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（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.      

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．      

地震前兆的象限性特征及其理论分析

在总结华北北部地区唐山、大同地震前地电阻率和形变前兆的象限性特征的基础上，分析并发现张北地震前的形变和地电阻率前兆也具有一定的象限性特征．说明前兆象限性的存在并非偶然，是与孕震体的存在有关．通过岩石实验与理论分析认为，在孕震过程中，前兆异常确实存在象限性特征．象限性的空间分布范围并不是固定不变，而是具有逐渐变大——最大——变小的过程．并且象限性的上升区与下降区（或压缩区与膨胀区）在近源区与远源区不同．如果基于对前兆象限性的认识，指导分析前兆异常不同形态异常的空间分布，对地震的可能发震地区预测将具有参考意义．      

水平层状粘弹性介质中震源应力-应变场的三维边值问题及相应的地电阻率前兆变化的数值模拟

本文应用关于粘弹介质的弹性力学三维有限元方法,研究了定常速率加载边界条件下以断层闭锁模拟震源的“孕震”过程,並将所求得的层状介质应力—应变场与视电阻率的“前兆”变化相关联,以此给出该“孕震”过程中地表视电阻率“前兆”变化的时空分布,从而揭示水平层状介质视电阻率的变化与震源区应变场之间的关系。计算结果表明,粘弹性介质的存在,对孕震过程起着相当重要的作用。介质中应力集中程度与材料粘弹性有着密切的关系。另一方面,对于视电阻率前兆而言,其时空分布不仅与大范围的应力—应变场有关,而且还与台站探测范围内介质的力学、电性结构条件相关联。     

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。     

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…     

强地震附近电阻率对称四极观测的探测深度

针对我国地震监测预报中固定地点和固定观测装置及参数的视电阻率观测,给出了半空间倾斜各向异性介质中电阻率对称四极观测的理论探测深度,研究了地震前兆信息的检测深度问题,得到：(1)在强地震、孕震晚期阶段,在震中区及附近可检测到地壳近地表较深部介质的电阻率变化,其深度大于或远大于均匀介质之;(2)震级、震中距、观测方向不同或在不同的孕震阶段,探测深度存在差异,甚至存在大的差异,且是动态变化的.并依据理论探测深度讨论了地震视电阻率前兆变化的复杂性、地电台址电性条件等问题.     

地电台址大范围介质条件的数值模拟研究

本文取两类震源模型,即“闭锁”模型和“膨胀”模型进行数值模拟,计算了大范围层状介质在多种不同组合情况下,其应力、应变场的分布,并进而计算了由附加应力、应变产生的视电阻率变化量。结果表明,不同介质组合对地电阻率前兆异常观测的影响不同,有利于发现前兆异常的大范围介质条件是:(1)坚硬层孕震;(2)孕育地震的高强度坚硬层要薄;(3)地表疏松覆盖层不能太厚。此外,计算结果还表明,地电台站探测范围内的介质力学,电性条件对前兆异常观测也有重大影响。     

岩石流变模型在孕震过程和前兆研究中的应用

本文用岩石流变模型讨论了地震孕育过程,以定常应变速率为地震孕育过程的基本条件.在解析解的基础上,计算了孕震过程中应力、应变、应变速率和能量等各种特征量随时间的变化曲线.在此基础上,分析了地震孕育过程的阶段性.本文还着重讨论了孕震过程中的各种前兆现象,探讨了多种前兆异常的综合机制,并初步给出了前兆现象和孕震过程之间的可能联系.      

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.     

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 (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 (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 (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.