normalize.ratios: Normalize isotope amount ratios to a common reference isotope

In CIAAWconsensus: Isotope Ratio Meta-Analysis

Description

This function converts the isotope amount ratios of an element from various studies to a single common reference isotope so that all isotope ratios can be directly compared to one another. The conversion involves a direct application of the law of propagation of uncertainty and this function discards the possible covariances between the isotope ratios.

Usage

normalize.ratios(dat, element, ref.isotope, expand = FALSE)

Arguments

dat	A data frame of results from each study where each study reports one or more isotope ratios (outcomes). The data frame must include the following named columns: Study, Year, Author, Outcome, Value, Unc, k_extra (see Details).
element	Lowercase english name of the element, e.g., "antimony"
ref.isotope	Desired reference isotope, e.g., "121Sb"
expand	(Logical) Specification of whether or not to expand the isotope ratio uncertainties using the values of dat$k_extra

Details

The isotope ratio vector R is transformed to the reference isotope R_{ref} by dividing each element of the set to the chosen reference isotope. The covariances of the transformed isotope ratios are obtained using the Law of Propagation of Uncertainty. This function assumes all isotope ratios reported by a given study as uncorrelated. While this is not strictly true in practice, such assumption is made largely because of the lack of reported correlations in the literature.

The format of dat data frame for a simple dataset is as follows:

Study	Year	Author	Outcome	Value	Unc	k_extra
1	1954	Howard	191Ir/193Ir	0.5949	0.0025	9
2	1991	Creaser	191Ir/193Ir	0.5948	0.0001	9
3	1992	Chang	191Ir/193Ir	0.59399	0.00103	6
4	1993	Walczyk	191Ir/193Ir	0.59418	0.00037	9
5	2017	Zhu	191Ir/193Ir	0.59290	0.00021	6

Value

R	A list of the normalized isotope amount ratios
u.R	A list of standard uncertainties for R
cov.R	A list of covariance matrices for R (forced to zero covariances)

Author(s)

Juris Meija <[e-mail]> and Antonio Possolo

References

J. Meija and Z. Mester (2008) Uncertainty propagation of atomic weight measurement results. Metrologia, 45, 53-62

J. Meija and A. Possolo (2017) Data reduction framework for standard atomic weights and isotopic compositions of the elements. Metrologia, 54, 229-238

Examples

## Normalize all platinum isotope data to platinum-195
normalize.ratios(platinum.data, "platinum", "195Pt")

Example output

$R
                  190Pt/195Pt 192Pt/195Pt 194Pt/195Pt 196Pt/195Pt 198Pt/195Pt
1956-White        0.000375700  0.02307700   0.9733730   0.7455620   0.2127220
1996-Taylor       0.000403000  0.02313400   0.9744450   0.7460980   0.2117400
2002-Wolff-Briche 0.000347374  0.02316166   0.9731083   0.7464467   0.2178755
2013-Creech       0.000381609  0.02349274   0.9710152   0.7485168   0.2163033

$u.R
                  190Pt/195Pt 192Pt/195Pt  194Pt/195Pt  196Pt/195Pt
1956-White        1.48000e-05 2.45000e-04 0.0055500000 0.0043400000
1996-Taylor       2.00000e-06 1.00000e-06 0.0000330000 0.0000080000
2002-Wolff-Briche 1.71991e-05 2.31531e-04 0.0055131280 0.0040929650
2013-Creech       1.89459e-06 1.32394e-05 0.0001650023 0.0004318382
                   198Pt/195Pt
1956-White        0.0011400000
1996-Taylor       0.0000130000
2002-Wolff-Briche 0.0012713790
2013-Creech       0.0003611509

CIAAWconsensus documentation built on May 2, 2019, 3:33 p.m.