Research On Coulomb Stress Change And Post-earthquake Strain Based On Spherical Earth Model

With the development of modern geodetic technology,observation technology such as GPS,In Sar and GRACE can detect significant seismic deformation.Through studying the characteristics of seismic deformation,one can not only analyze the viscous structure of the mantle,but also evaluate the strain accumulation on the fault zone and the Coulomb stress change on the fault plane,and further analyze the seismic hazard in the research area.Thus,the development of post-seismic strain change and internal deformation theory based on a realistic Earth model has important research significance and application value.This paper has studied the co-seismic internal deformation and post-seismic strain changes in a spherical layered Earth model,simultaneously taking self-gravitation,compressibility,and realistically stratified structure of the Earth into account.We further applied our method to the 2011 Mw9.0 Tohoku-Oki earthquake.The main research contents and conclusions are as follows:Based on the Reciprocal Theorem for solving differential equations,we studied the post-seismic strain changes in a spherically symmetric Earth model.Firstly,in the inverse Laplace transform,we used the closed rectangular integral on the complex plane,and derive the time-varying dislocation Love number.We found that as the degree of Love number increases,the impact of post-seismic is not obvious.Post-seismic Love number above 5000 degree can be replaced by co-seismic solution,it greatly improved the efficiency of post-earthquake deformation simulation.Then,we calculate the Green's Functions for post-seismic surface strain changes.Based on the proportional relationship between the mantle viscosity and the time of post-seismic deformation,a Green's Functions frame is prepared in advance,and the post-seismic Green's Functions at any time under any viscosity can be indirectly obtained by scaling the calculation time.Compared with the results calculated by viscoelastic half-space dislocation theory,we found the effect of curvature will increase significantly as the epicentral distance exceeds 15 °,and tend to stabilize over time.Finally,based on our Green's Functions,we simulated the post-seismic strain changes on the Japanese Islands and Northeast China induced by 2011 Mw9.0 Tohoku-Oki earthquake.By quantitatively comparing the results simulated by our Green's Function and the results calculated by GPS observation data in different epicentral distance regions,we found the relative errors decrease as the epicentral distance increases,revealing the importance of our spherical theory for far field research.Based on the dual numerical integral for the general solution and the particular solution for solving differential equations,we studied the co-seismic internal deformation in a spherically symmetric Earth model.In the study of internal deformation,it requires high-degree calculation if the depth of deformation was close to the source,however,when calculating the high-degree Love number for a deepsource,the integral of the general solution and the particular solution will overflow.Firstly,when solving the differential equations,we introduced a normalization method in the integration,separate the ratio coefficient from the propagation matrix during integration of each layer,to avoid numerical overflow,and derive the depth-varying dislocation Love number.We can calculate the internal deformation at an arbitrary depth caused by an arbitrary seismic source.Then,we calculate the Green's Functions for co-seismic internal strain changes,and found that the effects of a layered structure in internal deformations become small if the depth of the deformation approximates the seismic source.Finally,using the methods described above,we calculated the Coulomb stress changes at different depths on the Japanese Islands and Northeast China induced by the Tohoku-Oki Mw 9.0 earthquake.We found that the effect of layered structure plays a leading role on the near field,while curvature effect occupies a dominant position on the deep region of the far field.