5:15 PM - 6:45 PM
[SCG55-P12] Extension of the viscoelastic relaxation calculation method based on a self-gravitating spherical Earth model to non-linear rheology.
Keywords:satellite gravimetry, viscoelastic relaxation, rheology, postseismic deformation
Satellite gravimetry, such as GRACE, can capture mass change over land and sea, but the spatio-temporal resolution is lower than that of GNSS, at around 1 month and 300 km, which is insufficient to capture short-term variations on daily to weekly scales after a major earthquake. However, the current joint ESA/NASA gravity observation satellite development project (MAGIC) has a target spatio-temporal resolution of 3-5 days and 100 km. If this target is achieved, it may be possible to distinguish between co-seismic and post-seismic gravity changes with respect to major earthquakes in subduction zones, and to elucidate the mechanisms of short-term post-seismic deformation.
There are three types of post-seismic deformation mechanisms in subduction zones: afterslip, poroelastic rebound and viscoelastic relaxation. Seafloor geodetic observation after the 2011 Tohoku earthquake revealed that viscoelastic relaxation was predominant not only in the long term on the scale of years to decades but also in the short term immediately after a major earthquake. Geophysical models that reproduce such viscoelastic relaxation have been proposed taking various factors into account. Among these models, the one considering non-linear rheology (power-law creep) has reproduced the seafloor displacement pattern after a major earthquake well in several studies, but almost no studies have investigated its effect on gravity changes. In the non-linear case, co-seismic high stress changes lead to low effective viscosity, which promotes short-term viscoelastic relaxation and mass change after an earthquake. Therefore, this study aims to develop a viscoelastic relaxation calculation method that incorporates non-linear rheology and allows gravity changes to be discussed for future use on the MAGIC satellite.
We so far have developed a spectral finite-element method (SFEM) based on a spherical earth model with a 3D viscosity distribution for a linear rheology, which strictly treats the self-gravitation effects. In SFEM, isostasy effects arising from density contrasts beneath the Earth's surface layer are considered in the calculation of gravity changes. In this study, we extend this method to non-linear rheology. As in some previous studies incorporating non-linear rheology, the flow law for the viscous part of Maxwell model is replaced by the flow law obtained experimentally for dislocation creep of olivine, the main material in the upper mantle. Since SFEM solves the differential equations in the time domain without Laplace transform, defining the effective viscosity enables the non-linear constitutive equations to be apparently identical to the linear ones. Therefore, by adding a subroutine to calculate the effective viscosity at each time step using the stresses at each grid, non-linear effects can be incorporated without major changes to the algorithm. The presentation will show the outline of spectral finite element method, its extension to non-linear rheology, and numerical results of viscosity and gravity changes with time.
There are three types of post-seismic deformation mechanisms in subduction zones: afterslip, poroelastic rebound and viscoelastic relaxation. Seafloor geodetic observation after the 2011 Tohoku earthquake revealed that viscoelastic relaxation was predominant not only in the long term on the scale of years to decades but also in the short term immediately after a major earthquake. Geophysical models that reproduce such viscoelastic relaxation have been proposed taking various factors into account. Among these models, the one considering non-linear rheology (power-law creep) has reproduced the seafloor displacement pattern after a major earthquake well in several studies, but almost no studies have investigated its effect on gravity changes. In the non-linear case, co-seismic high stress changes lead to low effective viscosity, which promotes short-term viscoelastic relaxation and mass change after an earthquake. Therefore, this study aims to develop a viscoelastic relaxation calculation method that incorporates non-linear rheology and allows gravity changes to be discussed for future use on the MAGIC satellite.
We so far have developed a spectral finite-element method (SFEM) based on a spherical earth model with a 3D viscosity distribution for a linear rheology, which strictly treats the self-gravitation effects. In SFEM, isostasy effects arising from density contrasts beneath the Earth's surface layer are considered in the calculation of gravity changes. In this study, we extend this method to non-linear rheology. As in some previous studies incorporating non-linear rheology, the flow law for the viscous part of Maxwell model is replaced by the flow law obtained experimentally for dislocation creep of olivine, the main material in the upper mantle. Since SFEM solves the differential equations in the time domain without Laplace transform, defining the effective viscosity enables the non-linear constitutive equations to be apparently identical to the linear ones. Therefore, by adding a subroutine to calculate the effective viscosity at each time step using the stresses at each grid, non-linear effects can be incorporated without major changes to the algorithm. The presentation will show the outline of spectral finite element method, its extension to non-linear rheology, and numerical results of viscosity and gravity changes with time.