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  • Articles  (12)
  • regression analysis  (12)
  • 1970-1974  (12)
  • Geosciences  (12)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Architecture, Civil Engineering, Surveying
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  • Articles  (12)
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  • Geosciences  (12)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Architecture, Civil Engineering, Surveying
  • Mathematics  (12)
  • 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
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Nonlinear regression for dependent variables (1973)
    Springer
    Mathematical geology 5 (1973), S. 365-375 
    Details
    ISSN: 1573-8868
    Keywords: curve fitting ; regression analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Nonlinear regression methods can be used to fit functions for two related variables where both variables are subject to error. A computer program for nonlinear estimation described previously has been modified to fit such functions for a given set of data. A numerical example is provided for a second-degree equation in xand y.A closer fit to an observed set of data is possible if the error structure for the variables is specified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111987
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  • 7
    Electronic Resource
    Electronic Resource
    A piecewise exponential model for seismic well-logging data (1974)
    Springer
    Mathematical geology 6 (1974), S. 33-45 
    Details
    ISSN: 1573-8868
    Keywords: inversion of data ; mathematics ; numerical analysis ; regression analysis ; geophysics ; petroleum ; well logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Conventional methods of analyzing sonic log data do not always yield accurate information on each velocity segment of a well. It is shown here that the velocity-depth parameters and the sections of approximately constant velocity may be more precisely defined by using an exponential spline to model the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111925
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  • 8
    Electronic Resource
    Electronic Resource
    Efficiency of regression techniques for ore valuation at Kolar Gold Fields, India (1972)
    Springer
    Mathematical geology 4 (1972), S. 25-34 
    Details
    ISSN: 1573-8868
    Keywords: correlation ; lognormal distribution ; regression analysis ; statistics ; trend analysis ; mining ; ore valuation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The Kolar Gold Fields are some of the best known gold deposits in India. An example of ore valuation utilizing 49 ore blocks of the Oriental lode of the West Reefs, explored and developed in the Nundydroog mines, is given. In this reef system, there are large ore reserves of sulfidebearing quartz reefs, and the gold distribution is erratic both along strike and downdip. Ore valuation at present is based on the arithmetic mean of samples taken at peripheral positions of the blocks. Samples taken from internal portions of the blocks give a totally different picture of the value. To correct this discrepancy, normal regression and lognormal regression of internal block and total block values, over peripheral block values have been used to evaluate the deposits. The valuation efficiency criterion shows the logarithmic variance for distribution of ratios of unregressed and regressed block values with the corresponding arithmetic mean of internal stope values as observed inside the blocks. The studies have shown that the logarithmic variance is minimum if the logarithmic regression is used, thereby indicating maximum efficiency. Further, the undervaluation and overvaluation of low- and high-grade blocks is less for the logarithmic example. With help of the logarithmic regression equation an effective pay limit of 177.8 in.-dwt has been found for selective mining, for peripheral block values corresponding to the official pay limit of 240 in.-dwt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083190
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  • 9
    Electronic Resource
    Electronic Resource
    The statistical zap versus the shotgun approach (1974)
    Springer
    Mathematical geology 6 (1974), S. 311-332 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082354
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  • 10
    Electronic Resource
    Electronic Resource
    Efficiency of local polynomials in contour mapping (1972)
    Springer
    Mathematical geology 4 (1972), S. 291-305 
    Details
    ISSN: 1573-8868
    Keywords: mapping ; regression analysis ; trend analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract On the basis of samples taken from a known topographic surface, the parameters of two types of linear models are estimated. The first category is defined by polynomials or trigonometric functions, whose parameters are simultaneously computed from available data. In the second category a set of local centers is defined, and in the neighborhood of each center a fixed-degree polynomial is developed. An approximative resemblance index is calculated, and contour maps corresponding to various models are compared with the topographic map. It is found that with an increasing number of grid points, maps of local polynomials are converging both in continuity and in resemblance. For a sufficient number of grid points, this resemblance is always higher than those produced by models of the first category.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114091
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