Zharovskyi R. Mathematical modeling and statistical analysis of seismic signals using orthogonal filtering

The thesis is devoted to the problem of mathematical modeling and statistical analysis of seismic signals using orthogonal filtering. A new improved mathematical model of the seismic signal in the form of additive amount poliharmonic fading signal and random noise. This makes it possible to prove properties of generating seismic signals and take them into account as well as their changes in the distribution layer structures in the crust. Different types of seismic noise described by a stationary linear random process make it possible to take into account the specifics and characteristics of seismic experiments in different places. The efficiency of correlation orthogonal seismic data processing system based on orthogonal filters camp. The results improve the signal noise ratio of the system compared to the typical correlation system. A corresponding algorithmic and software statistical analysis of seismic signals, making it possible to carry out a wide range of computer simulation experiments. As a promising method of correlation orthogonal statistical analysis of seismic signals, an adaptive method was proposed to reduce the influence of seismic noise by using complex orthogonal Laguerre filters. The basic scientific and practical results of mathematical modeling and statistical analysis of seismic signals in correlation orthogonal systems were proposed.