On the existence of a periodic dislocation cycle in horizontally layered viscoelastic models

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Abstract
Horizontally stratified viscoelastic models are employed to characterize the lithosphere‐asthenosphere interaction following dislocation events occurring on long transcurrent faults. The aim is to investigate the ability of such models to reproduce the periodic behavior often assumed in the geophysical literature for the earthquake source process. If the lithosphere is elastic and the asthenosphere has a Maxwell rheology, the earthquake recurrence time is proved to become zero (model I) or infinity (model II) if boundary conditions of constant strain rate or limited tectonic stress, respectively, are imposed over the fault region. Model assumptions that may be responsible for these paradoxical results include the choice of boundary conditions, the half‐space two‐dimensional geometry, and the assumed rheological behavior. This third possibility has been investigated in some detail. The adoption of the standard linear solid for the asthenosphere (model III) yields a stationary nonvanishing recurrence time if constant strain rate is applied. Another possibility is to assign a viscoelastic rheology to the lithosphere also (model IV); in this case, an earthquake cycle is obtained whose period depends on the assigned boundary conditions. In any case, the results obtained clearly indicate the importance of past earthquakes in the earthquake cycle.

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