On the nonexistence of SP head waves at a solid-vacuum interface

ABSTRACT The theoretical study of geometric SP head waves propagating in an isotropic homogeneous traction-free half-space or half-plane reveals that these waves can satisfy the traction-free condition at the boundary plane if and only if the Lamé parameter λ vanishes, which makes the existence of this type of head wave almost impossible. The analysis is based on the Helmholtz decomposition of the displacement field, coupled with the stress and strain tensor decomposition into spherical and deviatoric parts. It can be anticipated that the obtained result on the nonexistence of this type of head wave can have applications in geophysics and earthquake engineering due to the exclusion of geometric SP head waves from consideration.