Global post-seismic deformation

We quantify the effects of post-seismic deformation on the radial and horizontal components of the displacement, in the near- and far-field of strike- and dip-slip point dislocations; these sources are embedded in the elastic top layer of a spherical, self-gravitating, stratified viscoelastic earth. Within the scheme of the normal mode technique, we derive the explicit analytical expression of the fundamental matrix for the toroidal component of the field equations; this component is propagated, together with its spheroidal counterpart, from the core-mantle boundary to the earth's surface. Viscosity stratification at 670km depth influences the radial and horizontal deformation accompanying viscoelastic relaxation in the mantle over time-scales of 103-104 yr, both in the near-field, ranging from 100 to 500 km and in the far-field, from 103 to 5 X 103 km. If the upper mantle is differentiated into a low-viscosity zone beneath the lithosphere and a normal upper mantle, faster relaxation is obtained. For an asthenospheric viscosity of 1020 Pa s we obtain, for a strike-slip dislocation and a seismic moment of 1022 N m characteristic of an average large earthquake, horizontal rates of 1-4 mm yr-1 in the near-field and 0.05-0.4 mm yr-1 in the far-field; these values are maintained over time-scales of 10-103 yr. Larger rates, with shorter duration, are obtained if the viscosity is reduced in the low-viscosity channel. As expected, strike-slip dislocations are the most effective in driving horizontal deformation in the far-field in comparison with dip-slip ones. It is noteworthy that horizontal velocities are maintained longer in the far-field in comparison with radial ones, which is not surprising since momentum is propagated in far regions essentially in the horizontal direction; radial deformation is generally lower in the far-field. VLBI techniques, with a precision of a few parts per billion over distances of 103 km, can detect global post-seismic deformation induced by large earthquakes. Our results affect the interpretation of the transfer of stress and seismic activity among different plate boundaries.