Actually, Penny is right to be skeptical about 
the advice she has received, at least in the way 
it is expressed here.  Consider this example: 
When reported on the PDB scale , Julie's offset 
between measured and expected values of d18O is 
0.02 per mil, or roughly 1 % of the absolute 
value (-2.2).   Julie's 'second method' would 
suggest this is the amount by which all data 
should be compressed to get them onto the PDB 
scale (i.e., a measured value of +100 should be 
turned into a reported value of ca. +99).   If, 
instead, Julie had discussed exactly the same 
data using the SMOW scale, her offset between 
expected and observed values would have been 
almost identical (~0.02 per mil), but divided by 
a much larger number (something like 30; I don't 
have my IAEA book on-hand!),  thus implying a 
much smaller proportional stretching factor (ca. 
0.066 %; i.e, turning a measured value of +100 
into +99.934 ”).  Nothing has changed about the 
actual isotope ratios measured, nor their 
proportional offset from expected ratios, but by 
arbitrarily changing the reference frame used to 
convert raw data to delta values, the slope of 
the 'stretching factor' has been changed by 15x.

Any method that is based on additions, 
subtractions, multiplications or divisions using 
data reported on an arbitrary delta scale is 
bound to encounter greater or lesser problems of 
this kind (though division and multiplication 
based on ratios of delta value is a particularly 
bad idea).

One way to deal with offsets of this kind, 
assuming they represent instrumental or 
analytical fractionation rather than some 
additive component (like a blank), is by applying 
a stretching factor based on the ratio of 
measured to expected isotope ratios, not delta 
values.  When delta values are near 0 and vary 
little (i.e., for typical O, C and N isotope 
data), this will result in a correction quite 
close to that obtained by just adding or 
subtracting delta values (Penny's first, and 
preferred method).  When delta values are far 
from 0 or vary greatly (as for most H isotope 
data), this method can differ considerably from 
simple additions or subtractions.  Jason's 
suggestion regarding stretching factors based on 
measured differences between two or more 
standards that differ greatly in delta value will 
yield a similar result (this is the norm for 
correction of instrument- or method-specific 
hydrogen isotope fractionations).

John

>The first method of simple addition and subtraction has no logical
>derivation.  If you have to do it, then the second method of
>normalization (multiplying by the ratio of true/measured) is
>appropriate.  Hope this helps.
>
>
>Paul
>Department of Earth and Environmental Science
>6900 N. Loop 1604 W.
>San Antonio, Texas 78249
>
>-----Original Message-----
>From: Stable Isotope Geochemistry [mailto:[log in to unmask]] On
>Behalf Of Penny Higgins
>Sent: Friday, July 01, 2005 2:57 PM
>To: [log in to unmask]
>Subject: [ISOGEOCHEM] Correcting to standards - procedure
>
>Greetings all,
>
>I hope this isn't a totally dumb question. What seemed pretty
>straight-forward to me has become a large discussion in our lab. Maybe
>I've
>been doing this wrong all along - I just want to be sure.
>
>We're running carbonate samples for d13C and d18O on a gasbench
>connected
>to a DeltaPlus XP. NBS-19 is the standard we're using.
>
>So, I run a bunch of samples with a few NBS-19s tossed in for good
>measure.
>The values for NBS-19 don't come out exactly as specified by Coplen 1994
>as
>d13C = 1.95 and d18O = -2.20. Instead, I get d13C = 1.98 and d18O =
>-2.22.
>
>Ordinarily, I'd just do simple adding or subtracting to all the samples
>in
>the run to make the NBS-19s "right." I subtract 0.03 from ALL the d13C
>values and subtract 0.02 from all the d18O values. My understanding is
>that
>then I can report my results as VPDB.
>
>I was just told that a more correct way to do it is to calculate the
>ratio
>between the real value and the measured value of NBS-19 and multiply
>that
>with all of my samples. That is, the ratio of "true" and measured d13C
>for
>NBS-19 is 0.986, which I multiply all my d13C values with. The ratio of
>"true" and measured d18O for NBS-19 is 0.990, and I multiply all my d18O
>values with that.
>
>This second method just seems wrong, because any measured sample near
>zero
>would not change. But it makes sense in the sense that everything we are
>measuring is done in terms of ratios.
>
>So, at the risk of wasting bandwidth, which is the correct method? Is
>there
>some instances where both methods are required? Am I delusional (it
>happens)?
>
>Stumped,
>
>~Penny
>
>*******************************************************************
>                        Dr. Pennilyn Higgins
>                         Research Associate
>
>                              "SIREAL"
>    Stable Isotope Ratios in the Environment Analytical Laboratory
>
>          Department of Earth and Environmental Sciences
>          University of Rochester
>          227 Hutchison Hall
>          Rochester, NY 14627
>
>                     [log in to unmask]
>
>Office: 209b Hutchison Hall               Lab: 209 Hutchison Hall
>Voice : (585) 275-0601               Outer lab: (585) 273-1405
>FAX   : (585) 244-5689              Inner lab: (585) 273-1397
>
>            http://www.earth.rochester.edu/SIREAL/index.html
>*******************************************************************