Propagation of one-dimensional non-stationary waves in viscoelastic half space

The problem of one-dimensional non-stationary wave propagation in viscoelastic half space is considered. Relaxation kernel is considered exponential. Initial conditions are set to zero, displacement is determined on the half space boundary.The solution is represented in the form of perturbation and surface Green function resultant. For determination of Green function time Laplace transform is used. Its inverse transform is carried out both analytically expanding Green function in series and numerically. A good coincidence of analytical and numerical Green function calculation results is shown. The final solution is determined analytically. Examples of calculations are represented.