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.
Investigation of earthquake jump distance for strike‐slip step overs based on 3‐D dynamic rupture simulations in an elastic half‐space
