The isocon diagram; a simple solution to Gresens' equation for metasomatic alteration

Gresens' (1967) method of analysis of changes in volume and concentrations during metasomatism have been applied in many studies of hydrothermal alteration. This paper provides a simple method of solution of Gresens' equations, for both volume (or mass) change and concentration changes, one which requires no significant manipulation of analytical data and is readily accomplished both graphically and on a computer spreadsheet. Gresens' equation is rearranged into a linear relationship between the concentration of a component in the altered rock and that in the original. Simultaneous solution of such equations for all components that show no relative gain or loss of mass defines an "isocon." On a graph of the concentrations in the altered rock against those in the original, an isocon is a straight line through the origin. The slope of the isocon defines the mass change in the alteration, and the deviation of a data point from the isocon defines the concentration change for the corresponding component. As is shown, this can be applied to several stages of alteration simultaneously, and to other kinds of mass transfer such as migmatization.