Theoretical solutions are derived for a model of faulting in elastic media and for the effect of lateral inhomogeneities on the earth's free oscillations. The solutions are used in a study of permanent tilts and strains observed a few hundred kilometers from earthquakes.
It is shown that the static deformational field due to a suitably chosen dislocation fault model is the same as that dueto introduction of a stress free surface into a prestressed medium. Formal mathematical solutions are derived for the static deformational fields due to dislocation fault models in a homogeneous elasticsphere and a layered elastic half-space. For the layered half-space explicit solutions are given in terms of integral transforms for the surface displacements, tilts, and strains due to a slip faultand a dilatational source. A perturbation procedure is developed for calculating the effects of lateral changes in elastic constantson the earth's free oscillations. The procedure is applied to obtain expressions for the effect of some simple inhomogeneity geometrieson the torsional free oscillations.
Numerical evaluation of the static, elastic, dislocationsolutions shows that the observed tilts and strains are large compared with theoretical predictions and sometimes show the opposite sign.The hypothesis that a weak layer in the lower crust or upper mantle can explain the observations is investigated. It is found that a very weak layer, approaching a liquid-like behavior, does help toexplain the observations. The compatibility of a very weak layer with observed surface wave dispersion is tested using the resultsof the perturbation calculations for the torsional free oscillations. A very weak layer is determined as compatible with observed surface wave dispersion only if very thin and with some frequency dependence in its elastic properties. It is concluded that although a regional weak layer in the lower crust or upper mantle can help to explain the observed tilts and strains, other regional or local structural effects or source complications must also be important.
