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  • Articles  (24)
  • cluster analysis  (12)
  • sampling  (7)
  • structure  (7)
  • 1970-1974  (24)
  • Geosciences  (24)
  • Architecture, Civil Engineering, Surveying
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  • Articles  (24)
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  • 1
    Electronic Resource
    Electronic Resource
    Statistical considerations for grain-size analyses of tills (1971)
    Springer
    Mathematical geology 3 (1971), S. 227-238 
    Details
    ISSN: 1573-8868
    Keywords: classification ; data processing ; graphics ; mapping ; mathematics ; plotting ; sampling ; statistics ; sedimentology ; stratigraphy ; grain-size analysis ; textural analysis ; glacial geology ; Pleistocene stratigraphy ; till
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Relative percentages of sand, silt, and clay from samples of the same till unit are not identical because of different lithologies in the source areas, sorting in transport, random variation, and experimental error. Random variation and experimental error can be isolated from the other two as follows. For each particle-size class of each till unit, a standard population is determined by using a normally distributed, representative group of data. New measurements are compared with the standard population and, if they compare satisfactorily, the experimental error is not significant and random variation is within the expected range for the population. The outcome of the comparison depends on numerical criteria derived from a graphical method rather than on a more commonly used one-way analysis of variance with two treatments. If the number of samples and the standard deviation of the standard population are substituted in at-test equation, a family of hyperbolas is generated, each of which corresponds to a specific number of subsamples taken from each new sample. The axes of the graphs of the hyperbolas are the standard deviation of new measurements (horizontal axis) and the difference between the means of the new measurements and the standard population (vertical axis). The area between the two branches of each hyperbola corresponds to a satisfactory comparison between the new measurements and the standard population. Measurements from a new sample can be tested by plotting their standard deviation vs. difference in means on axes containing a hyperbola corresponding to the specific number of subsamples used. If the point lies between the branches of the hyperbola, the measurements are considered reliable. But if the point lies outside this region, the measurements are repeated. Because the critical segment of the hyperbola is approximately a straight line parallel to the horizontal axis, the test is simplified to a comparison between the means of the standard population and the means of the subsample. The minimum number of subsamples required to prove significant variation between samples caused by different lithologies in the source areas and sorting in transport can be determined directly from the graphical method. The minimum number of subsamples required is the maximum number to be run for economy of effort.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045793
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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
    Numerical classification applied to certain Jamaican eocene nummulitids (1971)
    Springer
    Mathematical geology 3 (1971), S. 297-311 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; numerical taxonomy ; paleontology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Eighty-eight specimens of Eocene nummulitids from the Yellow Limestone Formation of northwestern Jamaica are classified according to quantitative measurements of morphologic parameters that are generally considered to be taxonomically useful. The specimens are grouped into homogeneous classes by the computer screening of differently oriented data projections. By this method, the use of similarity coefficients and the question of a priori weighting of characters, for which numerical taxonomy has been heavily criticized, are both avoided. The stability of the classes thus obtained is validated by discriminant analysis. These techniques provide an objective view of phenetic differences among specimens and show how the measured characters produce those differences. Tightness of coiling and total number of whorls, prove to be the most useful features in discriminating between groups but seem to have taxonomic value only at the specific and not at the generic level. This suggests that the generaOperculinoides andNummulites are synonymous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045797
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  • 4
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Numeric examination of multivariate soil samples (1971)
    Springer
    Mathematical geology 3 (1971), S. 1-14 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; principal components analysis ; numerical taxonomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Numerical methods for the examination of multivariate soil samples are presented in geometric terms. Techniques of coordinate representation by principal components, by nonmetric scaling, and by a new method are discussed, as are techniques for agglomerative hierarchic cluster analysis. These are illustrated by two sets of previously published data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047429
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  • 7
    Electronic Resource
    Electronic Resource
    Preliminary assessment of a nonlinear mapping algorithm in a geological context (1973)
    Springer
    Mathematical geology 5 (1973), S. 39-57 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; dimensionality reduction ; mapping ; multivariate analysis ; principal-components analysis ; general geology ; geochemistry ; paleontology ; petrology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114086
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  • 8
    Electronic Resource
    Electronic Resource
    Application of factor analysis to classification of engineering-geological environments (1974)
    Springer
    Mathematical geology 6 (1974), S. 17-31 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; factor analysis ; engineering geology ; soils
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The engineering-geological environment, as any other geological environment, can be described by a number of variables. A clustering of those variables or clustering of their quantities makes it possible to divide the environment into taxonomic types. It is also possible to determine factors which are functions of those variables and which characterize the environment or its parts. In this paper we have applied R-and Q-mode factor analysis to engineering-geological research, concentrating our attention on establishing criteria for subdividing an environment into various aspects by its engineering-geological characteristics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111924
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  • 9
    Electronic Resource
    Electronic Resource
    Multivariate oceanographic sampling (1971)
    Springer
    Mathematical geology 3 (1971), S. 43-50 
    Details
    ISSN: 1573-8868
    Keywords: dynamic programming ; sampling ; oceanography ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Increasing attention in recent years has been devoted to the application of statistical techniques in the analysis and interpretation of geologic and oceanographic data. Equally important, but less well explored, are methods for efficient experimental design. The theory of linear programming provides plans for optimal sampling of geologic and oceanographic phenomena. Of particular significance are solutions to problems of multivariate sampling. Often, a single field sample may be analyzed for a number of oxides, or a number of minerals, or a number of textural parameters. In general, these variables differ in the degree to which they are diagnostic of changes in the phenomenon of interest, and thus they must be known with different levels of precision if they are to be useful. Similarly, the variables differ in the ease with which they may be measured. If a sampling plan is to be most efficient, it must provide the requisite levels of precision for the minimum expenditure of time and effort. Sampling for a single variable may be optimized directly. Sampling for several variables simultaneously usually introduces special difficulties, but if the objective function can be generalized to hold for all variables, solutions can be determined even in this situation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047431
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  • 10
    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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