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 due
to 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 elastic
sphere 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 fault
and a dilatational source. A perturbation procedure is developed
for calculating the effects of lateral changes in elastic constants
on the earth's free oscillations. The procedure is applied to obtain
expressions for the effect of some simple inhomogeneity geometries
on the torsional free oscillations.
Numerical evaluation of the static, elastic, dislocation
solutions 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 to
explain the observations. The compatibility of a very weak layer
with observed surface wave dispersion is tested using the results
of 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.</p
