岩石圈介质结构的不均匀性对地震同震、震后位移影响的三维数值模拟
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摘要
地震同震位移场的模拟受很多参数控制,从震源角度看:诸如断层的几何结构,倾角的大小,位错的分布等;从介质结构角度看:如半空间均匀模型、横向分层以及纵向分层介质模型;从弹性参数角度看:如拉梅常数,弹性模量以及泊松比等。定量的分析这些参数对地震同震位移的影响有助于我们根据地震破裂过程了解地震造成的地表形变特征或利用观测的形变资料识别断层的活动特征。在粘弹性松弛的震后形变理论中,震后形变则受控于同震形变和介质的粘性结构。探讨各种粘性结构介质中震后位移场的特征,有助于我们利用震后形变资料研究岩石的粘性。
本文首先回顾了同震形变、震后形变理论研究的背景。然后介绍了有限元方法的基本理论。在此基础之上,定量探讨了介质的不均匀性对地震同震、震后位移场的影响。最后分别以大陆内部和俯冲区域发生的逆冲大地震:汶川地震、日本地震为例,构建符合当地发震区域的介质结构,在观测资料的约束下,定量的模拟介质的不均匀性对地震同震位移以及震后位移的影响。论文主要包括以下内容:
(Ⅰ)介质的不均匀性和断层倾角对同震位移场的影响
影响同震位移分布的主要因素包括断层的滑动分布、断层的几何参数以及介质的弹性参数。本项研究主要利用三维有限元数值模拟的方法,定量研究介质不均匀性和断层倾角变化对同震位移场的影响。而滑动分布则选用简单的有限矩形走滑、逆冲或正断层滑动。数值模拟显示:(1)在均匀及纵向分层介质模型中,对于垂直走滑断层地震,水平位移场分量与介质的泊松比呈较弱负相关,垂直位移场与介质的泊松比呈正相关,水平位移场与剪切模量呈正相关,垂直位移场与剪切模量呈负相关;(2)模型介质的横向变化对同震位移场具有较大影响,剪切模量的横向变化对地震的位移场影响最大,断层左侧块体地震位移场与左侧块体介质的剪切量呈负相关,在垂直走滑断层地震中,断层右侧块体弹性参数不变、左侧块体剪切模量减半可使左侧块体的最大垂直位移分量幅度增大55.6%;(3)倾角对同震位移场有重要影响,在断层附近,倾角对位移场有主要的控制作用,对于高倾角逆冲断层(60～90度),上盘断层附近区域的水平位移场出现反向区,反向区域的范围随倾角的增大而增大,当倾角为90度时,上盘水平位移场全部反向;断层倾角增大时,在断层附近下盘的水平位移场增大幅度较大。
(Ⅱ)介质粘弹性结构的不均匀性对震后位移场的影响
在粘弹性松弛震后形变理论中,介质的粘弹性结构在震后位移场的特征中起着重要的控制作用,传统的半解析解无法考虑介质粘性的横向差异。我们构建简单的走滑断层地震,采用有限元的数值方法,定量的分析不同的粘弹性介质及粘性结构不均匀介质中地震震后形变的特征。数值模拟显示:(1)麦克斯韦介质在模拟地震震后形变中存在不协调问题,当粘性较低(如1018Pa.s)时,粘弹性松弛会很快达到平衡,无法模拟时间跨度较长的震后形变,当粘性较高时,震后位移随时间成线性增大,不符合一般观测的震后位移呈指数变化特点,采用广义麦克斯韦体介质,能较好的改善这一问题;(2)纵向分层(果冻三明治模型、奶油焦糖布丁模型)的粘弹性介质模型中,震后位移随时间松弛趋势与半空间均匀介质中的震后位移松弛趋势一致。相对于上地幔,下地壳的粘性对震后位移场的影响较大,在相同时间内,较弱的下地壳模型要比较弱的上地幔模型中震后位移松弛幅度大;(3)在横向不均匀的粘弹性模型中,粘性相对较强的块体中断层附近震后位移分量呈现与同震位移运动方向相反的特点,在相同的时间内粘性较弱的块体中震后位移量大于粘性较强块体中的震后位移。(4)断层一侧块体含有粘性较弱的流动通道时,其震后位移的松弛特点与下地壳上地幔粘性横向不均匀模型中的震后位移松弛特征相同。
(Ⅲ)汶川Ms8.0地震的同震、震后位移场
汶川Ms8.0地震发震区域的介质背景以及断层破裂滑动分布比较复杂,我们采用有限元算法,分别利用由Ji and Hayes以及Nishimuru and Yaji给出的滑动分布模型,参考地震波反演给出的发震区域的介质参数,计算汶川地震的同震位移场,比较断层滑动分布对地震同震位移场的影响,并将地表同震位移场的计算值与GPS观测值对比。此外参考CRUST2.0构建汶川地震局部区域的纵向分层介质模型,比较介质结构的差异对汶川地震同震位移场的影响。在震后位移场的模拟中,分别构建粘性横向均匀、横向分层的广义麦克斯韦体粘弹介质模型,探讨粘性差异介质结构中震后位移场的特征,并与观测到的汶川地震的震后位移场做比较,从粘弹性松弛理论的角度对汶川地震的震后位移场进行一个定性的分析。数值结果显示:(1)断层附近两侧的水平位移场呈现明显的相向运动,随着离断层距离的增大,位移场逐渐衰减。破裂区的南部以断层的逆冲运动为主,北部区域以右旋走滑为主,在较远范围内计算结果与GPS及InSAR观测值符合较好;(2)介质的弹性参数对同震位移场同样有一定的影响,相对于采用发震区域的Crust2.0介质结构,采用地震波反演的介质结构在断层附近引起的位移分量差异约10%,但是由于地震波给出的介质参数中,青藏高原的上地壳剪切模量相对四川盆地较强,即使考虑到介质的横向差异无益改善断层附近的位移场的计算值与观测值的差异。(3)断层的滑动分布对同震位移场有显著的影响,采用Ji and Hayes和Nishimuru and Yaji给出的滑动模型计算所得同震位移场在水平方向以及垂直方向都有较大的差异,这表明有必要采用地震波数据和形变观测位移数据,比如GPS和InSAR观测的数据联合反演以获取更合适的滑动分布;(4)震后数值模拟结果发现采用粘性横向差异的粘弹性模型计算的汶川地震的震后位移场特征与GPS观测的震后形变特征大体一致,震后位移随时间呈指数变化,断层两侧震后位移幅度不一致,粘性较弱上盘震后位移松弛幅度要大于粘性较强的下盘位移松弛幅度。断层两侧块体的粘性差异越大,震后位移松弛幅度差异越大;(5)在考虑粘性横向差异的模型中,在以逆冲为主区域的断层附近震后水平位移呈现反向,我们认为,龙门山断层两侧粘性横向差异可能是导致基于GPS观测到的汶川地震断层附近震后位移场反向的原因。
(Ⅳ) 2011 Mw 9.0 Honshu地震的同震位移场
2011年Mw9.0 Honshu地震为发生在俯冲带区域的低倾角逆冲大地震,俯冲带两侧介质存在显著的横向差异,震后很多研究机构基于地震波反演给出了日本地震的滑动分布,在反演的结果中,断层的几何参数以及最大滑动分布差异比较大。本章将参考地震反演给出的日本地震发震区域介质结构,分别计算了不同的滑动分布产生的同震位移场。并将计算结果与GPS测定的日本同震位移场进行对比,选取符合较好的滑动分布模型。为研究日本2011 Mw 9.0 Honshu地震的震后形变机制以及探讨震后的应力变化提供一个较好的约束。此外,参考Crust2.0模型,构建纵向均匀介质模型,比较介质的差异对日本地震同震位移场的影响。数值模拟显示:
(1)日本地震的水平位移场以断层为中心,两侧位移相向运动,上盘位移远大于下盘位移。地表垂直位移场在断层区域呈现隆起,隆起两侧沉降。呈现典型的低倾角逆冲断层大地震的特征。
(2)地表同震位移随断层的距离呈指数衰减,在断层附近,相对于Wei et al (2011)给出的滑动分布计算结果,采用Shao et al (2011)给出的滑动模型计算的同震位移在断层附近的最大值较大(最大约21m)。由此可见,在反演断层的滑动分布时,应考虑近场形变的信息。
(3)介质的横向差异对日本地震的同震位移场影响显著,相对于采用纵向分层的Crust2.0介质模型,采用地震波反演给出的横向不均匀模型计算的位移分量要大0.57-1.77m,因此,对于日本地震,在同震位移场的正演以及利用观测形变资料反演断层的滑动分布的反演的工作中应当考虑到介质的横向差异。
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 deformation
The 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 deformation
Viscoelastic 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 China
Based 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 earthquake
2011 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.
本文首先回顾了同震形变、震后形变理论研究的背景。然后介绍了有限元方法的基本理论。在此基础之上,定量探讨了介质的不均匀性对地震同震、震后位移场的影响。最后分别以大陆内部和俯冲区域发生的逆冲大地震:汶川地震、日本地震为例,构建符合当地发震区域的介质结构,在观测资料的约束下,定量的模拟介质的不均匀性对地震同震位移以及震后位移的影响。论文主要包括以下内容:
(Ⅰ)介质的不均匀性和断层倾角对同震位移场的影响
影响同震位移分布的主要因素包括断层的滑动分布、断层的几何参数以及介质的弹性参数。本项研究主要利用三维有限元数值模拟的方法,定量研究介质不均匀性和断层倾角变化对同震位移场的影响。而滑动分布则选用简单的有限矩形走滑、逆冲或正断层滑动。数值模拟显示:(1)在均匀及纵向分层介质模型中,对于垂直走滑断层地震,水平位移场分量与介质的泊松比呈较弱负相关,垂直位移场与介质的泊松比呈正相关,水平位移场与剪切模量呈正相关,垂直位移场与剪切模量呈负相关;(2)模型介质的横向变化对同震位移场具有较大影响,剪切模量的横向变化对地震的位移场影响最大,断层左侧块体地震位移场与左侧块体介质的剪切量呈负相关,在垂直走滑断层地震中,断层右侧块体弹性参数不变、左侧块体剪切模量减半可使左侧块体的最大垂直位移分量幅度增大55.6%;(3)倾角对同震位移场有重要影响,在断层附近,倾角对位移场有主要的控制作用,对于高倾角逆冲断层(60～90度),上盘断层附近区域的水平位移场出现反向区,反向区域的范围随倾角的增大而增大,当倾角为90度时,上盘水平位移场全部反向;断层倾角增大时,在断层附近下盘的水平位移场增大幅度较大。
(Ⅱ)介质粘弹性结构的不均匀性对震后位移场的影响
在粘弹性松弛震后形变理论中,介质的粘弹性结构在震后位移场的特征中起着重要的控制作用,传统的半解析解无法考虑介质粘性的横向差异。我们构建简单的走滑断层地震,采用有限元的数值方法,定量的分析不同的粘弹性介质及粘性结构不均匀介质中地震震后形变的特征。数值模拟显示:(1)麦克斯韦介质在模拟地震震后形变中存在不协调问题,当粘性较低(如1018Pa.s)时,粘弹性松弛会很快达到平衡,无法模拟时间跨度较长的震后形变,当粘性较高时,震后位移随时间成线性增大,不符合一般观测的震后位移呈指数变化特点,采用广义麦克斯韦体介质,能较好的改善这一问题;(2)纵向分层(果冻三明治模型、奶油焦糖布丁模型)的粘弹性介质模型中,震后位移随时间松弛趋势与半空间均匀介质中的震后位移松弛趋势一致。相对于上地幔,下地壳的粘性对震后位移场的影响较大,在相同时间内,较弱的下地壳模型要比较弱的上地幔模型中震后位移松弛幅度大;(3)在横向不均匀的粘弹性模型中,粘性相对较强的块体中断层附近震后位移分量呈现与同震位移运动方向相反的特点,在相同的时间内粘性较弱的块体中震后位移量大于粘性较强块体中的震后位移。(4)断层一侧块体含有粘性较弱的流动通道时,其震后位移的松弛特点与下地壳上地幔粘性横向不均匀模型中的震后位移松弛特征相同。
(Ⅲ)汶川Ms8.0地震的同震、震后位移场
汶川Ms8.0地震发震区域的介质背景以及断层破裂滑动分布比较复杂,我们采用有限元算法,分别利用由Ji and Hayes以及Nishimuru and Yaji给出的滑动分布模型,参考地震波反演给出的发震区域的介质参数,计算汶川地震的同震位移场,比较断层滑动分布对地震同震位移场的影响,并将地表同震位移场的计算值与GPS观测值对比。此外参考CRUST2.0构建汶川地震局部区域的纵向分层介质模型,比较介质结构的差异对汶川地震同震位移场的影响。在震后位移场的模拟中,分别构建粘性横向均匀、横向分层的广义麦克斯韦体粘弹介质模型,探讨粘性差异介质结构中震后位移场的特征,并与观测到的汶川地震的震后位移场做比较,从粘弹性松弛理论的角度对汶川地震的震后位移场进行一个定性的分析。数值结果显示:(1)断层附近两侧的水平位移场呈现明显的相向运动,随着离断层距离的增大,位移场逐渐衰减。破裂区的南部以断层的逆冲运动为主,北部区域以右旋走滑为主,在较远范围内计算结果与GPS及InSAR观测值符合较好;(2)介质的弹性参数对同震位移场同样有一定的影响,相对于采用发震区域的Crust2.0介质结构,采用地震波反演的介质结构在断层附近引起的位移分量差异约10%,但是由于地震波给出的介质参数中,青藏高原的上地壳剪切模量相对四川盆地较强,即使考虑到介质的横向差异无益改善断层附近的位移场的计算值与观测值的差异。(3)断层的滑动分布对同震位移场有显著的影响,采用Ji and Hayes和Nishimuru and Yaji给出的滑动模型计算所得同震位移场在水平方向以及垂直方向都有较大的差异,这表明有必要采用地震波数据和形变观测位移数据,比如GPS和InSAR观测的数据联合反演以获取更合适的滑动分布;(4)震后数值模拟结果发现采用粘性横向差异的粘弹性模型计算的汶川地震的震后位移场特征与GPS观测的震后形变特征大体一致,震后位移随时间呈指数变化,断层两侧震后位移幅度不一致,粘性较弱上盘震后位移松弛幅度要大于粘性较强的下盘位移松弛幅度。断层两侧块体的粘性差异越大,震后位移松弛幅度差异越大;(5)在考虑粘性横向差异的模型中,在以逆冲为主区域的断层附近震后水平位移呈现反向,我们认为,龙门山断层两侧粘性横向差异可能是导致基于GPS观测到的汶川地震断层附近震后位移场反向的原因。
(Ⅳ) 2011 Mw 9.0 Honshu地震的同震位移场
2011年Mw9.0 Honshu地震为发生在俯冲带区域的低倾角逆冲大地震,俯冲带两侧介质存在显著的横向差异,震后很多研究机构基于地震波反演给出了日本地震的滑动分布,在反演的结果中,断层的几何参数以及最大滑动分布差异比较大。本章将参考地震反演给出的日本地震发震区域介质结构,分别计算了不同的滑动分布产生的同震位移场。并将计算结果与GPS测定的日本同震位移场进行对比,选取符合较好的滑动分布模型。为研究日本2011 Mw 9.0 Honshu地震的震后形变机制以及探讨震后的应力变化提供一个较好的约束。此外,参考Crust2.0模型,构建纵向均匀介质模型,比较介质的差异对日本地震同震位移场的影响。数值模拟显示:
(1)日本地震的水平位移场以断层为中心,两侧位移相向运动,上盘位移远大于下盘位移。地表垂直位移场在断层区域呈现隆起,隆起两侧沉降。呈现典型的低倾角逆冲断层大地震的特征。
(2)地表同震位移随断层的距离呈指数衰减,在断层附近,相对于Wei et al (2011)给出的滑动分布计算结果,采用Shao et al (2011)给出的滑动模型计算的同震位移在断层附近的最大值较大(最大约21m)。由此可见,在反演断层的滑动分布时,应考虑近场形变的信息。
(3)介质的横向差异对日本地震的同震位移场影响显著,相对于采用纵向分层的Crust2.0介质模型,采用地震波反演给出的横向不均匀模型计算的位移分量要大0.57-1.77m,因此,对于日本地震,在同震位移场的正演以及利用观测形变资料反演断层的滑动分布的反演的工作中应当考虑到介质的横向差异。
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 deformation
The 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 deformation
Viscoelastic 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 China
Based 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 earthquake
2011 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.
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