USE OF LINEAR-PROGRAMMING IN THE ANALYSIS OF PETROLOGICAL MIXING PROBLEMS

Petrological mixing problems such as modal analysis, magma mixing, and liquid line of descent calculations, can be solved using the methods of linear programming. If estimates of the standard error of the chemical data are introduced as weights into the set of equations, it is possible to assign confidence limits to the solutions which are obtained and to apply formal statistical tests to geological hypotheses based on the mixing model. This approach is applied to petrological data previously analysed by Wright and Doherty (1970) using a combination of linear programming and least squares methods. It is shown that some of the geological inferences which they drew were based on an overoptimistic assessment of the confidence limits on their solutions, and cannot be regarded as proven. © 1979 Springer-Verlag.