1887

Abstract

Summary

Here a mathematical approach which can be used for comparison of three methods for modeling Gaussian random fields is developed. Namely, the known methods of Sequential Gaussian Simulation and Spectral Modeling as well as new method based of Fourier transform and spectral modeling random fields of Fourier coefficients are considered. We show that these methods give equivalent result when specific Gaussian fields are modeled. Also we discuss advantages and limitations of these methods, their applicability in practice problems, computational complexity and ways for their effective realizations.

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/content/papers/10.3997/2214-4609.201902181
2019-09-02
2024-03-29
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References

  1. Baikov, V.A., Bakirov, N.K. and Yakovlev, A.A. [2010] New Approaches to the Geological and Hydrodynamic Modeling. Oil Industry Publishing house, 9, 56–59.
    [Google Scholar]
  2. Davis, M.W. [1987] Production of Conditional Simulations via the LU Triangular Decomposition of the Covariance Matrix. Mathematical Geology, 19(2), 91–98.
    [Google Scholar]
  3. Dietrich, C.R. and Newsam, G.N. [1996] A Fast and Exact Method for Multidimensional Gaussian Stochastic Simulations: Extensions to Realizations Conditioned on Direct and Indirect Measurements. Water Resources Research, 32(6), 1643–1652.
    [Google Scholar]
  4. Eaton, M.L. [2007] Multivariate Statistics: A Vector Space Approach. Institute of Mathematical Statistics, 53, 512.
    [Google Scholar]
  5. Gentle, J.E. [2009] Computational Statistics. New York: Springer, 727.
    [Google Scholar]
  6. Journel, A.G. and GoovaertsP. [1997] Geostatistics for Natural Resources Evaluation. New York, Oxford University Press, 483.
    [Google Scholar]
  7. Lang, A. and Potthoff, J. [2011] Fast Simulation of Gaussian Random Fields. Monte Carlo Methods Appl., 17, 195–214.
    [Google Scholar]
  8. Matheron, G. [1962] Traite de Geostatistique Appliquee. Tome1.Paris: Technip, 333.
    [Google Scholar]
  9. Park, M. and Tretyakov, M.V. [2015] A Block Circulant Embedding Method for Simulation of Stationary Gaussian Random Fields on Block-Regular Grids. International Journal for Uncertainty Quantification, 5(6), 527–544.
    [Google Scholar]
  10. Prigarin, S.M. [2005] Metody chislennogo modelirovaniya sluchainykh protsessov i polei [Methods of Numerical Simulation of Random Processes and Fields]. Novosibirsk: IVMiMG SO RAN Publishing house, 259
    [Google Scholar]
  11. Remy, N., Boucher, A. and Wu, J. [2009] Applied Geostatistics with SGeMS: A Users' Guide. Cambridge University Press, 284.
    [Google Scholar]
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