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

TLDR

Gresens' (1967) method for analyzing volume and concentration changes during metasomatism has been widely used in hydrothermal alteration studies. This paper offers a straightforward solution to Gresens' equations that requires minimal data manipulation and can be performed graphically or via spreadsheet. By rearranging Gresens' equation into a linear relationship between altered and original component concentrations, simultaneous solutions for all mass‑conserving components define an isocon. The isocon appears as a straight line through the origin on a concentration plot, with its slope indicating mass change and point deviations revealing component concentration changes, and it can be applied to multiple alteration stages and other mass‑transfer processes such as migmatization.

Abstract

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.