Abstract: The Fourier transformations about the azimuthal angle and Hankel transformation about the radial direction have been used to convert the basic equations of elasticity into a non-homogenous first-order ordinary differential equation system in cylindrical coordinates. By the use of the matrix method to solve this system of equations, the transmission matrices of the layered medium are established. The singular solution in frequency domain for an arbitrarilly buried source acting in the multilayered elastic ha...