Scattering of Impulsive Elastic Waves by a Rigid Cylinder

Abstract

The exact solution to the problem of the scattering of compressional elastic waves from a line source by a rigid, infinitely dense cylinder imbedded in an isotropic, homogeneous, perfectly elastic medium is obtained in integral form. The integrals are evaluated asymptotically obtain the motions on the wave fronts. In the illuminated zone the saddle point method of integration yields the geometrical optics approximation to the reflected field. In the shadow zone the diffracted field is obtained by evaluating the integrals by the method of Dougall and Watson. In the case of an incident P wave the observed events in the illuminated zone are (1) direct P, (2) reflected P, and (3) reflected S. In the shadow zone the observed events are (1) diffracted P and (2) diffracted S. Both diffracted wave fronts travel around the cylinder with the velocity of P waves.