地壳介质弹性、电性各向异性理论及对地震过程的联合解释
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摘要
本论文共分10章，第1章为引论，第2－6章为基础理论，第7－10章
为应用研究。主要研究内容可分为五个方面：
1．第1章引论部分综述了地壳介质各向异性现象和分类，从发展沿革、理论方
法及成果、存在的问题这个顺序分别论述了地壳介质弹性各向异性和电性备
向异性。在此基础上提出了本论文的研究思路和主题：将地震学中的S波分
裂法与电法中的大地电磁测深法联合起来解释地震过程中的各向异性动态特
征与发震应力场的关系。围绕这个主题设定了两个核心：一是建立地壳介质
电性各向异性微观模型，在此之前这方面的研究是一个空白；二是基于EDA
裂隙模型将S波分裂法与大地电磁测深法联合应用于对实际震例的分析研
究，该研究具有首创性。并对其它研究内容作了安排。
2．基础理论部分中第一项研究内容是本构关系的理论分析、推导。第2章讨论
弹性各向异性本构关系。除了引用前人给出的公式外，本论文有特色的工作
是：推导了一个应变能公式，给出了各种对称体系下的弹性本构形式，对前
人给出的结果作了验证，指出存在的个别错误；对EDA（广泛扩容各向异
性）构成的薄层介质各向异性弹性常数作了推导，给出了解析表达；对几
种类型的各向异性体系的角散式进行了推导并作了数值计算．第5章讨论电
性各向异性本构关系，本论文在此作了一个有创新性的工作，即本论文的
第一个核心，受弹性各向异性等效弹性模量（Hudson公式）和APE（各向
异性孔隙弹性）理论的启示，建立了等效的电性各向异性微观模型并给出
了数学推导，将此模型称之为电性各向异性裂隙方向性集中体积模型（简称
体积模型）；其它有特色的工作是从直流电法和大地电磁测深法来讨论薄层
各向异性和EDA各向异性的特征，并指出了直流电法中的“反常现象”．
3．基础理论部分的第二项研究内容是数值模拟．第3章是引用前人提出的伪谱
法对2.5维弹性波场作了数值模拟，并对快慢S波时间延迟、快S偏振方
向作了分析；第4章对第3章遗留的问题作了进一步研究。有特色的工作
是：全面推导了用特征值法处理伪谱法中各种边界条件的表达式，为以后
这方面的工作提供了便利．第6章是引用前人的方法，对层状EDA各向异
I
中国地震局地球物理研究所博士学位论文：地壳介质弹性、电性各向异性理论及对地震过程的联合解释
性作了大地电磁测深（MT）数值模拟，并对前人公式中的模糊之处作了说
明．数值模拟部分其重要性在本论文中占的份量较小，但工作量却很大，主
要工作是编程计算．这方面的研究目的就是从直观上提高对各向异性的认
识，为下续的研究工作打基础．
4t应用部分的第一项研究内容就是本论文的第2个核心，即基于EDA裂隙模
型联合应用S波分裂法和大地电磁测深法来分析研究地震过程中的前兆各向
异性现象和发震应力场随时间演化的关系。第7章引用前人的方法，对S
波分裂法中的旋转相关法、最大特征值法、波形识别算子作了论述椎导；对
大地电磁测深法资料处理的最小H乘法作了论述推导。第8章用CDSN兰
州台、中法合作朗索台的三分量数字记录小震资料，和中法合作松山台的电
磁连续观测资料，分析了1995年7月22日永登5，8级地震前后快S波偏
振方向、电性主轴方向与震源机制解P轴方向的关系，发现三者震前的协
调一致性；快慢S波时间延迟在时间上随地震的孕育而逐渐增大；从电性
主轴与频率的关系分析出地震孕育造成的动态各向异性在地壳深度一定范围
内是广泛存在的；还发现视电阻率的变化受发震应力场和台站处构造条件的
共同作用。第 9章用同样的方法对 1996年 6月 1日的天祝－古浪 5．4级地
震过程的各向异性现象作了联合解释，得到的结果与第8章是一致的，但
由于资料情况不同、背景应力场不同，震源机制不同，所以该次地震的各
向异性分析结果有自己的一些特点。
5．应用部分的第 h项研究内容（第 10章）是根据 EDA模型、APE理论和本
论文建立的电性模型，从各异性的角度来讨论直流视电阻率地震监测预报方
法的机理，着重点落在离震源较远的场兆问题上。通过讨论、简单计算，认
为根据新的电性模型可解释震前小应变下大的视电阻率变化，可以解释不
同方向观测值不同的原因，可以解释震前视电阻率既可以是下降变化也可
以出现上升变化的现象，排除了临震视电阻率突跳对大量进水或大量出水
的严重依赖性，这些问题是以往标量理论所不能及的。
总之，本论文在电性各向异性理论上有1个较大的创新，建立了一个新
的模型，弹性、电性的联合解释和对地电法机理的研究在应用上是二个鲜
明的创新。其余部分的工作大多是在前人基础上作了一些补充和改进，并
互互
This dissertation consists of l0 chapters, the first chapter is general illustration
and introduction, basic theories and formulas are discussed in following 5 chapters,
application studies are included in the last 4 chapters. The studied contents could be
divided into 5 aspects as following:
l. In chapter 1 the anisotropic phenomena and classification of earth crust media are
comprehensively discussed, from enisotropy study history and development to its
theory and method and to existing problems. On this basis the main research topic
is put forward, that is combing s-wave splitting method with MT to study and
explain the dynamic anisotropic phenomena of earthquake precursors and their
relations with seismic stress field development. Around the main topic, two most
important and creative research contents are designed: one is to set up an electrical
anisotropic micro model, because before this paper there were many scalar
presentations but no any tensor model with physical meaning; the other is to
combine s-wave splitting method with MT to study anisotrpic precursors of
practical earthquakes, this will be an creative work. The others study contens are
also arranged in chapter 1.
2. The first part of study in basic theories is to derive and explain formulas of
anisotropic constitutive relations. Chapter 2 discusses anisotropic elastic
constitutive relations of various symmetry systems. Interestihg works include three
parts, (1) deriving an elastic strain energy equation to discuss constitutive relations
of various elastic symmetry systems, and to check out some errors in previous
papers. (2)deriving effective elastic constants of EDA-PTL medium; (3)deriving
and numerically studying the elastic wave rays angle {dispersion phenomenon.
Chapter 5 discusses electrical anisotropic constitutive relations, Creative work is to
set up a new micro electrical anisotropic model and its equation. Ths model is'
named as cracks directional concentrated cubic model(simply called cubic
model). Other interesting work is to discuss PTL and EDA anisotropico behaviors in
apparent resistivity and MT methods respectively.
3. The second part of study in basic,theories is numerical simulation, Chapter 3 and
chapter 4 study s-wave splitting of 2.5D model by pseudo-spectrum approach and
thoroughly derive and analyze various boundary equations by eigenvalue method.
The time delay of splitting s-waves and polarization of fast s wave are also
analyzed. Chapter 6 numerically simulates layered anisotropic MT models by
using and modifying previous papers equations. The purpose of these numerical
simulations is to establish a basis for following researches.
4. The first part of study in application is the main topic of this dissertation, that is to
study seismic anisotropic phenomena and the development process of stress field
by integrating s-wave splitting method and MT approach based on EDA model.
Chaper 7 is to derive equations and write computer programs which are going to
be used in following two chapters, including rotation-correlation analysis,
maximum eigenvalue method, factors of wave type recognition used in s-wave
中国地震局地球物理研究所博士学位论文：地壳介质弹性、电性各向异性理论及对地震过程的联合解释
spl汕胆d吻sls。andlea幻 sqllares me山cd used In MT d扯a processmp．C帅ter 8
咖yzesandexplains selsmlcanddeCiCic幻amsotroplc precwsorsM山elr
众vd地memM山山ep rePrePmM。n毗hig尔ng砌曲叫毗e Ms 5．8。Co——d m1Ulys
22th，1995，nd heir relationsMth P axis ofe讪…e me血删m solWon．The
伽areOOlle恤RomL一u咖Langsuedopt8Iselsmograpmc sMlons毗
Songshan elemcal－m卿euc删＊．It Is discovered thatthe polariwion ofM s
wave，one of＊the main elemcal axis Wthe P axis re geneally identical； the s－
。e splittillg time delny Is Increasing ith time tmll ewtuake happens；
accodingto Requencycharawn犯c ofele以nd axis n Is concluded山幻伽
drpamlc nsotroplc vanationcaused byeanllquake pfaparauon Is exeslvely
distributed In certain
为应用研究。主要研究内容可分为五个方面：
1．第1章引论部分综述了地壳介质各向异性现象和分类，从发展沿革、理论方
法及成果、存在的问题这个顺序分别论述了地壳介质弹性各向异性和电性备
向异性。在此基础上提出了本论文的研究思路和主题：将地震学中的S波分
裂法与电法中的大地电磁测深法联合起来解释地震过程中的各向异性动态特
征与发震应力场的关系。围绕这个主题设定了两个核心：一是建立地壳介质
电性各向异性微观模型，在此之前这方面的研究是一个空白；二是基于EDA
裂隙模型将S波分裂法与大地电磁测深法联合应用于对实际震例的分析研
究，该研究具有首创性。并对其它研究内容作了安排。
2．基础理论部分中第一项研究内容是本构关系的理论分析、推导。第2章讨论
弹性各向异性本构关系。除了引用前人给出的公式外，本论文有特色的工作
是：推导了一个应变能公式，给出了各种对称体系下的弹性本构形式，对前
人给出的结果作了验证，指出存在的个别错误；对EDA（广泛扩容各向异
性）构成的薄层介质各向异性弹性常数作了推导，给出了解析表达；对几
种类型的各向异性体系的角散式进行了推导并作了数值计算．第5章讨论电
性各向异性本构关系，本论文在此作了一个有创新性的工作，即本论文的
第一个核心，受弹性各向异性等效弹性模量（Hudson公式）和APE（各向
异性孔隙弹性）理论的启示，建立了等效的电性各向异性微观模型并给出
了数学推导，将此模型称之为电性各向异性裂隙方向性集中体积模型（简称
体积模型）；其它有特色的工作是从直流电法和大地电磁测深法来讨论薄层
各向异性和EDA各向异性的特征，并指出了直流电法中的“反常现象”．
3．基础理论部分的第二项研究内容是数值模拟．第3章是引用前人提出的伪谱
法对2.5维弹性波场作了数值模拟，并对快慢S波时间延迟、快S偏振方
向作了分析；第4章对第3章遗留的问题作了进一步研究。有特色的工作
是：全面推导了用特征值法处理伪谱法中各种边界条件的表达式，为以后
这方面的工作提供了便利．第6章是引用前人的方法，对层状EDA各向异
I
中国地震局地球物理研究所博士学位论文：地壳介质弹性、电性各向异性理论及对地震过程的联合解释
性作了大地电磁测深（MT）数值模拟，并对前人公式中的模糊之处作了说
明．数值模拟部分其重要性在本论文中占的份量较小，但工作量却很大，主
要工作是编程计算．这方面的研究目的就是从直观上提高对各向异性的认
识，为下续的研究工作打基础．
4t应用部分的第一项研究内容就是本论文的第2个核心，即基于EDA裂隙模
型联合应用S波分裂法和大地电磁测深法来分析研究地震过程中的前兆各向
异性现象和发震应力场随时间演化的关系。第7章引用前人的方法，对S
波分裂法中的旋转相关法、最大特征值法、波形识别算子作了论述椎导；对
大地电磁测深法资料处理的最小H乘法作了论述推导。第8章用CDSN兰
州台、中法合作朗索台的三分量数字记录小震资料，和中法合作松山台的电
磁连续观测资料，分析了1995年7月22日永登5，8级地震前后快S波偏
振方向、电性主轴方向与震源机制解P轴方向的关系，发现三者震前的协
调一致性；快慢S波时间延迟在时间上随地震的孕育而逐渐增大；从电性
主轴与频率的关系分析出地震孕育造成的动态各向异性在地壳深度一定范围
内是广泛存在的；还发现视电阻率的变化受发震应力场和台站处构造条件的
共同作用。第 9章用同样的方法对 1996年 6月 1日的天祝－古浪 5．4级地
震过程的各向异性现象作了联合解释，得到的结果与第8章是一致的，但
由于资料情况不同、背景应力场不同，震源机制不同，所以该次地震的各
向异性分析结果有自己的一些特点。
5．应用部分的第 h项研究内容（第 10章）是根据 EDA模型、APE理论和本
论文建立的电性模型，从各异性的角度来讨论直流视电阻率地震监测预报方
法的机理，着重点落在离震源较远的场兆问题上。通过讨论、简单计算，认
为根据新的电性模型可解释震前小应变下大的视电阻率变化，可以解释不
同方向观测值不同的原因，可以解释震前视电阻率既可以是下降变化也可
以出现上升变化的现象，排除了临震视电阻率突跳对大量进水或大量出水
的严重依赖性，这些问题是以往标量理论所不能及的。
总之，本论文在电性各向异性理论上有1个较大的创新，建立了一个新
的模型，弹性、电性的联合解释和对地电法机理的研究在应用上是二个鲜
明的创新。其余部分的工作大多是在前人基础上作了一些补充和改进，并
互互
This dissertation consists of l0 chapters, the first chapter is general illustration
and introduction, basic theories and formulas are discussed in following 5 chapters,
application studies are included in the last 4 chapters. The studied contents could be
divided into 5 aspects as following:
l. In chapter 1 the anisotropic phenomena and classification of earth crust media are
comprehensively discussed, from enisotropy study history and development to its
theory and method and to existing problems. On this basis the main research topic
is put forward, that is combing s-wave splitting method with MT to study and
explain the dynamic anisotropic phenomena of earthquake precursors and their
relations with seismic stress field development. Around the main topic, two most
important and creative research contents are designed: one is to set up an electrical
anisotropic micro model, because before this paper there were many scalar
presentations but no any tensor model with physical meaning; the other is to
combine s-wave splitting method with MT to study anisotrpic precursors of
practical earthquakes, this will be an creative work. The others study contens are
also arranged in chapter 1.
2. The first part of study in basic theories is to derive and explain formulas of
anisotropic constitutive relations. Chapter 2 discusses anisotropic elastic
constitutive relations of various symmetry systems. Interestihg works include three
parts, (1) deriving an elastic strain energy equation to discuss constitutive relations
of various elastic symmetry systems, and to check out some errors in previous
papers. (2)deriving effective elastic constants of EDA-PTL medium; (3)deriving
and numerically studying the elastic wave rays angle {dispersion phenomenon.
Chapter 5 discusses electrical anisotropic constitutive relations, Creative work is to
set up a new micro electrical anisotropic model and its equation. Ths model is'
named as cracks directional concentrated cubic model(simply called cubic
model). Other interesting work is to discuss PTL and EDA anisotropico behaviors in
apparent resistivity and MT methods respectively.
3. The second part of study in basic,theories is numerical simulation, Chapter 3 and
chapter 4 study s-wave splitting of 2.5D model by pseudo-spectrum approach and
thoroughly derive and analyze various boundary equations by eigenvalue method.
The time delay of splitting s-waves and polarization of fast s wave are also
analyzed. Chapter 6 numerically simulates layered anisotropic MT models by
using and modifying previous papers equations. The purpose of these numerical
simulations is to establish a basis for following researches.
4. The first part of study in application is the main topic of this dissertation, that is to
study seismic anisotropic phenomena and the development process of stress field
by integrating s-wave splitting method and MT approach based on EDA model.
Chaper 7 is to derive equations and write computer programs which are going to
be used in following two chapters, including rotation-correlation analysis,
maximum eigenvalue method, factors of wave type recognition used in s-wave
中国地震局地球物理研究所博士学位论文：地壳介质弹性、电性各向异性理论及对地震过程的联合解释
spl汕胆d吻sls。andlea幻 sqllares me山cd used In MT d扯a processmp．C帅ter 8
咖yzesandexplains selsmlcanddeCiCic幻amsotroplc precwsorsM山elr
众vd地memM山山ep rePrePmM。n毗hig尔ng砌曲叫毗e Ms 5．8。Co——d m1Ulys
22th，1995，nd heir relationsMth P axis ofe讪…e me血删m solWon．The
伽areOOlle恤RomL一u咖Langsuedopt8Iselsmograpmc sMlons毗
Songshan elemcal－m卿euc删＊．It Is discovered thatthe polariwion ofM s
wave，one of＊the main elemcal axis Wthe P axis re geneally identical； the s－
。e splittillg time delny Is Increasing ith time tmll ewtuake happens；
accodingto Requencycharawn犯c ofele以nd axis n Is concluded山幻伽
drpamlc nsotroplc vanationcaused byeanllquake pfaparauon Is exeslvely
distributed In certain
引文
[1] Ajit Kumar Sinha & Prabhat K. Bhattacharya, 1967． Electric dipole over an anisotropic and inhomogeneous earth, Geophysics, 32:652-667．
[2] Alford,R. M., Shear-data in the presence of azimuthal anisotropy, 56th SEG Annual Metting Expanded Abstracts, 1986, 476-479．
[3] Ando, M., Ishikawa, Y. & Wada, H., 1980． S-wave anisotropy in the upper mantle under a volcanic area in Japan, Nature, 286:43-46．
[4] Archie, G. E. 1942． The electrical resistivity log as an aid in determining some reservoir characteristic, Trans. A. I.M. E. 146: 54-62．
[5] Aster, R. C., Shearer, P.M. & Berger, J., 1990． Quantitative measurements of shear wave polarization at the Anza seismic network, Southern California:implications for shear-wave splitting and earthquake prediction, J. Geophys. Res., 95:12449-12473．
[6] Bernard Budiansky & Richard J. O'Connell, 1976． Elastic moduli of a cracked Solid, Int. J. Solids Structures, 12: 81-97．
[7] Brace, W. F. et al., 1968． Electrical resistivity changes in saturated rocks during fracture and frictional sliding, J. Geophys. R. 73:1433-1445．
[8] Brace, W. F., 1975． Dilatancy-related electrical resistivity changes in rocks, Pure and Applied Geophysics, 113:207-217．
[9] Carbin, H. D. & Knopoff L., 1973． The congressional modulus of a material permeated by a random distribution of circular cracks, Q. appl. Math., 30: 453-464．
[10] Carbin, H. D. & Knopoff L. , 1975a. The shear modulus of a material permeated by a random distribution of circular cracks, Q. appl. Math. , 33:296-300．
[11] Carbin, H. D. & Knopoff L., 1975b. Elastic moduli of a medium with liquid-filled cracks, Q. appl. Math., 33:301-303．
[12] Cerveny, 1985b. Ray Synthetic Seismograms for Complex 2D and 3D structures, J. Geophys, 58: 2-26．
[13] Cerveny, 1972． Seismic rays and ray intensities in inhomogeneous anisotropic media, Geophys. J. R. astr. Soc., 29:1-31．
[14] Chen Kunhua, Propagating numerical model of elastic wave in anisotropic inhomogeneous media-finite element method. Symposium of SGE, 1984, 54 :S17． 6． [15] Crampin, S. & King, D. W., 1977． Evidence for anisotropy in the upper beneath Eurasia from generalized higher mode surface waves, Geophys. J. R. astr. Soc., 49:43-46．
[16] Crampin, S., Evans, R. & Atkinson, B. K., 1984a. Earthquake predictions new physical basis, Geophys. J. R. astr. Soc., 76: 147-156．
[17] Crampin S., Chesnokov,E. M. & Hipkin, R. G., 1984b. Seismic anisotropy the state of art II, Geophys. J. R. astr. Soc., 76: 1-16．
[18] Crampin, S., Evans, R., Ucer, B., Doyle, M., Davis, J. P., Yegorkina G. V .
& Miller, A., 1980． Observations of dilatancy-induced polarization anomalies and earthquake prediction, Nature, 286:874-877．
[19] Crampin, S., Evans, R., Ucer, B., 1985． Analysis of records of local earthquakes:the Turkish Dilantancy Projects (TDP1 and TDP2) , Geophys. J. R. astr. Soc., 83:31-45．
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[1]张家茹，邵学钟，雷胜利1982，利用波的偏振特性提高转换波震相识别的可靠性，地球物理学报，Vol．25，No．4，P352-P358．
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[11]Crampin S. &John H. Lovell, 1991. A decade of shear-wave splitting in the earth's crust: what does it mean? What use can we make of it? and what should we do next ? Geophysics, J Int., 107, 387-417.
[12]Crampin,S., Evans, R. & Atkinson, B.K., 1984a. Earthquake prediction:a new physical basis, Geophys. J.R. astr. Soc., 76: 147-156.
[13]Crampin S.,Chesnokov, E.M.& Hipkin, R.G., 1984b. Seismic anisotropy the state of art Ⅱ,Geophys. J.R. astr. Soc., 76: 1-16.
[14]Sergei V. Zatsepin & Stuart Crampin, 1997. Modelling the compliance of crustal rock- Ⅰresponse of shear-Wave splitting to differential stress, RAS,GJI, 129: 477-494.
[15]Stuart Crampin, 1998. Keynote Lecture:Going APE-Monitoring and Modelling Rock Deformation with Shear-Wave Splitting, personal communication.
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