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  • Articles  (26)
  • geostatistics  (26)
  • Springer  (26)
  • 2005-2009
  • 1980-1984  (26)
  • 1965-1969
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  • Geosciences  (26)
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  • Articles  (26)
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  • Springer  (26)
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  • 1
    Electronic Resource
    Electronic Resource
    The lognormal approach to predicting local distributions of selective mining unit grades (1980)
    Springer
    Mathematical geology 12 (1980), S. 285-303 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; lognormal distribution ; mine planning ; ore reserve estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract When planning highly selective mining operations, the challenge is to estimate mineable ore reserves that will be selected at the mining stage. From exploration data it is not possible to estimate accurately the grade (or thickness) of each future selective mining unit; however, it is possible to estimate the local distributions of these mining unit grades within large panels suitable for long-range mine planning. Application of a cut-off then allows estimation of the recovered ore tonnage and grade within each such panel. Derivation of local conditional distributions is rather simple when the grade is either normally or lognormally distributed. The geologically important lognormal case is fully described both in the stationary and the nonstationary case. Cross validations of these techniques using the exploration data of the Imouraren uranium deposit are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029417
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  • 2
    Electronic Resource
    Electronic Resource
    The random coin method: Solution of the problem of the simulation of a random function in the plane (1980)
    Springer
    Mathematical geology 12 (1980), S. 25-32 
    Details
    ISSN: 1573-8868
    Keywords: random function ; geostatistics ; simulation ; covariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper presents a new geostatistical method to obtain realizations of stationary random functions in the plane.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01039901
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  • 3
    Electronic Resource
    Electronic Resource
    Disjunctive kriging: Comparison of theory with actual results (1980)
    Springer
    Mathematical geology 12 (1980), S. 305-320 
    Details
    ISSN: 1573-8868
    Keywords: disjunctive kriging ; logarithmic kriging ; gold evaluation ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The method of disjunctive kriging is applied to the evaluation of blocks of ore in a gold mine, and the estimated block values are compared with the true block values. First the theory of disjunctive kriging as applicable to mine valuation is presented from the user's viewpoint. The theory is then applied to process sample values originating from a large gold mine. Using the computer simulation of a number of sampling programs, estimated values and true values are compared. The disjunctive kriging estimates are also compared with estimates obtained by other methods of evaluation, including logarithmic kriging. It is shown that the results obtained, using real world data, are in complete agreement with the results expected according to the geostatistical theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029418
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    The effect of drift on the experimental semivariogram (1982)
    Springer
    Mathematical geology 14 (1982), S. 309-319 
    Details
    ISSN: 1573-8868
    Keywords: Bias ; drift ; semivariogram ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract When nonlinear drift is present, the nature of the bias in the experimental semivariogram estimator of the semivariogram function is determined by the extent and density of the sampling as well as by the drift function itself. The bias caused by drift may affect the interpretation of the experimental semivariogram over its entire range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032592
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  • 6
    Electronic Resource
    Electronic Resource
    Prediction of local ore recoveries and ore-waste ratios at the silver bell uranium mine (1982)
    Springer
    Mathematical geology 14 (1982), S. 645-660 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; uranium ; production forecast
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geostatistical estimation techniques were customized to allow forecasting of production figures at the Silver Bell uranium mine (Uravan District).Surface drill hole data were used to provide a block model of kriged estimators of average uranium grades. Figures for recoverable ore grade and the ore-waste ratio are then deduced from regressive curves previously obtained from underground information and production data. Cross-validations of the entire model were performed and were found positive.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033885
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  • 7
    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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  • 8
    Electronic Resource
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    Nonparametric estimation of spatial distributions (1983)
    Springer
    Mathematical geology 15 (1983), S. 445-468 
    Details
    ISSN: 1573-8868
    Keywords: indicator kriging ; geostatistics ; nonparametric
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The indicator approach, whereby the data are used through their rank order, allows a nonparametric approach to the data bivariate distribution. Such rich structural information allows a nonparametric risk-qualified, estimation of local and global spatial distributions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031292
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  • 9
    Electronic Resource
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    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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  • 10
    Electronic Resource
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    The multigaussian approach and its applications to the estimation of local reserves (1983)
    Springer
    Mathematical geology 15 (1983), S. 259-286 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; local recovery ; conditional expectation ; multigaussian kriging ; disjunctive kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The performance of the geostatistical techniques of disjunctive kriging and multigaussian kriging for the estimation of local recovered reserves are compared using a simulated deposit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036070
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  • 11
    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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  • 12
    Electronic Resource
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    Regression revisited (1983)
    Springer
    Mathematical geology 15 (1983), S. 517-536 
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    ISSN: 1573-8868
    Keywords: Kriging ; geostatistics ; regression effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract One traditional method of estimating ore reserves is to allocate the arithmetic mean of local samples to each block or stope within the deposit. Thirty years ago, Krige showed that this method produced a “bias” in the estimates, in that high values were commonly overestimated and low values underestimated. This bias became known as the “regression effect” because it could usually be corrected by an empirical regression relationship derived from previously mined areas. This paper shows how the regression effect can be reconciled with the geostatistical method of kriging and how a simple regression line may be derived before any areas are mined out. The method is similar to kriging with known mean, but acknowledges that the overall mean of the deposit may not be known precisely.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031175
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  • 13
    Electronic Resource
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    Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity (1984)
    Springer
    Mathematical geology 16 (1984), S. 19-35 
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    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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  • 14
    Electronic Resource
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    Exact formulas for approximating variogram function integrals (1980)
    Springer
    Mathematical geology 12 (1980), S. 577-588 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; geostatistics ; estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01034745
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  • 15
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    On the estimation of the generalized covariance function (1982)
    Springer
    Mathematical geology 14 (1982), S. 57-64 
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    ISSN: 1573-8868
    Keywords: estimation ; generalized covariance function ; generalized increments ; geostatistics ; intrinsic random functions ; multicollinearity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The estimation of the generalized covariance function, K, is a major problem in the use of intrinsic random functions of order k to obtain kriging estimates. The precise estimation by least-squares regression of the parameters in polynomial models for K is made difficult by the nature of the distribution of the dependent variable and the multicollinearity of the independent variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01037447
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  • 16
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    A geostatistical approach to predicting the washability characteristics of coal in situ (1981)
    Springer
    Mathematical geology 13 (1981), S. 321-329 
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    ISSN: 1573-8868
    Keywords: coal washability ; disjunctive kriging ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The washability characteristics of coal are dependent on two basic relations: the ash assay vs. relative density curve, and the distribution by weight of the relative densities of coal particles. Armstrong and Whitmore (1980) demonstrated that the ash content and the yield of coal floating at a particular density can be predicted with reasonable accuracy using a simple inverse proportionality relation for the ash assay vs. density curve and a lognormal model for the distribution. In this paper, geostatistical techniques are used in conjunction with the two models to predict the washability characteristics of coal in situ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031517
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  • 17
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    Geostatistical estimation of parameters for hydrologic transport modeling (1981)
    Springer
    Mathematical geology 13 (1981), S. 415-428 
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    ISSN: 1573-8868
    Keywords: geostatistics ; hydrologic transport ; kriging ; radioactive waste disposal
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A significant part of the work of evaluating a geologic formation as a potential repository for hazardous wastes is the modeling of contaminant transport in the surrounding media in the event the repository is breached. The transport equations that are commonly used are deterministic functions. However, because the data can vary within the area being considered, there is a degree of uncertainty associated with the results obtained from the contaminant transport models. There are several ways to incorporate uncertainties into the transport equations, but they assume that distributions and parameters such as variances and covariances are known. This paper discusses the application of geostatistical spatial estimation techniques to estimate quantities used in transport modeling. The techniques are illustrated on data from an electric analog simulation of a two-dimensional ground water system. Geostatistical methods were used to estimate potential and hydraulic conductivity surfaces from data generated from the simulation of the ground water system. Although the two surfaces were highly dependent through Darcy's Law, they were estimated independently. Independent verification of the two surfaces showed that they approximately satisfied the required conservation of mass condition that: ∇ ⋅ v = 0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01079645
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  • 18
    Electronic Resource
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    Variogram models must be positive-definite (1981)
    Springer
    Mathematical geology 13 (1981), S. 455-459 
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    ISSN: 1573-8868
    Keywords: Variograms ; geostatistics ; positive-definite
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The aim of this short article is to stress the importance of using only positive-definite functions as models for covariance functions and variograms. The two examples presented show that a negative variance can easily be obtained when a nonadmissible function is chosen for the variogram model.
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    URL: http://dx.doi.org/10.1007/BF01079648
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  • 19
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    Studies of the effects of outliers and data transformation on variogram estimates for a base metal and a gold ore body (1982)
    Springer
    Mathematical geology 14 (1982), S. 557-564 
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    ISSN: 1573-8868
    Keywords: geostatistics ; variogram ; outliers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033879
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  • 20
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    Anisotropic hole-effect modeling (1982)
    Springer
    Mathematical geology 14 (1982), S. 217-239 
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    ISSN: 1573-8868
    Keywords: geostatistics ; variograms ; anisotropies ; tungsten
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The regionalization of tungsten grades at the χ deposit represents an ideal case for anisotropic hole-effect variogram modeling. The modeling technique is presented step by step and the consequences of the model on block kriging are indicated.
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    URL: http://dx.doi.org/10.1007/BF01032885
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  • 21
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    Sequential sampling to contour an uncertain function (1982)
    Springer
    Mathematical geology 14 (1982), S. 387-404 
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    ISSN: 1573-8868
    Keywords: geostatistics ; resource estimation ; geoexploration ; sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Sampling exploration of uncertain functions to locate critical contour levels is most effective if sampling decisions are made sequentially. A simple sequential exploration strategy, based on pseudo-Bayesian second-moment analysis, is proposed and compared with non-sequential systematic sampling. Repeated application to functions simulated pseudorandomly from stationary random processes on the line and on the plane indicates uniform superiority of the sequential strategy. The method is particularly advantageous when the function of interest,h(X), has an uncertain trend, and in general when the random process that quantifies prior uncertainty onh(X) is highly correlated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01077529
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  • 22
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    Geostatistical case studies of the advantages of lognormal-de Wijsian kriging with mean for a base metal mine and a gold mine (1982)
    Springer
    Mathematical geology 14 (1982), S. 547-555 
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    ISSN: 1573-8868
    Keywords: geostatistics ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Parallel variogram analyses, block kriging, and follow-up studies were effected for the lead content of part of the Prieska copper-zinc ore body and for the gold content of the highly variable Breef in a section of the Loraine gold mine, based first on untransformed values and second on logarithmically transformed values using the lognormal-de Wijsian model. For both models the effect was also analyzed of using the population mean or ignoring it. Practical follow-up comparisons confirm theoretical considerations and show that on these mines conditional biases can be eliminated conveniently by kriging with mean; also that the lognormal-de Wijsian model with mean gives the best results.
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    URL: http://dx.doi.org/10.1007/BF01033878
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  • 23
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    Automatic recognition of geologic prospects (1983)
    Springer
    Mathematical geology 15 (1983), S. 183-195 
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    ISSN: 1573-8868
    Keywords: Computers ; data files ; exploration ; geostatistics ; petroleum ; prospects ; spatial filtering ; trend analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Computer recognition of prospective areas through the processing of digital exploration data can be effective if the statistical tests for the determination of the prospects are pertinent to the presence of the desired mineral. Where exploration involves the application of polynomial trend analysis to structure contour maps in the search for petroleum and natural gas, standard analysis of variance tests may not indicate the best exploration maps. Variance tests may be completely invalid where isolated dips and clustered samples cause the surfaces generated by some of the most common trend programs to oscillate, creating a false impression of variance. On the other hand, tests that directly compare the position of residual features with areas of known production consistently indicate the best map for the determination of new prospects. They are simple to apply and appear to offer the most opportunity for the automatic recognition of prospective areas.
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    URL: http://dx.doi.org/10.1007/BF01030082
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  • 24
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    Kriging in a global neighborhood (1984)
    Springer
    Mathematical geology 16 (1984), S. 249-265 
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    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.
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    URL: http://dx.doi.org/10.1007/BF01032690
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  • 25
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    Testing variograms for positive-definiteness (1984)
    Springer
    Mathematical geology 16 (1984), S. 407-421 
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    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.
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    URL: http://dx.doi.org/10.1007/BF01029889
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  • 26
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    Multiobjective observation network design for regionalized variables (1983)
    Springer
    Geotechnical and geological engineering 1 (1983), S. 331-342 
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    ISSN: 1573-1529
    Keywords: Optimization ; geostatistics ; mining ; exploration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Summary In this paper mathematical programming models and special solution algorithms are presented for the optimal allocation of data points for regionalized variables. Two models are discussed; the first one minimizes the estimation variance subject to a given number of additional measurement points or additional measurement cost. The second model minimizes the number of additional points or additional cost subject to upper bounds given to the estimation variances. The models are based on the theory of kriging and the properties of the estimation variances, which lead to certain multiobject programming problems. As it can be shown, a special branch and bound algorithm can be used for solving the resulting nonlinear programming problems
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    URL: http://dx.doi.org/10.1007/BF00881549
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