Green's functions for vertical point load on an elastic half-space with depth-degrading stiffness

The response of an elastic, vertically non-homogeneous half-space to a time-harmonic surface point load is studied. The non-homogeneity is defined by a function that may describe both increasing and decreasing shear modulus with depth. The solution for the latter is obtained in the paper by simple transformations from the previously derived one for a half-space with increasing shear modulus with depth. The analysis shows that cut-off frequencies for the SV/P surface wave may occur. Graphs for the variation of the complex valued displacement field with distance from the source and frequency are presented for selected values of the non-homogeneity parameters.