Numerical solutions of unstable direct and inverse dynamic problems

Full text: Mathematical models of wave propagation theory give an instrument to determine the numerical values of the propagation speed and absorption coefficients of elastic waves. The more realistic and reliable is the mathematical model, the more accurate the determined are values of propagation speed and the absorption coefficient of elastic waves. At present the peculiarities of elastic wave absorption in media that have been established by now and the simultaneous manifestation of multiple electroseismic effects are not consistent with the simplest models. In the process of propagation, seismic waves dissipate, which is associated with energy absorption. In applied objective including earthquake prediction [1], mathematical apparatus of direct and inverse dynamic problems for equation's system is often used, and reflects condition of spreading those waves [2-3]. We obtain a solution to the linearized system of equations for the entire homogeneous space in the frequency domain in the case when wave processes are caused by a point source of the concentrated force type. To determine the seismic moment tensor, we use, in contrast to [3], a part of the components of the displacement vectors P - longitudinal and S - transverse waves measured only at one point source of the concentrated force type. The noise stability of the solutions to the inverse problems considered is investigated numerically with the use of the method of critical components. (author)