A kinematic model for the earthquake cycle at convergent plate boundaries has been constructed on the basis of dislocation theory. We model the lithosphere-asthenosphere system by a stratified semi-infinite medium under gravity, consisting of an elastic surface layer, an intervening layer with Maxwell viscoelasticity, and an elastic substratum. The steady motion of plate convergence is naturally represented by uniform slip at a constant rate on the upper boundary of the descending oceanic plate. The occurrence of interplate earthquakes is regarded as a perturbation of the steady state plate motion, and represented by a periodic sequence of step slips on a finite seismic zone of the plate interface. Based on dislocation theory we can show that the steady slip on the interface deeper than the lithosphere-asthenosphere boundary does not contribute to surface deformation in the steady state. Accordingly the surface deformation associated with the earthquake cycle is given by the superposition of viscoelastic responses to the steady slip on the interface shallower than the lithosphere-asthenosphere boundary, the steady backslip on the seismic zone, and the periodic sequence of seismic slips. We have computed cyclic patterns of vertical displacements at the free surface for two representative cases, taking account of gravity effects. The patterns of vertical displacements differ notably in the latter stage of the cycle depending on whether or not the seismic zone extends through the entire thickness of the lithosphere. After the completion of one earthquake cycle, our model yields a certain amount of permanent deformation resulting from the steady plate convergence. The pattern of the permanent deformation, that is characterized by steep uplift on the continental side, sharp subsidence at the plate boundary, and gentle uplift on the oceanic side, is irrespective of the cyclic process of stress accumulation and release repeated on the seismic zone. The earthquake cycle model developed here provides a possible explanation for the formation of earthquake-origin marine terraces.
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