The elastic wave equation in an isotropic homogeneous semi-infinite elastic medium has been transformed by a combination of Fourier and Laplace-transforms and the surface displacements due to general force-system in three mutually perpendicular directions have been directly obtained. By suitably specifying the force-system, the surface displacements for all possible types of point sources so far used, have been calculated, obtaining in particular, the results previously derived by Haskell for a dipolar point source of arbitrary direction. It has been shown that now the surface displacement for finite size of the source can be calculated for both body and surface waves. Expressions for the displacements at any point of the medium have been derived, giving in particular the displacements associated with incident wave in the medium, separately.

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