MONTE CARLO METHOD AND CAUCHY MODEL: IDENTIFYING CHALK LAYER DENSITY ON RIVNE NPP INDUSTRIAL AREA - Vyzhva, Z.; Demidov, V.; Vyzhva, A. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
The paper furthers the theory and methods of random process and field statistical simulation (Monte Carlo methods) based on spectral decomposition, and focuses on the application of the methods mentioned to environmental geophysical monitoring. A new effective statistical technique has been devised to simulate random fields in 3D space for chalk layer density on the Rivne NPP industrial site. There has been solved the problem of statistical simulation of "noise" for chalk layer density realizations as random fields in 3D space. 2D data were selected from 3D data on chalk layer density at three depth levels (28, 29, 30 m below the surface). The data were presented as the sum of deterministic and random components for each level. Deterministic 2D trend surface was constructed using spline interpolation. The random component ("noise" factor) is a 2D homogeneous isotropic random field. There has been formulated an algorithm to generate "noise" field realization for chalk layer density involving Cauchy correlation function, which has been devised on the mean-square approximation of random fields' estimator. There has been made a statistical model for Gaussian homogeneous and isotropic random fields in three-dimensional space, which were given by their statistical characteristics. There has been made Spectr 3 program based on the chosen statistical model and the formulated algorithm for statistical simulation of 3D random fields' realizations. Additionally simulated have been 300 values in the intervals between observation points for each level. The effective comparison of error simulation between the method proposed and ТВМ (turning band method) has been made. There has been introduced a method of random processes and fields in 3D space statistical simulation based on spectral decompositions in order to enhance map accuracy by the example of chalk layer density data. There has been developed a universal method of statistical simulation of geophysical data for generating random 3D fields' realizations on grids with required accuracy and regularity.
Keywords: environmental geophysical monitoring; chalk layer; statistical model