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  • Articles  (18)
  • geochemistry  (18)
  • 1975-1979  (18)
  • 1965-1969
  • 1945-1949
  • Geosciences  (18)
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  • Articles  (18)
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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of multivariate point distributions and chemical grouping of rocks (1975)
    Springer
    Mathematical geology 7 (1975), S. 191-214 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; mapping ; multivariate analysis ; pattern recognition ; point-density analysis ; geochemistry ; ore-bearing districts
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Large sets of rock compositions can be grouped by the analysis of corresponding point distributions in multidimensional space, where the separate dimensions represent the chemical variables. The point density around each composition is estimated in a small, multivariate, rectangular interval. Establishment of the identity of specimens contained in the interval, and systematic comparison of the point densities surrounding each of them, leads to the recognition of density maxima, which represent the statistical modes of the rock types present in the set. The remaining specimens by the same operations can be assigned to the groups formed. Experimental results are given for two sets, one comprising a wide variety of metasedimentary and metavolcanic rocks from the ore-bearing Skellefte district and adjacent parts of Västerbotten, Sweden, and the other representing a less variable population of basic rocks from Norrbotten, Sweden. Linear discriminant analysis and existing geological information indicate that the groups obtained are statistically and geologically valid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02312721
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  • 2
    Electronic Resource
    Electronic Resource
    Dynamical formulation of Broecker's model for marine cycles of biologically incorporated elements (1976)
    Springer
    Mathematical geology 8 (1976), S. 511-527 
    Details
    ISSN: 1573-8868
    Keywords: analogcomputer simulation ; systems analysis ; geochemistry ; oceanography
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Broecker presented a steady-state, two-box model which emphasizes the role of kinetic factors in determining the chemical composition of sea water. Unlike thermodynamic models, Broecker's model suggests that sizable temporal variation in the composition of sea water and rates of sedimentation may have taken place in the past 100 million years. To describe the evolution of the ocean's chemical system and interpret variations observed in the sedimentary record, we have formulated a dynamical model. Mass-balance consideration leads to a set of coupled nonlinear differential equations. The equations are linearized and solved for step function changes in the rate of river input and in the rate of vertical mixing. This simple model of the ocean's chemical system is shown to be stable against oscillations. Using data for the modern ocean, the response times for P, C, Si, Ca, and Ba are calculated to be of the order of 104 to 106 yr for changes in river and other inputs and of the order 101 to 102 yr for a change in the rate of vertical mixing. Analog-simulation techniques, discussed for the situation of the two-box model, provide a powerful tool for treating nonlinearities and systems with more than two components. In the final section, consequences of the dynamical formulation are compared with parameters appearing in Broecker's steady-state formulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01042991
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  • 3
    Electronic Resource
    Electronic Resource
    Mineral variation in anorthositic, troctolitic, and adamellitic rocks of the Barth Island layered structure in the Nain anorthosite complex, Labrador (1976)
    Springer
    Mathematical geology 8 (1976), S. 561-574 
    Details
    ISSN: 1573-8868
    Keywords: regression analysis ; trend analysis ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The Barth Island layered structure is an oval, 6 by 9 km body, consisting of rhythmically layered adamellitic rock in the center which grades outward through jotunite into troctolite. Farther outward the sequence repeats itself in reversed order, strongly reduced in magnitude and finer grained; the adamellitic zone is followed by jotunite which grades into coarse-grained leuconorite and into anorthosite of the Nain complex. The Barth Island structure, having an inverted conical base topped by a hemispherical depression, seems to represent a distorted sequence of rock layers with troctolite at the bottom, grading upward into adamellitic rocks which grade into anorthosite at the top. Trend-surface analysis demonstrates the regional variation of plagioclase and orthopyroxene compositions in the troctolite—adamellite sequence of the central part of the structure. The fits for the second- and third-degree surfaces are good and significant at the 99 percent level. The regression line for compositional variation in coexisting plagioclase and orthopyroxene in all analyzed rocks has a correlation coefficient of r2 = 0.78. The difference between the trends in the troctolite—adamellite sequence and the anorthosite—adamellite sequence is insignificant. The regression curve for compositional variation in coexisting orthopyroxene and olivine has a correlation coefficient of r2 = 0.98. The curve shows good correlation with the experimentally established partitioning curve of Medaris, which indicates that equilibrium conditions prevailed during formation of the olivine—ortho-pyroxene pairs. The results suggest that the troctolite—adamellite sequence and the anorthosite—adamellite sequence are products of fractional crystallization, possibly from the same parental magma.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01042994
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  • 4
    Electronic Resource
    Electronic Resource
    Application of correspondence factor analysis to the study of major and trace elements in the Erta Ale Chain (Afar, Ethiopia) (1975)
    Springer
    Mathematical geology 7 (1975), S. 13-30 
    Details
    ISSN: 1573-8868
    Keywords: correspondence analysis ; factor analysis ; geochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The lavas in the active volcanic chain of the Erta Ale were emplaced 1 million years ago on the new crust of oceanic character created by the separation of the Arabic plate and the African plate. This differentiated series ranges from the basalts to the hyperalkaline rhyolites, passing through all the intermediate members. It is characterized by an iron enrichment in the intermediate series, and the role of silica is secondary in the differentiation which is controlled by the fractionation of olivine, pyroxene, and calcic plagioclases. By applying correspondence factor analysis to the rock samples analyzed for major and trace elements, factors were found expressing the importance of certain associations between the samples and their elements. The variables were projected onto factorial axes and graphs were plotted automatically showing their positions. Ellipses corresponding to the groups based on the rock types, volcanoes, and the indices of Kuno were drawn so that their situation in relation to the oxides and trace elements could be seen. From the plan of the axes, the degree of differentiation of the samples in the considered series is indicated, and the petrological terminology of the rocks may be verified. Two graphs, representing the series, are proposed using indices for the oxides and traces obtained from the results of correspondence analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080631
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  • 5
    Electronic Resource
    Electronic Resource
    On the need, design, and prospects for an electronic information system serving igneous petrology (1975)
    Springer
    Mathematical geology 7 (1975), S. 363-371 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An information system is needed to restore access to published information, now so voluminous that suitable levels of familiarity with it cannot be maintained by conventional nonelectronic scholarly devices. The services of the system should be available to petrologists via mail or remote terminal, and should provide, as requested, either retrieval or reduction of data contained in its base. The base should contain chemical, geological, mineralogical, and petrographic information about specimens for which full descriptions have been published. Provisional plans for construction of such a base are briefly reviewed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080495
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  • 6
    Electronic Resource
    Electronic Resource
    Principal components analysis using the hypothetical closed array (1976)
    Springer
    Mathematical geology 8 (1976), S. 25-36 
    Details
    ISSN: 1573-8868
    Keywords: principal components analysis ; closure correlations ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The application of R-mode principal components analysis to a set of closed chemical data is described using previously published chemical analyses of rocks from Gough Island. Different measures of similarity have been used and the results compared by calculating the correlation coefficients between each of the elements of the extracted eigenvectors and each of the original variables. These correlations provide a convenient measure of the contribution of each variable to each of the principal components. The choice of similarity measure (variance-covariance or correlation coefficient)should reflect the nature of the data and the view of the investigator as to which is the proper weighting of the variables—according to their sample variance or equally. If the data are appropriate for principal components analysis, then the Chayes and Kruskal concept of the hypothetical open and closed arrays and the expected closure correlations would seem to be useful in defining the structure to be expected in the absence of significant departures from randomness. If the data are not multivariate normally distributed, then it is possible that the principal components will not be independent. This may result in significant nonzero covariances between various pairs of principal components.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01039682
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  • 7
    Electronic Resource
    Electronic Resource
    An abundance model resource appraisal for some Canadian commodities (1978)
    Springer
    Mathematical geology 10 (1978), S. 481-494 
    Details
    ISSN: 1573-8868
    Keywords: geochemistry ; crustal abundance ; resource analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An abundance model resource appraisal has been undertaken for 10 mineral commodities in Canada: nickel, copper, zinc, lead, molybdenum, uranium, silver, gold, chromium, and tin. The purpose of the appraisal was to investigate the applicability of the model to the Canadian situation. Resource appraisals for the first 6 of the commodities studied have been published following deposit modeling studies. For many other commodities studied have been published following deposit modeling appraisals. The demonstration of the relevance of the abundance model to Canada would allow its application in such cases. The data presented in this paper indicate that the approximate relation, resource (short tons)=abundance (%)×1010. holds true for all commodities studied except chromium and tin. As the resources versus abundances relationship observed on a global scale is observable in Canada, it is concluded that Canada is a sufficiently large fraction (∼7%) of the earth's continental crust to represent a valid sample of that crust. Canada appears to be relatively well endowed with resources of copper, molybdenum, lead, and zinc, and poorly endowed with chromium and tin. It is proposed that the intersection of national boundaries with the boundaries of the world's metallogenic provinces is of greater importance than the intensity of past search, a feature that has been suggested in other studies. If these areas overlap, a nation may be self sufficient in a commodity: if they do not, the nation must import, or find a nationally available substitute. The sources of information used in the appraisal are outlined together with an analysis of the problems encounterea and the time requirements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461979
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  • 8
    Electronic Resource
    Electronic Resource
    Application of a generalized power transformation to geochemical data (1979)
    Springer
    Mathematical geology 11 (1979), S. 45-62 
    Details
    ISSN: 1573-8868
    Keywords: geochemistry ; frequency distributions ; data transformation ; algorithm ; FORTRAN
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract In the context of analysis of variance, Box and Cox (1964) developed a generalized technique for power transformation of frequency distributions to normality. It is here applied to geochemical data, based on the nonlinear optimization of skewness and kurtosis. The transform appears to be particularly well suited to the preprocessing of geochemical data prior to multivariate analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01043245
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  • 9
    Electronic Resource
    Electronic Resource
    Correspondence factor analysis: An outline of its method (1975)
    Springer
    Mathematical geology 7 (1975), S. 3-12 
    Details
    ISSN: 1573-8868
    Keywords: correspondence analysis ; factor analysis ; mathematics ; principal components ; geochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Correspondence factor analysis is a multivariate technique that may be applied to any type of data and to any number of data points. It detects associations and oppositions existing between subjects and objects, measuring their contribution to the total inertia for each factor. The probabilistic character of the data matrix is taken into consideration, and together with the principle of distributional equivalence, results in stability. The projection of the subjects and the objects onto the same set of factorial axes enables two-dimensional graphs to be drawn which offer aid in the interpretation of the results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080630
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  • 10
    Electronic Resource
    Electronic Resource
    Association of proportions (1975)
    Springer
    Mathematical geology 7 (1975), S. 63-73 
    Details
    ISSN: 1573-8868
    Keywords: crossassociation ; crosscorrelation ; proportions ; geochemistry ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Simple correlation leads to misleading results when applied to the proportions of materials in mixtures, because of the constraint that the total of the proportions is less than one. A simple mainly graphical procedure to determine whether the proportions in mixtures are associated after allowing for the constraint is presented. No assumptions about the form of the underlying probability distributions are required. The technique is extended to problems where other constraints apply.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080634
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