ABOUT ALGORITHMS OF STATISTICAL SIMULATION OF SEISMIC NOISE IN THE OBSERVATION PROFILE FOR DETERMINATION THE FREQUENCY CHARACTERISTICS OF GEOLOGICAL ENVIRONMENT - Vyzhva, Z.; Fedorenko, K.; Vyzhva, A. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
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 seismic noise in the observation profile is under consideration for introduction into seismological researches for determination of the frequency characteristics of geological environment. Statistical model and numerical algorithm of simulation realizations of such random fields are built on the basis of modified Kotelnikov-Shennon interpolation decompositions for generating the adequate realizations of seismic noise. Real-valued random fields ξ(t, x), t ∈ R, x ∈ R , that are homogeneous with respect to time and homogeneous isotropic with respect to spatial variable 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  R R by a model with a bounded spectrum is presented. Estimates of the mean-square approximation of random fields in the space constructed with the help of the spectral decomposition and interpolation of 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 variable are developed. Teorems on the mean-square approximation of homogeneous in time and homogeneous isotropic with respect to the other variable random fields by special partial sums have been proved. A simulation method was used to formulate an algorithm of numerical simulation by means of these theorems. The spectral analysis methods of generated seismic noise realizations are considered. Universal methods of statistical simulation (Monte Carlo methods) of multi parameters seismology data for generating of seismic noise in the observation profile of required detail and regularity have been developed.