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This paper presents the results of numerical simulation of the propagation of HF radio waves in the artificially disturbed ionosphere during launch of the Tsyklon-3 carrier rocket from the Plesetsk cosmodrome on December 18, 1991, and an industrial high-power explosion with a magnitude of M = 2.4 on the Kola Peninsula on April 8, 1990. A specially developed software package in Python programming language allows three-dimensional modeling of ray trajectories in the geometric optics approximation by solving a bicharacteristic system for the eikonal equation. The geomagnetic field is specified according to the IGRF model, and the ionospheric electron density distribution is specified according to radio tomography data. The ionogram modeling is performed using a three-dimensional shooting method based on the Nelder-Mead simplex minimization. It is shown that the artificial ionospheric irregularities that arise during the periods of the considered events are quasi-wave perturbations that have a significant effect on the ray trajectories of HF radio waves and ionograms of vertical and oblique sounding. This effect manifests itself in the form of characteristic peculiarities of ray trajectories with multiple reflections from the local maxima of the electron density and additional traces on ionograms caused by the passage of traveling ionospheric disturbances above the sounding system.

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