Excitation of an elastic half-space by a buried line source of conical waves

A formal solution is obtained to the problem of a buried line source of conical waves propagating at a constant phase velocity c in an isotropic elastic half space. By applying the boundary conditions at the free surface, it is determined that the reflected field, in addition to the incident field, requires addition of a scalar potential and two components of the vector potential. The latter is in contrast to the case of cylindrical waves where only one component of the vector potential is needed. The formal solution for the conical wave source goes over to that for the two dimensional cylindrical wave case in the limit of infinite phase velocity c.