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  • Articles  (45)
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  • geostatistics  (45)
  • 1985-1989  (20)
  • 1980-1984  (25)
  • Mathematics  (45)
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  • Articles  (45)
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  • 1
    Electronic Resource
    Electronic Resource
    On the importance of choosing a change of support model for global reserves estimation (1988)
    Springer
    Mathematical geology 20 (1988), S. 1001-1019 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; change of support ; recoverable reserves ; selectivity ; normality index ; Cartier's formula ; affine correction ; discrete Gaussian model ; mosaic model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The practical problem considered here is: how can block distribution in an orebody be forecast from sample data? The task is arduous because information yielded by samples is too often insufficient to allow an accurate evaluation of blocks. In practice, necessary additional information is obtained via a model. Choosing that model is crucial; the value of results reflects the model, i.e., its adequacy to represent reality. In this paper, the importance of choosing the change of support model is illustrated with simulations and practical examples (especially deposits with a skewed sample distribution and a large spike at the origin). An attempt to quantify this importance is made also.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00892976
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  • 2
    Electronic Resource
    Electronic Resource
    Bayesian updating revisited (1989)
    Springer
    Mathematical geology 21 (1989), S. 285-308 
    Details
    ISSN: 1573-8868
    Keywords: Bayesian updating ; geostatistics ; Kriging ; linear inversion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Bayesian updating methods provide an alternate philosophy to the characterization of the input variables of a stochastic mathematical model. Here, a priori values of statistical parameters are assumed on subjective grounds or by analysis of a data base from a geologically similar area. As measurements become available during site investigations, updated estimates of parameters characterizing spatial variability are generated. However, in solving the traditional updating equations, an updated covariance matrix may be generated that is not positive-definite, particularly when observed data errors are small. In addition, measurements may indicate that initial estimates of the statistical parameters are poor. The traditional procedure does not have a facility to revise the parameter estimates before the update is carried out. alternatively, Bayesian updating can be viewed as a linear inverse problem that minimizes a weighted combination of solution simplicity and data misfit. Depending on the weight given to the a priori information, a different solution is generated. A Bayesian updating procedure for log-conductivity interpolation that uses a singular value decomposition (SVD) is presented. An efficient and stable algorithm is outlined that computes the updated log-conductivity field and the a posteriori covariance of the estimated values (estimation errors). In addition, an information density matrix is constructed that indicates how well predicted data match observations. Analysis of this matrix indicates the relative importance of the observed data. The SVD updating procedure is used to interpolate the log-conductivity fields of a series of hypothetical aquifers to demonstrate pitfalls and possibilities of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00893691
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  • 3
    Electronic Resource
    Electronic Resource
    Factorial kriging analysis applied to geological data from petroleum exploration (1989)
    Springer
    Mathematical geology 21 (1989), S. 683-691 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; factorial kriging analysis ; spectral analysis ; petroleum exploration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A regionalized variable, thickness of the reservoir layer, from a gas field is decomposed by factorial kriging analysis. Maps of the obtained components may be associated with depositional environments that are favorable for petroleum exploration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00893316
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  • 4
    Electronic Resource
    Electronic Resource
    Variography of submarine morphology: Problems of deregularization, and cartographical implications (1989)
    Springer
    Mathematical geology 21 (1989), S. 693-713 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; variography ; deregularization ; universal kriging ; bathymetry ; SEABEAM survey ; cartography
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract During the German Antarctic Expedition VI (leg 3, December 1987 to March 1988), bathymetric surveys were made in the Weddell Sea by the SEABEAM sonar system. For the first time geostatistical methods were applied in the SEABEAM-postprocessing. The investigations of variography that were necessary prior to the cartographical-geomorphological evaluation shed new light on classical geostatistical concerns. SEABEAM data provide a good example of a mean square, differentiable regionalized variable, where data are sampled over a two-dimensional support due to the technique of the sonar device. By deregularizations of the sample variograms, spatial continuity can be shown to be a property of seafloor depth as well as a point variable. The results are discussed in a sedimentological context. As an application of the regional variogram analyses, large-scale kriged bathymetric maps are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00893317
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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    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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  • 9
    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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  • 10
    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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