**Z****.**** Vyzhva****, ****Dr****. ****Sci****. ****(****Phys****.-****Math****.), Assos. P****rof.,**

**E-mail:
zoya_vyzhva@ukr.net**

**V.** **Demidov, ****Cand****. ****Sci. (****Phys****.-****Math****.),**** A****ssistant,**

**E-mail: ****fondadl@** **ukr.net**

**A. Vyzhva, Postgraduate
Student,**

**E-mail: ****motomustanger@ukr.net**

**Geological Faculty****, ****Taras Schevchenko National University of Kyiv**

**90****,**** ****Vasylkivska**** Str****., ****Kyiv****, 03022 ****Ukraine**

MONTE CARLO METHOD AND CAUCHY MODEL: IDENTIFYING CHALK LAYER DENSITY ON RIVNE NPP

INDUSTRIAL AREA

*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
ÒÂÌ (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.**

**Key
words: environmental geophysical monitoring,
chalk layer, statistical model.**