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# 14C calculations

Author Topic:   14C calculations
RAZD
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 Message 1 of 10 (714576) 12-23-2013 8:07 PM

In doing research for my new version of the age thread I came across this:
quote:
Modern standard
The principal modern radiocarbon standard is N.I.S.T (National Institute of Standards and Technology; Gaithersburg, Maryland, USA) Oxalic Acid I (C2H2O4). Oxalic acid I is N.I.S.T designation SRM 4990 B and is termed HOx1. This is the International Radiocarbon Dating Standard. Ninety-five percent of the activity of Oxalic Acid from the year 1950 is equal to the measured activity of the absolute radiocarbon standard which is 1890 wood. 1890 wood was chosen as the radiocarbon standard because it was growing prior to the fossil fuel effects of the industrial revolution. The activity of 1890 wood is corrected for radioactive decay to 1950. Thus 1950, is year 0 BP by convention in radiocarbon dating and is deemed to be the 'present'. 1950 was chosen for no particular reason other than to honour the publication of the first radiocarbon dates calculated in December 1949 (Taylor, 1987:97).
A radiocarbon measurement, termed a conventional radiocarbon age (or CRA) is obtained using a set of parameters outlined by Stuiver and Polach (1977), in the journal Radiocarbon. A time-independent level of C14 activity for the past is assumed in the measurement of a CRA. The activity of this hypothetical level of C14 activity is equal to the activity of the absolute international radiocarbon standard.
The Conventional Radiocarbon Age BP is calculated using the radiocarbon decay equation:
t=-8033 ln(Asn/Aon)
Where -8033 represents the mean lifetime of 14C (Stuiver and Polach, 1977). Aon is the activity in counts per minute of the modern standard, Asn is the equivalent cpm for the sample. 'ln' represents the natural logarithm.
A CRA embraces the following recommended conventions:
• a half-life of 5568 years;
• the use of Oxalic acid I or II, or appropriate secondary radiocarbon standards (e.g. ANU sucrose) as the modern radiocarbon standard;
• correction for sample isotopic fractionation (deltaC13) to a normalized or base value of -25.0 per mille relative to the ratio of C12/C13 in the carbonate standard VPDB (more on fractionation and deltaC13);
• the use of 1950 AD as 0 BP, ie all C14 ages head back in time from 1950;
• the assumption that all C14 reservoirs have remained constant through time.

Thus it appears that all the "14C-age" calculations are based on the old half-life value of 5568 years instead of the revised half-life of 5730 years ... and this is so (a) they can be compared to older dates so calculated and (b) to ensure that corrections would not be applied twice.
My interest is to convert graphs of "14C-age" vs calendar age to show ln[14C‰] vs calendar age.
It seems to me that Aon is a constant representing the 14C content in 1950 (although this is complicated by the 1890 wood standard correction for radioactive decay to 1950).
There also has to be a tie to 12C or total carbon .. ie Asn and Aon are counts of 14C/gram carbon (when using ALS) or similar, and this should result in the raw data via reversing the age formula:
Asn = Aon &bul; e^(-t/8033)
Anyone know what a good number for Aon is and what the volume of carbon it represents?

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 Message 2 of 10 (714578) 12-23-2013 10:18 PM

Thread Copied from Proposed New Topics Forum
Thread copied here from the 14C calculations thread in the Proposed New Topics forum.

Coyote
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Joined: 01-12-2008

 (1)
 Message 3 of 10 (714581) 12-24-2013 12:13 AM

In dealing with >600 radiocarbon dates I've obtained, I've always used either the measured age and calibrated using Calib. 4.3, or used the conventional age and calibrated using Calib. 5, 6, or now 7. Calib. 7 includes the new IntCal13 and Marine13 calibrations curves.
When you calibrate using the recent curves, such as IntCal13 and Marine13, a lot of factors are taken into account, so you don't have to deal with them individually.
[By the way, one of your quotes is from Taylor (1987). I worked with Taylor on a proposal for a radiocarbon project a number of years ago, but it never came together.]

Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.
Belief gets in the way of learning--Robert A. Heinlein
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If I am entitled to something, someone else is obliged to pay--Jerry Pournelle
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 Replies to this message: Message 4 by herebedragons, posted 12-24-2013 8:53 AM Coyote has replied Message 7 by RAZD, posted 12-24-2013 2:24 PM Coyote has seen this message but not replied

herebedragons
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 Message 4 of 10 (714590) 12-24-2013 8:53 AM Reply to: Message 3 by Coyote12-24-2013 12:13 AM

Examples?
Hi Coyote ...
Out of curiosity, could you give some examples using the 4 different calibration techniques you mention (measured age + Calib. 4.3; conventional age +Calib.5; c.a.+Calib. 6.; c.a.+Calib. 7) to compare the calibrated dates? Maybe give a couple different ranges of dates, say 2 kya, 6 kya, and 20 kya for example. I am just curious about how much these calibration curve updates have affected adjusted dates over the different revisions.
Maybe you could use some older data that you used one of the older systems on and then plug those numbers into the new system (?)
HBD

Whoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for. But until the end of the present exile has come and terminated this our imperfection by which "we know in part," I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca
"Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem.

 This message is a reply to: Message 3 by Coyote, posted 12-24-2013 12:13 AM Coyote has replied

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Coyote
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Posts: 6117
Joined: 01-12-2008

 Message 5 of 10 (714614) 12-24-2013 11:44 AM Reply to: Message 4 by herebedragons12-24-2013 8:53 AM

Re: Examples?
Sure!
Here is a radiocarbon date I received a few years ago. The measured age was 498040 and the conventional age was 539040.
The conventional age was calculated by the laboratory using a C13/C12 measurement of -0.1. This corrects for isotopic fractionation, as the heavier isotopes (C13 and C14) are taken up into the food chain at lower rates than C12. This sample was a piece of mussel shell. The C13/C12 figure for mussel shell, at -0.1, is very typical of what we see.
The laboratory gave a calibrated age of BC 3660-3490 (5610-5440 BP) at 2 sigma, with an intercept of 5560 BP. As this sample was shell, they used the marine reservoir correction (Delta-R) of 22535. Given that this sample was submitted several years ago, the calibration curve they used was IntCal09/Marine09.
Recalibrating this using Calib. 7.0 with the newer IntCal13/Marine13 gives the following at 2 sigma:
BC 3696-3449 and BP 5645-5398, with the intercept remaining at 5560 BP.
Calibrating this using the old Calib. 4.3 (using Marine98) gives the following:
BC 3659-3474 and BP 5608-5423, with the intercept at 5548.
So, the intercept changed by 12 years between the 1998 marine dataset and the two newer marine datasets. This is insignificant as we're dealing with 40 in the initial measurement anyway.

Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.
Belief gets in the way of learning--Robert A. Heinlein
How can I possibly put a new idea into your heads, if I do not first remove your delusions?--Robert A. Heinlein
It's not what we don't know that hurts, it's what we know that ain't so--Will Rogers
If I am entitled to something, someone else is obliged to pay--Jerry Pournelle
If a religion's teachings are true, then it should have nothing to fear from science...--dwise1

 This message is a reply to: Message 4 by herebedragons, posted 12-24-2013 8:53 AM herebedragons has not replied

 Replies to this message: Message 6 by RAZD, posted 12-24-2013 1:49 PM Coyote has replied

RAZD
Member (Idle past 952 days)
Posts: 20714
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 Message 6 of 10 (714624) 12-24-2013 1:49 PM Reply to: Message 5 by Coyote12-24-2013 11:44 AM

Re: Examples?
From the site in Message 1:
quote:
Three further terms are sometimes given with reported radiocarbon dates. d14C, D14C and deltaC13.
All are expressed in per mille notation rather than per cent notation (%).
d14C represents the per mille depletion in sample carbon 14 prior to isotopic fractionation correction and is measured by:
d14C=((Asn/Aon) - 1)1000 per mille
D14C represents the 'normalized' value of d14C. 'Normalized' means that the activity is scaled in relation to fractionation of the sample, or its deltaC13 value. All D14C values are normalized to the base value of -25.0 per mille with respect to the standard carbonate (VPDB). D14C is calculated using:
D14C=d14C - 2(dC13 + 25)(1 + d14C/1000) per mille
This value can then be used to calculate the CRA using the equation given above.

This still gives you an age based on the old half-life (-8033*ln(1/2) = 5,568)
If you want to use the modern value of 5730 then the multiplier is -8267, but this still doesn't correct for changes in atmospheric 14C levels over time.
... the conventional age was 539040.
And the 5730 age would be 5550 +/- 40 which then needs to be calibrated to atmosphere levels
Using the old values avoids the possibility of making this correction twice.
Enjoy

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 This message is a reply to: Message 5 by Coyote, posted 12-24-2013 11:44 AM Coyote has replied

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RAZD
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Posts: 20714
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 Message 7 of 10 (714626) 12-24-2013 2:24 PM Reply to: Message 3 by Coyote12-24-2013 12:13 AM

so
so it looks like the best I can do is convert to %Aon ...
t = -8033 ln(Asn/Aon)
-t/8033 = ln(Asn/Aon)
e^-(t/8033) = e^ ln(Asn/Aon) = Asn/Aon
For:
 0,000 1000 1,000 883 2,000 779.6 3,000 688.3 4,000 607.8 5,000 536.6 6,000 473.8 7,000 418.4 8,000 369.4 9,000 326.2 10,000 288 11,000 254.3 12,000 224.5 13,000 198.2 14,000 175 15,000 154.5 16,000 136.5 17,000 120.5 18,000 106.4 19,000 93.9 20,000 82.9 21,000 73.2 22,000 64.7 23,000 57.1 24,000 50.4 25,000 44.5 26,000 39.3 27,000 34.7 28,000 30.6 29,000 27 30,000 23.9 31,000 21.1 32,000 18.6 33,000 16.4 34,000 14.5 35,000 12.8 36,000 11.3 37,000 10 38,000 8.8 39,000 7.8 40,000 6.9 41,000 6.1 42,000 5.4 43,000 4.7 44,000 4.2 45,000 3.7 46,000 3.3 47,000 2.9 48,000 2.5 49,000 2.2 50,000 2
* compared to 1950 Aon standard
So the second column should represent the actual 14C measured compared to the 1950 Aon standard.
As you can see these amounts are getting quite small, especially when you compare this to the fraction of 14C to 12C at the 1950 standard.
... the conventional age was 539040.
This would be 511.2‰ of the 1950 Aon standard
Enjoy
Edited by RAZD, : near 1 half life

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 This message is a reply to: Message 3 by Coyote, posted 12-24-2013 12:13 AM Coyote has seen this message but not replied

Coyote
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 Message 8 of 10 (714627) 12-24-2013 2:25 PM Reply to: Message 6 by RAZD12-24-2013 1:49 PM

Re: Examples?
From the bottom of Beta Analysic's report page:
Dates are reported as RCYBP (radiocarbon years before present, "present"=AD 1950). By international convention, the modern reference standard was 95% the 14C activity of the National Institute of Standards (NIST) Oxalic Acid (SRM 4990C) and calculated using the Libby 14C half-life (5568 years). Quoted errors represent 1 relative standard deviation statistics (68% probability) counting errors based on the combined measurements of the sample, background, and modern reference standards. Measured 13C/12C ratios (delta 13C) were calculated relative to the PDB-1 standard.
The Conventional Radiocarbon Age represents the Measured Radiocarbon Age corrected for isotopic fractionation, calculated using the delta 13C. On rare occasions where the Conventional Radiocarbon Age was calculated using an assumed delta 13C, the ratio and the Conventional Radiocarbon Age will be followed by "*". The Conventional Radiocarbon Age is not calendar calibrated. When available, the Calendar Calibrated result is calculated from the Conventional Radiocarbon Age and is listed as the "Two Sigma Calibrated Result" for each sample.
I have never worried about the difference between the original half-life of 5568 and the modern one of 5730. As noted above, most reporting uses the old figure, and often there is a note saying to multiply by 1.03 if you want to convert to the new one.
Here is a page describing Beta Analytic's report procedures and report form:
Carbon-14 AMS Standard Deviation - Beta Analytic
Have fun!

Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.
Belief gets in the way of learning--Robert A. Heinlein
How can I possibly put a new idea into your heads, if I do not first remove your delusions?--Robert A. Heinlein
It's not what we don't know that hurts, it's what we know that ain't so--Will Rogers
If I am entitled to something, someone else is obliged to pay--Jerry Pournelle
If a religion's teachings are true, then it should have nothing to fear from science...--dwise1

 This message is a reply to: Message 6 by RAZD, posted 12-24-2013 1:49 PM RAZD has replied

 Replies to this message: Message 9 by RAZD, posted 12-24-2013 2:29 PM Coyote has replied

RAZD
Member (Idle past 952 days)
Posts: 20714
From: the other end of the sidewalk
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 Message 9 of 10 (714630) 12-24-2013 2:29 PM Reply to: Message 8 by Coyote12-24-2013 2:25 PM

Re: Examples?
I have never worried about the difference between the original half-life of 5568 and the modern one of 5730. As noted above, most reporting uses the old figure, and often there is a note saying to multiply by 1.03 if you want to convert to the new one.
Yes, this is what the website in Message 1 says, and it is the convention adopted to ensure that dates aren't double corrected.
Thanks.

we are limited in our ability to understand
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 This message is a reply to: Message 8 by Coyote, posted 12-24-2013 2:25 PM Coyote has replied

 Replies to this message: Message 10 by Coyote, posted 12-24-2013 2:58 PM RAZD has seen this message but not replied

Coyote
Member (Idle past 1653 days)
Posts: 6117
Joined: 01-12-2008

 (2)
 Message 10 of 10 (714633) 12-24-2013 2:58 PM Reply to: Message 9 by RAZD12-24-2013 2:29 PM

Re: Examples?
We have found there is far more error to be found in sample selection than in anything the laboratory can do.
Example: in our area, the oldest abalone shell has been dated at 5910 BP, while the oldest mussel shell is 9420 BP. The lndians started using mussels early, and abalones, which take a lot more work, much later. If you date only abalone shells you miss out on the earliest 3,500 years of our prehistory.
Another example: some archaeologists are still using multiple pieces of shell in their dates. In any site that has gophers or squirrels, that almost certainly guarantees an error. We dated one site, using single pieces of shell, and found that they were completely randomized with respect to depth. But those single pieces, even though they had been moved around, still gave good dates. Including a large number of shell fragments in your sample will completely homogenize your date: if you have a two component site, Early and Late, that's a good way to get Middle Period dates even though the site wasn't occupied at that time.
A really sneaky one: changing populations and patterns of exploitation over time resulted in early mussel shells generally being pretty thick and robust, but shells from later in time were thinner. This reflects over-exploitation of the mussel beds where the mussels aren't given a chance to grow up. For a while in trying to date one site we were selecting just the nice thick shells, and we kept getting Early Period dates. Only when we selected thin shells did we get more recent dates.
Given all of these sources of bias, and a few others, we don't worry so much about what the laboratory does. We worry far more about what we and other archaeologists are doing!

Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.
Belief gets in the way of learning--Robert A. Heinlein
How can I possibly put a new idea into your heads, if I do not first remove your delusions?--Robert A. Heinlein
It's not what we don't know that hurts, it's what we know that ain't so--Will Rogers
If I am entitled to something, someone else is obliged to pay--Jerry Pournelle
If a religion's teachings are true, then it should have nothing to fear from science...--dwise1

 This message is a reply to: Message 9 by RAZD, posted 12-24-2013 2:29 PM RAZD has seen this message but not replied

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