The paper presents the results of mathematical modeling of superpower vibrational sources for the global tomography of the Earth. A hydroresonance scheme of a seismovibrator is considered, in which an oscillating in the vertical shaft liquid column with the mass of several tens thousands tons serves a seismic waves source. A mathematical model of the shaft source has been constructed. This model reflects the most significant features for the considered process of seismic waves radiation. Being combined, the model includes an elastic half-space with a vertical cylindric cavity, a column of a compressible fluid, and the ideal gas volume at the bottom of the shaft. The problem has been formulated in general in terms of mathematics, thus reducing to a combination of three systems of equations – dynamic elasticity theory, compressible fluid dynamics, and ideal gas dynamics. The boundary conditions are the known stresses and velocities relations at the interfaces between different media. For low frequencies when the wavelength essentially exceeds the shaft diameter, it appeared possible to separate the problem the determination of pressure distribution in the fluid from the 1D problem of finite oscillations of the compressible fluid column on the gas volume with allowance for quasi-static elastic deformations of the shaft walls, and, further, the solution of the dynamic problem for the elastic half-space with determined stresses on the cylindrical cavity boundary as boundary conditions. The results of numerical calculations of the full wave field of the shaft source for various model of media are presented.

Abstract

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