The paper discusses the possibility of propagation of torsional surface waves in a heterogeneous half-space under a rigid layer. The study reveals that, under the assumed conditions, torsional surface waves propagate in the medium. The velocities of torsional surface waves have been calculated numerically and are presented in a graph. It is observed that as the density of the medium increases the velocity of torsional wave front increases too. As a particular case it has been shown that in a homogeneous half-space under a rigid layer, a torsional wave does not propagate.
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