地震孕育体源流变模型(二)——应变场及其应用.

在弹性包体理论的基础上，建立了流变介质包体模型理论的应变场的理论解，导出流变介质中的包体在任意一点产生的正应变、剪应变及体应变的粘弹性解析解，即正应变、剪应变和体应变的表达式. 通过计算三维粘弹性介质中球形硬包体与软包体在地面引起的体应变场的时空演化过程，得到了一些非常有意义的结果，即球形硬包体在地面产生的体应变随时间的变化曲线出现了特征不同的3个阶段(, , )，它与大量地形变资料出现的, , 阶段相似，而球形软包体却没有这个特征. 这些结果对地震前兆的形态特征、前兆的象限性、前兆时空演化的阶段性、短临前兆突发性以及前兆异常时间的地区性等的解释具有启示意义. 这为地震前兆物理模式的建立提供了理论基础，并将为实现地震的物理预测发挥作用.      

地震孕育体源流变模型(三)--前兆场

在三维流变介质体源孕震模型的粘弹性位移场与应变场理论基础上,建立了流变介质体源孕震模型的前兆场理论解,导出了流变介质中任意一点（x,y,z）的地倾斜、地下水位、电阻率的粘弹性解析解,并对地电阻率的应用作了初步分析,为地震孕育过程中前兆分析提供了一定的理论基础.      

包体流变模型体应变场时空演变的理论分析

基于包体流变模型的理论解,计算了三维粘弹性介质中球形硬包体与软包体在地面引起的体应变．结果表明,球形硬包体的地面体应变随时间的变化曲线表现出特征不同的３个阶段（,,）．它与大量地形变资料出现的,,阶段相似;而球形软包体却没有此特征．其中,阶段的前兆在近源区和远源区都向外扩展;阶段的前兆在近源区和远源区都处于极值状态;阶段前兆在远源区表现为向近源区收缩,而在近源区表现为向外扩展．这些结果对地震前兆的时空演化过程阶段性的解释具有一定的启示．      

地震孕育过程中形变趋势变化形态的理论分析

利用流变介质包体模型理论中体应变解析解计算分析了孕震过程中不同观测点的形态异常特征，结果表明，硬包体产生的体应变具有明显的3阶段过程，软包体却只有2个阶段的特点，但它们的形态特征不仅都具有象限性与地区性，而且还随震中距的不同而不同。岩石实验结果也表明，观测点距破裂面的距离不同，其形态特征也不同。在理论分析与岩石实验结果一致的基础上，分析了张北地震与景泰地震前形变异常的形态特征，即具有明显的地区性与象限性；并且形态特征随震中距的变化而不同；变化幅度也随震中距的增大而减小。基于对形变异常形态特征的理解，提出了利用形态特征预测、判断发震地点及孕震状态的思路。     

包体模型应力集中的定量研究

本采用二维弹性介质圆形包体模型,运用连续介和学理论求解出包体内外的应力场、位移场、平均应力、最大剪应力以及能量密度的解析解,从而讨论了硬、软件包体的应力集中特征;     

在围压作用下硬包体模型若干力学性质的研究

为全国了解硬包体力学模型的基本力学性质,本文对软、硬匀质介质模型,非匀质软、硬包体模型及含有软弱层或空穴的不连续介质模型进行了三维弹性有限元分析。在常规围压作用下,得到了各具不同特征的位移场、应力场及变形势能密度场,对硬包体模型的发震条件、震源分布及前兆机理进行了探讨性研究。     

加卸载响应比与其它地震前兆时空演化研究及其应用

本文重点研究了加卸载响应比的时空演化特征 ,并利用震例研究了长期地震活动性的时空演变特征的普适性。为了理解以上特征及地震前兆综合特征 ,应用解析、数值模拟等方法对二维圆形包体、二维硬软复合包体进行了研究 ,并推导出半无限流变介质中三维包体产生的粘弹性位移、应变、地倾斜解析表达式 ,详细地计算和分析了球形包体在地表产生的体应变的时空演变过程 ,从而使孕震模型理论化。应用理论研究结果 ,对地震前兆的时空演化进行了解释 ,提出了长期预测和中短期预测方法 ,并应用于实践 ,取得 5次地震的长期、中期预测的成效。主要结果如下…     

远场差异构造应力作用下包体-地层地应力分析

地应力场的不均匀分布是地球科学非常关心的问题,远场差异构造应力及介质本身的不均匀性对地应力场的不均匀分布都有重要影响.本文利用弹性力学理论,以地球科学的包体-地层系统为例,推导了边界差异构造应力条件下包体-地层系统位移场和应力场的解析表达式.将远场差异构造应力分解为均匀构造应力和偏构造应力两部分,通过边值问题的一般求解方法,分别得出了这两种情况下的理论解.通过将两部分理论解叠加,得到了边界差异构造应力条件下包体-地层系统的位移场、应力场和连接载荷.通过推导的解析解与有限元数值解进行比较,两者非常一致.通过分析包体-地层系统、材料参数、几何尺寸、远场构造应力的大小和方向等因素对包体-地层位移场和应力场分布的影响,可以用于探讨钻孔应变等包体应力(应变)计观测的地震应变阶、慢地震、地震孕育、火山喷发、地球自由振荡、地震波等现象的地球动力学机制.结果表明,远场地应力的分布主要受控于边界构造应力的大小和方向.在包体内部,应力场基本是均匀分布的;而在包体附近,由于介质差异,地应力场的不均匀性非常显著,并且有一定的优势方向,对地应力集中部位的分析为钻孔应变观测等地球动力学研究手段提供了基础理论参考.     

华北地区震群活动的阶段性特征

通过对华北地区1970年以来震群活动的分析表明，唐山地震的震群活动显示出一定的迁移性和阶段性。应用流变介质包体孕震模型的理论进行了初步力学分析。张北地震的预测检验表明，震群活动的迁移性与阶段性对强震的中期预测具有一定指导意义。     

含不同弹性模量包体复合模型中的应力及其变化

用光弹性法分别研究了一组含软包体,等模量包体,及硬包体的复合模型中的应力及其变化,结果表明,在硬包体中的应力更高,硬包体的存在的乃是复合模型中形成和积累高应力区的结构构成条件,从而为坚固体孕震模式的力学机制研究提供了基本的实验依据。     

3-D rheologic model of earthquake preparation (I)—Displacement field

Introduction The rock medium shows mainly elastic character under low-temperature, low-pressure and external force for short duration, yet it shows rheologic property under high-temperature, high-pressure and long-time external force. It is reasonable that the rapid earthquake generating process lasted for tens seconds is analyzed by the elastic theory. As for the earthquake generating process for hundreds or thousand years, nevertheless, the rheologic property of rock must be taken into accou…     

3-D rheologic model of earthquake preparation (Ⅰ)--Displacement field

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed athree-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By usingcorrespondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoe-lastic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i. e., U(r, t), V*(r, t) and W(r,t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linearrheologic model.     

3-D rheologic model of earthquake preparation (I) — Displacement field

Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using correspondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoelastic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i.e., U(r, t), V*(r, t) and W(r, t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Foundation item: Chinese Joint Seismological Science Foundation (101105)     

3-D rheologic model of earthquake preparation (II): Strain field and its applications

Introduction Based on the elastic theory of the hard inclusion (Dobrovolskii, 1991), we developed an inclusion theory of rheologic medium, and applied the results of bulk-strain field of a rheologic inclusion model to explain the spatial-temporal evolution process of earthquake precursors (SONG, et al, 2000). In the former paper (SONG, et al, 2003), we derived the viscoelastic displacement field of the rheologic inclusion model on the basis of the analytic expression of displacement field o…     

3-D rheologic model of earthquake preparation (Ⅱ):Strain field and its applications

On the basis of the three-dimensional elastic inclusion model, the analytic expression of viscoelastic strain field is derived, i.e., the analytic expression of viscoelastic strain at an arbitrary point (x, y, z) in x-axis, y-axis and z-axis produced by three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model, namely the normal strains εxx(r, t), εyy(r, t) and εzz(r, t), the shear strains εxy(r, t) and εyx(r, t), εyz(r, t)and εzy(r, t), εxz(r, t) and εzx(r, t), and the bulk-strain θ (r, t). By computing the spatial-temporal variation of bulk strain on the ground produced by a spherical rheologic inclusion in a semi-infinite rheologic medium, we obtained some significant results that the bulk-strain variation with time produced by a hard inclusion has three stages (α, β,γ) with different characteristics, which are similar to those of most geodetic deformation curves, but not the case for those by a soft inclusion. It is meaningful that these theoretical results have been applied to explain preliminarily the characteristics of stage variation of spatial-temporal evolution, the pattern and quadrant distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to found the physical model of earthquake precursors and a reference to predict physically the earthquakes.     

3-D rheologic model of earthquake prepa-ration (III): Precursor field

Introduction Based on the elastic theory of hard inclusion model proposed by Dobrovolskii (1991), we developed a rheologic inclusion model to study the spatial-temporal variation of earthquake pre-cursor by using the bulk-strain field resulted from rheologic inclusion model (SONG et al, 2000). Based on the elastic inclusion theory, the analytical expressions for the viscoelastic displacement field and strain field of rheologic inclusion model are derived (SONG et al, 2003, 2004). Further-m…     

3-D rheologic model of earthquake preparation (Ⅲ): Precursor field

On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for the three-dimensional rheologic model of earthquake preparation. We derive the viscoelastic analytical expressions of the ground tilt, underground water level, earth resistivity at an arbitrary point (x, y, z) in the rheologic medium, and analyzed the earth resistivity preliminarily, providing a certain theoretical basis for the precursor analysis of seismogenic process.     

3-D rheologic model of earthquake preparation （Ⅲ）： Precursor field

On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for the three-dimensional rheologic model of earthquake preparation. We derive the viscoelastic analytical expressions of the ground tilt, underground water level, earth resistivity at an arbitrary point （x, y, z） in the rheologic medium, and analyzed the earth resistivity preliminarily, providing a certain theoretical basis for the precursor analysis of seismogenic process.     

The Displacement and Strain Field of Three-dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains ε_xx (r, t), ε_yy (r, t) and ε_zz (r, t) and the bulk strain θ (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (α, β, γ) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.