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  • Articles  (30)
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  • general geology  (12)
  • regression analysis  (12)
  • factor analysis  (9)
  • 2015-2019
  • 1970-1974  (30)
  • Mathematics  (30)
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  • Articles  (30)
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  • 1
    Electronic Resource
    Electronic Resource
    An algorithm andFortran-iv program for large-scaleQ-mode factor analysis and calculation of factor scores (1971)
    Springer
    Mathematical geology 3 (1971), S. 61-77 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; principal components analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An algorithm andFortran-iv computer program,cabfac, forQ-mode factor analysis is described. The program will accept up to 1500 items and 50 variables on a moderate-size computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047433
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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
    Trend-surface analysis (1971)
    Springer
    Mathematical geology 3 (1971), S. 215-226 
    Details
    ISSN: 1573-8868
    Keywords: autocorrelation ; kriging ; regionalized variables ; trend analysis ; geostatistics ; general geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper is largely an exposition of the work of the French geostatistian G. Matheron and his school in English and at a simpler mathematical level. The probability theory on which it is based is essentially all contained in the references cited, most of which will be unfamiliar to mathematical geologists. The important method of ‘universal kriging” is explained intuitively. The genuine statistical problems, which have yet to be overcome, are pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045792
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  • 4
    Electronic Resource
    Electronic Resource
    A generalized set of discrete frequency distributions with Fortran program (1972)
    Springer
    Mathematical geology 4 (1972), S. 1-24 
    Details
    ISSN: 1573-8868
    Keywords: discrete frequency distributions ; statistics ; general geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geologists unfamiliar with the application of probability theory to discrete data in other fields of research are usually acquainted with only three discrete theoretical frequency distributions: Poisson, binomial, and negative binomial distributions. In some situations these distributions may fail to adequately describe a set of experimental data. Other distributions such as the Poisson with zeros, Neyman type A, logarithmic with zeros, Poisson-binomial, and Thomas double Poisson together with the more common Poisson, binomial, and negative binomial form a generalized subset of discrete theoretical distributions, one of which should fit almost any experimental data set. A computer program is presented which allows testing of any combination of these distributions against observed discrete data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083189
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  • 5
    Electronic Resource
    Electronic Resource
    Multiple regression with correlated independent variables (1972)
    Springer
    Mathematical geology 4 (1972), S. 203-218 
    Details
    ISSN: 1573-8868
    Keywords: correlated independent variables ; regression analysis ; ridge trace ; statistics ; trend analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Multiple linear regression analysis may be used to describe the relation of one geologic variable to a number of other (independent) variables, and also may be used to fit a trend surface to geographically distributed variables. The leastsquares estimates of the regression coefficients differ unpredictably from the true coefficients if the independent variables are correlated. The estimates can be too large in absolute value, and may have the wrong sign. Also, the least-squares solution may be unstable in that replicate samples can give widely differing values of the regression coefficients. Ridgeregression analysis is a technique for removing the effect of correlations from the regression analysis. The procedure involves addition of a small constant K to the diagonal elements of the standardized covariance matrix. The estimates obtained are biased but have smaller sums of squared deviations between the coefficients and their estimates. The ridge trace, a plot of the coefficients versus K, helps determine the value of K that stabilizes the estimates. Correlations between geologic variables are common, and regression coefficients based on these data may be suspect. In trendsurface analysis, correlations between the geographic coordinates may differ widely, and extreme correlations may be introduced if higher order terms are used in the trend. Ridgeregression analysis serves to guide the geologist to a more reliable interpretation of the results of multiple regression if the independent variables are correlated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02311718
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Some considerations in management of computer-processable files of geological data (1974)
    Springer
    Mathematical geology 6 (1974), S. 291-310 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; general geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Many sets of data in the natural sciences have a hierarchical structure that is either inherent in the data or that is imposed on them during collection. These data structures can be defined using mathematical set-theory notation. If data from two or more computer-processable files are accessed simultaneously, the application of operations of set union and intersection leads to emergence of certain criteria which must be adhered to when managing data files using a generalized, database management system. One of the situations in which these principles come into play is illustrated by the merging of two computer-processable files of geotechnical data, the data for both files having been derived from the same source but structured differently.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082353
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  • 8
    Electronic Resource
    Electronic Resource
    Automatic contouring of geological maps to detect target areas for mineral exploration (1974)
    Springer
    Mathematical geology 6 (1974), S. 373-395 
    Details
    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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  • 9
    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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  • 10
    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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