Multipolar elastic fields in a layered half space

Abstract

Hansen's expansion is used to derive integral expressions for the displacement field due to a localized buried source of the mth order in a layered half space. The dipolar case (m ≦ 2) is worked out in detail for arbitrary source-depth in the layer and in the substratum. A new type of representation of the source is used which gives the final results in a concise form. Explicit expressions for the displacements at the free surface are obtained for a center of explosion, a vertical strike-slip fault and a vertical dip-slip fault. The results for a horizontal thrust are found to be the same as for a vertical dip-slip fault. The relations between the Galerkin vector and the biharmonic eigenvectors are clarified. It is shown that the Galerkin-Boussinesq solution for the elastic half space cannot be extended to structures of higher complexity, except for a few simple sources. On the other hand, the Hansen Solution is valid for a wide class of sources and structures. Both dynamic and static regimes are considered.