Spherical versus flat models of coseismic and postseismic deformations

We perform an exhaustive study of coseismic and postseismic surface deformations induced by shear dislocations using flat and spherical Earth models. Our aim is to examine the effects of the spherical geometry, the vertical layering, and the self-gravitation on surface displacement field. For a 100 km long fault, spherical and flat models produce comparable coseismic deformations up to a distance of ∼300 km from the epicenter. This distance is sensibly reduced in the postseismic regime and when infinitely long strike-slip faults are considered. The differences between predictions based on flat and spherical models are due both to their global geometry and the effect of the gravity forces. Self-gravitation has a minor role with respect to that of sphericity for surface coseismic deformations, while in the postseismic regime its effects increase considerably. As a case study, we consider the coseismic and postseismic deformations due to the great 1960 Chilean earthquake. The results of the spherical stratified model differ sensibly from those of a flat uniform model. Moreover, within the framework of spherical Earth models, the rheological stratification plays a major role in determining the pattern of the displacement field. We show that the present-day rates of vertical and horizontal deformations are considerably large (∼10−2 m yr−1) for an asthenospheric viscosity ranging from 1019 to 1020 Pa s. These rates, which could possibly be detected by geodetic investigations, are found to be also sensitive to the rheological properties of the mantle beneath the asthenosphere.