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Preliminary assessment of a nonlinear mapping algorithm in a geological context (1973)

Howarth, R. J.

Springer

Mathematical geology 5 (1973), S. 39-57

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ISSN: 1573-8868

Schlagwort(e): classification ; cluster analysis ; dimensionality reduction ; mapping ; multivariate analysis ; principal-components analysis ; general geology ; geochemistry ; paleontology ; petrology ; stratigraphy

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract A new algorithm has been developed by J. W. Sammon for the nonlinear-point mapping of high-dimensional data in two dimensions such that the inherent structure of the data is approximately preserved. This paper describes results using several sets of geologic data including stratigraphic thickness, petrographic modal analysis, and morphological or geochemical measurements. Comparisons are made with hierarchical cluster analysis using dendrogram representation. Initial results are encouraging and suggest that the technique could have widespread geological applications.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02114086

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Digitale Medien

Thoughts on use of principal component analysis in petrogenetic problems (1973)

Till, Roger ; Colley, Howard

Springer

Mathematical geology 5 (1973), S. 341-350

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ISSN: 1573-8868

Schlagwort(e): principal components analysis ; geochemistry ; petrology

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract The use of principal component analysis in studying chemical trends in volcanic rock suites is described. It is suggested that eigenvectors generated from a correlation matrix, rather than a covariance matrix, could be used in this context. In the latter situation many elements are swamped by silicon's numerical size and range. In the former situation the alkalies and titanium begin to show their true importance.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02111985

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Estimation of parameters in petrologic materials balance equations (1973)

Gray, N. H.

Springer

Mathematical geology 5 (1973), S. 225-236

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ISSN: 1573-8868

Schlagwort(e): estimation ; materials balance ; mathematics ; mixing equations ; geochemistry ; petrology

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract A rigorous treatment of the least-squares estimation of the parameters in petrologic materials balance equations is developed to take into account the uncertainties inherent in the chemical analyses. The choice of the optimal estimation procedure for a particular problem is dependent upon the extent of the petrogenetic understanding of the exact nature of the materials balance involved. Some of the complications entailed in obtaining least-squares estimates are illustrated by the examples of magmatic differentiation and metamorphic reactions.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02111812

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A geomathematic investigation of syntexis in a Gabbroic formation (1973)

Potenza, Roberto

Springer

Mathematical geology 5 (1973), S. 321-339

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ISSN: 1573-8868

Schlagwort(e): factor analysis ; Fourier analysis ; mapping ; petrology

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geologie und Paläontologie , Mathematik

Notizen: Abstract Mathematical methods were employed in an investigation of syntexis in the “Gabbro di Sondalo,” a mafic igneous formation in the Central Alps (Italy). A set of 100 specimens was selected according to sampling criteria and analyzed by X-ray fluorescence for eight elements; Q-mode and R-mode factor analysis then was applied to these data. Results of the computations indicate that the general trend of differentiation is related to the syntexis of gneissic wall rocks (“Gneiss del Monte Tonale”) in the mafic melt. Ca and Mg are abundant in the gabbro, and Si and K in the gneiss; the independent variation trend of Fe and Ti may be related to a differentiation episode due to a magmatic phase. Spatial representation of multivariate data on differentiation also was performed on the main elements and a picture of the trend of syntexis was mapped.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02111984

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