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  • Articles  (10)
  • trend analysis  (10)
  • 1970-1974  (10)
  • Geosciences  (10)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Architecture, Civil Engineering, Surveying
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  • Articles  (10)
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  • Geosciences  (10)
  • Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
  • Architecture, Civil Engineering, Surveying
  • Mathematics  (10)
  • 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
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Spline-surface interpolation, spatial filtering, and trend surfaces for geological mapped variables (1973)
    Springer
    Mathematical geology 5 (1973), S. 111-126 
    Details
    ISSN: 1573-8868
    Keywords: contouring ; mapping ; trend analysis ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Spline surfaces are interpolated for top of the Dundee Limestone of the central Michigan Basin, USA. The requirement of gridded data render spline functions inappropriate tools for representing many types of geological mapped data. Comparisons are drawn with maps for the same Michigan data based on trend surfaces and spatial filtering.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111890
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  • 9
    Electronic Resource
    Electronic Resource
    Z-trend maps for quick recognition of geologic patterns (1971)
    Springer
    Mathematical geology 3 (1971), S. 171-181 
    Details
    ISSN: 1573-8868
    Keywords: Fourier analysis ; graphics ; mapping ; spatial filtering ; trend analysis ; stratigraphy ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Z-trend maps are a simplified lineprinter version of spatially filtered maps designed to give a quick visual appraisal of trends. The printout shows a “yes-no” configuration by a printed character or a blank so that the map has a conspicuous pattern. This pattern reflects the presence, position, and trend of the desired features. If a reasonable symbol density ratio is used the results can be visually pleasing thus enhancing trend recognition. Z-trending can be adapted to any map with stationary properties but is most easily applied to data that have been filtered with a bandpass operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045959
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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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