9:00 AM - 9:15 AM
[SCG61-13] Modelling post-seismic gravity change with nonlinear rheology for satellite gravimetry
Keywords:Viscoelastic relaxation, Rheology, Gravity change, Forward modelling, Satellite gravimetry
The post-seismic deformation of the 2011 Tohoku earthquake captured by geodetic observations suggests that viscosities of the upper mantle were significantly low (1017-1018 Pa s) in the early stage of the post-seismic deformation and continuously increased to a typical value (~1020 Pa s). Several studies have modelled this time evolution of viscosity with a laboratory-derived nonlinear flow law of olivine, where effective viscosity is inversely proportional to the applied deviatoric stress raised to an exponent close to 2, and successfully explained GNSS data. Meanwhile, post-seismic gravity changes following large earthquakes including the 2011 Tohoku earthquake have been detected by satellite gravimetry, such as GRACE, and these changes are primarily explained by viscoelastic relaxation of the mantle. Because satellite gravimetry provides broad and continuous observations over both land and ocean, it may constrain large-scale rheological structures more effectively than GNSS. However, it remains unclear whether post-seismic gravity changes observed by satellite gravimetry can also be explained by laboratory-derived nonlinear rheology. Given this background, the present study aims to model the post-seismic gravity change using laboratory-derived nonlinear rheology to compare with GRACE observations and investigate the broad rheological structure of the Japan subduction zone.
Since there has been no well-established method for calculating post-seismic gravity changes considering nonlinear rheology, we extended the Spectral-Finite Element Method (SFEM), which was originally developed for linear rheology, to the case of nonlinear rheology. Compared to standard finite element methods, SFEM enables more efficient computation of viscoelastic deformation in a self-gravitating Earth with a 3-D viscosity structure, due to its formulation based on spherical harmonics. We adopted a nonlinear Burgers model, in which nonlinear rheology is applied to the two dashpots of a conventional Burgers model. We employed the parameter sets and its spatial distributions for nonlinear rheology from Agata et al. (2019, Nat. Commun.) and Muto et al. (2019, Sci. Adv.), each of which successfully explained GNSS observations using laboratory-derived dislocation creep flow law of olivine.
We then compared our modeled ten-year post-seismic gravity changes following the 2011 Tohoku earthquake with monthly GRACE solutions (2011-2021) from the Center for Space Research, University of Texas. The maximum spherical harmonic degree was set to 60, and a 300 km Gaussian filter was applied to both model results and observations. Regarding the time series of gravity changes at a location where GRACE observed the peak of a positive gravity change, both nonlinear rheology models exhibit a good fit to observations. In particular, the one with enhanced transient deformation due to a larger pre-exponential factor in the Kelvin element (Muto et al. (2019)) better explains short-term variations within approximately three years. However, in terms of spatial distribution, our models predict broader positive gravity change areas extending from the offshore Tohoku to the Sea of Japan, whereas GRACE observations show that positive changes are primarily concentrated offshore Tohoku. This discrepancy suggests that additional factors in the mantle wedge, such as a cold nose, should be incorporated for a more accurate modelling of post-seismic gravity changes.
This study provides the first verification that nonlinear transient rheology, or nonlinear Burgers rheology using laboratory-derived flow law can reproduce post-seismic gravity changes after the 2011 Tohoku earthquake at a first-order level. In the presentation, we will also show calculation results that consider those additional factors in the mantle wedge.
Since there has been no well-established method for calculating post-seismic gravity changes considering nonlinear rheology, we extended the Spectral-Finite Element Method (SFEM), which was originally developed for linear rheology, to the case of nonlinear rheology. Compared to standard finite element methods, SFEM enables more efficient computation of viscoelastic deformation in a self-gravitating Earth with a 3-D viscosity structure, due to its formulation based on spherical harmonics. We adopted a nonlinear Burgers model, in which nonlinear rheology is applied to the two dashpots of a conventional Burgers model. We employed the parameter sets and its spatial distributions for nonlinear rheology from Agata et al. (2019, Nat. Commun.) and Muto et al. (2019, Sci. Adv.), each of which successfully explained GNSS observations using laboratory-derived dislocation creep flow law of olivine.
We then compared our modeled ten-year post-seismic gravity changes following the 2011 Tohoku earthquake with monthly GRACE solutions (2011-2021) from the Center for Space Research, University of Texas. The maximum spherical harmonic degree was set to 60, and a 300 km Gaussian filter was applied to both model results and observations. Regarding the time series of gravity changes at a location where GRACE observed the peak of a positive gravity change, both nonlinear rheology models exhibit a good fit to observations. In particular, the one with enhanced transient deformation due to a larger pre-exponential factor in the Kelvin element (Muto et al. (2019)) better explains short-term variations within approximately three years. However, in terms of spatial distribution, our models predict broader positive gravity change areas extending from the offshore Tohoku to the Sea of Japan, whereas GRACE observations show that positive changes are primarily concentrated offshore Tohoku. This discrepancy suggests that additional factors in the mantle wedge, such as a cold nose, should be incorporated for a more accurate modelling of post-seismic gravity changes.
This study provides the first verification that nonlinear transient rheology, or nonlinear Burgers rheology using laboratory-derived flow law can reproduce post-seismic gravity changes after the 2011 Tohoku earthquake at a first-order level. In the presentation, we will also show calculation results that consider those additional factors in the mantle wedge.