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 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 （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.     

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.      

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…     

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.      

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.      

2018年9月8日墨江地震及周边地区构造应力场特征分析

2018年9月8日,云南省墨江县发生M_S5.9地震并伴随一系列余震,探究该地震周围的应力场对于理解该地震的发生机制和后续地震的发展趋势具有着重要的参考意义.本研究收集了震源及其邻区中前人研究和Global CMT所给出的震源机制资料,对该地区进行了构造应力场反演,并同时利用反演得到的应力张量模拟墨江地区的震源机制解表现.结果表明：①在应力轴整体分布上,自西向东σ₁轴（压轴）从NNE-SSW向逐渐转向NNW-SSE向,σ₃轴（张轴）从WWN-EES向逐渐转向WWS-EEN向,张轴呈弧形分布,压轴呈放射状分布.②在应力轴倾伏角上,研究区域内的压应力轴和张应力轴倾伏角都比较小,即两轴均接近水平.③R值分布大体是在东南部相较于西北部大,结合当地地质背景分析得到,物质逃逸自西北向东南呈逐渐变缓的趋势.④利用反演得到的应力张量和应力状态计算墨江地震震源区的相对剪应力和相对正应力大小.由此推测,墨江地震恰好发生在相对剪切应力值和相对正应力正值最大的节面上.从而可以确定墨江地震的发震节面的基本参数：走向216.32°,倾角86.91°,滑动角0.27°,相对剪应力值0.9,相对正应力值0.3.本研究为此次墨江地震的发震背景和地震动力学研究提供了基础性资料.

     

Defining a model of 3D seismogenic sources for Seismic Hazard Assessment applications: The case of central Apennines (Italy)

Geology-based methods for Probabilistic Seismic Hazard Assessment (PSHA) have been developing in Italy. These methods require information on the geometric, kinematic and energetic parameters of the major seismogenic faults. In this paper, we define a model of 3D seismogenic sources in the central Apennines of Italy. Our approach is mainly structural-seismotectonic: we integrate surface geology data (trace of active faults, i.e. 2D features) with seismicity and subsurface geological–geophysical data (3D approach). A fundamental step is to fix constraints on the thickness of the seismogenic layer and deep geometry of faults: we use constraints from the depth distribution of aftershock zones and background seismicity; we also use information on the structural style of the extensional deformation at crustal scale (mainly from seismic reflection data), as well as on the strength and behaviour (brittle versus plastic) of the crust by rheological profiling. Geological observations allow us to define a segmentation model consisting of major fault structures separated by first-order (kilometric scale) structural-geometric complexities considered as likely barriers to the propagation of major earthquake ruptures. Once defined the 3D fault features and the segmentation model, the step onward is the computation of the maximum magnitude of the expected earthquake (M _max). We compare three different estimates of M _max: (1) from association of past earthquakes to faults; (2) from 3D fault geometry and (3) from geometrical estimate corrected by earthquake scaling laws. By integrating all the data, we define a model of seismogenic sources (seismogenic boxes), which can be directly used for regional-scale PSHA. Preliminary applications of PSHA indicate that the 3D approach may allow to hazard scenarios more realistic than those previously proposed.     

Strain field measurements of rubber by image analysis and design criteria for laminated rubber bearings (LRB)

Although seismic isolation rubber bearings in bridges and buildings have proven to be a very effective passive method for reducing earthquake‐induced forces, a detailed mechanical modeling of the rubber that is used in bearings under large strains has not been established. Therefore, a 3D model of failure behavior and the design criteria for the safety evaluation of seismic isolation bearings have not yet been developed. This paper presents: (1) correlation‐based template‐matching algorithms to measure large strain fields of continua; (2) a failure criterion for rubber; and (3) the design criteria for the safety evaluation of laminated algorithms, data‐validation algorithms were developed and implemented to eliminate possible unrealistic displacement vectors present in the measured displacement field. The algorithms were successfully employed in the strain field measurement of LRB and rubber materials that are subjected to failure. The measured local strains for rubber material at failure were used to develop a failure criterion for rubber. The validity of the proposed criterion was evaluated by applying it to the LRB; the criterion was introduced into a 3D finite element model of LRB, compared with the experimental results of bearings failure, and verified. Finally, design criteria are proposed for LRB for the safety evaluation. Copyright © 2003 John Wiley & Sons, Ltd.     

2016年M6.2呼图壁地震发震构造及其对天山构造带隆升的启示:来自中近场钻孔应变观测的证据

天山山脉在新生代经历了强烈的构造隆升和地壳缩短作用,其周缘发生的地震活动是了解这一构造模式的窗口.对2016年呼图壁地震的发震构造有两种解读：向南倾斜的低角度逆断层和向北倾斜的高角度逆断层.中近场四台钻孔应变仪记录到了本次地震的同震响应,本文采用均质模型对IGP-CEA和USGS震源机制解进行模拟,结果显示发震断层为向北陡倾的反冲断层,15个原始方位和8个N-S、E-W方位观测值全部与预测值一致.对比天山北缘常见的低角度逆冲断层,反冲断层对构造隆升的贡献更有效,以断层倾角70°和19°计算,二者对隆升和缩短贡献比例分别为2.89：1和1：2.76.这一结果表明天山构造带内部的反冲构造同样具有单独发震的可能性,它们对天山现今的隆升高度同样起着不可忽视的作用.

     

Rupture model of the 2013 M_W 6.6 Lushan (China) earthquake constrained by a new GPS data set and its effects on potential seismic hazard

Vertical records are critically important when determining the rupture model of an earthquake, especially a thrust earthquake. Due to the relatively low fitness level of near-field vertical displacements, the precision of previous rupture models is relatively low, and the seismic hazard evaluated thereafter should be further updated. In this study, we applied three-component displacement records from GPS stations in and around the source region of the 2013 MW6.6 Lushan earthquake to re-investigate the rupture model.To improve the resolution of the rupture model, records from both continuous and campaign GPS stations were gathered, and secular deformations of the GPS movements were removed from the records of the campaign stations to ensure their reliability. The rupture model was derived by the steepest descent method(SDM), which is based on a layered velocity structure. The peak slip value was about 0.75 m, with a seismic moment release of 9.89 × 10~(18) N·m, which was equivalent to an M_W6.6 event. The inferred fault geometry coincided well with the aftershock distribution of the Lushan earthquake. Unlike previous rupture models, a secondary slip asperity existed at a shallow depth and even touched the ground surface. Based on the distribution of the co-seismic ruptures of the Lushan and Wenchuan earthquakes, post-seismic relaxation of the Wenchuan earthquake, and tectonic loading process, we proposed that the seismic hazard is quite high and still needs special attention in the seismic gap between the two earthquakes.     

Seismotectonics and seismic quietness of the Oranie region (Western Algeria): The Mascara earthquake of August 18th 1994, Mw = 5.7, Ms = 6.0

The plate dynamics in the central western Mediterranean region is characterised by a collision between the Eurasian and African plates. In response to this dynamics, many systems of faults and folds having a NE-SW and E-W trending have been generated along the Tellian Atlas of Algeria. The Oranie region (north western Algeria) has experienced some significant earthquakes in the last centuries, the most important one is that of Oran city on February 9^th 1790, I_o = XI which destroyed the town completely and caused the loss of many lives. Since 1790 no other event was so disastrous except that of August 18^th 1994, M_w = 5.7, which struck Mascara province (Algeria) at 01 h 13 mn GMT. Since the beginning of this century the region has been dominated by a seismic quietness. Thus, no event with magnitude larger than 5.5 have occurred in this area. In relation with this recent event, a seismotectonic framework summarising the tectonic, seismicity and focal solution results is presented. The Maximum Observed Intensities Map (MOI) made for Algeria (Bezzeghoud et al., 1996) is also used to show that the Mascara region is located in an VIII-X intensity zone, which explain partially the casualties caused by the 18/08/1994 (M_w = 5.7) earthquake. This earthquake is not anomalous compared to historical records but is unusual compared to recorded seismicity of this century. The seismotectonic map made in this study and also the review of the focal solutions given by the EMSC, Harvard, and other authors shows that our event is probably associated with a source belonging to a system of faults located in the vicinity of the village of Hacine where the maximum damage was observed.