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  • Articles  (40)
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  • kriging  (40)
  • 1985-1989  (20)
  • 1980-1984  (20)
  • Mathematics  (40)
  • 1
    Electronic Resource
    Electronic Resource
    Statistical and geostatistical methods applied to the exploration work of the Nanisivik Zn-Pb mine, Baffin Island, Canada (1980)
    Springer
    Mathematical geology 12 (1980), S. 321-337 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; kriging ; variogram analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The Nanisivik Pb-Zn deposit at Strathcona Sound, northern Baffin Island, Canada, is an orebody that is an S-shaped lens 3000 m long, 75 m wide, and 2–20 m thick. It is an epigenetic karst channel filling. Total reserves are 6.9 million short tons of 14.12% Zn, 1.4% Pb, and 1.77 oz of Ag per ton. The mine was brought into production in 1976 at a rate of 2000 short tons per day. In the preproduction phase variogram studies based only on surface holes indicated a random distribution. For the evaluation of grades and for the determination of the confidence limits, classic statistical procedures were applied. Since the drilling density was different in different ore zones, a model was developed to test the effect of different drill hole spacings on the uncertainties in the present value in a discounted cash flow model. After the initial development and mining stage, structures could be recognized in semivariograms. Studies for a best drilling grid showed that the pattern of 25 ×20 m used in the mine could be extended to 35 ×35 m, taking into account that eight stopes are mined simultaneously. For ore reserve calculations weighing factors were calculated by kriging for six universally applicable geometric situations. Only the drill holes within a block and immediately surrounding it were taken into account. A test in a well-known zone yielded satisfactory results. A test to predict highs and lows of the grade accurately enough to optimally place the pillars failed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029419
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  • 2
    Electronic Resource
    Electronic Resource
    Lognormal kriging—the general case (1982)
    Springer
    Mathematical geology 14 (1982), S. 475-499 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; lognormal estimation ; conservation of lognormality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A theoretical study of the general case of the estimation of regionalized variables with a lognormal distribution is presented. The results of this study are compared to those obtained assuming conservation of lognormality. The numerical significance of the different solutions is illustrated by several simple examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01077535
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  • 3
    Electronic Resource
    Electronic Resource
    Variogram models for regional groundwater geochemical data (1982)
    Springer
    Mathematical geology 14 (1982), S. 629-644 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; kriging ; interpolation ; contouring ; inverse distance weighting ; geochemical gradient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Four variogram models for regional groundwater geochemical data are presented. These models were developed from an empirical study of the sample variograms for more than 10 elements in groundwaters from two geologic regions in the Plainview quandrangle, Texas. A procedure is given for the estimation of the variogram in the isotropic and anisotropic case. The variograms were found useful for quantifying the differences in spatial variability for elements within a geologic unit and for elements in different geologic units. Additionally, the variogram analysis enables assessment of the assumption of statistical independence of regional samples which is commonly used in many statistical procedures. The estimated variograms are used in computation of kriged estimates for the Plainview quadrangle data. The results indicate that an inverse distance weighting model was superior for prediction than simple kriging with the particular variograms used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033884
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  • 4
    Electronic Resource
    Electronic Resource
    The combination of sampling and kriging in the regional estimation of coal resources (1982)
    Springer
    Mathematical geology 14 (1982), S. 87-106 
    Details
    ISSN: 1573-8868
    Keywords: coal ; geostatistics ; kriging ; regional estimation ; systematic sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Two-dimensional systematic sampling of small plots followed by the kriging of those plots may be employed to obtain regional estimates of coal resources and measures of the accuracy of the estimates. The use of sampling makes large savings in computation possible. Two case studies involving the estimation of coal tonnage are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01083946
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  • 5
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Robust kriging—A proposal (1984)
    Springer
    Mathematical geology 16 (1984), S. 3-18 
    Details
    ISSN: 1573-8868
    Keywords: Geostatistics ; kriging ; robust estimation ; time series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geological data frequently have a heavy-tailed normal-in-the-middle distribution, which gives rise to grade distributions that appear to be normal except for the occurrence of a few outliers. This same situation also applies to log-transformed data to which lognormal kriging is to be applied. For such data, linear kriging is nonrobust in that (1)kriged estimates tend to infinity as the outliers do, and (2)it is also not minimum mean squared error. The more general nonlinear method of disjunctive kriging is even more nonrobust, computationally more laborious, and in the end need not produce better practical answers. We propose a robust kriging method for such nearly normal data based on linear kriging of an editing of the data. It is little more laborious than conventional linear kriging and, used in conjunction with a robust estimator of the variogram, provides good protection against the effects of data outliers. The method is also applicable to time series analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036237
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  • 8
    Electronic Resource
    Electronic Resource
    Smoothing and interpolation by kriging and with splines (1984)
    Springer
    Mathematical geology 16 (1984), S. 601-615 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; splines ; interpolation ; smoothing ; prediction ; Green's function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Let scalar measurements at distinct points x1, ⋯, xn be y1, ⋯, yn.We may look for a smooth function f(x)that goes through or near the points (xi, yi).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029320
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  • 9
    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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  • 10
    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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