## Wavefield and static deformation in depth-dependent elastic
models with seismic sources of finite dimensions: spectral approach

**Ctirad Matyska**
### Summary

A new formulation is presented to describe both the wave field and the
static coseismic deformation in depth-dependent elastic models generated by a priori
prescribed plane dislocation seismic source of finite dimensions, which is represented
by an arbitrary time-dependent slip function changable in both spatial
dimensions along the fault. Elastic moduli can change with depth
also in the source depth range.
By employing a special cartesian decomposition of displacement
and continuity of traction acting on the fault,
the partial differential equations of motion
are converted into a set of ordinary differential equations over the depth
for the displacement-stress vector,
where the horizontal wave numbers and the frequency play the role of parameters
and the slip function is transformed into the source term of the equations.
The resultant formulas thus represent a set of 1-D boundary-value problems,
where no Green functions are needed.
The pre-stress terms are considered in the equations of motion to obtain
correct static limit.

### Keywords

Somigliana dislocation, seismic source, 1-D elastic models,
waves and static response

*Geophys. J. Int.*, **155** (2003), 1105-1113.