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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 10 (1978), S. 289-299 
    ISSN: 1573-8868
    Keywords: classification ; discriminant analysis ; soil science ; autocorrelation ; boundary
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A linear discriminant function can be used to place the boundary between two mapping units, if multiple measurements are available for samples collected from both units. The function is calculated using samples of known group membership, then is applied to classify samples of unknown group identity. The plot of the discriminant index on a map of the study area locates the contact between the two groups. Boundary position can be evaluated by comparing data models based upon the boundary with the distributions of the original variables. This method is applied to locate the boundary between two soil mapping units. Samples of two contrasting soils were collected on a gridded sampling pattern positioned at the contact between two mapping units. Samples were analyzed for physical and chemical properties, including sand content, silt content, and pH. The boundary was located, then separately evaluated with respect to the sand, silt, and pH measurements. The discriminant score boundary corresponded closely to the sand content measurements, but did not match the silt or pH distributions.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 10 (1978), S. 111-139 
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; principal components ; morphometrics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An artificial data set is used to illustrate the morphologic properties of some common multivariate techniques and consideration of three common situations. The first concerns a sample showing no obvious groupings. In this situation principal components (or coordinates) and factor analyses give a logical ordination of form variation; cluster analysis produces sizedominated groups. The second situation considers an homogeneous sample where size and shape have important implications. Principal components are tested for association with size and shape, both of which can be isolated if isometry exists; if allometry is present, isolation of shape is possible only by size elimination, e.g., conversion to ratios. The third situation examines a sample of unknown groupings in which shape variation is the only interest. Aside from ratios, two other methods which produce shape-dominant clusters are assessed. Some of the options available in cluster analysis are also examined.
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  • 3
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; numerical taxonomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A method is described for testing the distinctness of two clusters in Euclidean space. One first calculates the projections, q,of the N1 and N2 members of the clusters onto the line joining the cluster centroids. From the distributions of qan index of disjunction, W,is calculated, which corresponds to an index of overlap, VG.The quantity W√(N1+N2)is distributed as noncentral tsubject to assumptions on the multivariate normal distribution of the clusters. This allows a test of whether the observed disjunction is significantly greater than a chosen figure, which is equivalent to testing whether the overlap of the clusters is significantly less than a corresponding value of VG.Two clusters that appear distinct may be produced simply by the partitioning of a homogeneous swarm into two contiguous regions. Provided that the clusters form a dichotomy in a dendrogram, and that the clustering method yields geometrically convex clusters, a conservative test of this situation can be derived by determining the excess of Wover the value expected for a rectangular distribution.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 9 (1977), S. 77-98 
    ISSN: 1573-8868
    Keywords: classification ; factor analysis ; association analysis ; binary data ; Recent carbonates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The shallow shelf area to a water depth of 40 m off Ras Burka, Gulf of Elat, comprises several depositional zones. In order of increasing water depth these include: sand dune (on shore); swash; dead reef platform; sand channel; live coral reef; Cymodoceaslope; reef knolls; and Halophilalawn. The abundance of 64 biogenic constituents, comprising 48 genera of Foraminifera and a variety of other taxa, was recorded in 16 samples representing the sediments presently forming in the various environments. Nodal ordination and association analysis were applied to classify the samples and to examine whether the present day zonation of sedimentary environments can be objectively recognized on the basis of the assemblages of biogenic constituents. The analyses classified the samples consistently into three classes, identified as the shallow near-shore, the upper slope, and the lower slope zones. Association analysis, utilizing only discrete binary presence or absence scores, yielded better results than nodal ordination analysis utilizing continuous metric modal data. In the study area, biogenic grains other than Foraminifera do not contribute to the environmental discrimination. The results suggest that crude presence scores, as contrasted with refined metric data, are informative enough for differentiating sedimentary environments.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 8 (1976), S. 597-616 
    ISSN: 1573-8868
    Keywords: classification ; Markov processes ; geomorphology ; hillslopes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract If considered as a sequence of morphological units, hillslopes can be treated as realizations of a stochastic process in which morphological units correspond to events and their attributes (e.g., slope)to values. A first-order, discrete-state, discrete-time Markov model, applied to a group of hillslopes measured in Calabria, explained a significant part of the hillslope morphology. A Markov property was determined to be present in the sequence of slopes and lengths of the morphological units. In the subsequent analysis of the Markov property in the sequence of slopes, an optimum transition scheme was developed. This indicated, inter alia,that concavity in the hillslope was most probable where the slope was in the range from 7° to 〈9°. The hillslopes were divided into classes based upon their geomorphological position. The resulting transition probability matrices and their derivatives were examined for significant differences.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 8 (1976), S. 75-84 
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; entropy ; facies analysis ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Criteria have been suggested for the optimal partitioning of a dendrogram into sample clusters. The implementation of these criteria by means of statistical and graphical measures is considered for two dendrograms. It is shown that the optimization of criteria is conditioned by research aims.
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  • 7
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; ordination analysis ; grain size ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A multivariate statistical strategy for classifying paleoenvironments is effective for studying modern sedimentary processes in western Great South Bay and South Oyster Bay, New York. The 13 whole phi weight percent variables were tested for redundancy with R-mode cluster analysis. The samples were partitioned statistically into five environmentally significant facies using Q-mode cluster analysis: (A)sandy gravel, (B)sandy silt, (C)silty sand, (D)slightly gravelly sand, and (E)fine sand. An ordination depicted gradational relationships among the samples and the facies. It was used to evaluate the environmental and textural parameter gradients within the sample space. Interpretations obtained in this manner and by examination of the grain-size curves suggest that these sediments were deposited by waves and currents on beaches and in wave zones (facies C and E),shoal areas (facies B),and tidal channels (facies A and D).Tidal currents, wave action, and eelgrass control the distribution of sediments within the two bays.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 8 (1976), S. 669-681 
    ISSN: 1573-8868
    Keywords: classification ; factor analysis ; economic geology ; mineralization ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geological descriptions of unmineralized and mineralized ultrabasic and basic complexes were collected on a world-wide basis from published literature in the framework of the research project “Basimine.”Its aim is the discovery of controls governing the existence of mineralization in certain complexes and subsequently the development of working hypotheses for nickel prospection. Files were created containing geological and petrological data for each complex. In order to gain an understanding into the relationship existing between variables and complexes, correspondence analysis was applied to various data sets taken from the files. The results indicated criteria, either favorable or unfavorable, for the presence of mineralization in the complexes, and pointed out certain unmineralized complexes which could well be mineralized due to their position as regards known ore deposits in the plan of the factorial axes.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 8 (1976), S. 413-427 
    ISSN: 1573-8868
    Keywords: Witwatersrand System ; geochemistry ; discriminant analysis ; classification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Powdered rock samples from strata of the Witwatersrand System's sedimentary succession have been analyzed by x-ray fluorescence and optical spectroscopy techniques for nineteen elements. Using discriminant analysis it is possible to identify strata based on their trace-element compositions.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 7 (1975), S. 191-214 
    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.
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