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  • geostatistics  (5)
  • Springer  (5)
  • Nature Publishing Group
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  • Springer  (5)
  • Nature Publishing Group
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  • 1
    Electronic Resource
    Electronic Resource
    Some exact sampling distributions for variogram estimators (1979)
    Springer
    Mathematical geology 11 (1979), S. 643-653 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; variogram estimation ; sampling distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract For equally spaced observations from a one-dimensional, stationary, Gaussian random function, the characteristic function of the usual variogram estimator $$\hat \gamma k$$ for a fixed lag k is derived. Because the characteristic function and the probability density function form a Fourier integral pair, it is possible to tabulate the sampling distribution of a function of a $$\hat \gamma k$$ using either analytic or numerical methods. An example of one such tabulation is given for an underlying model that is simple transitive.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031889
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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    Generating large stochastic simulations—The matrix polynomial approximation method (1987)
    Springer
    Mathematical geology 19 (1987), S. 99-107 
    Details
    ISSN: 1573-8868
    Keywords: geostatistics ; simulation ; Toeplitz matrices ; block Toeplitz matrices ; matrix polynomial approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An algorithm for producing a nonconditional simulation by multiplying the square root of the covariance matrix by a random vector is described. First, the square root of a matrix (or a function of a matrix in general) is defined. The square root of the matrix can be approximated by a minimax matrix polynomial. The block Toeplitz structure of the covariance matrix is used to minimize storage. Finally, multiplication of the block Toeplitz matrix by the random vector can be evaluated as a convolution using the fast Fourier transform. This results in an algorithm which is not only efficient in terms of storage and computation but also easy to implement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00898190
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Regionalization in geology by multivariate classification (1990)
    Springer
    Mathematical geology 22 (1990), S. 573-588 
    Details
    ISSN: 1573-8868
    Keywords: classification ; regionalization ; Bayes' theorem ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The concept of multivariate classification of “geological objects” can be combined with the concept of regionalized variables to yield a procedure for typification of geological objects, such as rock units, well records, or samples. Numerical classification is followed by subdivision of the area of investigation, and culminates in a regionalization or mapping of the classification onto the plane. Regions are subdivisions of the map area which are spatially contiguous and relatively homogeneous in their geological properties. The probability of correct classification of each point within a region as being part of that region can be assessed in terms of Bayesian probability as a space-dependent function. The procedure is applied to subsurface data from western Kansas. The geologic properties used are quantitative variables, and relationships are expressed by Mahalanobis' distances. These functions could be replaced by other metrics if qualitative or binary data derived from geological descriptions or appraisals were included in the analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00890505
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