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  • Articles  (5)
  • trend analysis  (5)
  • 1980-1984
  • 1970-1974  (5)
  • 1935-1939
  • 1972  (5)
  • Mathematics  (5)
  • Geosciences  (5)
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  • Articles  (5)
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  • 1980-1984
  • 1970-1974  (5)
  • 1935-1939
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  • Mathematics  (5)
  • Geosciences  (5)
  • 1
    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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    Paper (German National Licenses)
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  • 2
    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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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Trend-surface analysis of distribution of some heavy minerals in shelf sediments off Mangalore, India (1972)
    Springer
    Mathematical geology 4 (1972), S. 277-290 
    Details
    ISSN: 1573-8868
    Keywords: trend analysis ; mineralogy ; oceanography ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The mineralogy of the 0.062–0.125 and 0.125–0.25 mm fractions of 58 selected samples from a set of 78 samples collected at a spacing of 1–2 km in the inner shelf of Mangalore were studied. Trend-surface analysis of distribution of the heavy minerals, hornblende, muscovite, garnet, and sillimanite, were made to determine the various factors controlling the mineral-distribution patterns in the area. Parts of the area showing contrasting environments were analyzed separately to determine the relationship of the regional and local trends and the various factors controlling the trends. The linear, quadratic and cubic trends for hornblende, garnet, and sillimanite were controlled by the source, westerly river flow and southerly currents; for mica, the response to processes has been the main factor. The mineral distribution in this area is mainly the result of dynamic interaction of process and response elements and a process-response model is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114090
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  • 5
    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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