3-D Plane-fitting Program in 40Ar/39Ar Dating
Date Issued
2007
Date
2007
Author(s)
Wu, Chieh-Yu
DOI
zh-TW
Abstract
In an ideal K-Ar isotopic systematics, the measured concentrations of three argon isotope (36Ar, 39Ar, 40Ar) would satisfy a plane equation: 40Ar =α36Ar + β39Ar. In other words, the sample data should lie close to a plane in three-dimensional, XYZ space. If analytical errors are responsible for the scatter of data points on the 36Ar-39Ar-40Ar isotope correlation plot, the regression plane can be fitted using two steps. First, we employ matrix algebra to lay out the method of maximum likelihood for fitting a plane equation between any number of variables in the equation, all subject to analytical errors with known variances and covariances, although these may vary among the data points. In addition, the well-known Newton-Raphson method can subsequently be adopted in optimization. Secondly, in order to examine the maximum likelihood method of regression and to determine the standard errors of the parameters of a best-fit plane, the efficient-accurate methods can access standard errors, goodness-of-fit parameter, and MSWD (mean square weighted deviate) value. If the data are well fitted to the regression plane, the estimates of regression parameters α and β, will lead to estimates of the trapped argon composition and the radiometric age for sample.
To publish the above efficient algorithms and easy-to-use method, the present project designs a user-friendly Matlab-based graphical program, namely ArArPLOT, to perform the methods in age calculation and their corresponding diagrams (isotope abundance diagrams, isotope correlations diagrams) for 40Ar/39Ar geochronological studies. The program is portable between computer operating systems supported by Matlab. The major benefit of this program is capable of clarifying whether the data points from a single sample representing different isotopic systematics, using plane fitting methods in XYZ space, as mentioned above.
In contrast to 2-D isotope correlation diagrams which utilize projection technique, this 3-D plane fitting program exhibits the following advantages: (1) it allows to clearly display the spatial relation of data points, and to improve the precision of error calculations; (2) it can be used as means in clarifying different isotopic systematics in sample; (3) the interpretation of isotope abundance diagrams becomes much easier because of better visualization of data distribution in 3-D space. In summary, the current project successfully designs a user-friendly program which is powerful in data analysis in 40Ar/39Ar geochronology and is potentially useful to data analyses of other isotopes in compositional space.
Subjects
氬氬定年法
Ar-Ar dating
Type
thesis
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