Eduardo Kausel-Fundamental solutions in elastodynamics_ a compendium-Cambridge University Press (2006)

5.5 Half-plane, line blast load applied in its interior (Garvin’s problem) 77
This formula is valid for both an upper (z > 0) and a lower (z < 0) half-space, with z being
the coordinate of the source relative to the surface. For a lower half-space and at large
times, these displacements converge asymptotically to the static solution
2(1 − ν)
u x (x, 0, ∞) = sin θ z
(5.28a)
πµr
u y (x, 0, ∞) =
2(1 − ν)
cos θ z
πµr
(5.28b)