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data_processing [2010/04/30 07:09]
mdaeron created
data_processing [2013/01/22 04:15]
mdaeron [(2) Compute the composition of your sample gas]
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 ====== Data processing ====== ====== Data processing ======
  
-''​reduction ​and correction ​of raw IRMS data''​ +{{:​gas_corrections.zip|Python code for gas corrections in the "​imperial"​ reference frame}} 
-''​standardization issues''​+ 
 +===== CO2 data reduction ===== 
 +==== (1) Compute the isotopologue composition of your reference gas ==== 
 + 
 +...using the following parameters:​ 
 +  * δ<sup>13</​sup>​C<​sub>​Ref</​sub>:​ the nominal carbon isotope composition of your reference gas vs VPDB 
 +  * δ<​sup>​18</​sup>​O<​sub>​Ref</​sub>:​ the nominal oxygen isotope composition ​ of your reference gas vs VSMOW 
 +  * λ = 0.5164, the terrestrial mass-dependent fractionation parameter between <​sup>​17</​sup>​O ​and <​sup>​18</​sup>​O //[missing reference]//​ 
 +  * R<​sub>​13-VPDB</​sub>​ = 0.0112372, the abundance ratio of <​sup>​13</​sup>​C/<​sup>​12</​sup>​C for VPDB //[missing reference]//​ 
 +  * R<​sub>​17-VSMOW</​sub>​ = 0.0003799, the abundance ratio of <​sup>​17</​sup>​O/<​sup>​16</​sup>​O for VSMOW //[missing reference]//​ 
 +  * R<​sub>​18-VSMOW</​sub>​ = 0.0020052, the abundance ratio of <​sup>​18</​sup>​O/<​sup>​16</​sup>​O for VSMOW //[missing reference]//​ 
 + 
 +**(1.a) Compute abundance ratios of <​sup>​13</​sup>​C/<​sup>​12</​sup>​C,​ <​sup>​17</​sup>​O/<​sup>​16</​sup>​O and <​sup>​18</​sup>​O/<​sup>​16</​sup>​O** 
 + 
 +  * R<​sub>​13-Ref</​sub>​ = R<​sub>​13-VPDB</​sub>​ × (1 + δ<​sup>​13</​sup>​C<​sub>​Ref</​sub>/​1000) 
 +  * R<​sub>​18-Ref</​sub>​ = R<​sub>​18-VSMOW</​sub>​ × (1 + δ<​sup>​18</​sup>​O<​sub>​Ref</​sub>/​1000) 
 +  * R<​sub>​17-Ref</​sub>​ = R<​sub>​17-VSMOW</​sub>​ × (R<​sub>​18-Ref</​sub>​ / R<​sub>​18-VSMOW</​sub>​)<​sup>​λ</​sup>​ 
 + 
 +**(1.b) Compute abundances of <​sup>​12</​sup>​C,​ <​sup>​13</​sup>​C,​ <​sup>​16</​sup>​O,​ <​sup>​17</​sup>​O and <​sup>​18</​sup>​O** 
 + 
 +  * C<​sub>​12-Ref</​sub>​ = 1 / (1 + R<​sub>​13-Ref</​sub>​) 
 +  * C<​sub>​13-Ref</​sub>​ = R<​sub>​13-Ref</​sub>​ / (1 + R<​sub>​13-Ref</​sub>​) 
 +  * C<​sub>​16-Ref</​sub>​ = 1 / (1 + R<​sub>​17-Ref</​sub>​ + R<​sub>​18-Ref</​sub>​) 
 +  * C<​sub>​17-Ref</​sub>​ = R<​sub>​17-Ref</​sub>​ / (1 + R<​sub>​17-Ref</​sub>​ + R<​sub>​18-Ref</​sub>​) 
 +  * C<​sub>​18-Ref</​sub>​ = R<​sub>​18-Ref</​sub>​ / (1 + R<​sub>​17-Ref</​sub>​ + R<​sub>​18-Ref</​sub>​) 
 + 
 +**(1.c) Compute abundances of isotopologues with masses 44 to 49** 
 + 
 +...by making the assumption that your reference gas is stochastic (this is usually not true, but we correct for that later in the process). 
 +  * Mass 44: 
 +    * C<​sub>​12-16-16-Ref</​sub>​ = C<​sub>​12-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ 
 +  * Mass 45: 
 +    * C<​sub>​13-16-16-Ref</​sub>​ = C<​sub>​13-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ 
 +    * C<​sub>​12-17-16-Ref</​sub>​ = C<​sub>​12-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ × 2 
 +  * Mass 46: 
 +    * C<​sub>​12-18-16-Ref</​sub>​ = C<​sub>​12-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ × 2 
 +    * C<​sub>​13-17-16-Ref</​sub>​ = C<​sub>​13-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ × 2 
 +    * C<​sub>​12-17-17-Ref</​sub>​ = C<​sub>​12-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ 
 +  * Mass 47: 
 +    * C<​sub>​13-18-16-Ref</​sub>​ = C<​sub>​13-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ × C<​sub>​16-Ref</​sub>​ × 2 
 +    * C<​sub>​13-17-17-Ref</​sub>​ = C<​sub>​13-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ 
 +    * C<​sub>​12-18-17-Ref</​sub>​ = C<​sub>​12-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ × 2 
 +  * Mass 48: 
 +    * C<​sub>​13-18-17-Ref</​sub>​ = C<​sub>​13-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ × C<​sub>​17-Ref</​sub>​ × 2 
 +    * C<​sub>​12-18-18-Ref</​sub>​ = C<​sub>​12-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ 
 +  * Mass 49: 
 +    * C<​sub>​13-18-18-Ref</​sub>​ = C<​sub>​13-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ × C<​sub>​18-Ref</​sub>​ 
 + 
 +**(1.d) Compute binned abundances of isotopologues grouped by mass** 
 + 
 +  * C<​sub>​44-Ref</​sub>​ = C<​sub>​12-16-16-Ref</​sub>​ 
 +  * C<​sub>​45-Ref</​sub>​ = C<​sub>​13-16-16-Ref</​sub>​ + C<​sub>​12-17-16-Ref</​sub>​ 
 +  * C<​sub>​46-Ref</​sub>​ = C<​sub>​12-18-16-Ref</​sub>​ + C<​sub>​13-17-16-Ref</​sub>​ + C<​sub>​12-17-17-Ref</​sub>​ 
 +  * C<​sub>​47-Ref</​sub>​ = C<​sub>​13-18-16-Ref</​sub>​ + C<​sub>​13-17-17-Ref</​sub>​ + C<​sub>​12-18-17-Ref</​sub>​ 
 +  * C<​sub>​48-Ref</​sub>​ = C<​sub>​13-18-17-Ref</​sub>​ + C<​sub>​12-18-18-Ref</​sub>​ 
 +  * C<​sub>​49-Ref</​sub>​ = C<​sub>​13-18-18-Ref</​sub>​ 
 + 
 +==== (2) Compute the composition of your sample gas ==== 
 + 
 +**(2.a) Measure the abundance ratios of your sample gas for masses 45 to 49 (R<​sub>​45-Sample</​sub>,​ etc.)** 
 + 
 +...based on peak height measurements from your dual-inlet spectrometer:​ 
 +  * V<​sub>​44-Ref</​sub>​ ... V<​sub>​49-Ref</​sub>​ for your reference gas 
 +  * V<​sub>​44-Sample</​sub>​ ... V<​sub>​49-Sample</​sub>​ for your sample gas 
 + 
 +Ideally, these voltages reflect abundance ratios, so that: 
 +  * R<​sub>​45-Sample</​sub>​ = R<​sub>​45-Ref</​sub>​ × V<​sub>​45-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​45-Ref</​sub>​ 
 +  * R<​sub>​46-Sample</​sub>​ = R<​sub>​46-Ref</​sub>​ × V<​sub>​46-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​46-Ref</​sub>​ 
 +  * R<​sub>​47-Sample</​sub>​ = R<​sub>​47-Ref</​sub>​ × V<​sub>​47-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​47-Ref</​sub>​ 
 +  * R<​sub>​48-Sample</​sub>​ = R<​sub>​48-Ref</​sub>​ × V<​sub>​48-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​48-Ref</​sub>​ 
 +  * R<​sub>​49-Sample</​sub>​ = R<​sub>​49-Ref</​sub>​ × V<​sub>​49-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​49-Ref</​sub>​ 
 + 
 +And, using the conventional δ notation (relative to your reference gas): 
 +  * δ<​sub>​45</​sub>​ = 1000 × (1 - R<​sub>​45-Sample</​sub>/​R<​sub>​45-Ref</​sub>​) = 1000 × (1 - V<​sub>​45-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​45-Ref</​sub>​) 
 +  * δ<​sub>​46</​sub>​ = 1000 × (1 - R<​sub>​46-Sample</​sub>/​R<​sub>​46-Ref</​sub>​) = 1000 × (1 - V<​sub>​46-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​46-Ref</​sub>​) 
 +  * δ<​sub>​47</​sub>​ = 1000 × (1 - R<​sub>​47-Sample</​sub>/​R<​sub>​47-Ref</​sub>​) = 1000 × (1 - V<​sub>​47-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​47-Ref</​sub>​) 
 +  * δ<​sub>​48</​sub>​ = 1000 × (1 - R<​sub>​48-Sample</​sub>/​R<​sub>​48-Ref</​sub>​) = 1000 × (1 - V<​sub>​48-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​48-Ref</​sub>​) 
 +  * δ<​sub>​49</​sub>​ = 1000 × (1 - R<​sub>​49-Sample</​sub>/​R<​sub>​49-Ref</​sub>​) = 1000 × (1 - V<​sub>​49-Sample</​sub>​ / V<​sub>​44-Sample</​sub>​ × V<​sub>​44-Ref</​sub>​ / V<​sub>​49-Ref</​sub>​) 
 + 
 +**(2.b) Compute the bulk composition of your sample gas** 
 + 
 +One way to do that is to define: 
 + 
 +  * K = R<​sub>​17-VSMOW</​sub>​ × (R<​sub>​18-VSMOW</​sub>​)<​sup>​–λ</​sup>​ 
 + 
 +You can then compute <fc red>​R<​sub>​18-Sample</​sub></​fc>​ by numerically solving the following equation:  
 + 
 +  * –3K<​sup>​2</​sup>​ × (<fc red>​R<​sub>​18-Sample</​sub></​fc>​)<​sup>​2λ</​sup>​ + 2K × R<​sub>​45-Sample</​sub>​ × (<fc red>​R<​sub>​18-Sample</​sub></​fc>​)<​sup>​λ</​sup>​ + 2<fc red>​R<​sub>​18-Sample</​sub></​fc>​ - R<​sub>​46-Sample</​sub>​ = 0 
 + 
 +({{http://​dx.doi.org/​10.1002/​rcm.1012|Assonov & Brenninkmeijer,​ 2003}}) 
 + 
 +R<​sub>​17-Sample</​sub>​ and R<​sub>​13-Sample</​sub>​ may then be directly calculated:​ 
 + 
 +  * R<​sub>​17-Sample</​sub>​ = K × (R<​sub>​18-Sample</​sub>​)<​sup>​λ</​sup>​ 
 +  * R<​sub>​13-Sample</​sub>​ = R<​sub>​45-Sample</​sub>​ - 2R<​sub>​17-Sample</​sub>​ 
 + 
 +==== (3) Compute "raw" Δ values of your sample gas ==== 
 + 
 +**(3.a) "​Scramble"​ your sample gas** 
 + 
 +This means computing the abundance of each isotopologue of a gas with the same bulk composition as your sample, but in a stochastic state. This is done by following the steps (1.b) to (1.d) above: 
 + 
 +  * C<sub>12-Sample</​sub>​ = 1 / (1 + R<​sub>​13-Sample</​sub>​) 
 +  * C<​sub>​13-Sample</​sub>​ = R<​sub>​13-Sample</​sub>​ / (1 + R<​sub>​13-Sample</​sub>​) 
 +  * C<​sub>​16-Sample</​sub>​ = 1 / (1 + R<​sub>​17-Sample</​sub>​ + R<​sub>​18-Sample</​sub>​) 
 +  * C<​sub>​17-Sample</​sub>​ = R<​sub>​17-Sample</​sub>​ / (1 + R<​sub>​17-Sample</​sub>​ + R<​sub>​18-Sample</​sub>​) 
 +  * C<​sub>​18-Sample</​sub>​ = R<​sub>​18-Sample</​sub>​ / (1 + R<​sub>​17-Sample</​sub>​ + R<​sub>​18-Sample</​sub>​) 
 + 
 +Then (note the asterisk, here used to denote the stochastic state): 
 + 
 +  * Mass 44: 
 +    * C*<​sub>​12-16-16-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ 
 +  * Mass 45: 
 +    * C*<​sub>​13-16-16-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ 
 +    * C*<​sub>​12-17-16-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2 
 +  * Mass 46: 
 +    * C*<​sub>​12-18-16-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2 
 +    * C*<​sub>​13-17-16-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2 
 +    * C*<​sub>​12-17-17-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ 
 +  * Mass 47: 
 +    * C*<​sub>​13-18-16-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​16-Sample</​sub>​ × 2 
 +    * C*<​sub>​13-17-17-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ 
 +    * C*<​sub>​12-18-17-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × 2 
 +  * Mass 48: 
 +    * C*<​sub>​13-18-17-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​17-Sample</​sub>​ × 2 
 +    * C*<​sub>​12-18-18-Sample</​sub>​ = C<​sub>​12-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ 
 +  * Mass 49: 
 +    * C*<​sub>​13-18-18-Sample</​sub>​ = C<​sub>​13-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ × C<​sub>​18-Sample</​sub>​ 
 + 
 +Then: 
 + 
 +  * C*<​sub>​44-Sample</​sub>​ = C*<​sub>​12-16-16-Sample</​sub>​ 
 +  * C*<​sub>​45-Sample</​sub>​ = C*<​sub>​13-16-16-Sample</​sub>​ + C*<​sub>​12-17-16-Sample</​sub>​ 
 +  * C*<​sub>​46-Sample</​sub>​ = C*<​sub>​12-18-16-Sample</​sub>​ + C*<​sub>​13-17-16-Sample</​sub>​ + C*<​sub>​12-17-17-Sample</​sub>​ 
 +  * C*<​sub>​47-Sample</​sub>​ = C*<​sub>​13-18-16-Sample</​sub>​ + C*<​sub>​13-17-17-Sample</​sub>​ + C*<​sub>​12-18-17-Sample</​sub>​ 
 +  * C*<​sub>​48-Sample</​sub>​ = C*<​sub>​13-18-17-Sample</​sub>​ + C*<​sub>​12-18-18-Sample</​sub>​ 
 +  * C*<​sub>​49-Sample</​sub>​ = C*<​sub>​13-18-18-Sample</​sub>​ 
 + 
 +Ending up with the following "​stochastic abundance ratios":​ 
 + 
 +  * R*<​sub>​45-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​ 
 +  * R*<​sub>​46-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​ 
 +  * R*<​sub>​47-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​ 
 +  * R*<​sub>​48-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​ 
 +  * R*<​sub>​49-Sample</​sub>​ = C*<​sub>​45-Sample</​sub>​ / C*<​sub>​44-Sample</​sub>​ 
 + 
 +**(3.b) Compute raw Δ values** 
 + 
 +These Δ values are called "​raw"​ because they have not yet been corrected for a number of analytical artifacts. Most importantly,​ we have assumed that your reference gas is in a stochastic state, which is unlikely. This is why raw Δ<​sub>​47</​sub>​ values are typically underestimated by roughly the actual Δ<​sub>​47</​sub>​ value of your reference gas. 
 + 
 +  * rawΔ<​sub>​47</​sub>​ = 1000 × [ (R<​sub>​47-Sample</​sub>/​R*<​sub>​47-Sample</​sub>​ - 1) - (R<​sub>​46-Sample</​sub>/​R*<​sub>​46-Sample</​sub>​ - 1) - (R<​sub>​45-Sample</​sub>/​R*<​sub>​45-Sample</​sub>​ - 1) ] 
 +  * rawΔ<​sub>​48</​sub>​ = 1000 × [ (R<​sub>​48-Sample</​sub>/​R*<​sub>​48-Sample</​sub>​ - 1) - 2 × (R<​sub>​46-Sample</​sub>/​R*<​sub>​46-Sample</​sub>​ - 1) ] 
 +  * rawΔ<​sub>​49</​sub>​ = 1000 × [ (R<​sub>​49-Sample</​sub>/​R*<​sub>​49-Sample</​sub>​ - 1) - 2 × (R<​sub>​46-Sample</​sub>/​R*<​sub>​46-Sample</​sub>​ - 1) - (R<​sub>​45-Sample</​sub>/​R*<​sub>​45-Sample</​sub>​ - 1) ] 
 + 
 +({{http://​dx.doi.org/​10.1016/​j.gca.2005.08.021|Affek & Eiler, 2006}}) 
 + 
 +==== (4) Correct for non-linearity,​ stretching, and other effects ==== 
 + 
 +...using equilibrated CO<​sub>​2</​sub>​ standards prepared using various [[recipes]]. 
 + 
 +//(to be continued soon)//
data_processing.txt · Last modified: 2013/01/22 04:15 by mdaeron