Oleksandr V. Development of methods and tools for modeling oscillating processes in nonlinear randomly excited systems

The thesis is dedicated to analysis of random environmental influences and noise of instrumentation on the oscillating processes in the systems for measuring physical properties of geologic rocks during seismic or acoustic researches of fields, and also to development of methods and tools for simulation of random oscillations in these systems. A constructive algorithm for solving the problem has been developed, its programmatic implementation offered. The methods and algorithms of simulating quasiperiodic oscillations under the influences of random external disturbances have been used to improve the Geological Interpretation Systems packages "GeoPoisk" and "Tesseral-2D". Specialized utilities for the preliminary analysis of data obtained from geophysical investigations and their preparation for input into geological simulation packages have also been developed. Keywords: mathematical simulation, nonlinear oscillations, white noise, difference-differential equation, seismic exploration.