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  • kriging  (5)
  • Springer  (5)
  • American Institute of Physics (AIP)
Collection
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  • Springer  (5)
  • American Institute of Physics (AIP)
Years
  • 1
    Electronic Resource
    Electronic Resource
    Prediction of hydrocarbons in sedimentary basins (1993)
    Springer
    Mathematical geology 25 (1993), S. 925-936 
    Details
    ISSN: 1573-8868
    Keywords: basin analysis ; sedimentary basin ; hydrocarbon exploration ; probability ; multivariate classification ; kriging ; regionalization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract To estimate the undiscovered hydrocarbon potential of sedimentary basins, quantitative play assessments specific for each location in a region may be obtained using geostatistical methods combined with the theory of classification of geological objects, a methodology referred to as regionalization. The technique relies on process modeling and measured borehole data as well as probabilistic methods to exploit the relationship between geology (the “predictor”) and known hydrocarbon productivity (the “target”) to define prospective stratigraphic intervals within a basin. It is demonstrated in case studies from the oil-producing region of the western Kansas Pennsylvanian Shelf and the gas-bearing Rotliegend sediments of the Northeast German Basin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00891051
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  • 2
    Electronic Resource
    Electronic Resource
    Estimation of regionalized compositions: A comparison of three methods (1995)
    Springer
    Mathematical geology 27 (1995), S. 105-127 
    Details
    ISSN: 1573-8868
    Keywords: closed data ; log-ratio ; basis method ; oil field ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence—induced by the constant sum constraint—is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083570
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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
    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
    A fast method for the solution of a system of simultaneous linear equations—A method adapted to a particular problem (1978)
    Springer
    Mathematical geology 10 (1978), S. 369-374 
    Details
    ISSN: 1573-8868
    Keywords: linear equations ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract In mineral deposit evaluation, the estimation of block values can involve the solution of as many as 100,000 systems of linear equations. To minimize computing costs it is important that the program to solve the linear systems be as efficient as possible. Standard library routines tend to contain very general stable methods using pivoting and iteration to ensure high accuracy solutions. Here, a particular method has been developed that gives a substantial improvement in run time at the occasional expense of accuracy and stability. The method is not new—just a simple application of Gaussian elimination in the symmetric case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031741
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