Skip to content

E. Step 3: Interpolated ratios

Jump to bottom
sbodorkos edited this page Mar 20, 2017 · 3 revisions

Calculation of interpolated ratios of measured species

The next step is to calculate 'isotopic ratios', which in this context refers strictly to ratios in which both the numerator and the denominator correspond to species which have been directly measured as part of the SHRIMP data acquisition process. The following routine expects the index of the species constituting the numerator (denoted NUM) and the index of the species constituting the denominator (denoted DEN) to be defined. Indices from 1 to Nspecies are based on the order (within a scan) in which the species were acquired during analysis, which by convention (but not compulsorily) is in order of increasing mass within a scan. In the demo XML, species 196(Zr2O) has index 1 because it was acquired first, 204Pb = 2, background = 3, 206Pb = 4, 207Pb = 5, ..., 270(UO2) = 10.

The list of isotopic 'ratios of interest' is user-specified in SQUID, but is hard-wired here for prototyping purposes. The SQUID processing of the demo XML used a 'recipe' in which 10 'ratios of interest' were defined (this has nothing to do with the fact that Nspecies = 10 in the demo XML: just a coincidence), as follows (see columns T–AM on the worksheet 'StandardData' in the SQUID-book 100142_G6147_original_frozen.xls):

  • 204Pb/206Pb (i.e. NUM = 2, DEN = 4; an example where DEN > NUM: see below)
  • 207Pb/206Pb (i.e. NUM = 5, DEN = 4; an example where NUM > DEN: see below)
  • 208Pb/206Pb (i.e. NUM = 6, DEN = 4)
  • 238U/196(Zr2O) (i.e. NUM = 7, DEN = 1)
  • 206Pb/238U (i.e. NUM = 4, DEN = 7)
  • 254(UO)/238U (i.e. NUM = 9, DEN = 7)
  • 248(ThO)/254(UO) (i.e. NUM = 8, DEN = 9)
  • 206Pb/270(UO2) (i.e. NUM = 4, DEN = 10)
  • 270(UO2)/254(UO) (i.e. NUM = 10, DEN = 9)
  • 206Pb/254(UO) (i.e. NUM = 4, DEN = 9)

Note that there is no significance in the sequence of the 'ratios of interest' specified above; it simply reflects a user-tendency to look at the lower-mass species at the top of the SHRIMP analytical run-table before looking at the higher-mass species at the base.

For each analysis, we need three sets of data calculated in Step 2, and a further two harvested directly from the XML:

  1. NetPkCps from Step 2, as an array of size [Nscans, Nspecies] i.e. 6 x 10 in the demo XML
  2. SBMcps from Step 2, as an array of size [Nscans, Nspecies] i.e. 6 x 10 in the demo XML
  3. PkFerr from Step 2, as an array of size [Nscans, Nspecies] i.e. 6 x 10 in the demo XML
  4. time_stamp_sec from XML, as an array of size [Nscans, Nspecies] i.e. 6 x 10 in the demo XML
  5. count_time_sec from XML, as a vector of length [Nspecies] i.e. 10 in the demo XML

These calculations are outlined in detail here.

Calamari CSV (SQUID_03…)

In Calamari, these calculations culminate in the Calamari CSV file ‘SQUID_03…”, which is an array matching as closely as possible the ‘Within-Spot Ratios’ worksheet of a SQUID-workbook. The CSV has one row per ‘interpolated time’ (i.e. ‘Ndod’, where Ndod = Nscans – 1), and 3 columns per predefined ‘ratio of interest’ (comprising interpolated time, ‘ratio of interest’ value, and 1sigma absolute error in the ratio-value). Its structure is described in detail here.

Value-by-value comparisons of the Step 3 outputs from SQUID 2.50 and Calamari for a specified demonstration XML file are documented at G. Synthesis of Steps 1–4: Cell-by-cell comparisons of SQUID 2.50 and Calamari output.

Next: F. Step 4: Calculation of 'mean' ratio for each measured species for each analysis

Clone this wiki locally