Malytskyy D. Matrix method and its modifications in the problems of determining the earthquake's wave field and source parameters

The thesis is devoted the mathematical modeling of seismic waves in the inhomogeneous media. The review of basic methods that are used in seismology for calculation of synthetic seismograms has been performed. The approaches have been developed, based on matrix method and its modifications, for determining the far and near field displacements on the surface of layered medium when the source of seismic waves is represented by the arbitrarily oriented force and the tensor of seismic moment. Analytic-numeric approaches to determining the tensor of seismic moment have been formulated with application of eigenvector analysis reducing the problem to system of linear equations. I propose using singular decomposition in case of badly conditioned matrices. It has been demonstrated that determining the moment tensor as a function of time enables to estimate a source duration of seismic event. The suggested approaches have been implemented in a program package and numerical experiments have been conducted to determine a solution of direct and inverse dynamical problems of seismology using the synthetic data and the real records by one or more stations enabling to determine the source mechanism of the earthquake. Key words: mathematical modeling, wave field, inhomogeneous medium, matrix method, effective-point dislocation, tensor of seismic moment, source time function.