Numerical Solutions of Unstable Direct and Inverse Dynamic Problems

A solution to a system of equations for a homogeneous space in the time and frequency domains for the case of a point source is obtained. Ray representations of waves of various types in an inhomogeneous elastic-porous medium are obtained. Inverse problems of determining the parameters of the medium and seismic moment tensor are considered. This is done by using the information about: 1) component parts of the displacement vectors of P - and S - waves at a fixed point of space; 2) measured at six fixed points of space for all times. The noise stability of the solutions to the inverse problems considered is investigated numerically with the use of the method of critical components.