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

#### THE INVESTIGATION OF CHALK LAYER DENSITY ON RIVNE NPP INDUSTRIAL AREA TERRITORY BY MONTE CARLO METHOD USING 3D MODELS

*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.

- Vyzhva Z.O.
*Statystychne modelyuvannya vypadkovykh protsesiv ta poliv*[The statistical simulation of random processes and fields]. Kyiv,*Obriyi*, 2011, 388 p. - Vyzhva Z.O., Demidov V.K., Vyzhva A.S.
*Doslidzhennya hustyny kreydyanoyi tovshchi metodom Monte-Karlo na prommaydanchyku Rivnens’koyi AES iz zastosuvannyam modeli Koshi*[The investigation of chalk layer density on Rivne NPP industrial area territory by Monte Carlo method using Cauchy model].*Visnyk Kyivs’koho natsional’noho universytetu im.**T.**Shevchenka. Seriya Heolohiya*, 2014, no. 65. - Vyzhva S.A., Vyzhva Z.O., Demidov V.K.
*Statystychne modelyuvannya karstovo-sufoziynykh protsesiv na terytoriyi potentsiyno-nebezpechnykh ob’yektiv*[The statistical simulation of karst-suffusion phenomenon on the на territory of potential-dangerous objects].*Geoinformatika*[Geoinformatics (Ukraine)], 2004, no. 2, pp. 78-85. - Vyzhva S.A., Vyzhva Z.O., Demidov V.K.
*Statystychne modelyuvannya tryvymirnykh vypadkovykh poliv u zadachakh monitorynhu heolohichnoho seredovyshcha*[The statistical simulation of three-dimensional random fields on the problems of geological environment monitoring].*Trudy “Teoretychni ta prykladni aspekty heoinformatyky”*[Proc. “Theoretical and applying aspects of Geoinformatics”]. Kyiv,*TOV “Karbon-servis”*, 2006, pp. 173-184. - Vyzhva S.A., Vyzhva Z.O., Demidov V.K.
*Tryvymirne statystychne modelyuvannya metodom randomizatsiyi v zadachakh monitorynhu heolohichnoho seredovyshcha*[The three-dimensional statistical simulation by randomszation method on the problems of geological environment monitoring].*Geoinformatika*[Geoinformatics (Ukraine)], 2008, no. 2, pp. 78-85. - Ermakov S.M., Mykhaylov H.A.
*Statystycheskoe modelyrovanye*[The Statistical Simulation]. Moscow,*Nauka*, 1982, 296 p. - Yadrenko M.I., Gamalij O.G.
*Statystychne modelyuvannya odnoridnykh ta izotropnykh tryvymirnykh vypadkovykh poliv ta otsinky pokhybok modelyuvannya*[Statistical simulation of a homogeneous isotropic random field in the space 3D and estimates of simulation errors].*Teoriya ymovirnostey ta matematychna statystyka*[Theory of Probability and Mathematical Statistics], 1999, no. 59, pp. 171-175. - Chiles J-P., Delfiner P. Geostatistics: Modeling Spatial Uncertainty. N.Y., Toronto,
*John Wiley & Sons*, 2012, 734 p. - Gneiting T. Symmetric Positive Definite Functions with Applications in Spatial Statistics. Von der Universitдt Bayeuth zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung [From the University Bayreuth to obtain the degree of Doctor of Natural Sciences (Dr. rer. nat.) Approved treatise], Bayreuth University, 1997, 107p.
- Mantoglou A., Wilson L.J. Simulation of random fields with turning bands method.
*MIT Ralph M. Parsons Lab. Hydrol. and Water Syst. Rept.*, 1981, no. 264, 199 p.

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