Open AccessPost‐seismic relaxation theory on a laterally heterogeneous viscoelastic model
Author(s) -
Pollitz Fred F.
Publication year - 2003
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.2003.01980.x
Subject(s) - viscoelasticity , discretization , isotropy , laplace transform , correspondence principle (sociology) , relaxation (psychology) , standard linear solid model , geology , constitutive equation , deformation (meteorology) , moment (physics) , coupling (piping) , mechanics , mathematical analysis , physics , mathematics , classical mechanics , materials science , finite element method , optics , psychology , social psychology , oceanography , economics , metallurgy , market economy , thermodynamics
SUMMARY Investigation was carried out into the problem of relaxation of a laterally heterogeneous viscoelastic Earth following an impulsive moment release event. The formal solution utilizes a semi‐analytic solution for post‐seismic deformation on a laterally homogeneous Earth constructed from viscoelastic normal modes, followed by application of mode coupling theory to derive the response on the aspherical Earth. The solution is constructed in the Laplace transform domain using the correspondence principle and is valid for any linear constitutive relationship between stress and strain. The specific implementation described in this paper is a semi‐analytic discretization method which assumes isotropic elastic structure and a Maxwell constitutive relation. It accounts for viscoelastic–gravitational coupling under lateral variations in elastic parameters and viscosity. For a given viscoelastic structure and minimum wavelength scale, the computational effort involved with the numerical algorithm is proportional to the volume of the laterally heterogeneous region. Examples are presented of the calculation of post‐seismic relaxation with a shallow, laterally heterogeneous volume following synthetic impulsive seismic events, and they illustrate the potentially large effect of regional 3‐D heterogeneities on regional deformation patterns.