SH Waves in a Wedge-shaped Medium

Summary This paper contains the solution of the problem of a line source of harmonic SH waves within a wedge-shaped medium, the upper surface being free and the lower boundary rigidly fixed. The solution is extended to the problem of an SH pulse. It includes the effect of diffraction at the apex of the wedge; the approximate form of the diffracted pulse is worked out. In the latter part of the paper it is shown that Love waves exist in the wedge if the apex angle is small, being formed by constructive interference at large distances from the source of the disturbance. The period equation and the amplitudes of the Love waves are found to the first order of smallness. I. Analysis of the problem The main purpose of this paper is to investigate the propagation of Love waves in a layer whose upper and lower faces are slowly converging. We shall therefore consider the simplest problem, which is that of Love waves in a wedgeshaped region with a free upper surface and the lower face held rigid. The situation may be described by cylindrical polar coordinates (r, 8, x) with the x-axis along the apex of the wedge, as in Figure I ; the free surface is defined to be the half-plane 8 = 0, and the lower boundary, 8 = cc. We shall investigate the effect within the wedge of a line murce, S, of SH waves, lying in the layer, parallel with the apex. The initial, and therefore all subsequent, displacements are in the z-direction only and are independent of the z-coordinate (we assume that the elastic medium is isotropic and homogeneous).