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  • Journals
  • Articles  (5)
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  • kriging  (5)
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  • 1983  (5)
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  • Nature of Science, Research, Systems of Higher Education, Museum Science
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  • Springer  (5)
  • American Association for the Advancement of Science (AAAS)
  • American Chemical Society
  • American Chemical Society (ACS)
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  • 2015-2019
  • 1980-1984  (5)
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  • Geosciences  (5)
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  • Mathematics  (5)
  • 1
    Electronic Resource
    Electronic Resource
    Geostatistics as a tool to define various categories of resources (1983)
    Springer
    Mathematical geology 15 (1983), S. 131-143 
    Details
    ISSN: 1573-8868
    Keywords: Geostatistics ; resource classification ; mineral resources ; kriging ; resource definitions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Definition of “measured” and “indicated” resources tend to be vague. Yet, the calculation of such categories of resources in a mineral deposit calls for specific technical criteria, the selection of which depends upon the method of evaluation. This paper discusses how a geostatistical methodology provides the technical criteria required to classify reasonably assured resources by levels of assurance of their existence. A preliminary discussion concludes that the reasonably assured resources of a mineral deposit should be classified locally as in the traditional approach. However, the size of local volumes should not correspond to the elementary grid unit of drill holes but if possible to the minimum unit of selection that can be supported by the chosen mining method. The “level of confidence” of the reasonably assured resources can be quantitatively represented and determined by the estimation variance, one of the most important tools of geostatistics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030079
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  • 2
    Electronic Resource
    Electronic Resource
    Kriging of water levels in the Souss aquifer, Morocco (1983)
    Springer
    Mathematical geology 15 (1983), S. 537-551 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; drift ; least squares ; residuals ; water table
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Universal kriging is applied to water table data from the Souss aquifer in central Morocco. The procedure accounts for the spatial variability of the phenomenon to be mapped. With the use of measured elevations of the water table, an experimental variogram is constructed that characterizes the spatial variability of the measured water levels. Spherical and Gaussian variogram models are alternatively used to fit the experimental variogram. The models are used to develop contour maps of water table elevations and corresponding estimation variances. The estimation variances express the reliability of the kriged water table elevation maps. Universal kriging also provides a contour map of the expected elevation of the water table (drift). The differences between the expected and measured water table elevations are called residuals from the drift. Residuals from the drift are compared with residuals obtained by more traditional least-squares analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031176
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  • 3
    Electronic Resource
    Electronic Resource
    Cross validation of kriging in a unique neighborhood (1983)
    Springer
    Mathematical geology 15 (1983), S. 687-699 
    Details
    ISSN: 1573-8868
    Keywords: cross validation ; kriging ; moving neighborhood ; unique neighborhood
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Cross validation is an appropriate tool for testing interpolation methods: it consists of leaving out one data point at a time, and determining how well this point can be estimated from the other data. Cross validation is often used for testing “moving neighborhood” kriging models; in this case, each unknown value is predicted from a small number of surrounding data. In “unique neighborhood” kriging algorithms, each estimation uses all the available data; as a result, cross validation would spend much computer time. For instance, with ndata points it would cost at least the resolution of nsystems of n × nlinear equations (each with a different matrix).Here, we present a much faster method for cross validation in a unique neighborhood. Instead of solving nsystems n × n,it only requires the inversion of one n × nmatrix. We also generalized this method to leaving out several points instead of one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033232
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  • 4
    Electronic Resource
    Electronic Resource
    Two methods with different objectives: Splines and kriging (1983)
    Springer
    Mathematical geology 15 (1983), S. 245-257 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; splines ; measurement errors ; generalized covariance ; structural identification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract When drawing a contour map from a set of irregularly spaced data points, two methods are often used: The first corresponds to a rather aesthetic criterion and consists of obtaining contour lines which will be as “smooth”as possible and will honor the data points. This generally is the objective of the draftsman, and it can be automatically performed by the method of spline interpolation. The other method, used in kriging, is to compute the Best Linear Unbiased Estimator (B.L.U.E.),that is, to obtain a map as accurate as possible. Is it possible, in practice, to predict whether the aesthetic map will also be accurate? In this paper, we first examine the theoretical point of view: Spline interpolation is equivalent to kriging with a given (generalized)covariance. We then take an example to show how this question can be answered in practice: by testing how well the spline covariance is suited to the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036069
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  • 5
    Electronic Resource
    Electronic Resource
    Integration of mineral resource data for Kasmere Lake area, Northwest Manitoba, with emphasis on uranium (1983)
    Springer
    Mathematical geology 15 (1983), S. 25-45 
    Details
    ISSN: 1573-8868
    Keywords: Discriminant analysis ; autocorrelation ; kriging ; multiple regression ; uranium ; mineral resources
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geological and geophysical data digitized by Fabbri (1981)are augmented by eleven lakesediment geochemical variables in a quantitative study of the Kasmere Lake—Whiskey Jack Lake area, NW Manitoba. Each of 33 geological map units (Archean and Aphebian igneous and metamorphic rocks)have a fairly distinct multivariate geochemical and geophysical signal, as shown by discriminant analysis which is able to “recover” the geological map from the geophysical and geochemical data. Autocorrelation analysis of the geochemical variables, after removing a quadratic trend, indicate that copper, nickel, uranium, and cobait have a zone of influence from 15 to 30 km or more, with a marked anisotropy parallel to geological, geophysical, and structural trends which run NE-SW, parallel to the Wollaston fold belt. The observed uranium autocorrelation coefficients are modeled as a two-dimensional exponential function with elliptical contours. A trend-signal-noise model is applied to the lake-sediment uranium using kriging on residuals from the quadratic trend. A map comparing the resulting lake-sediment uranium signal with radiometric uranium/thorium patterns indicates considerable overlap and a generally good prediction of known uranium occurrences. In areas with a strong lake-sediment uranium signal, Aphebian metasediments have a somewhat different multivariate geochemical character from Archean and Hudsonian igneous and metamorphic rocks, suggesting a method of removing areas from the signal underlain by granites that may be economically uninteresting. Logistic and stepwise regression experiments based on a control area which includes most of the presently reported occurrences are used to predict areas favorable for uranium exploration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030074
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