Global postseismic deformation: Deep earthquakes

We study the global viscoelastic deformations associated with a shear dislo cation on a fault embedded in a viscoelastic mantle. To address this proble m, we extend the theory of the quasi-static deformations of a Maxwell, sphe rical, N-layer incompressible Earth, previously limited to the modeling of the effects of earthquakes occurring only within the elastic lithosphere. P ermanent postseismic deformations, which can be generated by lithospheric s ources, cannot be sustained if the source region is viscoelastic; however, the transient response of the mantle strongly depends on the viscosity of t he source region. We use the technique developed here to investigate thorou ghly the quasi-static surface deformations induced by seismic events of var iable depth. We show that owing to the combined effect of sphericity and vi scoelastic mantle relaxation, the surface displacements do not systematical ly decrease as the depth of the source increases. Instead, with increasing source depth we predict an increasing efficiency of mantle relaxation in tr iggering postseismic deformations of large size. Most of our results are ba sed on a. simple four-layer model, with a 100-km-thick lithosphere, upper a nd lower mantle separated by the 670-km discontinuity, and a fluid core; th e last part of this work is devoted to a study of the effects of a low-visc osity asthenosphere on the rates of deformation detected at the Earth's sur face. The findings reported here may be useful for the interpretation of th e transient motions of the Earth's surface in response to deep-focus earthq uakes.