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  • Articles  (26)
  • discriminant analysis  (13)
  • petrology  (12)
  • Chemistry
  • EARTH RESOURCES AND REMOTE SENSING
  • General Chemistry
  • 1980-1984  (9)
  • 1970-1974  (17)
  • 1950-1954
  • 1935-1939
  • Geosciences  (26)
  • 1
    Electronic Resource
    Electronic Resource
    The importance of energetic particle precipitation on the chemical composition of the middle atmosphere (1980)
    Springer
    Pure and applied geophysics 118 (1980), S. 128-151 
    Details
    ISSN: 1420-9136
    Keywords: Galactic cosmic rays ; Solar proton events ; Particle precipitation ; Chemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract An assessment is made of the relative contribution of certain classes of energetic particle precipitation to the chemical composition of the middle atmosphere with emphasis placed on the production of odd nitrogen and odd hydrogen species and their subsequent role in the catalytic removal of ozone. Galactic cosmic radiation is an important source of odd nitrogen in the lower stratosphere but since the peak energy deposition occurs below the region where catalytic removal of O3 is most effective, it is questionable whether this mechanism is important in the overall terrestrial ozone budget. The precipitation of energetic solar protons can periodically produce dramatic enhancement in upper stratospheric NO. The long residence time of NO in this region of the atmosphere, where catalytic interaction with O3 is also most effective, mandates that this mechanism be included in future modelling of the global distribution of O3. Throughout the mesosphere the precipitation of energetic electrons from the outer radiation belt (60°≲Λ≲70°) can sporadically act as a major local source of odd hydrogen and odd nitrogen leading to observable O3 depletion. Future satellite studies should be directed at simultaneously measuring the precipitation flux and the concomitant atmosphere modification, and these results should be employed to develop more sophisticated models of this important coupling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586448
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  • 2
    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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  • 3
    Electronic Resource
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    Ideal granite and its properties. I. The stochastic model (1972)
    Springer
    Mathematical geology 4 (1972), S. 89-102 
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    ISSN: 1573-8868
    Keywords: crystallization ; stochastic model ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Investigation of granitic rocks in the search for hidden ore deposits, restoration of their history, and understanding their special properties requires comparison of intrusive bodies. Comparisons are best made to some standard. The conception of an ideal magmatic granite as a standard is introduced in this paper. Investigation indicates that sequences of quartz grains potassium feldspars, and plagioclases of an ideal magmatic granite have definite mathematical properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080295
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  • 4
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    Computer program to analyze directional data, based on the methods of Fisher and Watson (1972)
    Springer
    Mathematical geology 4 (1972), S. 177-202 
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    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
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    Some problems of interpreting the correlations between the modal variables in granitic rocks (1974)
    Springer
    Mathematical geology 6 (1974), S. 245-258 
    Details
    ISSN: 1573-8868
    Keywords: correlation between proportions ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Correlation coefficients of modal variables from several suites of granitic rocks have been calculated and tested for significance using the Chayes-Kruskal and Chayes methods. The results show that although Chayes' remaining-space transformation does, in general, weaken the original proportion correlations, the positive and low-negative original proportion correlations tend to increase in absolute value because of a tendency of positive increment of the covariance by such transformation. However, no satisfactory procedure for choosing the variable to be transformed (V2)could be determined, and testing of the significance of remaining-space correlations is found to be highly problematic. It is shown also that the Vistelius-Sarmanov procedure of calculation of correlation coefficients from closed-table data does not effectively eliminate the closure effect. It is concluded that assigning statistical significance to the correlation coefficients between modal variables is, in general, unsatisfactory, except where the number of variables ⩾8,the sample size is large (say, ⩾30),and there is no negative element in the variance vector of the corresponding open variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082890
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  • 6
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    Automatic contouring of geological maps to detect target areas for mineral exploration (1974)
    Springer
    Mathematical geology 6 (1974), S. 373-395 
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    ISSN: 1573-8868
    Keywords: contouring ; discriminant analysis ; logistic model ; regression analysis ; geological maps ; mineral exploration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Various statistical methods for predicting mineral potential from geological maps are reviewed. It is pointed out that, if the features are coded in more detail for relatively small cells, several new problems arise because of the dichotomous nature of the resulting variables. The objective of this paper is to present a method for the automatic contouring of both discovered and undiscovered deposits of a given type in terms of the geological framework. It is based on the assumption that the probability of occurrence of a deposit is fully determined by a combination of functions of the mappable geological attributes in a region. Application of the logistic model is proposed for the situation in which relatively few deposits of a given type are known to exist in the study region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082358
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  • 7
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    Extensions of linear discriminant analysis for statistical classification of remotely sensed satellite imagery (1980)
    Springer
    Mathematical geology 12 (1980), S. 367-376 
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    ISSN: 1573-8868
    Keywords: discriminant analysis ; remote sensing ; satellite imagery
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Linear discriminant analysis is a commonly used statistical tool for the classification of surface features using satellite surface reflectance data. Extensions of this basic tool promise substantial improvements. In particular, we examine the added effectiveness of the integration of spatial autocorrelation into the discriminant model, the resolution of nonhomogeneous pixels, and data based prior probability estimates of class membership.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029421
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  • 8
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    A new look in exploration and development of old producing properties (1980)
    Springer
    Mathematical geology 12 (1980), S. 377-398 
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    ISSN: 1573-8868
    Keywords: discriminant analysis ; petroleum exploration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Stepwise linear discriminant analysis and regression function techniques were used to classify and analyze the data from 224 oil, gas, and dry holes drilled to the base of the Silurian Geologic System in southeast Ohio, U.S.A., from 1968 to 1975. These are 8.7% of all wells drilled in the same geographical area over the time interval. The wells were divided into six groups depending on the amount of control the drilling company had over their ultimate completion. Thirteen environmental (geologic and engineering) factors plus location data were collected about each well. Successive groupings of oil and gas wells were used to determine an environmental index which was used to establish the hydrocarbon producing potential of the next group. Discriminant analysis was used to determine whether the wells within each group were classified properly and regression analysis was used to determine a production estimating function. Geophysical well data were used to estimate whether gas or oil was expected. With this dichotomy, production estimating functions which explain 74% of the variation for oil wells and 78% of the variation for gas wells were formulated. Using the discriminant function for these groups as a ranking function the following results were obtained: For oil wells, 18.5% Type II errors for the productive group and 24.4% Type II errors for the nonproductive group; for gas wells, 5.4% Type II errors for the productive group and 17.1% Type II errors for the nonproductive group. By accepting the above Type II errors one is significantly able to reduce the number of noneconomic wells completed that originally should have been considered dry holes. The inverse was tested with three wells and yielded 33% Type II errors. Any area in which adequate data are available is amenable to these types of analysis with their attendant diagnostic capabilities.
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    URL: http://dx.doi.org/10.1007/BF01029422
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  • 9
    Electronic Resource
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    Counting error in petrographic point-count analysis: A theoretical and experimental study (1971)
    Springer
    Mathematical geology 3 (1971), S. 15-41 
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    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.
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    URL: http://dx.doi.org/10.1007/BF02047430
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  • 10
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    Effect of trends on correlation in open and closed three-component systems (1972)
    Springer
    Mathematical geology 4 (1972), S. 317-330 
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    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.
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    URL: http://dx.doi.org/10.1007/BF02114093
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  • 11
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    Preliminary assessment of a nonlinear mapping algorithm in a geological context (1973)
    Springer
    Mathematical geology 5 (1973), S. 39-57 
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    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.
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    URL: http://dx.doi.org/10.1007/BF02114086
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  • 12
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    Quantitative discrimination between magmatic units of the singhbhum granite (1971)
    Springer
    Mathematical geology 3 (1971), S. 123-133 
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    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.
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    URL: http://dx.doi.org/10.1007/BF02045956
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  • 13
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    Multivariate discriminant analysis of bioclastic turbidites (1972)
    Springer
    Mathematical geology 4 (1972), S. 249-261 
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    ISSN: 1573-8868
    Keywords: cluster analysis ; discriminant analysis ; principal-components analysis ; geochemistry ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A piston core from the southern Blake Basin penetrated nine distinct bioclastic carbonate turbidites separated by pelagic terrigenous clay units. X-ray diffraction analysis of the carbonate mineralogy of the graded, laminated, and homogenous units of the individual turbidite units indicated a general loss of unstable carbonates in the homogenous unit beyond that contained in the lower two units. Univariate and multivariate statistical tests were employed to determine the significance of the changes and to determine if different units of a turbidite sequence could be consistently grouped by statistical methods. Principal components, discriminant function, and cluster analysis were used in the multivariate tests. The graded and laminated units were closely related in mineralogy with little significant differences. The mineralogy of the homogenous units was significantly different than that of the other two units except in one example. Cluster analysis generated five groupings of the samples with the end members consisting of graded and laminated units at one end and homogenous units at the other.
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    URL: http://dx.doi.org/10.1007/BF02311721
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  • 14
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    The statistical zap versus the shotgun approach (1974)
    Springer
    Mathematical geology 6 (1974), S. 311-332 
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    ISSN: 1573-8868
    Keywords: canonical correlation ; cluster analysis ; correlation ; discriminant analysis ; factor analysis ; multivariate analysis ; numerical taxonomy ; principal coordinates ; regression analysis ; statistics ; allometry ; eurypterids ; integration and coordination ; ontogeny ; paleontology ; relative growth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Multivariate analysis is used in the search for one or more types of structure. The statistical zap applies a single method to determine one preselected type of structure. Several zaps suffice to ascertain several types of structure. The statistical shotgun represents an alternative approach. Here, a series of methods is applied to the data with the intent of ascertaining all possible types of structure that may exist. If strong structure is present, an appropriate zap will probably reveal it, and a variety of techniques will determine the same general structure. If only the main structure is required, the zap is adequate. In this situation, the shotgun will display a basic consistency which is at least reassuring. However, zaps may fail to detect a more subtle secondary structure of geological interest which will be displayed by the shotgun. For weakly structured data, a zap will only determine one type of structure but the shotgun reveals all. Study of the ontogeny of Parastylonurus myops(Clarke), a Lower Silurian eurypterid from New York (USA) shows the virtues of the statistical shotgun.
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    URL: http://dx.doi.org/10.1007/BF02082354
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  • 15
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    Use of discriminant analysis for classification of strata in sedimentary successions (1973)
    Springer
    Mathematical geology 5 (1973), S. 163-177 
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    ISSN: 1573-8868
    Keywords: classification ; discriminant analysis ; geochemistry ; numerical taxonomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The technique of instrumental neutron activation analysis (INAA) has been used to analyze chip samples of geological material for 12 elements. Discriminant analysis has been used to classify the unknown chip samples to the correct stratum in a sedimentary succession.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111893
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  • 16
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    Thoughts on use of principal component analysis in petrogenetic problems (1973)
    Springer
    Mathematical geology 5 (1973), S. 341-350 
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    ISSN: 1573-8868
    Keywords: principal components analysis ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The use of principal component analysis in studying chemical trends in volcanic rock suites is described. It is suggested that eigenvectors generated from a correlation matrix, rather than a covariance matrix, could be used in this context. In the latter situation many elements are swamped by silicon's numerical size and range. In the former situation the alkalies and titanium begin to show their true importance.
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    URL: http://dx.doi.org/10.1007/BF02111985
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  • 17
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    Application of discriminant analysis and generalized distance measures to uranium exploration (1980)
    Springer
    Mathematical geology 12 (1980), S. 539-558 
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    ISSN: 1573-8868
    Keywords: discriminant analysis ; variable selection ; uranium favorability ; generalized distance measures ; regional variables ; geochemical fingerprint
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The National Uranium Resource Evaluation (NURE) Program has as its goal the estimation of the nation's uranium resources. It is possible to use discriminant analysis methods on hydrogeochemical data collected in the NURE Program to aid in formulating geochemical models that can be used to identify the anomalous areas used in resource estimation. Discriminant analysis methods have been applied to data from the Plainview, Texas Quadrangle which has approximately 850 groundwater samples with more than 40 quantitative measurements per sample. Discriminant analysis topics involving estimation of misclassification probabilities, variable selection, and robust discrimination are applied. A method using generalized distance measures is given which enables the assignment of samples to a background population or a mineralized population whose parameters were estimated from separate studies. Each topic is related to its relevance in identifying areas of possible interest to uranium exploration. However, the methodology presented here is applicable to the identification of regions associated with other types of resources.
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    URL: http://dx.doi.org/10.1007/BF01034743
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  • 18
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    Harmonic analysis of cephalopod suture patterns (1981)
    Springer
    Mathematical geology 13 (1981), S. 23-35 
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    ISSN: 1573-8868
    Keywords: harmonic analysis ; cephalopod sutures ; discriminant analysis ; norm of reaction ; heterochrony
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Harmonic (Fourier) analysis provides a series of multivariate descriptors that exactly quantifies the shapes of cephalopod suture patterns in the Subclasses Nautiloidea and Bactritoidea, and in four of the eight orders of the Ammonoidea. The method allows the calculation and graphic display of the mean suture patterns of the subclasses and orders studied, and exactly measures the morphological differences between groups. Discriminant analysis provides significant differentiation of the four ammonoid orders using only the harmonic amplitudes of the sutures. Discriminant analysis also indicates significant differences between the two symmetric halves of sutures in Acanthoclymenia neapolitana, and thereby measures the withingenotype norm of reaction in that species. Twelve sutural harmonic amplitudes are significantly correlated with ontogenetic changes in apertural size and shape in Koenenites cooperi. Specific harmonic amplitudes increase monotonically in the ontogeny of K. cooperi, but do not change within the phylogeny of its family, the Gephuroceratidae. This method permits statistical testing of assumptions of heterochronous evolution in cephalopod lineages.
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    URL: http://dx.doi.org/10.1007/BF01032007
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  • 19
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    A prior probability method for smoothing discriminant analysis classification maps (1982)
    Springer
    Mathematical geology 14 (1982), S. 433-444 
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    ISSN: 1573-8868
    Keywords: smoothing ; discriminant analysis ; remote sensing ; satellite imagery
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A statistical method is presented for smoothing discriminant analysis classification maps by including pixel-specific prior probability estimates that have been determined from the frequency of tentative class assignments in a window moving across an initial per-point classification map. The class at the center of the window is reevaluated using the data for that location and the prior probability estimates obtained from the window area. An example using Landsat spectral data demonstrates the effectiveness of the method and shows an increase in classification accuracy after smoothing.
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    URL: http://dx.doi.org/10.1007/BF01077532
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  • 20
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    Computerized vision for the geologist (1983)
    Springer
    Mathematical geology 15 (1983), S. 3-23 
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    ISSN: 1573-8868
    Keywords: Geology ; petrology ; geological maps ; geological surveys ; image analysis ; image processing ; binary images ; component labels ; phase labels ; erosion ; dilatation ; logical operations ; spatial operations ; GIAPP ; Prospector ; CHARAN ; SIMSAG
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The digital computer can be a tireless friend and assistant to the geologist. The computer has no innate intelligence, but given adequate programs to analyze and interrelate the information on maps, photos, surveys, and other material, the computer can serve as an analytical tool and consultant. To the geologist's qualitative knowledge, theories, and models can be added the possibility of the computer's mathematically precise numerical answers, confirming or refuting the original ideas. In the interactive mode in particular, a dialogue between the geologist and the computer is established, where the geologist and the computer can complement each other's abilities. The basic principles of processing two-dimensional geological data, such as maps, charts, photos, and survey results, are discussed. Some comparisons are also made between the rule-based methods of Prospector, developed at Stanford Research Institute, and the more intuitively guided image-based procedures of GIAPP, developed on the equipment at the National Research Council of Canada, in collaboration with the Geological Survey of Canada and the University of Ottawa.
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    URL: http://dx.doi.org/10.1007/BF01030073
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  • 21
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    Multivariate models for landslide hazard evaluation (1983)
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    Mathematical geology 15 (1983), S. 403-426 
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    ISSN: 1573-8868
    Keywords: slope instability ; landslide hazard ; multivariate models ; discriminant analysis ; multiple regression analysis ; land evaluation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract As part of a long-term project aimed at a better understanding of the geological and geomorphological factors that control slope instability phenomena in Southern Italy, multivariate models for assessing landslide incidence hazard were developed and tested in two Calabrian sample areas characterized by different geological-geomorphological conditions. Discriminant analysis, based on a large set of mappable geological and geomorphical variables, is able to discriminate rather successfully between stable and unstable areas or slope units. Multiple regression analysis has also proved to be a useful tool in predicting actual and potential landslide hazard. Consequently, geomathematical models may provide a feasible approach to environmental hazard assessment, particularly when applied within the framework of a wider multidisciplinary project for land evaluation and planning.
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    URL: http://dx.doi.org/10.1007/BF01031290
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  • 22
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    Spatial pattern recognition by decomposition (1984)
    Springer
    Mathematical geology 16 (1984), S. 217-236 
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    ISSN: 1573-8868
    Keywords: nonlinear regression ; discriminant analysis ; decomposition of mixtures ; pattern recognition ; geochemistry ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The decomposition problem—the assignment of sample observations to component populations—is studied in a spatial context. The observations are spatially located and the assignment to component populations takes into account the value of each observation as well as the values of neighboring observations. Both parameter estimation and assignment rules use a new method that integrates a standard multivariate decomposition algorithm with nonlinear regression. The method is illustrated and tested with artificial data. The distribution of the trace component Cr2O3 in recent Lake Michigan sediments is, then, analyzed by the method. It yields a pattern of component populations that is correlated with the Lake's bottom structure and depositional environments.
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    URL: http://dx.doi.org/10.1007/BF01032688
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  • 23
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    Estimation of parameters in petrologic materials balance equations (1973)
    Springer
    Mathematical geology 5 (1973), S. 225-236 
    Details
    ISSN: 1573-8868
    Keywords: estimation ; materials balance ; mathematics ; mixing equations ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A rigorous treatment of the least-squares estimation of the parameters in petrologic materials balance equations is developed to take into account the uncertainties inherent in the chemical analyses. The choice of the optimal estimation procedure for a particular problem is dependent upon the extent of the petrogenetic understanding of the exact nature of the materials balance involved. Some of the complications entailed in obtaining least-squares estimates are illustrated by the examples of magmatic differentiation and metamorphic reactions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111812
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  • 24
    Electronic Resource
    Electronic Resource
    A multivariate analytical strategy for classifying paleoenvironments (1974)
    Springer
    Mathematical geology 6 (1974), S. 333-352 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; multivariate analysis ; ordination ; numerical taxonomy ; paleoecology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A multivariate analytical strategy is proposed for aiding the investigator in extracting maximum information from environmental data. Data are carefully coded and scaled and are tested for redundancy using R-mode cluster analysis. The samples are partitioned into environmental classes using Q-mode cluster analysis. Q-mode ordination facilitates interpretations, which usually can be verified by comparison with field relationships. Discriminant analysis serves as an identification procedure for extending the classification to unknown samples. The strategy is demonstrated by application to Cape Hatteras microorganism distributions and Devonian sedimentary facies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082355
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  • 25
    Electronic Resource
    Electronic Resource
    A geomathematic investigation of syntexis in a Gabbroic formation (1973)
    Springer
    Mathematical geology 5 (1973), S. 321-339 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; Fourier analysis ; mapping ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Mathematical methods were employed in an investigation of syntexis in the “Gabbro di Sondalo,” a mafic igneous formation in the Central Alps (Italy). A set of 100 specimens was selected according to sampling criteria and analyzed by X-ray fluorescence for eight elements; Q-mode and R-mode factor analysis then was applied to these data. Results of the computations indicate that the general trend of differentiation is related to the syntexis of gneissic wall rocks (“Gneiss del Monte Tonale”) in the mafic melt. Ca and Mg are abundant in the gabbro, and Si and K in the gneiss; the independent variation trend of Fe and Ti may be related to a differentiation episode due to a magmatic phase. Spatial representation of multivariate data on differentiation also was performed on the main elements and a picture of the trend of syntexis was mapped.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111984
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  • 26
    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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