Estimating Proportions in Petrographic Mixing Equations by Least-Squares Approximation

Petrogenetic hypotheses involving fractional crystallization, assimilation, or mixing of magmas may be expressed and tested as problems in leastsquares approximation. The calculation uses all of the data and yields a unique solution for each model, thus avoiding the ambiguity inherent in graphical or trial-and-error procedures. The compositional change in the 1960 lavas of Kilauea Volcano, Hawaii, is used to illustrate the method of calculation.