smaller, less dispersed, and errors smaller.  The latter means that fluctuations beyond error are detected more sensitively using 4-red.  The small variation in co 206 detected indicates that for at least some analyses, the individual correction should be applied rather than the mean surface blank.  
	Note that ’7-red’ means assigning (fixed) ages for AS3 of 1099 Ma and 378 Ma for all UNKs.  In other words, zero age Pb loss is assumed rather than the expectation that all points fall on Concordia.  

207/206 ages, 204-reduced, combined GA838 and GA842
	All agree within error (mswd 1.5) and have weighted mean of 381.5 ± 8.4 Ma.  

Notes on Snobs session 5/6/02

Correlation between UO2/UO, UO/U
	Previous two sessions, 25/09/01 and 23/11/01, gave 0.57 ± .03 and .58 ± .03 for ln UO2/UO vs ln UO/U.  Mswd for the regressions using calculated errors are 5.7 and 6.2 respectively, which shows that other errors are mainly responsible for the scatter.  If the errors for each ratio are augmented by 0.9%, Mswd drops to unity and the regression slopes change to 0.59 ± .03 and 0.60 ± .03.  On face value, the extra error should be applicable to Pb/UO, Pb/UO2, which may have serious effects on the calibration factor and resolution of Pb loss and inheritance.
 	The 5/6/02 session is noticeably more scattered than the previous two, and needs an extra error of ±1.5%.  It gives 0.93 ± .07 for the slope when this is added.  
	PRAWN has evidently failed to register the full errors in the ratios for the three Snob’s sessions.  

Ln Pb/UO vs ln UO/U	
	GA838 and TEM resp. give 1.10 ± .15 and 0.97 ± .13, wtd mean is 1.03 ± .10.  The latter predicts 0.10 ± .12 for the slope between ln Pb/O2 vs ln UO/U, and 0.11 ± .12 for ln Pb/O2 vs ln UO2/U.  

Ln Pb/UO2 vs ln UO/U
 The slopes observed for GA838 and TEM are 0.31 ± .15 and 0.26 ± .08, giving weighted mean of  0.28 ± .06.   
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Ages Temora using Pb/UO2 
	Accepted empirical 0.28 ± .06 slope.  Used 207-correction.  Deleted one older outlier, averaged rest at 411.8 Ma.  Adjusted mean to 417 Ma by factor 1.0130 ± .0035.  Used this factor for GA838 ages.  Temora mean and precision are not changed by the 1.5% extra error.  All ages except one fit to within error (Mswd 0.84)

Ages GA838 using 1.
	(a) Calculated errors 
Processed same as TEM.  Deleted 2 younger outliers leaving N=23.  Mean of rest is 377.0 ± 1.3 Ma, MSWD 5.6, SD 1.7%.   Delete 2 oldest, get MSWD 3.4, mean 376 ± 1.3 Ma, SD 1.6%.  Mix-modelling for N=23 and internal errors gives 372.4 ± 0.8 Ma (53%), with 6 older at 386.0 ± 1.3 Ma and 4 older at 378 ± 2. 
	(b) Augmented errors
 For all ages, Mswd is 2.44.  Progressively delete two youngest to find Mswd 0.88 and weighted mean age 376.6 ± 1.4 Ma.  
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Ages Temora using Pb/UO
	Accepted standard 1.0 slope.  Used 207-correction.  Deleted one older outlier, averaged rest at 408.5 Ma.  Adjusted mean to 417 Ma by factor 1.0215 ± .006.  Used this factor for GA838 ages using Pb/UO.  

Ages GA838 using 2.
	Processed same as TEM.  Deleted 1 older, 1 younger outlier leaving N=23.  Mean of rest is 381.0 ± 1.9 Ma, MSWD 5.3.  Several subjective deletions (see 838 1. stats) reduce MSWD to 2.1 (still significant), but age of majority hovers around 381 Ma.   This is older than Pb/UO2 mean.  Mix-modelling for N=23 gives 381.7 ± 0.9 Ma (69%), with 2 older at 400 ± 3 Ma and 5 younger (369 Ma).  Conclusion:  In this instance, use of the mean (plus inferred bigger analytical errors) and use of internal errors with mix-modelling give the same answer.   
	With the added 1.5% to input errors, the Temora statistics are unchanged and the GA838 statistics become simpler.  The single old GA838 age continues to be older than rest but deletion of the youngest is marginal.  Mean age is 379.1 ± 2.8 Ma for N=24 and Mswd 1.28.   With youngest deleted, it is 381.0 ± 1.9 Ma with Mswd 0.93.  

Observed and expected correlations between UO/U, UO2/UO, Pb/UO and Pb/UO2 

(a) SHRIMP empirical observations:
Pb/U = a*(UO/U)m, 

which leads to 	      ln(Pb/U) = ln a + m*ln(UO/U).  

(b)  Write Pb/UO as (Pb/U) / (UO/U).
  Then
ln (Pb/UO) = ln (Pb/U) - ln (UO/U) = ln a + m*ln(UO/U) - ln (UO/U)
       = ln a + (m - 1)*ln(UO/U)

Thus, if the slope m for the Pb/U vs UO/U correlation is 2.0, it becomes 1.0 for the Pb/UO.  

(c) Similarly,  write Pb/UO2 as (Pb/UO)/(UO2/UO), so that 

ln (Pb/UO2) = ln (Pb/UO)  - ln (UO2/UO)……………………………………(1)

By empirical observation, UO2/UO is well correlated with UO/U, which can be expressed conveniently as
     UO2/UO = b*( UO/U)p

Thus, ln (UO2/UO) = ln b + p*ln (UO/U)……………………………………………(2)

Substituting for ln (Pb/UO) and ln (UO2/UO) in (1)

ln (Pb/UO2) = ln a + (m - 1)*ln(UO/U) - ln b - p*ln (UO/U)
        = ln a - ln b + (m - 1 - p)*ln (UO/U)……………………………(3)

For SHRIMP, p has been evaluated at 0.6.  Thus the slope expected between ln (Pb/UO2) and ln (UO/U becomes (≥1.7 - 1 -.6), which is ≥ 0.1.  

(d)  Express (1) in terms of UO2/UO rather than UO/U.  
From (2) get
		ln (UO/U) = (ln (UO2/UO) - ln b) / p

Substitute in (3) to get

    ln (Pb/UO2) = ln a + (m - 1) * (ln (UO2/UO) - ln b)/p - ln (UO2/UO)
			= ln a -(ln b)/p + ((m - 1)/p -1) * ln (UO2/UO)………………(4)

For the SHRIMP evaluations, this gives an expected slope for the plot of ln (Pb/UO2) vs ln (UO2/UO) of ca 0.2 but the value is sensitive to the exact parameters.  For example, if the slope for ln Pb/UO vs ln UO/U is 1.0 rather than 0.7, it becomes 0.7. 

(e)  Of the three sets of ratios that can be used, the plot ln (Pb/UO2) against ln (UO/U) has the smallest value for slope.  It follows that (real) variation in slope within or between sessions has the least effect on ln (Pb/UO2).