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.     

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.      

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 (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 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)     

地震孕育体源流变模型（一）-位移场

为了研究地震孕育过程，在弹性包体理论的基础上建立了流变介质的体源包体模型理论．本文基于弹性包体模型的位移场的解析解，运用流变力学理论中的对应原理，导出流变体介质中，包体在任意一点的3个方向分别产生的位移的粘弹性解析解.      

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.     

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.     

Theoretical analysis of the spatio-temporal evolution of the bulk-strain field based on a rheologic inclusion model

ntroductionThe rock medium shows mainly elastic character under low-temperature, low-pressure and external force of short duration, but it shows rheologic property under high-temperature, high-pressure and long-time external force. It is right that rapid earthquake faulting process of only about ten seconds is analyzed by the elastic theory. But for the earthquake generating process continuing over hundreds or thousand years, the rheologic property of rock must be considered (ZHANG, 1987; YI…     

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。     

唐山地震前兆场的分布特征

本文对唐山地震昌黎等七个台的地电阻率日均值时间序列进行了关联维计算．取每年为一个时间段，其目的在于探索分数维对地震各个阶段的反应，以便达到利用分数维进行地震预报的目的。计算结果表明大部分地电台的地电阻率在地震前有明显的降维特征。通过地震前后七个台的地电阻率分数维的变化，得到了地震前后前兆场的分布特征，这一结果对于未来震源区的判定有重要意义。     

APE理论与地电阻率前兆

介绍了含裂隙介质的ＡＰＥ理论（ａｎｉｓｏｔｒｏｐｉｃ ｐｏｒｏ－ｅｌａｓｔｉｃｉｔｙ）。根据ＡＰＥ理论,对裂隙膨胀提出了新的看法,认为当岩石不产生大量破裂时,裂隙的扩张和闭合是互为依存、彼此平衡的。用笔者建立的裂隙方面性集中体积模型的各向异性电导率张量表达式,研究了应力场导致裂隙纵横比变化与地壳岩石电阻率变化的关系。结果表明,即使地壳岩石的平均体应变很小或不产生新的裂隙,也可以出现电阻率大的突变。     

地电阻率正常变化的初步研究

观测地壳浅层电阻率随时间变化以寻找地震信息是地电阻率方法的目的。实际工作中,在保证观测精度的前提下,发现正常（无震）情况的地电阻率仍然存在着复杂的变化,给定量和定性分析地震异常带来相当大的困难。 本文分析了一些台站正常地电阻率的变化规律,并在此基础上提出“变化电性剖面模式”,来阐明一些台站正常地电阻率变化的复杂过程及其产生的可能原因。从此观点出发,导出以二层电性剖面为特征的台站正常地电阻率相对似年变化幅度公式。通过典型计算,提出获取平稳的正常原始资料是解决上述困难问题的方向,并指出了获取平稳正常变化资料的具体途径。     

地电阻率年变化与气象因素及水位的关系

为了消除d_s 观测资料中的年周期变化,对宝坻、塘沽地震台的地电阻率观测资料与台站附近地区的气压、气温、相对湿度、水位及海水水位的同期资料进行了相关处理分析, 并对地电阻率年周期变化产生的原因进行了分析,认为产生地电阻率与气象要素年周期变化的外因是同一源场作用的结果。 而地电阻率变化的内因,则是基于地下咸水层厚度的改变及地壳应力场的变化。 采用最小二乘法由气象参量和水位变化拟合出地电阻率模型值, 并计算出观测值与拟合值的残差,以消除电阻率观测资料中的年周期变化。结果表明, 近年来华北地区发生的 6级左右地震前,在宝坻、塘沽地震台的观测资料中均存在明显的短期前兆异常。     

Strain-geoelectric resistivity precursor and the virtual dislocation model to the Tangshan earthquake

The complete records of geoelectric resistivity before two earthquakes were analyzed, including 16 stations within 240 km around the Tangshan earthquake and 2 stations within 50–60 km from theM6.1 Datong earthquake. By eliminating various disturbances in the records and realizing the precursory anomalies to be reliable, the authors studied the distribution of the geoelectric precursor field, which proves to be physically related to the earthquake source stress field. Comparision of the sign distribution of coseismic resistivity changes with the solution of earthquake source mechanism indicates that, the coseismic resistivity changes are of opposite sign but similar spatial distribution with respect to the corresponding resistivity precursor changes. Therefore, from the resistivity observations we are of the opinion that the Tangshan earthquake is an elastic rebound process. A virtual dislocation model of geoelectric precursor for the Tangshan earthquake is proposed, in which the geoelectric precursors are supposed to be caused by the strain accumulation due to a virtual dislocation, which is opposite in sign to the actual slip taking place at the earthquake occurrence. Taking into account of the non-linear characteristics of the amplification factorK=(Δρ/ρ)/ɛ in a range of 10⁻⁷–10⁻⁵ strain changes, the theoretical distribution of geoelectric precursors for the Tangshan earthquake was calculated based on the theory of fracture mechanics and reasonably selected dislocation parameters. The results show that the semi-quantitative theoretical values are in good agreement with the observed, suggesting that the virtual dislocation model of the geoelectric precursor is appropriate to the Tangshan earthquake. Contribution No. 96A0023, Institute of Geophysics, SSB, China. This work was supported by the National Natural Science Foundation of China and the Science and Technology Department of SSB.     

九江Ms5.7地震前地电阻率异常分析

2005年9月合肥地震台地电阻率出现明显异常变化,11月26日九江、瑞昌交界地区发生Ms5.7地震,经核实分析,确认该地电异常是九江地震的震兆异常,为今后华东地区分析和确定地电异常提供了重要参考.     

吉林省地电阻率观测干扰分析研究

本文主要利用吉林省内3个地电阻率台站的数据,对观测中出现的自然干扰、测量线路干扰等进行了分析研究,为正确排除数字化地电数据中的干扰和准确识别其中的震兆信息提供借鉴和参考。     

Quadrant characteristics of earthquake precursors and its theoretical analysis

IntroductionMigration and inhomogeneity are important two of the characteristics in the temporal-spatial distribution of earthquake precursors, which have been dealt with by MEI, et al (1993) comprehensively with their proposed explanation. The obvious quadrant feature in spatial distribution of earthquake precursors has been drawn with the explanation for its mechanism developed in some case studies in recent years. This paper deals mainly with the quadrant features derived from the analysis…