Dislocation Theory in a 3-dimensional Viscoelastic Earth Model

This study presents a new method to calculate displacement and potential changes caused by an earthquake in a three-dimensional viscoelastic earth model. It is the first time to compute co- and post-seismic deformation in a spherical earth with lateral heterogeneities. Such a method is useful to investigate the 3-dimensional viscoelastic structure of the earth by interpreting precise satellite gravity and GPS data. Firstly, we concern with Maxwell’s constitutive equation, the linearized equation of momentum conservation and Poisson’s equation, and obtain the solution in the Laplace domain in a spherical symmetric viscoelastic earth model. Furthermore, we employ the perturbed method to deal with the effect of lateral heterogeneities and obtain the relation between the solutions of the spherical symmetric earth model, the three-dimension earth model with lateral inhomogeneity and the auxiliary solutions. Then, using the given surface boundary conditions to determine the auxiliary solutions, we obtain the perturbed solutions of lateral increment in the Laplace domain. Finally, taking the inverse Laplace transforms of solutions in a spherical symmetric viscoelastic earth model and perturbed solutions with respect to lateral hetergeneities, we obtain the solutions of deformation in a three-dimensional viscoelastic earth model.