Quasi-static deformations due to an inclined, rectangular fault in a viscoelastic half-space

Abstract

Analytical expressions of the quasi-static, surface deformations (displacement, strain and tilt) due to an inclined, rectangular fault in a viscoelastic halfspace are obtained by applying a “correspondence principle” to the solutions of the associated elastic problem. The medium is assumed to be elastic dilatational and Maxwell deviatric, and the time dependence of a dislocation source is taken to be of a step function type. From the analytical expressions, it is directly found that the viscoelastic part of the deformation field vanishes exactly for both an arbitrary slip on a horizontal fault plane and a dip-slip faulting on a vertical plane. In other cases, the viscoelastic part has a time dependence prescribed by a factor, 1 —exp(—t/τ), where τ denotes the relaxation time determined from the Lamé's elastic constants and the viscosity of the medium. Patterns of the elastic and the viscoelastic parts of the deformation field are respectively shown for two representative fault models. As an example, postseismic vertical displacements associated with the Kanto earthquake of 1923 are computed by the fault model determined from the coseismic geodetic data, and compared with the observed crustal movements for the period of 1931–1950. © 1980, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan. All rights reserved.