Two-dimensional crack model of faulting in a layered elastic half-space

Crack models of faulting are presented in a layered medium. A free surface bounds a layer of low rigidity, in welded contact with a higher rigidity half-space, cut by an antiplane vertical shear crack reaching the interface between the two media. For comparison, the case is also considered of a homogeneous half-space. Solutions are found following an efficient numerical method which employes the integral properties of Jacobi and Chebyshev polynomials respectively in the two cases. Solutions for the slip amplitude on the crack surface and for the displacement field at the free surface show the importance of taking properly into account the presence of soft sedimentary layers when geodetic data are inverted for fault parameters after an earthquake. The major differences regard the maximum value of the displacement and its distance from the fault strike.