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  • Articles  (10)
  • geostatistics  (10)
  • Springer  (10)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Institute of Electrical and Electronics Engineers
  • Molecular Diversity Preservation International
  • Springer Nature
  • Springer Science + Business Media
  • 2020-2022
  • 2010-2014
  • 1985-1989  (5)
  • 1980-1984  (5)
  • 1960-1964
  • 2020
  • 1985  (5)
  • 1984  (5)
  • Geosciences  (10)
  • Mathematics  (9)
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  • Articles  (10)
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  • Springer  (10)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Institute of Electrical and Electronics Engineers
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  • 2020-2022
  • 2010-2014
  • 1985-1989  (5)
  • 1980-1984  (5)
  • 1960-1964
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  • Geosciences  (10)
  • Mathematics  (9)
  • 1
    Electronic Resource
    Electronic Resource
    Comparison of geostatistical calculations with the results of open pit mining at the Iharkut bauxite district, Hungary: A case study (1984)
    Springer
    Mathematical geology 16 (1984), S. 173-191 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; reserve evaluation ; bauxite prospecting ; open-pit mining
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geostatistical calculations were carried out on two completely exhausted open-pit bauxite mines in the Iharkut bauxite district, Hungary. Fictitious regular drilling grids were laid on the maps, and horizontal variograms were calculated for drilling grids evaluating the bauxite surface, footwall surface, and bauxite thickness. Point kriging was carried out for all three parameters. Bauxite reserves were calculated using block kriging for bauxite thickness. The total estimation variance of the reserves has been established. Results were compared with real reserves obtained from the mine maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032215
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  • 2
    Electronic Resource
    Electronic Resource
    Conditional estimation variances: An empirical approach (1984)
    Springer
    Mathematical geology 16 (1984), S. 327-350 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; estimation variance ; recoverable reserves
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract One of the tasks routinely carried out by geostatisticians is the evaluation of global mining reserves corresponding to a given cutoff grade and size of selective mining units. A long with these recovery figures, the geostatistician generally provides an assessment of the global estimation variance, which represents the precision of the overall average grade estimate, when no cutoff is applied. Such a global estimation variance is of limited interest for evaluating mining projects; what is required is the reliability of the estimate of recovered reserves or, in other words, the conditional estimation variance. Unfortunately, classical linear geostatistical methods fail to provide an easy way to estimate this variance. Through the use of simulated deposits (representing various types of regionalization)the present paper reviews and discusses the effects of changes in cutoff grade and selective mining unit size on the conditional estimation variance. It is shown that, when the cutoff grade is applied to a pointsupport (sample-size)distribution, the conditional estimation variance appears to be readily accessible by classical formulas, once the conditional semivariogram is known. However, the evaluation of the conditional estimation variance seems to be less straightforward for the general case when a cutoff is applied to the average grade distribution of selective mining units. Empirical approximation formulas for the conditional estimation variance are tentatively proposed, and their performance in the case of the simulated deposits is shown. The limitations of these approximations are discussed, and possible ways of formalizing the problem suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029885
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  • 3
    Electronic Resource
    Electronic Resource
    Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity (1984)
    Springer
    Mathematical geology 16 (1984), S. 19-35 
    Details
    ISSN: 1573-8868
    Keywords: groundwater ; geostatistics ; cokriging ; kriging ; transmissivity ; specific capacity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper presents a new application of the cokriging technique for constructing maps of aquifer transmissivity from field measurements of transmissivity and specific capacity. The technique is illustrated using data from Yolo Basin, California. Cokriging is well-suited for estimating undersampled variables. To improve the accuracy of the estimation, cokriging considers the spatial auto-correlation of the variable to be estimated and the spatial cross-correlation between the variable to be estimated and other, better-sampled variables. Consequently, in regions that lack data of the variable to be estimated, accurate estimation can still be made on the basis of auto- and cross-correlation. In addition, estimation variances can be obtained with a little additional computation effort.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036238
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  • 4
    Electronic Resource
    Electronic Resource
    Minimum-variance unbiased quadratic estimation of covariances of regionalized variables (1985)
    Springer
    Mathematical geology 17 (1985), S. 195-208 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; covariance estimation ; optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033154
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  • 5
    Electronic Resource
    Electronic Resource
    Global estimation variance: Formulas and calculation (1985)
    Springer
    Mathematical geology 17 (1985), S. 785-796 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; kriging ; estimation variance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper discusses the combination of kriging variances, which have been considered heretofor unfeasible since linearity of the problem and considerable simplifications which follow were overlooked. A simplified expression for global estimation variance is presented and an algorithm discussed with respect to precision and computer cost. A case study is presented, and, finally, an optimum calculation method is recommended.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01034061
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  • 6
    Electronic Resource
    Electronic Resource
    Kriging in a global neighborhood (1984)
    Springer
    Mathematical geology 16 (1984), S. 249-265 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; moving neighborhood ; global neighborhood ; geostatistics ; automatic contouring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The kriging estimator is usually computed in a moving neighborhood; only the data near the point to be estimated are used. This moving neighborhood approach creates discontinuities in mapping applications. An alternative approach is presented here, whereby all points are estimated using all the available data. To solve the resulting large linear system the kriging estimator is expressed in terms of the inverse of the covariance matrix. The covariance matrix has the advantage of being positive definite and the size of system which can be solved without encountering numerical instability is substantially increased. Because the kriging matrix does not change, the estimator can be written in terms of scalar products, thus avoiding the more time-consuming matrix multiplications of the standard approach. In the particular case of a covariance which is zero for distances greater than a fixed value (the range), the resulting banded structure of the covariance matrix is shown to lead to substantial computational savings in both run time and storage space. In this case the calculation time for the kriging variance is also substantially reduced. The present method is extended to the nonstationary case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032690
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  • 7
    Electronic Resource
    Electronic Resource
    Testing variograms for positive-definiteness (1984)
    Springer
    Mathematical geology 16 (1984), S. 407-421 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; geostatistics ; positive-definite ; Bochner's theorem ; Hankel transforms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A method based on Bochner's theorem is described for demonstrating the positive-definiteness of variogram models and for generating classes of valid variogram functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029889
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  • 8
    Electronic Resource
    Electronic Resource
    The deterministic side of geostatistics (1985)
    Springer
    Mathematical geology 17 (1985), S. 1-15 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; stationarity ; ergodicity ; spatial average ; deterministic kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The probabilistic approach is but one language used by geostatisticians to characterize spatial variability and to express a very simple criterion for goodness of estimation. Notions such as stationarity and ergodicity are important for the consistency of the probabilistic language but are irrelevant to the real problem, that of estimating a well-defined deterministic spatial average. The kriging algorithm is established without any recourse to probabilistic modeling or notation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030363
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  • 9
    Electronic Resource
    Electronic Resource
    Two-dimensional simulation by turning bands (1985)
    Springer
    Mathematical geology 17 (1985), S. 81-90 
    Details
    ISSN: 1573-8868
    Keywords: simulation ; turning bands ; covariance ; semivariogram ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Journel (1974) developed the turning-bands method which allows a three-dimensional data set with specified covariance to be obtained by the simulation of several one-dimensional realizations which have an intermediate covariance. The relationship between the threedimensional and one-dimensional covariance is straightforward and allows the one-dimensional covariance to be obtained immediately. In theory a dense uniform distribution of lines in three-dimensional space is required along which the one-dimensional realizations are generated; in practice most workers have been content to use the fifteen axes of the regular icosahedron. Many mining problems may be treated in two dimensions, and in this paper a turning-bands approach is developed to generate two-dimensional data sets with a specified covariance. By working in two dimensions, the area on which the data is simulated may be divided as finely as desired by the lines on which the one-dimensional realizations are first generated. The relationship between the two-dimensional and one-dimensional covariance is derived as a nontrivial integral equation. This is solved analytically for the onedimensional covariance. The method is applied to the generation of a two-dimensional data set with spherical covariance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030369
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  • 10
    Electronic Resource
    Electronic Resource
    Some limitations in the geostatistical evaluation of ore deposits (1985)
    Springer
    Geotechnical and geological engineering 3 (1985), S. 155-159 
    Details
    ISSN: 1573-1529
    Keywords: Estimation variance ; geostatistics ; interpolation ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Conclusions The foregoing discussion indicates that geostatistical estimation of ore deposits is not local; it is not objective; it is not sensitive to local data trends; and it is not unrestrained by the range of data values. Kriging, as an interpolation method, is a variant of IDW least squares linear fit. As such, it suffers from the limitations of all IDW linear interpolation methods that employ only data values. The estimation variance, currently used to calculate the confidence limits of values for individual mining blocks, is hypothetical and globally derived. It is more closely related to sampling density than to local variation in the data set. Geostatistical methods, of course, have a real place in ore deposit assessment, e.g. global, comparative evaluation to assist decisions on development and investment. What is questioned here is the validity of employing a global method to assess detail (mining blocks) within an ore deposit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00881627
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