Higuchi (1932) considered a medium consisting of two quarter-spaces in welded contact, each having a single homogeneous layer of the same thickness overlying a homogeneous half-space, and gave conditions on the rigidities and densities of the two layers and two half-spaces in such a way that the plane Love waves normally incident on the vertical plane generate only reflected and transmitted Love waves without mode conversion or body-wave scattering.
In this paper, we generalize Higuchi's results to two layers overlying a half-space divided by a vertical plane. On one side of the vertical plane, the shear velocities and rigidities for the top and the bottom surface layers, and for the half-space are β1, μ1, β2(>β1), μ2(>μ1), and β3(>β2), μ3(>μ2), respectively. On the other side, the corresponding shear velocities and rigidities for the two layers and the half-space are given by the primed quantities with β3′ > β2′ > β1′ and μ3′ > μ2′ > μ1′. We show that if the following conditions are satisfied
then plane Love waves normally incident on the vertical plane generate only reflected and transmitted Love waves without mode conversion or body-wave scattering. These conditions for the special case under consideration provide a valuable check for various analytical and numerical approximations which ignore the body-wave contributions in similar diffraction problems.