Seismic dislocation theory of spherical Earth model and its application
-
摘要: 地震位错理论是研究地震断层滑动与地球物理场变化之间关系的理论，是震源机制、地球内部构造、地震预测等基本地球物理问题与大地测量、地球物理观测数据之间的联系纽带。被广泛使用的半无限空间介质模型的位错理论，由于其几何模型的限制，在地震变形和地球动力学等应用研究中会导致一定程度的误差。此外，现代大地测量技术可以在全球和区域尺度上精确地观测地震变形，亟需一个适用于全球地震变形研究的地震位错理论。为此，本团队基于球形地球模型，经过多年系统性研究，建立了地震位错理论新体系。所构建的球形地球模型的地震位错理论，促进了全球地震变形和地球动力学变化的研究，是近年来地球物理学领域取得的重要理论进展之一。本文简要地介绍了国内球形地球模型地震位错理论的发展及其应用研究。首先，介绍了弹性球形地球模型、三维不均匀地球模型和黏弹地球模型的位错理论；其次，介绍球形地球模型的位错理论在地球动力学变化研究、断层与地下介质结构反演和地震大地测量学研究方面的相关应用；最后，对球形地球模型的位错理论的发展方向作出展望。Abstract: Seismic dislocation theory is the theory of studying the relationship between seismic fault slip and geophysical field change, and also it is the link between the source mechanism, the internal structure of the Earth, earthquake forecasting and other basic geophysical problems and geodetic-geophysical observation. The widely used dislocation theory of the semi-infinite medium model, due to the limitation of its geometric attribute, will riskily result in a certain degree of oversight and even fault in the application of seismic deformation and geodynamics analysis. In addition, modern geodesy technology can accurately observe seismic deformation on global and regional scales, and a suitable seismic dislocation theory born for global seismic deformation study is urgently required. For this purpose, our team has developed a new system of seismic dislocation theory based on the spherical Earth model through many years of systematic research. The establishment of such theory has promoted the study of global seismic deformation and geodynamic process, and expanded the study of earthquake-induced global geodynamic changes. This informative article briefly introduces the domestic development and application of seismic dislocation theory of spherical Earth model. The first section introduces the dislocation theory of elastic spherical Earth model, three-dimensional inhomogeneous Earth model and viscoelastic Earth model. The second section introduces the relevant applications of the dislocation theory of spherical Earth model in geodynamic change, fault and underground structure inversion and others in seismological geodesy. The seismic dislocation theory of the spherical Earth model has promoted the study of global seismic deformation and geodynamic changes. It is one of the important theoretical advances in the field of geophysics in recent years.
-
引言
2022年1月8日1时45分，青海省海北州门源县发生MS6.9地震，震中位置为（37.8°N，101.3°E），这是中国大陆2022年第一个接近M7.0的强震。该次地震发生在青藏高原东北缘祁连地块中的托莱山—冷龙岭断裂附近（图1）。据中国地震台网中心（2022）的速报结果，该地震震中距离门源县城大约54 km，震源深度为10 km，震源深度重定位结果为12.9 km （Fan et al，2022）。截至2022年1月19日8时整，共记录到M≥3.0余震20次，其中MS4.0—4.9地震5次，MS≥5.0地震2次，最大为1月12日18时20分MS5.2地震。
![]()
图 1 青藏高原东北缘区域构造背景与地震台站分布Figure 1. Tectonic settings of the northeastern Tibetan Plateau and distribution of seismic stations门源地区位于祁连地块中东部，由于受到印度板块和欧亚板块持续碰撞、挤压的远程作用，区域内活动断裂发育、构造变形强烈。祁连地块内部发育了一系列以挤压逆冲为主兼具左旋走滑特征的活动断裂带，其中主要受到阿尔金和祁连—海原两条大型边界走滑断裂控制（袁道阳等，2004）。2022年门源MS6.9地震发生在冷龙岭断裂西端、托莱山断裂东端，基本上将冷龙岭断裂与托莱山断裂连接起来（图2），这两条断裂与海原断裂、老虎山断裂、毛毛山断裂、金强河断裂等构成了长约1 000 km的祁连—海原断裂带。祁连—海原断裂带不仅控制着青藏高原东北缘地区的几何和构造格局（Zheng et al，2013；Shi et al，2020），同时也调节着青藏地块相对于阿拉善地块的向东运动（Gaudemer et al，1995；Lasserre et al，2002）。
![]()
图 2 门源MS6.9地震及余震分布2022年地震序列定位结果引自Fan等（2022），2016年门源地震位置引自梁姗姗等（2017），1986年门源地震位置引自兰州地震研究所青海省地震局联合考察队（1987）。F1：龙首山南缘断裂东段；F2：河西堡—四道山断裂；F3：榆木山东缘断裂；F4：民乐—永昌断裂；F5：肃南—祁连断裂；F6：民乐—大马营断裂；F7：皇城—双塔断裂；F8：托莱山断裂；F9：冷龙岭断裂；F10：金强河断裂；F11：毛毛山断裂；F12：天桥沟—黄羊川断裂；F13：玛雅雪山北缘断裂；F14：大通山北缘断裂；F15：木里—江仓断裂；F16：日月山断裂；F17：门源断裂；F18：达坂山断裂；F19：黑林河断裂Figure 2. The distribution of Menyuan MS6.9 earthquake and its aftershocksThe location of 2022 seismic sequence is from Fan et al （2022），the location of 2016 Menyuan earthquake is from Liang et al （2017），and the location of 1986 Menyuan earthquake is from Lanzhou Institute of Seismology and Seismological Bureau of Qinghai Province （1987）. F1：Eastern segment of southern Longshoushan fault；F2：Hexipu-Sidaoshan fault；F3：Yumushan eastern marginal fault；F4：Minyue-Yongchang fault； F5：Su’nan-Qilian fault；F6：Minyue-Damaying fault；F7：Huangcheng-Shuangta fault；F8：Tuolaishan fault；F9：Lenglongling fault；F10：Jinqianghe fault；F11：Maomaoshan fault；F12：Tianqiaogou-Huangyangchuan fault；F13：Mayaxueshan northern marginal fault；F14：Datongshan northern marginal fault；F15：Muli-Jiangcang fault；F16：Riyueshan fault； F 17：Menyuan fault；F18：Dabanshan fault；F19：Heilinhe fault1900年以来，祁连—海原断裂带附近多次发生M6.0以上地震，位置相近的有1986年MS6.4地震和2016年MS6.4地震（图2），其中2016年门源MS6.4地震发生在冷龙岭北侧断裂（胡朝忠等，2016），与此次门源地震序列中的1月12日MS5.2余震位置相差约9 km。两次门源地震虽然相距不远，但其发震机制表现不同，即2016年门源地震为冷龙岭北侧断裂上的逆冲型地震，2022年门源地震则为道沟断裂上的走滑型地震（中国地震局地质研究所，2022），表明该地区的地质构造特征比较复杂。相关研究表明，在剪切变形较大的区域更易发生地震（Jin et al，2019）。位于青藏东北缘的祁连地块是新生代再次活跃的早古生代岛弧、微陆块拼合体（Yin，Harrison，2000），当前仍以12 mm/a的速率沿NNE−SSW方向水平缩短（Zhang et al，2004）。这种NE方向的推挤对阿尔金断裂带东部和河西走廊产生一定的加载作用，可能是导致2016年门源MS6.4地震发生的原因（胡朝忠等，2016）。2022年门源MS6.9地震发生后，中国地震局组织了考察工作，初步结果显示：此次门源MS6.9地震极震区的烈度可能达Ⅸ以上（中国地震局地球物理研究所，2022）；地震序列在托莱山—冷龙岭断裂附近产生了四条地表破裂带，其中断裂带南、北两侧破裂程度差异较大，北侧明显高于南侧（中国地震局地质研究所，2022）。
结构成像研究显示，强震更容易发生在高、低速变化的过渡带，例如青藏东南缘（王琼，高原，2014），青藏东北缘地区的岷漳MS6.7地震和九寨沟MS7.0地震的震源也都位于高、低速的过渡带（夏思茹等，2021）。为解剖强震发生的深部构造背景，本文收集了速度结构等资料，拟通过分析地壳结构与地震分布之间的关系，探讨门源MS6.9地震的深部孕震构造背景。
1. 接收函数揭示的门源地区地壳厚度和vP/vS不均匀分布
地壳厚度和泊松比是描述地壳结构和物质成分的两个重要参数，可以为地壳的地质演化过程提供重要的约束，同时有益于对地震孕震环境的研究。Wang等（2016）使用来自中国地震台网2007年8月至2013年10月间的三分量宽频带地震数据，对震级M＞5.0，震中距为30°—90°且震相清晰、初动尖锐的地震记录进行接收函数计算，得到了青藏高原东北缘地区的地壳厚度和波速比。Wang等（2017）使用来自中国科学台阵Ⅱ期和鄂尔多斯地块内流动台阵的资料（共724个台站）得到了青藏高原东北缘的地壳厚度和波速比。为了分析此次门源MS6.9地震的发震位置与深部结构之间的关系，本文根据两种数据结果重绘了门源地区的地壳厚度和vP/vS的分布图像（图3）。
![]()
从图3可以看到，研究区域内地壳厚度约为30—70 km，变化非常剧烈，青藏高原东北部的地壳比周缘区域厚。地壳厚度与地形起伏变化比较一致，从东向西呈梯度加深的趋势。门源台（MEY）的地壳厚度为59.3 km，与王椿镛等（1995）的基于门源—平凉—渭南人工地震测深剖面得到的门源地壳厚度（58 km）较为一致。吴立辛等（2011）运用小波多尺度分析也观察到青藏高原东北缘地壳厚度呈现由东北向西南增厚的趋势，且门源地区位于梯度变化较大的区域。通过本文的数据再分析，门源地区处于地壳厚度由西向东剧烈减薄的地带，而门源MS6.9地震的震中位于地壳厚度南厚北薄的局部急剧变化过渡带上，同时又处于波速比（vP/vS）东高西低快速变化的过渡带，揭示了门源MS6.9地震与深部结构的不均匀分布有关，特别是与物性参数的快速变化有关。
由于使用不同的资料和方法，Wang等（2016）和Wang等（2017）的结果在门源地区存在一些差异，也揭示了该区域地壳物性在小范围内的不均匀分布，表明关键地域密集台阵观测的必要性。这些结果虽然呈现不均匀分布的具体形态差异，但它们都揭示了门源MS6.9地震震源区深部结构存在剧烈的（或快速的）物性变化。
2. 体波成像揭示的P波、S波速度和泊松比分布
基于2009年至2017年青藏高原东北缘区域固定台网记录到的3万9 971次地震的初至P波和S波走时数据，利用双差成像方法对2万9 491次地震进行了重新定位，获取了青藏高原东北缘地壳的波速和泊松比结构（肖卓，高原，2017）。为了探究门源MS6.9地震的深部发震结构，对门源地震震源区的深部结构进行了重绘放大，得到了门源地震震源区的P波速度、S波速度以及泊松比在不同深度的横向和垂向分布图像，结果如图4和图5所示。
![]()
图 4 门源地区P波速度（a）、S波速度（b）和泊松比（c）红色星形表示2022年MS6.9门源主震，红色圆点表示其余震，地壳深度标于子图的左下角，下同Figure 4. P-wave velocity （a），S-wave velocity （b） and Poisson’s ratio （c） in the Menyuan regionThe red star represents the 2022 Menyuan MS6.9 earthquake，the red solid circle represents its aftershock，and the crustal depth is labled at the lower-left corner of the subfigure，the same below![]()
图 5 穿过门源地震震源区的P波速度（a）、S波速度（b）和泊松比（c）的垂向剖面图剖面方向根据图4白色实线绘制，剖面数据来自肖卓和高原（2017）Figure 5. Vertical profiles of P-wave velocity （a），S-wave velocity （b） and Poisson’s ratio （c） through the source region of Menyuan earthquakeThe section direction is drawn according to the white line in Fig. 4，and the profile data is from Xiao and Gao （2017）P波速度分布显示，门源地震震源区的结构存在明显的垂向变化和横向变化，特别是在垂向上，上地壳顶部（0—10 km）的P波速度较高，但随着深度的增加（10—20 km），P波速度逐渐转变为低速异常（图4，5）。根据门源地震序列重新定位结果（Fan et al，2022），MS6.9主震的震源深度为12.9 km。在震源区，P波速度在5—15 km深度由高速变为低速（图5）。S波速度和泊松比分布显示，门源地震震源区的结构存在明显的横向变化。在10—15 km深度，门源地震震源区东西两侧分别呈现为高S波速度、低泊松比和低S波速度、高泊松比异常（图4）。门源地震震源区泊松比（图4）在东西方向的变化特征与接收函数得到的vP/vS变化（图3）具有很好的一致性，揭示了地壳介质物性在东西方向上的快速变化很可能主要分布在10—20 km深度范围。
夏思茹等（2021）使用青藏高原东北缘71个固定台和418个流动台站得到了更高分辨率的三维P波速度结构，本文使用其数据绘制了两个跨过震中位置的垂向剖面图（图6）。从图6可以看到，门源地震发生在上地壳高低速变化过渡区，震源下方存在明显低速体。从这一点上看，图6与图5的P波速度垂向变化结果基本一致。
![]()
图 6 穿过门源地震震源区P波速度垂向剖面图剖面方向根据图1中白色实线绘制，剖面数据来自夏思茹等（2021）Figure 6. Vertical P-wave velocity profile through the source region of Menyuan earthquakeThe section direction is drawn according to the white line in Fig. 1，and the prolife data is from Xia et al （2021）人工地震测深剖面（王椿镛等，1995）和远震面波成像（Li et al，2017）均揭示，祁连造山带下方中地壳存在S波低速层；地震与速度结构之间关系的研究结果表明，地震的发生往往与壳内低速度层存在明显的关联性（Zhao et al，2002；李永华等，2014）；重力资料多阶小波分析也显示，重力异常分布与大地震发生的位置有关联性（Wu，Gao，2019）；王新胜等（2013）利用分离的布格重力异常揭示大地震多发生在高、低密度异常边界区域或者下地壳低密度层之上，结果显示这次门源MS6.9震源区下方下地壳表现为强烈的低密度异常；赵凌强等（2019）通过大地电磁探测剖面发现冷龙岭断裂下方存在高导层，认为该断裂下方可能形成了明显的力学强度软弱区，这种力学强度软弱区的存在易导致地震蠕动、滑移与发生。由此可见，地震带下方壳内薄弱层的存在很可能使其上覆脆性上地壳物质易于形成应力集中而发生强震。
3. 背景噪声成像揭示的相速度和方位各向异性分布
利用青藏高原东北缘地区固定地震台网三分量连续波形数据，采用Yao等（2006）发展起来的背景噪声数据处理技术，使用瑞雷波能量较强的垂向记录，反演得到了青藏高原东北缘地区相速度和方位各向异性（王琼，高原，2018）。为了分析门源地震与深部结构的关系，本文重绘了门源地震震源区的区域相速度和方位各向异性结构（图7）。
![]()
图 7 门源地震震源区相速度和方位各向异性分布Figure 7. Phase velocity and azimuthal anisotropy distribution in the source region of the Menyuan earthquake（a） T＝8 s；（b） T＝12 s根据门源MS6.9地震的震源深度结果，把门源地震标示在周期8 s和12 s的相速度图（图7）上。可以看到，MS6.9门源地震发生在高低速的过渡区，方位各向异性也呈现出方向和幅值的变化。郭瑛霞（2017）利用布设在祁连山断裂带的40个短周期流动台站和38个宽频带固定台站的记录，采用背景噪声成像得到了祁连地块S波速度结构，结果同样显示门源震源区处于高速与低速的过渡区域。王琼和高原（2014）分析青藏高原东南缘地区强震活动与速度结构关系时发现，M5.0—6.9地震主要发生在高低速过渡区和低速异常区，M≥7.0地震则主要发生在高低速过渡区但更深入到高速异常区里。房立华等（2009）认为，速度变化强烈的地区存在应力集中，介质比较脆弱，更易于释放应力而触发较大的地震。
地震各向异性可以揭示壳幔内部构造变形等信息（高原，滕吉文，2005）。连续记录的背景噪声数据不依赖于地震信号，更有利于获得地壳的结构特征。从图7可以看到，以冷龙岭断裂为界，各向异性快波方向呈现不同特征：断裂以北，快波方向主要呈北东方向，与区域平均最大主压应力方向一致（许忠淮，2001）；断裂以南，快波方向主要呈北西方向，表明各向异性形态可能受到区域断裂带的影响，揭示门源地区地壳（至少上地壳）介质各向异性可能受到区域构造应力和局部断裂（构造）的双重约束。
祝意青等（2016）关于2011—2015年流动重力观测资料的分析结果显示，重力变化在冷龙岭断裂两侧出现正负边界带，重力变化梯度带与冷龙岭断裂的走向一致，冷龙岭北侧的重力变化以正值为主，南侧则以负值为主，表明冷龙岭断裂有地震孕育的构造背景。赵凌强等（2019）结合现今水准、重力、GPS速度场及大地电磁测深结果，认为冷龙岭断裂所处的祁连—海原断裂带是青藏高原东北缘的边界断裂，目前正承受着巨大的NE向挤压力。Gao等（1996）和高锐等（1998）根据深地震反射剖面结果认为青藏高原在向北扩展过程中处于双向挤压应力作用之下，同时受到印度板块向北俯冲和阿拉善地块沿宽滩山断裂插入到祁连山之下的动力作用。在双向挤压力作用下，上地壳岩片发生逆冲叠覆，岩层发生脆性变形，使上地壳缩短增厚，因此对于祁连造山带内低速高导层的存在，可能与地壳增厚和地表抬升有关。Wang （2001）提出，由于壳幔流变性质的差异，地壳的增厚升温可以降低岩石层的整体强度。新生代祁连造山带地壳的增厚和构造演化可能导致放射性生热元素含量增加，产生相对较高的热流值。羌塘地块和松潘—甘孜地块的热流值较低（44—45 mW/m2），柴达木盆地的热流值为54 mW/m2，而祁连造山带的热流值高达66 mW/m2 （Wang，2001），说明祁连山的局部低速异常可能由上地壳增厚、生热元素含量增加引起，而门源地震同时也处于地壳厚度快速变化的区域（图3），容易造成应力的集中，具有发生大地震的深部构造背景。
4. 讨论与结论
本文根据地壳厚度、vP/vS比值、P波和S波速度结构、面波相速度及方位各向异性结果，结合密集地震台阵探测、人工地震测深、深地震反射、大地电磁探测、区域重力场等地球物理资料，初步探讨了门源MS6.9地震的深部构造背景。
此次门源MS6.9地震发生在地壳厚度和vP/vS值都出现快速空间变化的区域。门源MS6.9地震震源位于P波速度从浅到深由高速变低速的垂向过渡区，也是S波速度和泊松比分布呈现明显横向变化的过渡区域，该过渡区域大致处于10—20 km深度范围内。背景噪声成像结果显示，冷龙岭断裂两侧相速度和方位各向异性变化明显。这些现象表明，地震活动与地壳结构有较强的对应关系。通常情况下，地震波速度的变化可能代表岩石强度的变化，而大的破裂或强烈的地壳变形往往都集中在地壳强度（或地震波速度）反差较大的地方（Tian et al，2021）。
1月12日的MS5.2余震震中与2016年MS6.4地震震中很近，表明这次门源MS6.9地震及其余震导致冷龙岭断裂的破裂比较充分，两次门源地震之间及邻近地区短时间内难以积累更大的能量，即意味着短时间内发生更大地震的可能性不大。
本文结果显示，不同资料、不同方法及不同数据处理得到的结果可能存在差异，需要甄别大的形态一致性与小的局部不同。重要的是强震震源区处于地壳介质物性快速变化的过渡区，这是不同的研究结果给出了共同的认识。对于小区域深部结构的准确成像，需要密集台阵观测资料的支持。此外，P波与S波速度分布不同，可能表明岩性、组分或流体充填状态等的不同。
受到印度板块和欧亚板块持续碰撞、挤压的远程作用，青藏高原东北缘祁连地块的地壳显著增厚，但陇西盆地没有明显增厚（Tian et al，2021），而祁连地块东部正处于地壳厚度横向变化较为剧烈的区域，容易形成应力集中和积累，具有发生大地震的深部构造背景。
中国地震局地球物理研究所王兴臣副研究员提供了地壳厚度和波速比数据，石磊副研究员和硕士研究生夏思茹提供了P波速度剖面图件，审稿专家提出的宝贵意见使本文的质量有了明显改善，作者在此一并表示衷心的感谢。
-
陈飞,刘泰,付广裕,佘雅文. 2020. 震后GPS观测数据揭示的日本MW9.0地震周边地区地幔黏滞性结构垂向变化[J]. 地球物理学报,63(6):2210–2220. doi: 10.6038/cjg2020N0170 Chen F,Liu T,Fu G Y,She Y W. 2020. Variation of the mantle viscosity around the Tohoku-Oki MW9.0 earthquake revealed by post-seismic GPS data[J]. Chinese Journal of Geophysics,63(6):2210–2220 (in Chinese).
陈俊勇. 2003. 现代大地测量学的进展[J]. 测绘科学,28(2):1–5. doi: 10.3771/j.issn.1009-2307.2003.02.001 Chen J Y. 2003. On the development of modern geodesy[J]. Science of Surveying and Mapping,28(2):1–5 (in Chinese).
陈运泰,林邦慧,林中洋,李志勇. 1975. 根据地面形变的观测研究1966年邢台地震的震源过程[J]. 地球物理学报,18(3):164–182. Chen Y T,Lin B H,Lin Z Y,Li Z Y. 1975. The focal mechanism of the 1966 Hsingtai ( 邢台) earthquake as inferred from the ground deformation observations[J]. Acta Geophysica Sinica,18(3):164–182 (in Chinese). Chen Y T, Lin B H, Lin Z Y, Li Z Y. 1975. The focal mechanism of the 1966 Hsingtai （邢台） earthquake as inferred from the ground deformation observations[J]. Acta Geophysica Sinica, 18（3）: 164-182 （in Chinese）.
陈运泰,林邦慧,王新华,黄立人,刘妙龙. 1979. 用大地测量资料反演的1976年唐山地震的位错模式[J]. 地球物理学报,22(3):201–217. doi: 10.3321/j.issn:0001-5733.1979.03.001 Chen Y T,Lin B H,Wang X H,Huang L R,Liu M L. 1979. A dislocation model of the Tangshan (唐山) earthquake of 1976 from the inversion of geodetic data[J]. Acta Geophysica Sinica,22(3):201–217 (in Chinese). Chen Y T, Lin B H, Wang X H, Huang L R, Liu M L. 1979. A dislocation model of the Tangshan （唐山） earthquake of 1976 from the inversion of geodetic data [J]. Acta Geophysica Sinica, 22（3）: 201-217 （in Chinese）.
付广裕,孙文科. 2012a. 地球横向不均匀结构对地表以及空间固定点同震重力变化的影响[J]. 地球物理学报,55(8):2728–2746. Fu G Y,Sun W K. 2012a. Effects of earth’s lateral heterogeneity on co-seismic gravity changes at deformed earth surface and space-fixed point[J]. Chinese Journal of Geophysics,55(8):2728–2746 (in Chinese).
付广裕,孙文科. 2012b. 球体位错理论计算程序的总体设计与具体实现[J]. 地震,32(2):73–87. Fu G Y,Sun W K. 2012b. Overall design and specific structures of the computing codes for coseismic deformations on a layered spherical earth[J]. Earthquake,32(2):73–87 (in Chinese).
胡明城. 2000. 现代大地测量学[J]. 测绘通报,(5):3. doi: 10.3969/j.issn.0494-0911.2000.05.021 Hu M C. 2000. Modern geodesy[J]. Bulletin of Surveying and Mapping,(5):3 (in Chinese).
李建成,宁津生,晁定波,姜卫平. 2006. 卫星测高在大地测量学中的应用及进展[J]. 测绘科学,31(6):19–23. doi: 10.3771/j.issn.1009-2307.2006.06.003 Li J C,Ning J S,Chao D B,Jiang W P. 2006. The applications and progress of satellite altimetry in geodesy[J]. Science of Surveying and Mapping,31(6):19–23 (in Chinese).
梁明,王武星,张晶. 2018. 联合GPS和GRACE观测研究日本MW9.0地震震后变形机制[J]. 地球物理学报,61(7):2691–2704. doi: 10.6038/cjg2018L0356 Liang M,Wang W X,Zhang J. 2018. Post-seismic deformation mechanism of the MW9.0 Tohoku-Oki earthquake detected by GPS and GRACE observations[J]. Chinese Journal of Geophysics,61(7):2691–2704 (in Chinese).
林晓光,孙文科. 2014. 地形效应和局部地质构造对计算同震形变的影响:以2011年日本东北大地震(MW9.0)为例[J]. 地球物理学报,57(8):2530–2540. doi: 10.6038/cjg20140814 Lin X G,Sun W K. 2014. Effects of topography and local geological structure on computing co-seismic deformation:A case study of the 2011 Japan Tohoku earthquake (MW9.0)[J]. Chinese Journal of Geophysics,57(8):2530–2540 (in Chinese).
刘泰,付广裕,周新,苏小宁. 2017. 2011年日本MW9.0地震震后形变机制与震源区总体构造特征[J]. 地球物理学报,60(9):3406–3417. doi: 10.6038/cjg20170911 Liu T,Fu G Y,Zhou X,Su X N. 2017. Mechanism of post-seismic deformations following the 2011 Tohoku-Oki MW9.0 earthquake and general structure of lithosphere around the source[J]. Chinese Journal of Geophysics,60(9):3406–3417 (in Chinese).
刘泰,付广裕,邹镇宇. 2019. 2004年苏门答腊地震粘滞性松弛效应对华南地区地壳水平活动的影响[J]. 地震,39(2):37–45. doi: 10.3969/j.issn.1000-3274.2019.02.005 Liu T,Fu G Y,Zou Z Y. 2019. Effect of viscoelastic relaxation following the 2004 Sumatra earthquake on horizontal crustal movement in South China[J]. Earthquake,39(2):37–45 (in Chinese).
孙文科. 1989. 空间大地测量技术在板块构造及地壳形变中的应用[J]. 地球物理学报,32(3):339–346. doi: 10.3321/j.issn:0001-5733.1989.03.010 Sun W K. 1989. Applications of spatial geodetic in plate structure and crust deformation[J]. Acta Geophysica Sinica,32(3):339–346 (in Chinese).
孙文科. 2002. 低轨道人造卫星(CHAMP、GRACE、GOCE)与高精度地球重力场:卫星重力大地测量的最新发展及其对地球科学的重大影响[J]. 大地测量与地球动力学,22(1):92–100. Sun W K. 2002. Satellite in low orbit (CHAMP,GRACE,GOCE) and high precision earth gravity field:The latest progress of satellite gravity geodesy and its great influence on geoscience[J]. Journal of Geodesy and Geodynamics,22(1):92–100 (in Chinese).
孙文科. 2012a. 地震位错理论[M]. 北京: 科学出版社: 14–56. Sun W K. 2012a. Seismic Dislocation Theory[M]. Beijing: Science Press: 14–56 （in Chinese）.
孙文科. 2012b. 地震位错理论在地震学研究中的作用与存在的问题[J]. 国际地震动态,(6):17. Sun W K. 2012b. Application of dislocation theories in seismological study and existing problems[J]. Recent Developments in World Seismology,(6):17 (in Chinese).
唐河,孙文科. 2021. 黏弹地球地震变形理论研究进展和展望[J]. 地球与行星物理论评,52(1):11–26. Tang H,Sun W K. 2021. Progress and prospect of deformation theory in the viscoelastic earth[J]. Reviews of Geophysics and Planetary Physics,52(1):11–26 (in Chinese).
汪汉胜,李国营,许厚泽. 1997. SNRVEI地球模型连续分布的简正模及其意义[J]. 地球物理学报,40(1):78–84. doi: 10.3321/j.issn:0001-5733.1997.01.009 Wang H S,Li G Y,Xu H Z. 1997. Continuously distributed modes of SNRVEI earth model and their effects[J]. Acta Geophysica Sinica,40(1):78–84 (in Chinese).
许厚泽,王广运. 1989. 动力大地测量学:研究地球动态变化的新学科[J]. 地球科学进展,4(4):9–15. Xu H Z,Wang G Y. 1989. Dynamic geodesy:A new discipline for studying the dynamic changes of the earth[J]. Advances in Earth Science,4(4):9–15 (in Chinese).
杨君妍,孙文科. 2020. 利用大地测量数据反演地震位错Love数和格林函数的理论与方法[J]. 地球物理学报,63(8):2912–2923. doi: 10.6038/cjg2020N0356 Yang J Y,Sun W K. 2020. The theory and method of determining dislocation Love number and Green’s function using geodetic data[J]. Chinese Journal of Geophysics,63(8):2912–2923 (in Chinese).
姚宜斌,杨元喜,孙和平,李建成. 2020. 大地测量学科发展现状与趋势[J]. 测绘学报,49(10):1243–1251. doi: 10.11947/j.AGCS.2020.20200358 Yao Y B,Yang Y X,Sun H P,Li J C. 2020. Geodesy discipline:Progress and perspective[J]. Acta Geodaetica et Cartographica Sinica,49(10):1243–1251 (in Chinese).
张国庆,付广裕,周新,徐长仪. 2015. 利用震后黏弹性位错理论研究苏门答腊地震(MW9.3)的震后重力变化[J]. 地球物理学报,58(5):1654–1665. doi: 10.6038/cjg20150517 Zhang G Q,Fu G Y,Zhou X,Xu C Y. 2015. Retrieve post-seismic gravity changes induced by Sumatra earthquake (MW9.3) based on the viscoelastic dislocation theory[J]. Chinese Journal of Geophysics,58(5):1654–1665 (in Chinese).
张岚,孙文科. 2022. 重力卫星GRACE Mascon产品的应用研究进展与展望[J]. 地球与行星物理论评,53(1):35–52. Zhang L,Sun W K. 2022. Progress and prospect of GRACE Mascon product and its application[J]. Reviews of Geophysics and Planetary Physics,53(1):35–52 (in Chinese).
周江存,孙和平,徐建桥,崔小明,陈晓东. 2017. 重力位能同震变化及其构造意义:以青藏高原地区为例[J]. 地球物理学报,60(6):2493–2499. doi: 10.6038/cjg20170636 Zhou J C,Sun H P,Xu J Q,Cui X M,Chen X D. 2017. Co-seismic change of gravitational potential energy and its tectonic implications:A case study of the Tibetan Plateau[J]. Chinese Journal of Geophysics,60(6):2493–2499 (in Chinese).
周硕愚,吴云,姚运生,杜瑞林. 2008. 地震大地测量学研究[J]. 大地测量与地球动力学,28(6):77–82. Zhou S Y,Wu Y,Yao Y S,Du R L. 2008. Research of earthquake geodesy[J]. Journal of Geodesy and Geodynamics,28(6):77–82 (in Chinese).
周硕愚,吴云,江在森. 2017. 地震大地测量学及其对地震预测的促进:50年进展、问题与创新驱动[J]. 大地测量与地球动力学,37(6):551–562. Zhou S Y,Wu Y,Jiang Z S. 2017. Earthquake geodesy and earthquake prediction:Progress,innovations and problems over fifty years[J]. Journal of Geodesy and Geodynamics,37(6):551–562 (in Chinese).
周新. 2017. 利用大地测量数据反演断层滑移分布的MCMC方法[J]. 大地测量与地球动力学,37(10):996–1002. Zhou X. 2017. Markov Chain Monte Carlo method used to invert for fault slip from geodetic data[J]. Journal of Geodesy and Geodynamics,37(10):996–1002 (in Chinese).
周新,万晓云,申旭辉. 2018. 主喜马拉雅逆冲带的震间与同震重力场变化[J]. 遥感学报,22(增刊1):100–113. Zhou X,Wang X Y,Shen X H. 2018. Coseismic and interseismic gravity field change along the Main Himalaya Thrust[J]. Journal of Remote Sensing,22(S1):100–113 (in Chinese).
Abidin H Z,Andreas H,Kato T,Ito T,Meilano I,Kimata F,Natawidjaya D H,Harjono H. 2009. Crustal deformation studies in Java (Indonesia) using GPS[J]. J Earthq Tsunami,3(2):77–88. doi: 10.1142/S1793431109000445
Adam D. 2002. Amazing GRACE[J]. Nature,416(6876):10–11. doi: 10.1038/416010a
Aki K. 1964. Study of Love and Rayleigh waves from earthquakes with fault plane solutions or with known faulting. Part 1. A phase difference method based on a new model of earthquake source[J]. Bull Seismol Soc Am,54(2):511–527. doi: 10.1785/BSSA0540020511
Allen R M,Ziv A. 2011. Application of real-time GPS to earthquake early warning[J]. Geophys Res Lett,38(16):L16310.
Alterman Z,Jarosch H,Pekeris C L. 1959. Oscillations of the earth[J]. Proc R Soc Lond A:Math Phys Sci,252(1268):80–95.
Amoruso A,Crescentini L. 2009. Slow diffusive fault slip propagation following the 6 April 2009 L’Aquila earthquake,Italy[J]. Geophys Res Lett,36(24):L24306. doi: 10.1029/2009GL041503
Anderson D L. 1974. Earthquakes and the rotation of the Earth[J]. Science,186(4158):49–50. doi: 10.1126/science.186.4158.49
Anderson D L,O’Connell R. 1967. Viscosity of the Earth[J]. Geophys J Int,14(1/2/3/4):287–295.
Argus D F,Peltier W R,Blewitt G,Kreemer C. 2021. The viscosity of the top third of the lower mantle estimated using GPS,GRACE,and relative sea level measurements of glacial isostatic adjustment[J]. J Geophys Res:Solid Earth,126(5):e2020JB021537.
Ben-Menahem A,Toksöz M N. 1962. Source-mechanism from spectra of long-period seismic surface-waves:1. The Mongolian earthquake of December 4,1957[J]. J Geophys Res,67(5):1943–1955. doi: 10.1029/JZ067i005p01943
Ben-Menahem A,Singh S J. 1968. Multipolar elastic fields in a layered half space[J]. Bull Seismol Soc Am,58(5):1519–1572. doi: 10.1785/BSSA0580051519
Beresnev I A. 2003. Uncertainties in finite-fault slip inversions:To what extent to believe?(a critical review)[J]. Bull Seismol Soc Am,93(6):2445–2458. doi: 10.1785/0120020225
Biggs J,Wright T J. 2020. How satellite InSAR has grown from opportunistic science to routine monitoring over the last decade[J]. Nat Commun,11(1):3863. doi: 10.1038/s41467-020-17587-6
Bock Y,Melgar D. 2016. Physical applications of GPS geodesy:A review[J]. Rep Prog Phys,79(10):106801. doi: 10.1088/0034-4885/79/10/106801
Braitenberg C. 2018. The deforming and rotating Earth:A review of the 18th International Symposium on Geodynamics and Earth Tide,Trieste 2016[J]. Geod Geodyn,9(3):187–196. doi: 10.1016/j.geog.2018.03.003
Cambiotti G,Barletta V R,Bordoni A,Sabadini R. 2009. A comparative analysis of the solutions for a Maxwell Earth:The role of the advection and buoyancy force[J]. Geophys J Int,176(3):995–1006. doi: 10.1111/j.1365-246X.2008.04034.x
Cambiotti G. 2020. Joint estimate of the coseismic 2011 Tohoku earthquake fault slip and post-seismic viscoelastic relaxation by GRACE data inversion[J]. Geophys J Int,220(2):1012–1022.
Cathles L M. 1975. Viscosity of the Earth’s Mantle[M]. Princeton: Princeton University Press: 267.
Chao B F. 2003. Geodesy is not just for static measurements any more[J]. Eos,Trans AGU,84(16):145–150.
Chao B F,Gross R S. 1987. Changes in the Earth’s rotation and low-degree gravitational field induced by earthquakes[J]. Geophys J Int,91(3):569–596. doi: 10.1111/j.1365-246X.1987.tb01659.x
Chen C H,Yeh T K,Liu J Y,Wang C H,Wen S,Yen H Y,Chang S H. 2011. Surface deformation and seismic rebound:Implications and applications[J]. Surv Geophys,32(3):291–313. doi: 10.1007/s10712-011-9117-3
Cheng H H,Zhang B,Huang L Y,Zhang H,Shi Y L. 2019. Calculating coseismic deformation and stress changes in a heterogeneous ellipsoid earth model[J]. Geophys J Int,216(2):851–858. doi: 10.1093/gji/ggy444
Chinnery M A. 1961. The deformation of the ground around surface faults[J]. Bull Seismol Soc Am,51(3):355–372. doi: 10.1785/BSSA0510030355
Cornelio C,Violay M. 2020. Effect of fluid viscosity on earthquake nucleation[J]. Geophys Res Lett,47(12):e2020GL087854.
Dahlen F A. 1968. The normal modes of a rotating,elliptical Earth[J]. Geophys J Int,16(4):329–367. doi: 10.1111/j.1365-246X.1968.tb00229.x
Dahlen F A. 1974. On the static deformation of an Earth model with a fluid core[J]. Geophys J Int,36(2):461–485. doi: 10.1111/j.1365-246X.1974.tb03649.x
Dahlen F A. 1977. The balance of energy in earthquake faulting[J]. Geophys J Int,48(2):239–261. doi: 10.1111/j.1365-246X.1977.tb01298.x
Dai C L,Shum C K,Wang R J,Wang L,Guo J Y,Shang K,Tapley B. 2014. Improved constraints on seismic source parameters of the 2011 Tohoku earthquake from GRACE gravity and gravity gradient changes[J]. Geophys Res Lett,41(6):1929–1936. doi: 10.1002/2013GL059178
Diao F Q,Wang R J,Wang Y B,Xiong X,Walter T R. 2018. Fault behavior and lower crustal rheology inferred from the first seven years of postseismic GPS data after the 2008 Wenchuan earthquake[J]. Earth Planet Sci Lett,495:202–212. doi: 10.1016/j.jpgl.2018.05.020
Diao F Q,Xiong X,Wang R J,Walter T R,Wang Y B,Wang K. 2019. Slip rate variation along the Kunlun fault (Tibet):Results from new GPS observations and a viscoelastic earthquake-cycle deformation model[J]. Geophys Res Lett,46(5):2524–2533. doi: 10.1029/2019GL081940
Dong J,Sun W K,Zhou X,Wang R J. 2014. Effects of Earth’s layered structure,gravity and curvature on coseismic deformation[J]. Geophys J Int,199(3):1442–1451. doi: 10.1093/gji/ggu342
Dziewonski A M,Anderson D L. 1981. Preliminary reference Earth model[J]. Phys Earth Planet Inter,25(4):297–356. doi: 10.1016/0031-9201(81)90046-7
Fang M,Hager B H. 1996. The sensitivity of post-glacial sea level to viscosity structure and ice-load history for realistically parameterized viscosity profiles[J]. Geophys Res Lett,23(25):3787–3790. doi: 10.1029/96GL03622
Fernández J,Pepe A,Poland M P,Sigmundsson F. 2017. Volcano geodesy:Recent developments and future challenges[J]. J Volcanol Geoth Res,344:1–12. doi: 10.1016/j.jvolgeores.2017.08.006
Forte A M,Peltier W R,Dziewonski A M. 1991. Inferences of mantle viscosity from tectonic plate velocities[J]. Geophys Res Lett,18(9):1747–1750. doi: 10.1029/91GL01726
Freed A M,Bürgmann R. 2004. Evidence of power-law flow in the Mojave desert mantle[J]. Nature,430(6999):548–551. doi: 10.1038/nature02784
Freed A M,Hashima A,Becker T W,Okaya D A,Sato H,Hatanaka Y. 2017. Resolving depth-dependent subduction zone viscosity and afterslip from postseismic displacements following the 2011 Tohoku-Oki,Japan earthquake[J]. Earth Planet Sci Lett,459:279–290. doi: 10.1016/j.jpgl.2016.11.040
Freymueller J T. 2021. GPS, tectonic geodesy[G]//Encyclopedia of Solid Earth Geophysics. Dordrecht: Springer: 558–578.
Fu G Y,Sun W K. 2006. Global co-seismic displacements caused by the 2004 Sumatra-Andaman earthquake (MW9.1)[J]. Earth Planets Space,58(2):149–152. doi: 10.1186/BF03353371
Fu G Y,Sun W K. 2007. Effects of lateral inhomogeneity in a spherical Earth on gravity Earth tides[J]. J Geophys Res:Solid Earth,112(B6):B06409.
Fu G Y,Sun W K. 2008. Surface coseismic gravity changes caused by dislocations in a 3-D heterogeneous earth[J]. Geophys J Int,172(2):479–503. doi: 10.1111/j.1365-246X.2007.03684.x
Fu G Y,Sun W K. 2009. Effects of Earth’s lateral inhomogeneous structures on coseismic gravity changes[J]. Pure Appl Geophys,166(8):1343–1368.
Fu G Y,Sun W K,Fukuda Y,Gao S H. 2010. Coseismic displacements caused by point dislocations in a three-dimensional heterogeneous,spherical earth model[J]. Geophys J Int,183(2):706–726. doi: 10.1111/j.1365-246X.2010.04757.x
Gautam P K,Rajesh S,Kumar N,Dabral C P. 2020. GPS measurements on pre-,co- and post-seismic surface deformation at first multi-parametric geophysical observatory,Ghuttu in Garhwal Himalaya,India[J]. J Geod Sci,10(1):136–144. doi: 10.1515/jogs-2020-0114
Gilbert F,MacDonald G J F. 1960. Free oscillations of the Earth:1. Toroidal oscillations[J]. J Geophys Res,65(2):675–693. doi: 10.1029/JZ065i002p00675
Gilbert F,Backus G E. 1966. Propagator matrices in elastic wave and vibration problems[J]. Geophysics,31(2):326–332. doi: 10.1190/1.1439771
Gilbert F, Backus G E. 1968. Elastic-gravitational vibrations of a radially stratified sphere[G]//Dynamics of Stratified Solids. New York: American Society of Mechanical Engineers: 82–95.
Gilbert F,Dziewonski A M. 1975. An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra[J]. Philos Trans R Soc Lond A:Math Phys Eng Sci,278(1280):187–269.
Giorgi G,Schmidt T D,Trainotti C,Mata-Calvo R,Fuchs C,Hoque M M,Berdermann J,Furthner J,Günther C,Schuldt T,Sanjuan J,Gohlke M,Oswald M,Braxmaier C,Balidakis K,Dick G,Flechtner F,Ge M,Glaser S,König R,Michalak G,Murböck M,Semmling M,Schuh H. 2019. Advanced technologies for satellite navigation and geodesy[J]. Adv Space Res,64(6):1256–1273. doi: 10.1016/j.asr.2019.06.010
Glennie C L,Carter W E,Shrestha R L,Dietrich W E. 2013. Geodetic imaging with airborne LiDAR:The Earth’s surface revealed[J]. Rep Prog Phys,76(8):086801. doi: 10.1088/0034-4885/76/8/086801
Gómez D D,Bevis M,Pan E N,Smalley R. 2017. The influence of gravity on the displacement field produced by fault slip[J]. Geophys Res Lett,44(18):9321–9329. doi: 10.1002/2017GL074113
Han S C,Shum C K,Bevis M,Ji C,Kuo C Y. 2006. Crustal dilatation observed by GRACE after the 2004 Sumatra-Andaman earthquake[J]. Science,313(5787):658–662. doi: 10.1126/science.1128661
Haskell N A. 1953. The dispersion of surface waves on multilayered media[J]. Bull Seismol Soc Am,43(1):17–34. doi: 10.1785/BSSA0430010017
Herring T A,Melbourne T I,Murray M H,Floyd M A,Szeliga W M,King R W,Phillips D A,Puskas C M,Santillan M,Wang L. 2016. Plate boundary observatory and related networks:GPS data analysis methods and geodetic products[J]. Rev Geophys,54(4):759–808. doi: 10.1002/2016RG000529
Hu Y,Wang K L,He J H,Klotz J,Khazaradze G. 2004. Three-dimensional viscoelastic finite element model for postseismic deformation of the great 1960 Chile earthquake[J]. J Geophys Res:Solid Earth,109:B12403. doi: 10.1029/2004JB003163
Ide S. 2007. Slip inversion[G]//Earthquake Seismology: Treatise on Geophysics Volume 4. Amsterdam: Elsevier: 193–223.
Imanishi Y,Sato T,Higashi T,Sun W K,Okubo S. 2004. A network of superconducting gravimeters detects submicrogal coseismic gravity changes[J]. Science,306(5695):476–478. doi: 10.1126/science.1101875
Israel M,Ben-Menahem A. 1974. Residual displacements and strains due to faulting in real Earth models[J]. Phys Earth Planet Inter,8(1):23–45. doi: 10.1016/0031-9201(74)90107-1
Ito T,Simons M. 2011. Probing asthenospheric density,temperature,and elastic moduli below the western United States[J]. Science,332(6032):947–951. doi: 10.1126/science.1202584
Jiang Z S,Wang M,Wang Y Z,Wu Y Q,Che S,Shen Z K,Bürgmann R,Sun J B,Yang Y L,Liao H,Li Q. 2014. GPS constrained coseismic source and slip distribution of the 2013 MW6.6 Lushan,China,earthquake and its tectonic implications[J]. Geophys Res Lett,41(2):407–413. doi: 10.1002/2013GL058812
Jovanovich D B,Husseini M I,Chinnery M A. 1974a. Elastic dislocations in a layered half-space: Ⅰ . Basic theory and numerical methods[J]. Geophys J Int,39(2):205–217. doi: 10.1111/j.1365-246X.1974.tb05451.x
Jovanovich D B,Husseini M I,Chinnery M A. 1974b. Elastic dislocations in a layered half-space: Ⅱ . The point source[J]. Geophys J Int,39(2):219–239. doi: 10.1111/j.1365-246X.1974.tb05452.x
Kennett B L N,Engdahl E R. 1991. Traveltimes for global earthquake location and phase identification[J]. Geophys J Int,105(2):429–465. doi: 10.1111/j.1365-246X.1991.tb06724.x
Krynski J. 2012. Gravimetry for geodesy and geodynamics-brief historical review[J]. Rep Geod,92(1):69–86.
Larson K M. 2019. Unanticipated uses of the global positioning system[J]. Annu Rev Earth Planet Sci,47(1):19–40. doi: 10.1146/annurev-earth-053018-060203
Li X X,Ge M R,Dai X L,Ren X D,Fritsche M,Wickert J,Schuh H. 2015. Accuracy and reliability of multi-GNSS real-time precise positioning:GPS,GLONASS,BeiDou,and Galileo[J]. J Geod,89(6):607–635. doi: 10.1007/s00190-015-0802-8
Love A E H. 1911. Some Problems of Geodynamics[M]. Cambridge: Cambridge University Press: 102–118.
Ma X Q,Kusznir N J. 1992. 3-D subsurface displacement and strain fields for faults and fault arrays in a layered elastic half-space[J]. Geophys J Int,111(3):542–558. doi: 10.1111/j.1365-246X.1992.tb02111.x
Marchandon M,Hollingsworth J,Radiguet M. 2021. Origin of the shallow slip deficit on a strike slip fault:Influence of elastic structure,topography,data coverage,and noise[J]. Earth Planet Sci Lett,554:116696. doi: 10.1016/j.jpgl.2020.116696
Marotta A M. 2003. Benefits from GOCE within solid Earth geophysics[J]. Space Sci Rev,108:95–104. doi: 10.1023/A:1026273832697
Maruyama T. 1964. Statical elastic dislocations in an infinite and semi-infinite medium[J]. Bull Earthq Res Inst Univ Tokyo,42:289–368.
Masterlark T. 2003. Finite element model predictions of static deformation from dislocation sources in a subduction zone:Sensitivities to homogeneous,isotropic,Poisson-solid,and half-space assumptions[J]. J Geophys Res:Solid Earth,108(B11):2540. doi: 10.1029/2002JB002296
Matsuo K,Heki K. 2011. Coseismic gravity changes of the 2011 Tohoku-Oki earthquake from satellite gravimetry[J]. Geophys Res Lett,38(7):L00G12.
Meigs A. 2013. Active tectonics and the LiDAR revolution[J]. Lithosphere,5(2):226–229. doi: 10.1130/RF.L004.1
Melini D,Cannelli V,Piersanti A,Spada G. 2008. Post-seismic rebound of a spherical Earth:New insights from the application of the Post-Widder inversion formula[J]. Geophys J Int,174(2):672–695. doi: 10.1111/j.1365-246X.2008.03847.x
Mindlin R D,Cheng D H. 1950. Nuclei of strain in the semi-infinite solid[J]. J Appl Phys,21(9):926–930. doi: 10.1063/1.1699785
Molodenskiy S M. 1980. The effect of lateral heterogeneities upon the tides[J]. BIM Fevrier,80:4833–4850.
Ni S D,Kanamori H,Helmberger D. 2005. Energy radiation from the Sumatra earthquake[J]. Nature,434(7033):582. doi: 10.1038/434582a
Nur A,Mavko G. 1974. Postseismic viscoelastic rebound[J]. Science,183(4121):204–206. doi: 10.1126/science.183.4121.204
Okada Y. 1985. Surface deformation due to shear and tensile faults in a half-space[J]. Bull Seismol Soc Am,75(4):1135–1154. doi: 10.1785/BSSA0750041135
Okada Y. 1992. Internal deformation due to shear and tensile faults in a half-space[J]. Bull Seismol Soc Am,82(2):1018–1040. doi: 10.1785/BSSA0820021018
Okubo S. 1991. Potential and gravity changes raised by point dislocations[J]. Geophys J Int,105(3):573–586. doi: 10.1111/j.1365-246X.1991.tb00797.x
Okubo S. 1992. Gravity and potential changes due to shear and tensile faults in a half-space[J]. J Geophys Res:Solid Earth,97(B5):7137–7144. doi: 10.1029/92JB00178
Okubo S. 1993. Reciprocity theorem to compute the static deformation due to a point dislocation buried in a spherically symmetric Earth[J]. Geophys J Int,115(3):921–928. doi: 10.1111/j.1365-246X.1993.tb01501.x
Okubo S. 2020. Advances in gravity analyses for studying volcanoes and earthquakes[J]. Proc Jpn Acad Ser B:Phys Biol Sci,96(2):50–69. doi: 10.2183/pjab.96.005
Pan E N. 2019. Green’s functions for geophysics:A review[J]. Rep Prog Phys,82(10):106801. doi: 10.1088/1361-6633/ab1877
Panet I,Mikhailov V,Diament M,Pollitz F,King G,De Viron O,Holschneider M,Biancale R,Lemoine J M. 2007. Coseismic and post-seismic signatures of the Sumatra 2004 December and 2005 March earthquakes in GRACE satellite gravity[J]. Geophys J Int,171(1):177–190. doi: 10.1111/j.1365-246X.2007.03525.x
Peltier W R. 2021. Mantle viscosity[G]//Encyclopedia of Solid Earth Geophysics. Dordrecht: Springer: 1107–1115.
Pepe A,Calò F. 2017. A review of interferometric synthetic aperture RADAR (InSAR) multi-track approaches for the retrieval of Earth’s surface displacements[J]. Appl Sci,7(12):1264. doi: 10.3390/app7121264
Piersanti A,Spada G,Sabadini R,Bonafede M. 1995. Global post-seismic deformation[J]. Geophys J Int,120(3):544–566. doi: 10.1111/j.1365-246X.1995.tb01838.x
Pollitz F F. 1992. Postseismic relaxation theory on the spherical earth[J]. Bull Seismol Soc Am,82(1):422–453.
Pollitz F F. 1996. Coseismic deformation from earthquake faulting on a layered spherical Earth[J]. Geophys J Int,125(1):1–14. doi: 10.1111/j.1365-246X.1996.tb06530.x
Pollitz F F. 1997. Gravitational viscoelastic postseismic relaxation on a layered spherical Earth[J]. J Geophys Res:Solid Earth,102(B8):17921–17941. doi: 10.1029/97JB01277
Press F. 1965. Displacements,strains,and tilts at teleseismic distances[J]. J Geophys Res,70(10):2395–2412. doi: 10.1029/JZ070i010p02395
Reid H F. 1910. Mechanics of the Earthquake, the California Earthquake of April 18, 1906[R]. Washington D C: The State Investigation Commission, Carnegie Institution of Washington: 29–31.
Reilinger R E,Ergintav S,Bürgmann R,McClusky S,Lenk O,Barka A,Gurkan O,Hearn L,Feigl K L,Cakmak R,Aktug B,Ozener H,Töksoz M N. 2000. Coseismic and postseismic fault slip for the 17 August 1999,M=7.5,Izmit,Turkey earthquake[J]. Science,289(5484):1519–1524. doi: 10.1126/science.289.5484.1519
Rolandone F,Dreger D,Murray M,Bürgmann R. 2006. Coseismic slip distribution of the 2003 MW6.6 San Simeon earthquake,California,determined from GPS measurements and seismic waveform data[J]. Geophys Res Lett,33(16):L16315. doi: 10.1029/2006GL027079
Roth F. 1990. Subsurface deformations in a layered elastic half-space[J]. Geophys J Int,103(1):147–155. doi: 10.1111/j.1365-246X.1990.tb01759.x
Rundle J B. 1980. Static elastic-gravitational deformation of a layered half space by point couple sources[J]. J Geophys Res: Solid Earth,85(B10):5355–5363. doi: 10.1029/JB085iB10p05355
Ryder I,Parsons B,Wright T J,Funning G J. 2007. Post-seismic motion following the 1997 Manyi (Tibet) earthquake:InSAR observations and modelling[J]. Geophys J Int,169(3):1009–1027. doi: 10.1111/j.1365-246X.2006.03312.x
Sabadini R,Yuen D A,Boschi E. 1984. The effects of post-seismic motions on the moment of inertia of a stratified viscoelastic earth with an asthenosphere[J]. Geophys J Int,79(3):727–745. doi: 10.1111/j.1365-246X.1984.tb02865.x
Salvi S,Stramondo S,Funning G J,Ferretti A,Sarti F,Mouratidis A. 2012. The Sentinel-1 mission for the improvement of the scientific understanding and the operational monitoring of the seismic cycle[J]. Remote Sens Environ,120:164–174. doi: 10.1016/j.rse.2011.09.029
Savage J C,Hastie L M. 1969. A dislocation model for the Fairview Peak,Nevada,earthquake[J]. Bull Seismol Soc Am,59(5):1937–1948. doi: 10.1785/BSSA0590051937
Savage J C,Burford R O. 1973. Geodetic determination of relative plate motion in central California[J]. J Geophys Res,78(5):832–845. doi: 10.1029/JB078i005p00832
Savage J C,Prescott W H. 1978. Asthenosphere readjustment and the earthquake cycle[J]. J Geophys Res:Solid Earth,83(B7):3369–3376. doi: 10.1029/JB083iB07p03369
Savage J C. 1983. A dislocation model of strain accumulation and release at a subduction zone[J]. J Geophys Res:Solid Earth,88(B6):4984–4996. doi: 10.1029/JB088iB06p04984
Scholz C H. 1998. Earthquakes and friction laws[J]. Nature,391(6662):37–42. doi: 10.1038/34097
Segall P,Davis J L. 1997. GPS applications for geodynamics and earthquake studies[J]. Annu Rev Earth Planet Sci,25(1):301–336. doi: 10.1146/annurev.earth.25.1.301
Soldati G,Spada G. 1999. Large earthquakes and Earth rotation:The role of mantle relaxation[J]. Geophys Res Lett,26(7):911–914. doi: 10.1029/1999GL900144
Spaans K,Hooper A. 2016. InSAR processing for volcano monitoring and other near-real time applications[J]. J Geophys Res:Solid Earth,121(4):2947–2960. doi: 10.1002/2015JB012752
Spada G,Sabadini R,Yuen D A,Ricard Y. 1992. Effects on post-glacial rebound from the hard rheology in the transition zone[J]. Geophys J Int,109(3):683–700. doi: 10.1111/j.1365-246X.1992.tb00125.x
Steketee J A. 1958. On Volterra’s dislocations in a semi-infinite elastic medium[J]. Can J Phys,36(2):192–205. doi: 10.1139/p58-024
Suito H,Freymueller J T. 2009. A viscoelastic and afterslip postseismic deformation model for the 1964 Alaska earthquake[J]. J Geophys Res:Solid Earth,114:B11404.
Sun W K. 1992. Potential and gravity changes caused by dislocations in spherically symmetric Earth models[J]. Bull Earthq Res Inst Univ Tokyo,67(2):89–238.
Sun W K. 2003. Asymptotic theory for calculating deformations caused by dislocations buried in a spherical earth:Geoid change[J]. J Geod,77(7/8):381–387.
Sun W K. 2004a. Asymptotic solution of static displacements caused by dislocations in a spherically symmetric Earth[J]. J Geophys Res:Solid Earth,109(B5):B05402.
Sun W K. 2004b. Short note:Asymptotic theory for calculating deformations caused by dislocations buried in a spherical earth-gravity change[J]. J Geod,78(1/2):76–81.
Sun W K,Okubo S. 1993. Surface potential and gravity changes due to internal dislocations in a spherical Earth: Ⅰ . Theory for a point dislocation[J]. Geophys J Int,114(3):569–592. doi: 10.1111/j.1365-246X.1993.tb06988.x
Sun W K,Okubo S. 1998. Surface potential and gravity changes due to internal dislocations in a spherical Earth: Ⅱ . Application to a finite fault[J]. Geophys J Int,132(1):79–88.
Sun W K,Okubo S. 2002. Effects of earth’s spherical curvature and radial heterogeneity in dislocation studies:For a point dislocation[J]. Geophys Res Lett,29(12):46-1–46-4.
Sun W K,Okubo S. 2004. Coseismic deformations detectable by satellite gravity missions:A case study of Alaska (1964,2002) and Hokkaido (2003) earthquakes in the spectral domain[J]. J Geophys Res:Solid Earth,109(B4):B04405.
Sun W K,Zhou X. 2012. Coseismic deflection change of the vertical caused by the 2011 Tohoku-Oki earthquake (MW9.0)[J]. Geophys J Int,189(2):937–955. doi: 10.1111/j.1365-246X.2012.05434.x
Sun W K,Dong J. 2013. Relation of dislocation Love numbers and conventional Love numbers and corresponding Green’s functions for a surface rupture in a spherical earth model[J]. Geophys J Int,193(2):717–733. doi: 10.1093/gji/ggt030
Sun W K,Dong J. 2014. Geo-center movement caused by huge earthquakes[J]. J Geodyn,76:1–7. doi: 10.1016/j.jog.2014.02.008
Sun W K,Okubo S,Fu G Y. 2006a. Green’s functions of coseismic strain changes and investigation of effects of Earth’s spherical curvature and radial heterogeneity[J]. Geophys J Int,167(3):1273–1291. doi: 10.1111/j.1365-246X.2006.03089.x
Sun W K,Okubo S,Sugano T. 2006b. Determining dislocation Love numbers using satellite gravity mission observations[J]. Earth Planets Space,58(5):497–503. doi: 10.1186/BF03351946
Sun W K,Okubo S,Fu G Y,Araya A. 2009. General formulations of global co-seismic deformations caused by an arbitrary dislocation in a spherically symmetric earth model:Applicable to deformed earth surface and space-fixed point[J]. Geophys J Int,177(3):817–833. doi: 10.1111/j.1365-246X.2009.04113.x
Sun X D,Hartzell S. 2014. Finite-fault slip model of the 2011 MW5.6 Prague,Oklahoma earthquake from regional waveforms[J]. Geophys Res Lett,41(12):4207–4213. doi: 10.1002/2014GL060410
Takeuchi H,Hasegawa Y. 1965. Viscosity distribution within the Earth[J]. Geophys J Int,9(5):503–508. doi: 10.1111/j.1365-246X.1965.tb06321.x
Tanaka Y,Okuno J,Okubo S. 2006. A new method for the computation of global viscoelastic post-seismic deformation in a realistic earth model ( Ⅰ ):Vertical displacement and gravity variation[J]. Geophys J Int,164(2):273–289. doi: 10.1111/j.1365-246X.2005.02821.x
Tanaka Y,Okuno J,Okubo S. 2007. A new method for the computation of global viscoelastic post-seismic deformation in a realistic earth model ( Ⅱ ):Horizontal displacement[J]. Geophys J Int,170(3):1031–1052. doi: 10.1111/j.1365-246X.2007.03486.x
Tanaka Y,Klemann V,Fleming K,Martinec Z. 2009. Spectral finite element approach to postseismic deformation in a viscoelastic self-gravitating spherical Earth[J]. Geophys J Int,176(3):715–739. doi: 10.1111/j.1365-246X.2008.04015.x
Tang H,Sun W K. 2018a. Asymptotic co- and post-seismic displacements in a homogeneous Maxwell sphere[J]. Geophys J Int,214(1):731–750. doi: 10.1093/gji/ggy174
Tang H,Sun W K. 2018b. Closed-form expressions of seismic deformation in a homogeneous Maxwell earth model[J]. J Geophys Res:Solid Earth,123(7):6033–6051. doi: 10.1029/2018JB015594
Tang H,Sun W K. 2019. New method for computing postseismic deformations in a realistic gravitational viscoelastic earth model[J]. J Geophys Res:Solid Earth,124(5):5060–5080. doi: 10.1029/2019JB017368
Tang H, Dong J, Sun W K. 2020a. An approximate method to simulate post-seismic deformations in a realistic earth model[C]//International Association of Geodesy Symposia. Berlin, Heidelberg: Springer: 1−7.
Tang H,Zhang L,Chang L,Sun W K. 2020b. Optimized approximate inverse Laplace transform for geo-deformation computation in viscoelastic Earth model[J]. Geophys J Int,223(1):444–453. doi: 10.1093/gji/ggaa322
Tapley B D,Watkins M M,Flechtner F,Reigber C,Bettadpur S,Rodell M,Sasgen I,Famiglietti J S,Landerer F W,Chambers D P,Reager J T,Gardner A S,Save H,Ivins E R,Swenson S C,Boening C,Dahle C,Wiese D N,Dobslaw H,Tamisiea M E,Velicogna I. 2019. Contributions of GRACE to understanding climate change[J]. Nat Climate Change,9(5):358–369. doi: 10.1038/s41558-019-0456-2
Thomson W T. 1950. Transmission of elastic waves through a stratified solid medium[J]. J Appl Phys,21(2):89–93. doi: 10.1063/1.1699629
Tian Z,Freymueller J T,Yang Z Q. 2021. Postseismic deformation due to the 2012 MW7.8 Haida Gwaii and 2013 MW7.5 Craig earthquakes and its implications for regional rheological structure[J]. J Geophys Res:Solid Earth,126:e2020JB020197.
Valsa J,Brančik L. 1998. Approximate formulae for numerical inversion of Laplace transforms[J]. Int J Numer Model:Electron Netw Dev Fields,11(3):153–166. doi: 10.1002/(SICI)1099-1204(199805/06)11:3<153::AID-JNM299>3.0.CO;2-C
Van Camp M,de Viron O,Watlet A,Meurers B,Francis O,Caudron C. 2017. Geophysics from terrestrial time-variable gravity measurements[J]. Rev Geophys,55(4):938–992. doi: 10.1002/2017RG000566
Vermeersen L L A,Sabadini R,Spada G. 1996. Analytical visco-elastic relaxation models[J]. Geophys Res Lett,23(7):697–700. doi: 10.1029/96GL00620
Vernant P. 2015. What can we learn from 20 years of interseismic GPS measurements across strike-slip faults?[J]. Tectonophysics,644/645:22–39. doi: 10.1016/j.tecto.2015.01.013
Wang H S. 1999. Surface vertical displacements,potential perturbations and gravity changes of a viscoelastic earth model induced by internal point dislocations[J]. Geophys J Int,137(2):429–440.
Wang K L. 2007. Elastic and viscoelastic models of crustal deformation in subduction earthquake cycles[G]//The Seismogenic Zone of Subduction Thrust Faults. New York: Columbia University Press: 540−577.
Wang K L,Hu Y,He J H. 2012. Deformation cycles of subduction earthquakes in a viscoelastic Earth[J]. Nature,484(7394):327–332. doi: 10.1038/nature11032
Wang M,Shen Z K. 2020. Present-day crustal deformation of continental China derived from GPS and its tectonic implications[J]. J Geophys Res:Solid Earth,125(2):e2019JB018774.
Wang R J,Martín F L,Roth F. 2003. Computation of deformation induced by earthquakes in a multi-layered elastic crust:Fortran programs EDGRN/EDCMP[J]. Comput Geosci,29(2):195–207. doi: 10.1016/S0098-3004(02)00111-5
Wang R J,Martín F L,Roth F. 2006. PSGRN/PSCMP:A new code for calculating co- and post-seismic deformation,geoid and gravity changes based on the viscoelastic-gravitational dislocation theory[J]. Comput Geosci,32(4):527–541. doi: 10.1016/j.cageo.2005.08.006
Wang W X,Shi Y L,Sun W K,Zhang J. 2011. Viscous lithospheric structure beneath Sumatra inferred from post-seismic gravity changes detected by GRACE[J]. Science China Earth Science,54(8):1257–1267. doi: 10.1007/s11430-011-4217-y
Wang W X,Sun W K,Wu Y Q,Gu G H. 2014. Modification of fault slip models of the MW9.0 Tohoku earthquake by far field GPS observations[J]. J Geodyn,75:22–33. doi: 10.1016/j.jog.2014.01.005
Wason H R,Singh S J. 1972. Static deformation of a multilayered sphere by internal sources[J]. Geophys J Int,27(1):1–14. doi: 10.1111/j.1365-246X.1972.tb02342.x
Wdowinski S, Eriksson S. 2009. Geodesy in the 21st century[J]. EOS Trans AGU, 90（18）: 153-155.
Weertman J, Weertman J R. 1964. Elementary Dislocation Theory[M]. New York: Macmillan: 1–15.
Weertman J,Weertman J R. 1975. High temperature creep of rock and mantle viscosity[J]. Annu Rev Earth Planet Sci,3(1):293–315. doi: 10.1146/annurev.ea.03.050175.001453
Wiesemeyer H, Nothnagel A. 2021. Very long baseline interferometry[G]//Encyclopedia of Solid Earth Geophysics. Dordrecht: Springer: 1902–1907.
Williams C A,Wallace L M. 2015. Effects of material property variations on slip estimates for subduction interface slow-slip events[J]. Geophys Res Lett,42(4):1113–1121. doi: 10.1002/2014GL062505
Xu C Y. 2021. Coseismic changes in the kinetic rotational energy of the Earth from 1976 to 2019[J]. Geophys J Int,224(2):1127–1132.
Xu C Y,Sun W K. 2014. Earthquake-origin expansion of the Earth inferred from a spherical-Earth elastic dislocation theory[J]. Geophys J Int,199(3):1655–1661. doi: 10.1093/gji/ggu364
Xu C Y,Chao B F. 2015. Seismological versus geodetic reference frames for seismic dislocation:Consistency under momentum conservations[J]. Geophys J Int,200(2):1000–1004. doi: 10.1093/gji/ggu439
Xu C Y,Chao B F. 2017. Coseismic changes of gravitational potential energy induced by global earthquakes based on spherical-Earth elastic dislocation theory[J]. J Geophys Res:Solid Earth,122(5):4053–4063. doi: 10.1002/2017JB014204
Xu C Y,Chao B F. 2019. Seismic effects on the secular drift of the Earth’s rotational pole[J]. J Geophys Res:Solid Earth,124(6):6092–6100. doi: 10.1029/2018JB017164
Xu C Y,Sun W K,Chao B F. 2014. Formulation of coseismic changes in Earth rotation and low-degree gravity field based on the spherical Earth dislocation theory[J]. J Geophys Res:Solid Earth,119(12):9031–9041. doi: 10.1002/2014JB011328
Xu C Y,Wei D P,Sun W K. 2016. Contribution of coseismic deformations on the current expansion of the Earth[J]. J Geodyn,99:10–15. doi: 10.1016/j.jog.2016.05.001
Xu C Y,Su X N,Liu T,Sun W K. 2017. Geodetic observations of the co- and post-seismic deformation of the 2013 Okhotsk Sea deep-focus earthquake[J]. Geophys J Int,209(3):1924–1933. doi: 10.1093/gji/ggx123
Yabuki T,Matsu’ura M. 1992. Geodetic data inversion using a Bayesian information criterion for spatial distribution of fault slip[J]. Geophys J Int,109(2):363–375. doi: 10.1111/j.1365-246X.1992.tb00102.x
Yamasaki T,Houseman G A. 2012. The crustal viscosity gradient measured from post-seismic deformation:A case study of the 1997 Manyi (Tibet) earthquake[J]. Earth Planet Sci Lett,351/352:105–114. doi: 10.1016/j.jpgl.2012.07.030
Yang J Y,Sun W K. 2020. Determining dislocation Love number of vertical displacement using GPS observations:Case study of 2011 Tohoku-Oki earthquake (MW9.0)[J]. Geophys J Int,222(2):965–977. doi: 10.1093/gji/ggaa163
Yang J Y,Zhou X,Yi S,Sun W K. 2015. Determining dislocation Love numbers using GRACE satellite mission gravity data[J]. Geophys J Int,203(1):257–269. doi: 10.1093/gji/ggv265
Zhou J C,Sun W K,Sun H P,Xu J Q. 2013. Reformulation of co-seismic polar motion excitation and low degree gravity changes:Applied to the 2011 Tohoku-Oki earthquake (MW9.0)[J]. J Geodyn,63:20–26. doi: 10.1016/j.jog.2012.09.004
Zhou J C,Sun W K,Sun H P,Xu J Q,Cui X M. 2014a. Co-seismic change of length of day based on the point dislocation theory for a SNREI Earth[J]. J Geodyn,79:18–22.
Zhou J C,Sun W K,Dong J. 2015. A correction to the article “Geo-center movement caused by huge earthquakes” by Wenke Sun and Jie Dong[J]. J Geodyn,87:67–73. doi: 10.1016/j.jog.2015.02.003
Zhou J C,Sun W K,Jin S G,Sun H P,Xu J Q. 2016. Rotation change in the orientation of the centre-of-figure frame caused by large earthquakes[J]. Geophys J Int,206(2):999–1008. doi: 10.1093/gji/ggw182
Zhou J C,Pan E N,Bevis M. 2019a. A point dislocation in a layered,transversely isotropic and self-gravitating Earth. Part Ⅰ :Analytical dislocation Love numbers[J]. Geophys J Int,217(3):1681–1705. doi: 10.1093/gji/ggz110
Zhou J C,Pan E N,Bevis M. 2019b. A point dislocation in a layered,transversely isotropic and self-gravitating Earth. Part Ⅱ :Accurate Green’s functions[J]. Geophys J Int,219(3):1717–1728. doi: 10.1093/gji/ggz392
Zhou J C,Pan E N,Bevis M. 2020. A point dislocation in a layered,transversely isotropic and self-gravitating Earth. Part Ⅲ :Internal deformation[J]. Geophys J Int,223(1):420–443. doi: 10.1093/gji/ggaa319
Zhou X,Cambiotti G,Sun W,Sabadini R. 2014b. The coseismic slip distribution of a shallow subduction fault constrained by prior information:The example of 2011 Tohoku (MW9.0) megathrust earthquake[J]. Geophys J Int,199(2):981–995. doi: 10.1093/gji/ggu310
Zhou X,Cambiotti G,Sun W K,Sabadini R. 2018. Co-seismic slip distribution of the 2011 Tohoku (MW9.0) earthquake inverted from GPS and space-borne gravimetric data[J]. Earth Planet Phys,2(2):120–138. doi: 10.26464/epp2018013
Zhu X X,Montazeri S,Gisinger C,Hanssen R F,Bamler R. 2016. Geodetic SAR tomography[J]. IEEE Trans Geosci Remote Sens,54(1):18–35. doi: 10.1109/TGRS.2015.2448686
-
期刊类型引用(3)
1. 赵庆旭，王延伟，莫红艳，曹振中. 基于多输入高斯过程回归的震级快速估算方法. 地震学报. 2024(05): 806-824 . 
本站查看
2. 李子昊，赵国为，郭攀，赵亚楠，王晓睿. 人工智能在地震学中的应用. 防灾减灾学报. 2024(04): 84-90 . 百度学术
3. 徐繁树，王保云，韩俊. 一种沟谷型潜在泥石流危险性评价方法：基于多源数据融合的卷积神经网络. 地球信息科学学报. 2023(03): 588-605 . 百度学术
其他类型引用(2)
下载:
计量
- 文章访问数: 620
- HTML全文浏览量: 446
- PDF下载量: 222
- 被引次数: 5
