Vyzhva Z. Theory and methodology of random process and field statistical simulation in environmental geophysical monitoring.

The thesis is devoted to the theory and methodology 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. There have been developed universal methods of statistical simulation (Monte Carlo methods) of geophysical data for generating random processes and fields on 2D and 3D grids of required detail and regularity. There has been proved a theorem on the mean-square approximation of homogeneous and isotropic random 3D fields by special partial sums. A randomization method was used to formulate an algorithm of statistical simulation by means of this theorem. A new effective statistical technique has been devised to simulate random fields in 3D space (randomization method, spectral coefficients method and others) for environmental geophysical monitoring of chalk layer density on Rivne NPP industrial area territory. There has been introduced random processes and fields in 2D space statistical simulation based on spectral decompositions in order to enhance map accuracy by the example of aeromagnetic survey data in the Ovruch depression. Statistical models and numerical simulation algorithms have been developed on the basis of Kotelnikov-Shennon theorem for homogeneous in time limited spectra isotropic random fields (in cylinder and sphere), for homogeneous in time as well as homogeneous and isotropic in space coordinates random fields (2D), for separable random processes and fields (2D and multi-dimensional) on an irregular observation grid. A new effective technique of statistical simulation of random processes and fields in 2D space with a regular interpolation grid has been introduced into seismic research into frequency characteristics of under-building-site geophysical environment (by the example of Odessa city).