The same formulation can be used for the interference monitors (particularly Ca) but further discussion of these will be deferred to Section 8 and Appendix A.Because the measurements are done simultaneously on all five detectors, any random variation in, say, the filament voltage or trap current will simultaneously affect all signals, resulting in correlated residuals. This assumption cannot be correct because both R and J are calculated using the same mass fractionation corrections, detector calibrations, interference corrections and radioactive decay corrections.The analytical uncertainty associated with each of these factors results in correlated errors between R and J.Partition coefficients between minerals and hydrous fluids as low as 10−6 lead fluid inclusions to dominate the radiogenic argon budget, particularly in low potassium minerals.Melt inclusions are less dominant but become critical in dating younger samples.To illustrate the profound implications of this point, consider the simple situation of a K-bearing sample containing neither Ca nor Cl.
The meaning of this equation and the significance of the subscripts will be elaborated in later sections of this paper.
Error correlations occur when calculating J-factors (Section 11) and, as we have already seen at the beginning of this section, when applying the J-factor to solve the age equation (Section 12).
Error correlations must also be taken into account when calculating the weighted mean of several in which ‘a’ stands for ‘air’, ‘ca’ for ‘Ca-salt’, ‘k’ for ‘K-glass’, and ‘cl’ for ‘Cl decay products’.
The zero value problem can be avoided by performing generalised linear regression of the ratios (using a logarithmic link function to ensure positive intercepts, Nelder and Wedderburn, 1972), or to cast the regression problem into a more sophisticated maximum likelihood form (Wood, 2015).
A comprehensive discussion of these alternative methods falls outside the scope of the present paper and will be deferred to a future publication.