QUASI-STATIC DISPLACEMENTS DUE TO FAULTING IN A LAYERED HALF-SPACE WITH AN INTERVENIENT VISCOELASTIC LAYER

Abstract

This paper presents a method for the computation of quasi-static surface displacements caused by the sudden appearance of a dislocation in a stratified elastic half-space with an intervenient, Maxwellian viscoelastic layer. Integral representations of the displacements are derived from those in the associated elastic case by applying the correspondence principle of linear viscoelasticity. Evaluation of the integral is carried out by using a method of approximating a part of the integrand by an analytical function.
The surface motion consists of an instantaneous elastic rebound at the time of faulting and a transient viscoelastic movement after the event. Time dependent properties of the viscoelastic movement are formally prescribed by a certain number of time constants, those are functions of a wave number determined by the rheological structure of the medium.
General features of the viscoelastic movement are investigated from various aspects. First, changes in the displacement profiles with dip-angle are examined for the point dislocation sources located in the elastic surface layer of a three-layered model at different depths. Second, variations of the displacement profiles with time are examined for various structure models with different thicknesses of the viscoelastic layer. Finally, the vertical and horizontal displacement fields due to a finite-dimensional fault are calculated for a three-layered model, and compared with those for different types of structure models, such as a viscoelastic half-space model and a two-layered model which consists of an elastic layer overlying a viscoelastic half-space.