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  • Articles  (25)
  • regression analysis  (12)
  • trend analysis  (10)
  • numerical taxonomy  (8)
  • 1970-1974  (25)
  • Geosciences  (25)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Architecture, Civil Engineering, Surveying
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  • Articles  (25)
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  • Geosciences  (25)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Architecture, Civil Engineering, Surveying
  • Mathematics  (25)
  • 1
    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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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    Application of autocorrelation criteria to the analysis of mapped geologic data from the coal measures of central England (1971)
    Springer
    Mathematical geology 3 (1971), S. 281-295 
    Details
    ISSN: 1573-8868
    Keywords: analysis of variance ; autocorrelation ; simulation ; trend analysis ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is proposed that the variance in mapped geologic data should be formally considered to be composed of three components which arise on different geographic scales. The three components (regional, local, and residual) should be defined solely in terms of the parameters of the sample data set. A two-step analysis is required to separate three components. Applying autocorrelation criteria, trend-surface analysis has been used, in the first step, to remove the residual component and, in the second step, to separate regional and local components from the resulting noise-free data. This procedure has made it possible to quantify local components in stratigraphic thickness data from the East Midlands coalfield (central England) which can be identified in terms of the known geology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045796
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  • 4
    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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  • 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
    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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  • 7
    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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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    Cyclic characteristics of sediments in the Moon Island Beach Subgroup, Newcastle Coal Measures, New South Wales (1973)
    Springer
    Mathematical geology 5 (1973), S. 91-110 
    Details
    ISSN: 1573-8868
    Keywords: Markov processes ; regression analysis ; time-trend analysis ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Cyclic characteristics of a sequence of Permian coal-measure sediments have been studied using Markov chain analysis on borehole data. Fining-upwards and oscillating sequences can be distinguished, and depositional regimes are proposed to explain the observed sequences. However, there is no clearly defined relationship of sequence type to tectonosedimentary environment. The relationship of the number of coal-defined and fining-upwards cycles to total thickness and mean cycle thickness is examined using linear regression. The relationships for coal-defined and fining-upwards cycles are essentially the same. Significant positive correlations are present between the number of cycles and total thickness and significant inverse relationships are present for the number of cycles and the mean cycle thickness.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114089
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  • 10
    Electronic Resource
    Electronic Resource
    Long-term growth of the oil industry in the United States (1973)
    Springer
    Mathematical geology 5 (1973), S. 237-267 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; generalized logistic curve ; Gompertz curve ; petroleum ; regression analysis ; time series ; time-trend analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A number of growth models have been developed and used in an attempt to project the historical pattern of oil activities to some estimate of their upper limit. Techniques are outlined for the estimation of parameters of the logistic and Gompertz curves. Factor analysis indicated a close relationship between production and demand, whereas annual discoveries and discoveries classified by year of discovery tended to comprise unique factors which were indifferent to changes in time. The growth models projected relatively high values for ultimate demand and production in comparison to the figures for ultimate reserves. Inasmuch as these trends seemed to be occurring independently, some reconciliation of the results was necessary. Using the highest projections of estimates for reserves suggests that over 420 billion barrels of oil in place will eventually be discovered in the United States, with perhaps 200 billion barrels of this eventually to be proved in the form of reserves. Projections for production were higher, corresponding to a trend indicating high levels in demand for crude oil. The only credible long-term estimate of demand was given by a bounded exponential growth model, in which ultimate cumulative demand for crude oil would reach about 416 billion barrels. These figures imply that over 150 billion barrels of oil would be imported into the United States from 1970 to 2070. Provided the time pattern for one of the variables has been determined, then estimates of the other variables probably would be facilitated because of the high interrelationship between variables. Models are suggested in which accurate pivotal forecasting in the short term might be possible—assuming the particular future trend in some of the “independent” variables has been predetermined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111813
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