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[SSS05-P01] Estimation of Afterslip Distribution and Viscoelastic Deformation by MCMC Method
Keywords:The 2011 off the Pacific coast of Tohoku Earthquake, Postseismic deformation, Markov Chain Monte Carlo method
Summary
Postseismic deformation of the 2011 off the Pacific coast of Tohoku Earthquake is still observed about ten years after the main rupture. Afterslip and viscoelastic deformation triggered by the main rupture are considered to be the mechanisms of the postseismic deformation. In this study, following Tomita et al. (2020), we estimate contributions of the afterslip and viscoelastic deformation including viscosity value simultaneously from the spatial pattern of the postseismic deformation obtained by the geodetic observation.
Calculation method
The displacements by afterslip and Viscoelastic are given by:
d0=Ge s0
d1=Gv,10 s0+Ge s1
where d0 and d1 are coseismic (t=0) and postseismic (t=t1) displacements, s0 and s1 are the coseismic slip and afterslip at t=t1, and Ge, Ge,10 are the elastic Green’s functions and viscoelastic Green’s functions at t=t1 by cosesimic slip. In this study, we use only two timesteps (t=0, t1), and do not consider the viscoelastic deformation induced by the afterslip.
We calculate elastic and viscoelastic Green’s functions of 600 fault patches, which are aligned with the Pacific Plate interface, using the code of Fukahata and Matsu’ura (2005). We assume a half-space consisting of an elastic surface layer with thickness of 50 km and a Maxwell viscoelastic substratum.
Inland postseismic displacements are derived from the F3 solutions of the 448 GEONET sites, by removing linear velocities and annual/semi-annual signals estimated from preseismic data. We also use seafloor observation data of Japan Coast Guard by removing the linear velocities estimated from preseismic data and fitting the timeseries by logarithm functions (Yokota et al. 2018). In addition, coseismic deformation data of three seafloor observation points of the Tohoku University are also used (Sato et al. 2011, Kido et al. 2011, Ito et al. 2011).
We use Markov Chain Monte Carlo (MCMC) method to estimate the fault slip parameters as well as hyperparameters for the smoothness of the slip distributions (Fukuda and Johnson 2008).
Results
Fig. 1 shows estimated slip distribution five years after the main rupture. The contribution of the afterslip dominates that of the viscoelastic deformation in the coastal region near the rupture area, where the sites show eastward and upward deformation. Far from the rupture area, the contribution of viscoelastic deformation becomes relatively larger. On the other hand, on the seafloor near the rupture area, the afterslip and viscoelastic deformation contribute in opposite sense, making moderate deformation on the seafloor observation points.
The effect of the viscoelastic deformation can be canceled by the afterslip for a wide range of viscosity in the coastal region near the rupture area. However, it is difficult to explain the deformation on the seafloor and far inland area for too large or small viscosity. As the result, the optimal viscosity, which makes smallest residuals between observed and calculated displacements, is estimated to be around 1019 Pa s (Fig. 2).
Note that our estimated slip distributions would not include the effect of plate interface coupling, since the preseismic velocities are subtracted from the data. This could be the reason why our estimated slip shows slightly larger seaward compared with the result of Tomita et al. (2020), in which they used the velocities relative to the continental plate. Nevertheless, the optimal viscosity in our result is very close to that of Tomita et al. (2020).
In our presentation, we will also show the results using different observation periods.
<Fig. 1> Estimated slip distribution five years after the 2011 off the Pacific coast of Tohoku Earthquake. Upper left and lower left figure respectively shows the horizontal and vertical displacements of observation (black) and calculation (white). Upper right and lower right figure respectively shows the contribution of the afterslip (magenta) and viscoelastic deformation (green) to the calculated displacements. In this calculation, the viscosity of 1019 Pa s is used. The estimated slip distribution of the main rupture (black contour), epicenter (star), and CMT solutions of the main shock and large aftershocks by JMA are also plotted.
<Fig. 2> Mean values of the residuals with respect to the viscosity.
Postseismic deformation of the 2011 off the Pacific coast of Tohoku Earthquake is still observed about ten years after the main rupture. Afterslip and viscoelastic deformation triggered by the main rupture are considered to be the mechanisms of the postseismic deformation. In this study, following Tomita et al. (2020), we estimate contributions of the afterslip and viscoelastic deformation including viscosity value simultaneously from the spatial pattern of the postseismic deformation obtained by the geodetic observation.
Calculation method
The displacements by afterslip and Viscoelastic are given by:
d0=Ge s0
d1=Gv,10 s0+Ge s1
where d0 and d1 are coseismic (t=0) and postseismic (t=t1) displacements, s0 and s1 are the coseismic slip and afterslip at t=t1, and Ge, Ge,10 are the elastic Green’s functions and viscoelastic Green’s functions at t=t1 by cosesimic slip. In this study, we use only two timesteps (t=0, t1), and do not consider the viscoelastic deformation induced by the afterslip.
We calculate elastic and viscoelastic Green’s functions of 600 fault patches, which are aligned with the Pacific Plate interface, using the code of Fukahata and Matsu’ura (2005). We assume a half-space consisting of an elastic surface layer with thickness of 50 km and a Maxwell viscoelastic substratum.
Inland postseismic displacements are derived from the F3 solutions of the 448 GEONET sites, by removing linear velocities and annual/semi-annual signals estimated from preseismic data. We also use seafloor observation data of Japan Coast Guard by removing the linear velocities estimated from preseismic data and fitting the timeseries by logarithm functions (Yokota et al. 2018). In addition, coseismic deformation data of three seafloor observation points of the Tohoku University are also used (Sato et al. 2011, Kido et al. 2011, Ito et al. 2011).
We use Markov Chain Monte Carlo (MCMC) method to estimate the fault slip parameters as well as hyperparameters for the smoothness of the slip distributions (Fukuda and Johnson 2008).
Results
Fig. 1 shows estimated slip distribution five years after the main rupture. The contribution of the afterslip dominates that of the viscoelastic deformation in the coastal region near the rupture area, where the sites show eastward and upward deformation. Far from the rupture area, the contribution of viscoelastic deformation becomes relatively larger. On the other hand, on the seafloor near the rupture area, the afterslip and viscoelastic deformation contribute in opposite sense, making moderate deformation on the seafloor observation points.
The effect of the viscoelastic deformation can be canceled by the afterslip for a wide range of viscosity in the coastal region near the rupture area. However, it is difficult to explain the deformation on the seafloor and far inland area for too large or small viscosity. As the result, the optimal viscosity, which makes smallest residuals between observed and calculated displacements, is estimated to be around 1019 Pa s (Fig. 2).
Note that our estimated slip distributions would not include the effect of plate interface coupling, since the preseismic velocities are subtracted from the data. This could be the reason why our estimated slip shows slightly larger seaward compared with the result of Tomita et al. (2020), in which they used the velocities relative to the continental plate. Nevertheless, the optimal viscosity in our result is very close to that of Tomita et al. (2020).
In our presentation, we will also show the results using different observation periods.
<Fig. 1> Estimated slip distribution five years after the 2011 off the Pacific coast of Tohoku Earthquake. Upper left and lower left figure respectively shows the horizontal and vertical displacements of observation (black) and calculation (white). Upper right and lower right figure respectively shows the contribution of the afterslip (magenta) and viscoelastic deformation (green) to the calculated displacements. In this calculation, the viscosity of 1019 Pa s is used. The estimated slip distribution of the main rupture (black contour), epicenter (star), and CMT solutions of the main shock and large aftershocks by JMA are also plotted.
<Fig. 2> Mean values of the residuals with respect to the viscosity.