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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