An analytical method for solving elastic system in inhomogeneous orthotropic media

In this paper, the three-dimensional initial value problem for elastic system in inhomogeneous orthotropic media is considered and an analytical method is studied to solve this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type, whose solution is obtained by the method of successive approximations. Finally, using the real Paley-Wiener theorem, it is shown that the solution of the initial value problem can be found by the inverse Fourier transform.