**Z.
Vyzhva**^{1}**,
Dr. Sci. (Phys.-Math.), Assoc. Prof.****,
****E-mail:
zoya_vyzhva@ukr.net;**

**K.
Fedorenko**^{1}**,
Postgraduate Student****,
****E-mail:
slims_mentol@mail.ru;**

**A.
Vyzhva**^{1}**,
Postgraduate Student****,
****E-mail:
motomustanger@ukr.net**

**THE
ADVANCED ALGORITHM OF STATISTICAL SIMULATION OF SEISMIC NOISE**

**IN
THE MULTIDIMENSIONAL AREA FOR DETERMINATION THE FREQUENCY**

**CHARACTERISTICS
OF GEOLOGICAL ENVIRONMENT**

^{1
}**Institute
of Geology, Taras Shevchenko National University of Kyiv****,
****90
Vasylkivska Str., Kyiv, 03022 Ukraine**

**The
article is devoted to the theory and methods of random process and
field statistical simulation on the basis of their spectral****
****decomposition
and modified Kotelnikov-Shennon interpolation sums, as well as using
these methods in environmental geophysical****
****monitoring.
The problem of statistical simulation of the multivariate random
fields (homogeneous in time and homogeneous isotropic****
****with
respect to the n other variables) is considered for introducing into
seismological researches for determination the frequency****
****characteristics
of geological environment. Statistical model and advanced numerical
algorithm of simulation realizations of such****
****random
fields are built on the basis of modified interpolation
Kotelnikov-Shennon decompositions for generating the adequate****
****realizations
of seismic noise. Real-valued random fields ξ (t, x), t ϵ**
**R, x ϵ**
**R n, that are
homogeneous with respect to time and****
****homogeneous
isotropic with respect to spatial variables in the multidimensional
spase are studied. The problem of approximation of****
****such
random fields by random fields with a bounded spectrum is considered.
An analogue of the Kotelnikov–Shannon theorem for****
****random
fields with a bounded spectrum is presented. Improved estimates of
the mean-square approximation of random fields in the****
****space
R x** **R
n by a model constructed with the help of the spectral decomposition
and interpolation Kotelnikov–Shannon formula are****
****obtained.
Some procedures for the statistical simulation of realizations of
Gaussian random fields with a bounded spectrum that are****
****homogeneous
with respect to time and homogeneous isotropic with respect to
spatial variables in the multidimensional spase are****
****developed.
There has been proved theorems on the mean-square approximation of
homogeneous in time and homogeneous isotropic****
****with
respect to the n other variables random fields by special partial
sums. A simulation method was used to formulate an advanced****
****algorithm
of numerical simulation by means of this theorems. The spectral
analysis methods of generated seismic noise realizations are****
****considered.
There have been developed universal methods of statistical simulation
(Monte Carlo methods) of multi parameters****
****seismology
data for generating of seismic noise on 2D and 3D grids of required
detail and regularity.**

**Keywords:
statistical simulation, spectral analyzes, seismic noise.**

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