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  • Articles  (6)
  • mineralogy  (6)
  • Springer  (6)
  • American Meteorological Society
  • 1970-1974  (6)
  • Geosciences  (6)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Energy, Environment Protection, Nuclear Power Engineering
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  • Articles  (6)
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  • Springer  (6)
  • American Meteorological Society
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Year
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  • Geosciences  (6)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Energy, Environment Protection, Nuclear Power Engineering
  • Mathematics  (6)
  • 1
    Electronic Resource
    Electronic Resource
    An empirical discriminant method applied to sedimentary-rock classification from major-element geochemistry (1971)
    Springer
    Mathematical geology 3 (1971), S. 51-60 
    Details
    ISSN: 1573-8868
    Keywords: entropy ; principal components analysis ; geochemistry ; mineralogy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Classification of sandstones, greywackes, pelites, limestones, dolomites, and acid-igneous and basicigneous rocks, using a literature sample of 183 post-1920 analyses for the 11 major oxides has achieved an 80-percent success rate. The method is based on nonparametric estimation of a probability density function for each category to be classified, using the Bayes decision rule. The method is suitable for use with small training sets and gives much improved results over a linear discriminant function. Classification following data compression using principal components also has given satisfactory recognition rates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047432
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  • 2
    Electronic Resource
    Electronic Resource
    Counting error in petrographic point-count analysis: A theoretical and experimental study (1971)
    Springer
    Mathematical geology 3 (1971), S. 15-41 
    Details
    ISSN: 1573-8868
    Keywords: modal analysis ; sampling ; statistics ; mineralogy ; petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The binomial model, commonly used to estimate counting error in point-count analysis, misestimates this error when the observation points on a grid are positively or negatively correlated. A model, called the “cell model,” is proposed as an alternative to the binomial model for use in studies, especially with coarse-grained rocks, in which such correlation is known or thought to exist. In the new model the thin section is conceptually partitioned into a number of cells (six is recommended), and the assumption is made that the proportions in the individual cells are statistically independent and that their variance does not differ from cell to cell. Empirical relations obtained from a suite of 200 thin sections of limestones are in reasonable support of the prediction that large particle size adversely affects counting error estimates based on the binomial model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047430
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  • 3
    Electronic Resource
    Electronic Resource
    Effect of trends on correlation in open and closed three-component systems (1972)
    Springer
    Mathematical geology 4 (1972), S. 317-330 
    Details
    ISSN: 1573-8868
    Keywords: linear correlation ; mapping ; trend analysis ; general geology ; mineralogy ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is well known among geologists that closure of an open-number system, as when stratigraphic rock thicknesses are converted to percentages, introduces correlations among the components even in the absence of correlations in the open system. In closed three-component systems the covariances are single-valued functions of the closed variances and are exactly predictable. If the open system has “inherent” correlation (point correlations) among its components the corresponding closed covariances reflect their presence in a predictable manner. If areal trends are present in the open system, the open covariances are themselves affected, but this “trend effect” can be completely removed to recover the initial point correlations among the components. Areal trends in open systems strongly influence the structure of the closed variance-covariance matrices, and the situation becomes increasingly complicated if the open system has both point correlations and areal trends. The paper considers the problems involved, and includes Monte Carlo runs to compare computed and predicted variances and covariances as data sets are followed from open systems with correlation but no trend to the closed equivalent of open systems with point correlations and trends.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114093
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  • 4
    Electronic Resource
    Electronic Resource
    Quantitative discrimination between magmatic units of the singhbhum granite (1971)
    Springer
    Mathematical geology 3 (1971), S. 123-133 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; distance functions ; mineralogy ; petrology ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The weight-percent values of four mineralogic variables (quartz, K feldspar, color index, and muscovite) for 10 sets of granitic rocks (20–50 samples in each set) from magmatic units of the Singhbhum granite were used for (1) computation of the Mahalanobis' generalized distance functions (D 2) between all pairs of the 10 sets, (2) testing significance of the difference between the multivariate means, and (3) computation of the linear discriminant functions between all possible pairs of the sets. The 10 data sets are for six magmatic units which belong to three successive but closely related phases of emplacement. The multivariate means for all sets are significantly different except for those between two of the sets of phase I. Cluster analysis on the basis of theD 2 values enables the 10 sets to be placed into four distinct groups. Group A includes two subgroups, one of which consists of two sets representing typical members of phase I; the other subgroup includes two sets which are typical of phase II. Group B includes two sets which are typical of phase III. The other four sets do not group with the typical representatives of the three phases, probably because of certain special conditions of their emplacement. A separate series ofD 2 computation from the same data, but excluding the color index, was unsuccessful in making the four aberrant sets group with the typical members of the respective phases. Efficient LDF's could be determined for discrimination between most pairs of the 10 sets of granite rocks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045956
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  • 5
    Electronic Resource
    Electronic Resource
    Trend-surface analysis of distribution of some heavy minerals in shelf sediments off Mangalore, India (1972)
    Springer
    Mathematical geology 4 (1972), S. 277-290 
    Details
    ISSN: 1573-8868
    Keywords: trend analysis ; mineralogy ; oceanography ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The mineralogy of the 0.062–0.125 and 0.125–0.25 mm fractions of 58 selected samples from a set of 78 samples collected at a spacing of 1–2 km in the inner shelf of Mangalore were studied. Trend-surface analysis of distribution of the heavy minerals, hornblende, muscovite, garnet, and sillimanite, were made to determine the various factors controlling the mineral-distribution patterns in the area. Parts of the area showing contrasting environments were analyzed separately to determine the relationship of the regional and local trends and the various factors controlling the trends. The linear, quadratic and cubic trends for hornblende, garnet, and sillimanite were controlled by the source, westerly river flow and southerly currents; for mica, the response to processes has been the main factor. The mineral distribution in this area is mainly the result of dynamic interaction of process and response elements and a process-response model is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114090
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  • 6
    Electronic Resource
    Electronic Resource
    Operator error in petrographic point-count analysis: A theoretical approach (1972)
    Springer
    Mathematical geology 4 (1972), S. 35-43 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; sampling ; statistics ; mineralogy ; petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Operator error in petrographic point-count analysis introduces bias into the estimates of proportion in a thin section. A correction for this bias, leading to an unbiased estimator of the true proportion in that thin section, is here proposed. Operator error also affects the confidence interval, and in this situation, too, an adjustment is possible. The approach proposed requires that the probabilities associated with operator error, categorized into A-type and B-type errors, are known or assumed. The A-type operator error tends to underestimate the true proportion in a thin section, whereas the B-type operator error tends to overestimate it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083191
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