Displacement, strain and stress within a viscoelastic half-space due to a rectangular fault.

In this paper, we treat quasi-static deformations of a viscoelastic half-space due to a rectangular fault. Analytical expressions of displacement and strain fields are derived by applying the correspondence principle of linear viscoelasticity. The rheology of the medium is assumed to be elastic dilatational and Maxwell or Voigt deviatoric, and the time function of the displacement dislocation is taken to be of a step type. The quasi-static deformation consists of an instantaneous response at the time of faulting and a transient deformation after the event. In the case of either the Maxwell or Voigt solids, the time dependence of the transient part is characterized by two time constants. Expressions of the quasi-static stresses are obtained from those of the strains on the basis of the Laplace transform. Features of the quasi-static deformations in a viscoelastic half-space are investigated in a vertical plane which bisects a rectangular fault. First, we examine the deformation fields in the Maxwell solid. In the case of a strike-slip fault, the transient viscoelastic movement progresses so as to decrease the instantaneous elastic response. Such a tendency is not remarkable in the case of a dip-slip fault, and the viscoelastic displacement field shows a more complicated pattern than the elastic deformation. The total stress field in the Maxwell solid tends to zero as time increases. Next, we examine the quasi-static deformations in the Voigt solid, and compare the results with those for the Maxwell solid. The pattern of quasi-static deformation due to the strike-slip fault does not strongly depend on the rheological properties of the medium. In the case of the dip-slip fault, on the other hand, both instantaneous and transient parts of the deformation field show different patterns from those in the Maxwell solid. The total stress field in the Voigt solid converges to the elastic stress field with increase of time.