Development of a calculation method for viscoelastic relaxation incorporating nonlinear rheology in a self-gravitating spherical Earth model

Space geodetic techniques such as GNSS have been used to observe co- and post-seismic crustal deformation in subduction zones with high spatio-temporal resolution. However, it is difficult to observe such crustal deformations in oceanic regions. Satellite gravimetry, on the other hand, can detect co- and post-seismic mass changes both over land and ocean. However, the spatio-temporal resolution of these satellites is insufficient to distinguish co- and post-seismic effects. The planned MAGIC mission aims to achieve a 3-day, 100 km resolution, enabling their separation. This advancement is expected to provide a more precise understanding of the mechanisms of post-seismic deformations following major earthquakes.

 

Geodetic observations have so far shown that there are three mechanisms of post-seismic deformations: afterslip, poroelastic rebound, and viscoelastic relaxation. The last one, viscoelastic relaxation has not been considered to contribute to short-term deformations unlike other two mechanisms. However, seafloor geodetic observations after the 2011 Tohoku earthquake captured the characteristic deformation even one year after the earthquake, which cannot be interpreted without a contribution of viscoelastic relaxation. Geophysical models that reproduce such viscoelastic relaxation have been proposed considering surface topography and 3D viscoelastic and density structure including a subducting oceanic slab. However, there are only a few models incorporating a nonlinear rheology to calculate post-seismic gravity changes. In the nonlinear case, the effective viscosity changes in space and time with stress evolution. In particular, co-seismic high stress changes lead to low effective viscosity, which promotes short-term viscoelastic relaxation after an earthquake. Hence, it is essential to discuss the extent to which this mechanism can be constrained when satellite gravity data with high spatio-temporal resolution become available by MAGIC.

 

Previous physical models to calculate post-seismic deformation have often treated the self-gravitation effects only approximately or ignored it. To represent the effects naturally, we have developed a spectral finite-element method based on a spherical earth model with a 3D viscosity distribution for a linear rheology.　In this study, we extend this method to a nonlinear rheology. This method computes the deformation in the time domain. Therefore, one can easily obtain the deformation for the nonlinear case by evaluating effective viscosity at each time step without major changes in the algorithm for the linear case. In the presentation, the spectral finite element method will be introduced, and numerical results will be shown, including viscosity distributions corresponding to co-seismic stress changes and their time evolution, and gravity signals reflecting a nonlinear rheology.