On strike-slip Somigliana dislocations in a layered elastic half-space

We consider a vertical strike-slip fault which is embedded in an elastic layer overlying an elastic half-space. The layer and the half-space have different rigidities. In such a model, dislocations on the fault are usually taken to occur with uniform slip, due to the difficulty of solving analytically the general problem of variable-slip (Somigliana) dislocations in this case. We adopt the Somigliana dislocation representing a crack in a homogeneous half-space and examine under which conditions this can be considered a good approximation to a crack in the layered medium. Better approximations can be obtained by super-positions of Chebyshev polynomials of the first kind and odd degree.