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Geoinformatika 2014; 3(51) : 47-56 (in Ukrainian)


Z.A. Vyzhva, V.K. Demidov, A.S. Vyzhva

Taras Shevchenko National University of Kyiv, Vasylkivska str. 90, Kyiv 03022, Ukraine, e-mail: zoya_vyzhva@ukr.net, fondad@ukr.net, motomustanger@ukr.net

The article is devoted to the application of the theory and methods of 3D random fields statistical simulation (Monte Carlo methods) to environmental geophysical monitoring problems. To investigate chalk layer density on the Rivne NPP industrial site a new effective statistical technique has been devised to simulate random fields in 3D space, based on spectral decomposition. The 2D data were selected from 3D density data of chalk rock strata at three depth levels (28, 29, 30 m from the surface). At each level, the data were presented as the sum of deterministic and random components. The deterministic 2D trend surface was constructed using spline interpolation. The random component (the so called “noise”) is a 2D homogeneous isotropic random field. The authors considered the problem of statistical simulation of “noise” for chalk layer density realizations as random fields in 3D space. Statistical models have been constructed for the gauss random fields in three-dimensional space given by their statistical characteristics. Using these models, formulated algorithms and created programs, the authors have obtained 3D random fields realization with difference Bessel types, Cauchy types, and hole effect with certain parameters values. 300 additional values were simulated in the intervals between observation points for each level by constructing original programs Spectr 3 and Spectr 3_1 based on the chosen statistical models. The authors compared mean-square errors of simulation made by the proposed methods and the ТВМ (turning band method) method. Statistical simulation method of random processes and fields in 3D space was I  ntroduced based on spectral decompositions, in order to enhance map accuracy with chalk layer density data. The paper suggests a universal method of statistical simulation of geophysical data to generate random 3D fields’ realizations on grids with required accuracy and regularity.

Keywords: statistical simulation, random field, correlations function, statistical model.



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