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  • Articles  (11)
  • kriging  (11)
  • Springer  (11)
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  • Articles  (11)
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  • Springer  (11)
  • American Geophysical Union
  • American Meteorological Society
  • American Physical Society (APS)
  • Springer Nature
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  • 2010-2014
  • 2000-2004
  • 1995-1999
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  • Geosciences  (11)
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  • 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
    Bayesian kriging—Merging observations and qualified guesses in kriging (1987)
    Springer
    Mathematical geology 19 (1987), S. 25-39 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; kriging ; Bayesian statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Frequently a user wants to merge general knowledge of the regionalized variable under study with available observations. Introduction of fake observations is the usual way of doing this. Bayesian kriging allows the user to specify a qualified guess, associated with uncertainty, for the expected surface. The method will provide predictions which are based on both observations and this qualified guess.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01275432
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  • 3
    Electronic Resource
    Electronic Resource
    Production of conditional simulations via the LU triangular decomposition of the covariance matrix (1987)
    Springer
    Mathematical geology 19 (1987), S. 91-98 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; kriging ; conditional simulation ; fast Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper reviews the turning band method and fast Fourier transform method of producing a nonconditional simulation of a multinormal random function with a given covariance structure. A review of the two common methods of conditioning the simulation to honor the data shows that they are formally equivalent. Another method for directly pondering a conditional simulation based on the LU triangular decomposition of the covariance matrix is presented. Computational and implementation difficulties are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00898189
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  • 4
    Electronic Resource
    Electronic Resource
    Interval-valued random functions and the kriging of intervals (1988)
    Springer
    Mathematical geology 20 (1988), S. 145-165 
    Details
    ISSN: 1573-8868
    Keywords: interval-valued data ; random function ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Estimation procedures using data that include some “values” known to lie within certain intervals are usually regarded as problems of constrained optimization. A different approach is used here. Intervals are treated as elements of a positive cone, obeying the arithmetic of interval analysis, and positive interval-valued random functions are discussed. A kriging formalism for interval-valued data is developed. It provides estimates that are themselves intervals. In this context, the condition that kriging weights be positive is seen to arise in a natural way. A numerical example is given, and the extension to universal kriging is sketched.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00890251
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  • 5
    Electronic Resource
    Electronic Resource
    Spatial prediction and ordinary kriging (1988)
    Springer
    Mathematical geology 20 (1988), S. 405-421 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; nugget effect ; range ; sill ; variogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Suppose data {Z(s i ):i=1, ..., n} are observed at spatial locations {s i :i=1, ..., n}. From these data, an unknownZ(s 0) is to be predicted at a known locations 0c, or, ifZ(s0) has a component of measurement error, then a smooth versionS(s 0) should be predicted. This article considers the assumptions needed to carry out the spatial prediction using ordinary kriging, and looks at how nugget effect, range, and sill of the variogram affect the predictor. It is concluded that certain commonly held interpretations of these variogram parameters should be modified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00892986
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  • 6
    Electronic Resource
    Electronic Resource
    New distance measures: The route toward truly non-Gaussian geostatistics (1988)
    Springer
    Mathematical geology 20 (1988), S. 459-475 
    Details
    ISSN: 1573-8868
    Keywords: Projection theorem ; kriging ; scalar product ; heteroscedasticity ; outlier resistance ; variogram ; distance measure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The projection or minimum error norm algorithm does not require that the distance measure be a variogram. In non-Gaussian cases, the traditional variogram distance measure leading to minimization of an error variance offers no definite advantage. Other distance measures, more outlierresistant than the variogram, are proposed which fulfill the condition of the projection theorem. The resulting minimum error norms provide the same data configurations ranking as traditionally obtained from kriging variances. A case study based on actual digital terrain data is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00892989
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  • 7
    Electronic Resource
    Electronic Resource
    Bootstrapped models for intrinsic random functions (1988)
    Springer
    Mathematical geology 20 (1988), S. 699-715 
    Details
    ISSN: 1573-8868
    Keywords: Regionalized variables ; kriging ; interpolation ; sample reuse ; nonparametric error estimates ; confidence intervals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Use of intrinsic random function stochastic models as a basis for estimation in geostatistical work requires the identification of the generalized covariance function of the underlying process. The fact that this function has to be estimated from data introduces an additional source of error into predictions based on the model. This paper develops the sample reuse procedure called the “bootstrap” in the context of intrinsic random functions to obtain realistic estimates of these errors. Simulation results support the conclusion that bootstrap distributions of functionals of the process, as well as their “kriging variance,” provide a reasonable picture of variability introduced by imperfect estimation of the generalized covariance function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00890586
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  • 8
    Electronic Resource
    Electronic Resource
    Robust estimation of the variogram: I (1980)
    Springer
    Mathematical geology 12 (1980), S. 115-125 
    Details
    ISSN: 1573-8868
    Keywords: Geostatistics ; kriging ; robust estimation ; variogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is a matter of common experience that ore values often do not follow the normal (or lognormal) distributions assumed for them, but, instead, follow some other heavier-tailed distribution. In this paper we discuss the robust estimation of the variogram when the distribution is normal-like in the central region but heavier than normal in the tails. It is shown that the use of a fourth-root transformation with or without the use of M-estimation yields stable robust estimates of the variogram.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01035243
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  • 9
    Electronic Resource
    Electronic Resource
    Random vectors and spatial analysis by geostatistics for geotechnical applications (1987)
    Springer
    Mathematical geology 19 (1987), S. 467-479 
    Details
    ISSN: 1573-8868
    Keywords: random vectors ; spatial analysis ; vector variogram ; kriging ; rock fracture orientation ; structural modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geostatistics is extended to the spatial analysis of vector variables by defining the estimation variance and vector variogram in terms of the magnitude of difference vectors. Many random variables in geotechnology are in vectorial terms rather than scalars, and its structural analysis requires those sample variable interpolations to construct and characterize structural models. A better local estimator will result in greater quality of input models; geostatistics can provide such estimators: kriging estimators. The efficiency of geostatistics for vector variables is demonstrated in a case study of rock joint orientations in geological formations. The positive cross-validation encourages application of geostatistics to spatial analysis of random vectors in geoscience as well as various geotechnical fields including optimum site characterization, rock mechanics for mining and civil structures, cavability analysis of block cavings, petroleum engineering, and hydrologic and hydraulic modelings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00896915
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  • 10
    Electronic Resource
    Electronic Resource
    Estimation of the generalized covariance function: II. A response surface approach (1987)
    Springer
    Mathematical geology 19 (1987), S. 769-783 
    Details
    ISSN: 1573-8868
    Keywords: Cross-validation ; geostatistics ; intrinsic random functions of orderk ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A procedure is proposed that employs first-moment estimation (kriging), cross-validation, and response surface analysis to estimate parameters of a generalized covariance function. Results from application of this procedure to two data sets are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00893014
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