The Propagation of an SH‐pulse in a layered medium

Abstract

An exact solution is given for the problem of the propagation of an SH‐wave due to a sudden application of a concentrated torsional stress at the surface of a layered medium. The solution is obtained in terms of elliptic integrals. The form of the displacement in the direct wave is like the time‐derivative of the applied stress. The beginning of the refracted waves is like that of the stress. At moderate distances from the source the internally reflected waves are large and increase in relative magnitude with the abruptness of the stress. Figure 1 shows the displacement at r = 4H due to the application of a stress‐pulse of the indicated form. It is suggested that the arrival‐time of a totally reflected SH‐wave should be taken at the point of maximum amplitude of the phase rather than at its beginning.