Portal de Periódicos da CAPES

Linked evolutionary data arrays: A logical structure for petrologic modeling of multisource, multiprocess magmatic systems

1986; American Geophysical Union; Volume: 91; Issue: B6 Linguagem: Inglês

10.1029/jb091ib06p05891

2156-2202

W. B. Bryan,

Mineral Processing and Grinding

Models of multiprocess, open magmatic systems can be tested in a stepwise procedure in which two‐dimensional data arrays representing a single stage in the set of processes are linked to a specific member of another array that represents either a preceding or a subsequent step in the model. Data within each array may be ordered according to variation in one or more components known or inferred to be especially sensitive to the process in question. In some cases, several processes operating concurrently, such as mixing plus crystal fractionation, can be accommodated within a single array. The essential steps in organizing data and testing models are (1) grouping sample data according to their assumed association with each process; (2) ordering of data within each array to reflect the “degree of evolution” or the extent to which the process has operated; and (3) defining the composition or compositions that represent the “branch points” linking each array to other arrays representing a previously completed or a subsequent process. This leads to a conceptual structure of linked evolutionary arrays, which collectively relate the starting and final compositions of a given magmatic system. Variation within major element data arrays and the linkage between them can be tested using an extension of the least squares algorithm, which selects the “best” branch point according to the minimum sum of squared residuals criterion. These capabilities have been incorporated in a program called MULTIFIT, written in Microsoft BASIC for use in an IBM or compatible microcomputer. A subroutine based on the Rayleigh equations permits evaluation of trace element variation consistent with the best major element result. It is emphasized that, while MULTIFIT utilizes concepts that are familiar to most petrologists and geochemists, and can be applied to a variety of problems, it may not be the best approach for poorly constrained models involving partial melting or complex mixing. An adaptation of inverse modeling methods may be more appropriate for such problems. Advantages and disadvantages of the materials balance approach used in MULTIFIT are discussed, a simple example is given, and the equations utilized by MULTIFIT are summarized. It is shown that an extension of the same concept may be useful for defining trace element partition coefficients in magmatic systems.