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MagPath: An Excel-based Visual Basic program for forward modeling of mafic magma crystallization

2011; Elsevier BV; Volume: 37; Issue: 11 Linguagem: Inglês

10.1016/j.cageo.2011.02.017

1873-7803

Kyle R. Mayborn, Charles E. Lesher,

Statistical and numerical algorithms

Mass balance calculation is a fundamental approach in geosciences. In petrology and geochemistry, it is widely used for quantitative characterization of phase transition and mass transfer. In a routine petrological practice, this method is commonly used to calculate proportions of the minerals formed from initial or parental bulk composition, or to quantify the reaction coefficients for minerals involved in a chemical reaction that achieves equilibria. In this paper, we present a new mass balance calculation program, GeoBalance, which is written with Visual Basic for Applications (VBA) and built in a macro-enabled Excel™ worksheet. The working algorithm is based on solving the least square problem using pseudo-inverse of matrix and singular value decomposition (SVD) of matrix. Both unconstrained and constrained solution methods are implemented in the program and can be chosen by the user. In addition, input data (e.g. compositions of the minerals) can be different data types, such as cations, oxides, moles of oxides, or moles of mineral endmembers. As a result of calculation, phase proportions are presented as percentages on 100%-normalized basis with residuals (for each chemical component), and a sum of squared estimate of errors (SSE). Monte Carlo simulation of error propagation for evaluating calculation uncertainty is also implemented as an optional function. An additional advantage of our program is that it enables users to perform mass balance calculations for complicated systems with a flexible number of phases and/or chemical components.