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  • Articles  (12)
  • structure  (7)
  • mineralogy  (6)
  • 1970-1974  (12)
  • Geosciences  (12)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Architecture, Civil Engineering, Surveying
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  • Articles  (12)
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  • 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
    Statistical analysis of tectonic patterns in areal volcanism: The bunyaruguru volcanic field in West Uganda (1971)
    Springer
    Mathematical geology 3 (1971), S. 335-355 
    Details
    ISSN: 1573-8868
    Keywords: nearest neighbor analysis ; regression analysis ; statistics ; trend analysis ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A quantitative analysis was made of the spatial arrangement of 149explosion craters in the western rift of Uganda. A variety of methods demonstrate that the spatial pattern of the craters reveals significant structural patterns that have guided volcanism to the surface. It is shown that the east-west elements in the field affected location, and the main rift fault is resolved into two main components. Tentatively, a possible dextral transform fault is identified that affected the relative location of the two main zones of activity. Grouping techniques demonstrate that crater groups obey an exponential rank-size rule and allow a mapping of the craters into energy classes that reveals a concentric pattern of energy in the field. The effect of the topography on energy levels and crater size show that only topography greater than 11,000ft could have prevented all eruptive activity, but the smaller energies and craters are sensitive to height differences on the order of the height of the rift wall, about 1000ft. Total energy in each crater class size is roughly constant, and the field energy could create one or two single craters comparable in size to small central volcanoes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083356
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  • 3
    Electronic Resource
    Electronic Resource
    Computer program to analyze directional data, based on the methods of Fisher and Watson (1972)
    Springer
    Mathematical geology 4 (1972), S. 177-202 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; factor analysis ; mapping ; statistics ; petrology ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Based on the methods of Fisher and Watson,Fortran iv computer programs are presented for the following analyses of directional observations on the sphere: (1) to determine if points are randomly distributed; (2) to estimate the azimuth and inclination of the center (mean direction) of a cluster and to estimate the precision (closeness) with which points are clustered; (3) to determine if two or more clusters have the same mean direction; (4) to determine if two clusters have the same precision of clustering; and (5) to locate the pole of a greatcircle girdle of points. Limitations of these analyses for undirected directional observations on the hemisphere also are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02311717
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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Spline-surface interpolation, spatial filtering, and trend surfaces for geological mapped variables (1973)
    Springer
    Mathematical geology 5 (1973), S. 111-126 
    Details
    ISSN: 1573-8868
    Keywords: contouring ; mapping ; trend analysis ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Spline surfaces are interpolated for top of the Dundee Limestone of the central Michigan Basin, USA. The requirement of gridded data render spline functions inappropriate tools for representing many types of geological mapped data. Comparisons are drawn with maps for the same Michigan data based on trend surfaces and spatial filtering.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111890
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  • 9
    Electronic Resource
    Electronic Resource
    Z-trend maps for quick recognition of geologic patterns (1971)
    Springer
    Mathematical geology 3 (1971), S. 171-181 
    Details
    ISSN: 1573-8868
    Keywords: Fourier analysis ; graphics ; mapping ; spatial filtering ; trend analysis ; stratigraphy ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Z-trend maps are a simplified lineprinter version of spatially filtered maps designed to give a quick visual appraisal of trends. The printout shows a “yes-no” configuration by a printed character or a blank so that the map has a conspicuous pattern. This pattern reflects the presence, position, and trend of the desired features. If a reasonable symbol density ratio is used the results can be visually pleasing thus enhancing trend recognition. Z-trending can be adapted to any map with stationary properties but is most easily applied to data that have been filtered with a bandpass operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045959
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  • 10
    Electronic Resource
    Electronic Resource
    Stratigraphic correlation of subsurface geologic data by computer (1972)
    Springer
    Mathematical geology 4 (1972), S. 331-343 
    Details
    ISSN: 1573-8868
    Keywords: cross correlation ; mapping ; plotting ; statistics ; stratigraphy ; structure ; electric logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Manual, semiautomatic, and fully automatic procedures for correlating subsurface data are reviewed. Special emphasis is placed on the use of electric-log data, including that of the dipmeter log, in this discussion. The Holgate method is described for its use in “fine-tuning” or refining gross correlations. A procedure for creating a matrix map for empirically establishing correlation between sets of data is described, and idealized models are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114094
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