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