Three-Dimensional Numerical Simulations On The Influences Of Elastic-heterogeneity On Co-seismic And Post-seismic Deformation

Factors influencing co-seismic displacements include fault slip distribution, fault geometry, rock's elastic property, and so on. Quantifying their effects on the co-seismic deformation helps to understand the relationship between the surface deformation and the fault rupture process, thus help to recognize the characteristics of the fault with deformation observations. Post-seismic deformation is mainly controlled by the co-seismic deformation and rock's viscoelastic property. Knowledges about the dependence of post-seismic deformation on different viscoelastic properties help to understand the rheology of the lower crustal and upper mantle form geodetic measurements such as postseismic deformation.In this paper, after a brief review on researches about co-seismic and post-seismic deformation, I briefly introduced the basics of finite element solutions to the elastic and viscoelastic deformation and the finite element program--pylith. Then the effects of elastic heterogeneities on the co-seicmic deformation and viscoelastic heterogeneities on post-seismic deformation are discussed in details based on numerical simulations in chapter 3 and chapter 4 respectively. Discussions on the effects of elastic or viscoelastic heterogeneities on the co-seismic or post-seismic deformation of the 2008 Ms 8.0 Wenchuan earthquake and the 2011 Mw9.0 Honshu earthquake are presented in chapter 5 and chapter 6 respectively. Main contributions of this paper are as follows.(1)The influences of elastic heterogeneity and the dip of the fault on co-seismic deformationThe effects of elastic heterogeneity and the dip of the fault on the co-seismic deformation have been studied in a three-dimensional finite element numerical model. In this part, the fault slip models include finite rectangular strike-slip, thrust and normal faults. The numerical results show that: (1) for a vertical strike-slip earthquake in homogeneous or horizontally homogeneous medium, the co-seismic deformation is slightly depend on the Poisson's ratio, with increases in Posson's ratio, the horizontal displacements decrease and the vertical displacements increase. The analysis for the relationship between coseismic deformation and shear modulus shows that horizontal displacements increase with shear modulus while vertical displacements decrease with shear modulus; (2) In horizontally heterogeneous medium, the shear modulus plays a significant role on the surface displacements, the relationship between shear modulus is negative, in the case of the elastic parameters on the right block of fault remain unchanged, the increase extent of maximum vertical displacements on the left block of fault reaches 55.6% due to halving the shear modulus of the left block of fault. Horizontal displacements on the hanging wall, the range of opposite direction region increase with dip-angle; and the increase extent of coseismic displacements on the foot wall are obvious.(2)The influences of viscoelastic heterogeneities on the post-seismic deformationViscoelastic properties control the post-seismic deformation in viscoelastic relaxation model. Conventional semi-analytic solutions can not account for lateral variations in viscoelastic properties. In this part, the influence of viscoelastic heterogeneity on postseismic deformation was studied with the aid of finite element numerical method. In our models, the fault motion is supposed to be simple finite rectangular strike-slip. The numerical results show that: (1) the maxwell viscoelastic medium was limited in simulating the post-seismic deformation. Post-seismic viscoelastic relaxation would reach balance too soon in the case of low viscousity (e.g. 1018Pa.s), thus can't interpret the observed post-seismic deformation in long time scales; the post-seismic displacements will relax linearly with time if the viscousity set too high ,thus can't account for post-seimic displacements relax exponentially with time. Using the General maxwell's body may get a better improvement. (2) In the vertically-layered viscoelastic model (e.g. jelly sandwich or crème brulee model), the tendency of post-seismic displacements relax with time is consistent with that in the model with elastic layer over a homogeneous viscoelastic half-space. Compare with the viscoelastic upper mantle, the viscousity in the lower crust dominate the character- rristics of the post-seismic displacements.In the same time, the relax displacements within the model of low viscousity in the lower crust is great than that within the model of low viscousity in the upper mantle; (3) in the lateral variations viscoelastic model, the post-seismic displacements near the fault move in the opposite direction compare with co-seismic displacements within the relatively strong viscoustiy block,In the same time, the relax displacements within lower viscousity block are great than that within stronger viscousity block. (3)The co-seismic and post-seismic deformation of the 2008 MS8.0 Wenchuan earthquake in ChinaBased on the finite element numerical algorithm, the coseismic displacements of the Wenchuan MS8.0 earthquake are calculated with the rupture slip vectors derived by Ji and Hayes as well as Nishimura and Yaji. Except in a narrow strip around the rupture zone, the coseismic displacements are consistent with those from GPS observ- ation and InSAR interpretation. Numerical results show that rupture slip vectors and elastic properties have profound influences on the surface coseismic deformation. Results from models with different elastic parameters indicate that;(1) in homogeno- us elastic medium, the surface displacements are weakly dependent on Poisson's ratio and independent of the elastic modulus;(2) in horizontally homogeneous medium with a weak zone at its middle, the thickness of the weak zone plays a significant role on calculating the surface displacements;(3) in horizontally and vertically heterogeneous medium, the surface displacements depend on both Poisson's ratio and elastic modulus. Calculations of coseismic deformation should take account of the spatial variation of the elastic properties. The misfit of the numerical results with that from the GPS observations in the narrow strip around the rupture zone suggests that a much more complicated rupture model of the Wenchuan earthquake needs to be established in future study ;( 4) the characteristic of post-seismic deformation calculated by applying lateral variations viscoelastic model is in accordance with that from the GPS observed for the Wenchuan earthquake, the post-seismic displacement relax exponentially with time,in the same time, the relax post-seismic displacements within lower viscousity uping wall are great than that within stronger viscousity down wall;(5) the post-seismic displacements near the fault domainated by reverse move in the opposite direction compare with co-seismic displacements within the relatively strong viscoustiy down wall,and the observed opposite direction in post-seismic displacement near the fault may be induced by lateral variations in viscoelastic properties(4)The coseismic deformation of the 2011 Mw 9.0 Honshu earthquake2011 Mw 9.0 Honshu earthquake is a megathrust earthquake which occurred on the subduction zone. The lateral variations of medium on the both sides of subduction fault are obvious. Many research institutions have given the fault slip model by inversion. The inversion results show some discrepancy in the fault angle and maximum final slip. In this section, we will calculate the displacements induced by different fault slip within the lateral variations medium based on the seismic inversion results and compare the calculated results with the GPS observations of co-seismic displacements. We will select a fault slip model of which induced displacements fit the GPS observed displacements best to give constraints for the research of post-seismic deformation mechanism. Furthermore, the other vertically-layered earth model was introduced refer to the with the purpose of comparing the effect of lateral variations medium on the 2011 Mw 9.0 Honshu earthquake's co-seismic deformation. The numerical results show that :(1) the horizontal displacements show that there is a significant opposite movement near the rupture zone after the Honshu earthquake The displacements amplitude on the hanging wall is lager than that on the foot wall. In the vicinity of rupture zone, the displacements are mainly upward and the displacements in the two sides of the rupture zone are mainly downward, all of which are the characteristic of displacements of the megathrust earthquake; (2) the amplitude of the movements decreases with the distance to the rupture zone increasing and the maximum amplitude of displacements induced by different fault slip differ greatly, the maximum displacements calculated by Jichen's slip model is 21m, therefore it is necessary to combine the seismic wave and surface deformation information to obtain proper fault slip vector in the fault; (3) the effect of lateral variations in elastic properties on the displacements of the 2011 Mw 9.0 Honshu earthquake is obvious.the maximum difference of displacement induce by the lateral variations in elastic medium can reach to 1.77m, So it is necessary to consider the lateral variations in elastic medium for the 2011 Mw 9.0 Honshu earthquake when inversing the fault slip and calculating the co-seismic deformation and post-seismic deformation.