Viscoelastic Response of a Self‐Gravitational Spherical Earth to Shear Dislocation Obtained Using the Fixed‐Talbot Method

Abstract

AbstractViscoelastic dislocation theory is important to understanding fundamental geodynamics and validating numerical models in the study of earthquake deformation. Available mathematical solutions differ in assumed Earth geometry and formulation of gravity terms, but the main challenge they commonly face is Inverse Laplace Transform (ILT). Limitations in previously used ILT methods tend to degrade the performance and/or accuracy of the solutions. To overcome these limitations, we have derived new Green's functions for a layered spherical Earth based on the Fixed‐Talbot ILT method. The new solution uses a precise density‐gravity relation, includes pre‐stress advection, buoyancy, and self‐gravitation, invokes the bi‐viscous Burgers rheology, and yields deformational and gravitational changes both at the surface and in the interior of the Earth. The Fixed‐Talbot ILT method, which involves a left‐open parabolic integration path in the complex plane, greatly improves computing efficiency and allows convenient use of a large number of Earth layers. Comparison with other existing solutions demonstrates the excellent performance of the new solution. Taking the postseismic deformation of the 2004 Sumatra Mw 9.2 earthquake as an example, we illustrate how to integrate numerically our Green's functions to represent realistic slip distribution over a three‐dimensionally curved fault. The combination of computational efficiency, mathematical completeness in modeling gravitational effects, adaptability to any radial structure of the Earth, and ability to provide results at any depth including the surface enables a powerful tool for forward and inverse modeling of viscoelastic earthquake cycles in a self‐gravitating spherical Earth.