Green functions for an incompressible linearly nonhomogeneous half-space

Time-harmonic vibrations of an incompressible half-space having shear modulus linearly increasing with depth are studied. The half-space is subjected to a surface load which has vertical or horizontal direction. The general solution of the time-harmonic, in the vertical direction nonhomogeneous problem is constructed for arbitrary angular distribution in the horizontal plane. Numerical results concerning surface displacements due to a point force are given for the case of nonzero shear modulus at the surface. These results show that nonhomogeneity can considerably increase amplitudes at large distances from the applied force.