Purpose. The aim is to conduct mathematical modeling of disturbances and seismic wave field propagation in horizontally layered isotropic elastic half-space; summarizing the results obtained in the case of absorbing media; numerical implementation of the method of calculation of seismic waves in horizontally layered medium with absorption, perturbed point source in a simple force that depends on time; build sustainable programs and algorithms for numerical calculations for synthetic seismograms; and conducting numerical experiments for verification of results. Methodology. The method comprises administering primary wave fields, perturbed idle power on or within horizontally layered isotropic elastic half-space with absorption. It is based on the use of integrals Bessellya-Mellin, matrix Thomson-Haskell method and its modifications. Results. The effective and sustainable method of calculating synthetic seismograms for stratified horizontally layered isotropic medium with absorption was carried out. The method takes into account the availability of the free surface, the presence of a point source in a simple force placed on or within half-space interference phenomena associated with tonkosharuvatistyu. To increase the stability calculation of the wave field the transition was made from the characteristic matrix of fourth order matrix to sixth order. The modeling of the phenomenon of resonance in horizontal layered half-space was caused by the presence of low speeds in the upper layer. Originality. After entering primary wave field perturbations idle power on or within the horizontally-layered half-space, the developed numerical and analytical approach to modeling of waves in horizontally layered isotropic elastic media was imperfect. Algorithms and software were used for the calculation of synthetic seismograms at the free surface of environments. Practical significance. The practical significance of the developed method is the ability to analytically and numerically explore the wave processes occurring in layered media. The calculation of synthetic seismograms and allocating them to different types of waves allow analysis and accurate interpretation of the wave pattern that is recorded during seismic observations
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