Study Of Post-seismic Displacements Induced By The 2011 Tohoku-Oki M_w9.0 Earthquake

Due to the development of modern geodetic techniques,the post-seismic deformation caused by earthquakes can be observed by the GPS and InSAR,which provide data support for the study of earth's internal structure and seismogenic mechanism.We extracted the post-seismic displacements caused by the 2011 Tohoku-Oki Mw 9.0 earthquake from 215 GPS continuous observation stations that distribute evenly on Japan.After the pre-seismic trends and the regional structure characteristics were eliminated,we obtained the time series of displacement within 4.5 years post-seismic observed in the continuous GPS stations,the data spans from 12 March 2009 to 12 September 2015.We optimized the thickness of the lithosphere and the viscosity of the mantle around the epicenter of the 2011 Tohoku-Oki Mw9.0 earthquake,as well as the evolution of the after-slips,and the post-seismic displacements within 4.5 years after the main shock by using a relatively perfect spherical dislocation viscoelastic theory.First we updated the software of Tanaka by using a segment-summation scheme,which improved the computation accuracies in the near-field.In this study,we introduce an updated code to compute post-seismic deformations,including displacements as well as geoid and gravity changes,caused by an arbitrary seismic source at any position,for an arbitrary time that passes by after an event.The code consists of three parts.The first part is 32 sets of the numerical frames of the dislocation green function(DGF).Each frame contains a set of two-dimensional discrete numerical frames of DGFs on a symmetric earth model,according to a time point after the event.The second part is an interpolation program.Based on the above 32 sets of the numerical frame of DGF,the program can be used to calculate a set of DGF,according to an arbitrary time point after the event.The third part is an integration function,which performs bi-quadratic spline interpolation operations on the calculated frame of DGFs.We calculated the co-seismic displacements caused by the 2011 Tohoku-Oki Mw9.0 earthquake,using the viscoelastic dislocation theory ofTanaka and elastic spherical dislocation theory of Sun,respectively.The results show that two sets of the co-seismic displacements agree with each other very well,and the differences of the two sets of the co-seismic displacements are within the uncertainty of the computation.As demonstrate the correction of our new software.Given the viscosity of 1×1019 Pa s,we interpolated the DGFs of horizontal displacements of four independent seismic sources for 4.5 years after the main shock with a depth of 32 km and calculated them by Tanaka's viscoelastic spherical dislocation theory,respectively.Two sets of results agree with each other very well.This verifies the correction of our new codes.Using the viscoelastic dislocation theory,we simulated the post-seismic displacements between 3 and 4.5 years after the main shock,which are caused completely by the viscoelastic relaxation of the mantle.Comparing the observed displacement with the simulated ones,we found that the optimal viscosity of the mantle and the thickness of the lithosphere are about 6×1018 Pa s and 30 km,respectively.Then,we simulated the viscoelastic relaxation induced by the 2011 Tohoku-Oki Mw 9.0 earthquake from 12 March 2011 to 12 September 2015 according to the optimal viscosity of the mantle and the thickness of the lithosphere,and then removed the displacement induced by viscoelastic relaxation from the GPS observations within 3 years after the main shock,consequently acquired the post-seismic displacements induced by after-slip.Finally,we inversed the temporal and spatial evolution process of after-slips following the 2011 Tohoku-Oki Mw 9.0 earthquake utilizing the inversion algorithm based on spherical dislocation theory.We analyzed the post-seismic displacements distribution caused by two different mechanisms within 4.5 years after the main shock.We found that after-slips following this earthquake changed significantly in 0.5 years and decayed completely in the area of the main shock after 2 years.However,the after-slips still existed in northeastern and southwestern area of the fault model.The cumulative moment of after-slips in 2 years achieved up to 8.59.The total displacements caused by the viscoelastic relaxation of the mantle would exceed the one caused by after-slips in approximately 4 years after the great earthquake.