A least-squares approach to mass transport calculations using the isocon method

Abstract

A statistically rigorous approach based on the isocon method (Grant, 1986) to evaluate mass transport is presented. Chemical analyses of multiple samples of unaltered (parent) and altered rock are used to calculate the average oxide or element concentration and its standard deviation for each rock population. In a typical application, the uncertainties in element concentration associated with the lack of homogeneity in each population outweigh the analytical uncertainty. An efficient algorithm is presented to select the immobile elements by identifying the maximum number of elements that are, within their uncertainties, compatible with the same isocon. The actual isocon is constructed by forcing a line through the origin and optimizing its slope using a weighted least-squares procedure for the selected immobile elements. Thus, individual uncertainties for each immobile element are taken into account. As an illustration, the procedure is applied to a published set of data on potassic and sericitic alterations of quartz monzonite of the Bingham porphyry copper system. The surprising result indicates that the apparent increase of potassic alteration phases is a consequence of acid leaching of calcium and sodium. No mass transport of potassium is indicated. Silica, water, and sulfur were added during alteration. The best fit isocon requires a small mass increase during each alteration process which, however, is within the uncertainty obtained for the slope of the isocon. A software package is available from the authors in the form of a FORTRAN 77 source code.