Applications Of The Spherical Earth Dislocation Theory In The Tohoku-Oki Mw9.0 Earthquake

The occurrence of the Tohoku-Oki Mw9.0 earthquake not only caused huge co-seismic and post-seismic deformation in the Japanese archipelago,but also had some impact on the far-field areas of China,Korea and North Korea.With the rapid development of GPS technology,using GPS data to study post-seismic deformation has become a new normal.Based on the viscoelastic spherical earth theory dislocation and the observation data of 23 GPS stations on the Japanese island in the near field and 8 GPS stations in the far field from 2.5 to 4.5 years after the earthquake,this paper studies the effect of mantle viscoelastic relaxation,and reveals the vertical variation of the mantle viscosity around the Tohoku-Oki Mw9.0 earthquake.We also research the co-seismic Coulomb stress changes on the northern Tanlu fault zone caused by the Tohoku-Oki Mw9.0 earthquake,by using spherical earth dislocation theory.And the influence of the earth's curvature in the far field is evaluated.In this paper,we research quantitatively the variation of the mantle viscosity around the Tohoku-Oki Mw9.0 earthquake by using the post-seismic GPS data that is widely distributed,as well as the viscoelastic spherical earth dislocation theory.At first,combined land and seafloor GPS data,we inverse the co-seismic slip distribution of the Tohoku-Oki Mw9.0 earthquake by using Bayesian inversion method as well as the Green's functions of the spherical earth dislocation theory.The maximum of the slip is about 59 m.Then,under the assumption of a uniform model,we inverse the viscosity of mantle around the Tohoku-Oki Mw9.0 earthquake.The root mean square error between the calculated post-seismic displacements and the observed ones reaches up to 0.81 cm in the far field.Next,we establish a model of the mantle viscous structure varying with the change of the depth,and inverse the mantle viscosity in this region by using far-field and near-field GPS data.As a result,the optimal solution of the lithosphere thickness the around the epicenter is 40 km.The optimal viscosity of the mantle between 40 km to 220 km is about 6×1018 Pa?s,and changes to be 1.5×1019 Pa?s between 220 km to 670 km.Such a viscous structure of mantle makes the root mean square error between the observations and calculations in the far field to be as small as 0.12 cm,about 15 % of the one under the assumption of uniform mantle viscosity.The accuracy of the theoretical result is improved.Finally,the analysis of root mean square error between the observed value and the simulated value indicates that the near-field data of post-seismic deformation mainly constrain the viscous structure of the shallow mantle,while the far-field data of post-seismic deformation mainly constrain the viscous structure of the deep mantle.Based on the spherical earth dislocation theory and a fault slip model of the Tohoku-Oki Mw9.0 earthquake,we calculate the co-seismic Coulomb failure stress changes(?CFS)on the northern Tanlu fault zone at a depth of 0 ~ 40 km.By comparing two sets of results from the spherical earth dislocation theory and the semi-infinite space one,we quantitatively analyze the influence of earth's curvature on the calculation results.In order to accurately reflect the spatial variation of Coulomb stress changes on the northern Tanlu fault zone.At first,we systematically summarize previous researches related to the northern Tanlu fault zone,divide the fault zone as detailed as possible,give the geometric parameters of each segment,and establish a segmented structural model of the northern Tanlu fault zone.Second,we calculate the ?CFS caused by the great earthquake on the northern Tanlu fault zone by using the spherical earth dislocation theory.The result shows that the ?CFS is no more than 0.003 MPa,which proves that the great earthquake didn't significantly change the stress state of the fault zone.Finally,we quantitatively analyze the disparities between the results of semi-infinite space dislocation theory and the spherical earth one.We find that the overall disparity between them is about 7.7% on the northern Tanlu fault zone.The disparity is 16.8% on the Fangzheng graben and the maximum disparity on the fault reaches up to 25.5%.It indicates that the influence of earth's curvature can't be ignored.In view of this,it's necessary to use the spherical earth dislocation theory instead of the semi-infinite space one to research the ?CFS in the far field(like the Tanlu fault zone).