The effects of displacement discontinuity derivatives on wave propagation—III: Body and point forces in elastic half-spaces

Based on previous work, the displacements due to arbitrary body force fields in half-spaces with, respectively, traction-free and zero-displacement surfaces are derived. The expressions allow indentification of all wave components. In particular, the contributions due to the body force at the point of observation and a contribution arising essentially from the unbounded solid case can be discerned. For the special case of a point force in the half-space with a traction-free surface, this latter contribution is compared with the exact displacements on the surface. The point force is neither normal nor tangential to the surface. Agreement seems to vary directly with the depth of the point force. When the point force is on the surface, agreement seems weakest, perhaps due to the presence of Rayleigh waves in the exact solution.