Abstract
Trace element concentration data can be used in a systematic way for the study of igneous processes by means of constructing models of such processes which satisfactorily account for the observations. We propose to treat the problem as an inverse problem. The concept of trace element paths (TEP) is introduced as a representation of the solution to the direct problem. The inverse problem consists of estimating, by a resolution of the equations, the various parameters of a model so as to provide a best fit to observed TEP. A detailed account of the theory is given in the case of equilibrium fractional crystallization. The estimated parameters are then those figuring in the Rayleigh distillation law, namely, 1) the initial concentrations of trace elements in the parental magma, 2) the bulk partition coefficients of the elements, and 3) the degree of crystallization corresponding to each sample of the magmatic suite analyzed.
A slightly generalized maximum likelihood method is used to solve the linearized equation by a stable, iterative algorithm. Information theory is then shown to yield an account of the distribution and flow of information during the process of solving the inverse problem. The concept of Data Importances is generalized, and its use in optimizing the study justified. The technique is successfully applied to a synthetic data set, and then illustrated on a data set from Terceira (Azores). The results are used to refine the conclusions reached in part I, and permit a more detailed discussion of the model.
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Now at Dept. Geological and Planetary Sciences, California Institute of Technology, Pasadena, Calif., USA
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Minster, J.F., Minster, J.B., Treuil, M. et al. Systematic use of trace elements in igneous processes. Contr. Mineral. and Petrol. 61, 49–77 (1977). https://doi.org/10.1007/BF00375945
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DOI: https://doi.org/10.1007/BF00375945