Trajectory of fault-plane-induced tensile crack in relation to the primary stress field

Summary The predetermination of the trajectory of a tensile crack induced at the tip of a stress-free fault plane (open slit, in two dimensional approximation) was investigated. Both the primary field of the tensile component of principal stress and the primary field of the strain energy density factor were computed and compared with the trajectory of the subsequent tensile crack. It was found that it is not the field of the strain energy density factor, but the field of the tensile component of principal stress which determines the trajectory of the tensile crack. Moreover, this field is responsible for the trajectory of the tensile crack not only in its seismoactive phase of its development, but also in the following aseismic stage characterized by slow stable growth.     

Seismic regime of a single fault model

A special experimental technique enabled us to study in detail seismic events on a fault model in a uniaxial stress field. The recording system used made it possible to investigate the radiation pattern for all the events observed including the precise determination of the dislocation origin.The aim of the present paper is (1) to find the relation between shear and tensile displacements, (2) to check a possible influence of the process of tensile crack generation on the seismic energy release and (3) to compare the seismic regime of a single fault before and after the tensile crack generation, respectively.Results prove the dominating importance of shear mechanism for the seismic energy release. The tensile displacement can be seismoactive only under special contact conditions on the fault plane.The existence of tensile cracks at the fault tips changed the pattern of seismic energy radiation. This feature is probably caused by subsequent changes in contact conditions on the fault plane and in the stress field around the fault.A comparison of some results of the present model experiments with the already published results of geological and seismological measurements and investigations shows the analogous character in laboratory and in nature of the process of tectonic earthquake preparation, the displacement course on the fault during the earthquake and the manner of seismic energy release on faults.     

Radiation pattern ofP and Rayleigh waves for an experimental strike-slip fault model

Summary The spatial radiation pattern of P and Rayleigh waves for microtremors, produced in a seismoactive source by a suitable modelling technique, was investigated. The results indicate that the source simulates a strike-slip fault of finite dimensions slipping along the fault plane.     

Fault interaction and seismicity: Laboratory investigation and its seismotectonic interpretation

Systems of two parallel linear faults of the same length with the angle of inclination =45° were investigated under uniaxial linearly increasing load. Perspex plates were used as models. For each treated fault configuration the morphology of tensile cracks and the sequence of seismoacoustic events of shear and tensile origin were studied.It is shown that the seismic regime of a fault system is strongly influenced by the contact conditions on a fault plane; it is different in the faults with the aseismic contact, represented by open slits, and in the faults with the seismoactive contact, represented by filled slits, respectively.The experiments proved the dominating role of a fast shear displacement of the stick-slip type in the regime of seismic energy release of a fault system. The tensile crack generation seems to be only of little—if not negligible—importance. On the other hand, the existence of tensile cracks in a fault system can play an important role in the course of subsequent loading cycles because the stick-slip displacements can take place not only along the primary faults but also along the planes of tensile cracks.A comparison of some results of model experiments and the already published results of geological and seismological investigations indicated that the way of seismic energy relase on faults in nature and in the laboratory could be of the same character. Several analogies between the seismic regime of a fault model and of real seismic regions were found concerning the morphology of faults, off-fault fore- and aftershocks, and earthquake doublets, respectively.     

Improvement in the Fault Boundary Conditions for a Staggered Grid Finite-difference Method

The staggered grid finite-difference method is a powerful tool in seismology and is commonly used to study earthquake source dynamics. In the staggered grid finite-difference method stress and particle velocity components are calculated at different grid points, and a faulting problem is a mixed boundary problem, therefore different implementations of fault boundary conditions have been proposed. Viriuex and Madariaga (1982) chose the shear stress grid as the fault surface, however, this method has several problems: (1) Fault slip leakage outside the fault, and (2) the stress bump beyond the crack tip caused by S waves is not well resolved. Madariaga et al. (1998) solved the latter problem via thick fault implementation, but the former problem remains and causes a new issue; displacement discontinuity across the slip is not well modeled because of the artificial thickness of the fault. In the present study we improve the implementation of the fault boundary conditions in the staggered grid finite-difference method by using a fictitious surface to satisfy the fault boundary conditions. In our implementation, velocity (or displacement) grids are set on the fault plane, stress grids are shifted half grid spacing from the fault and stress on the fictitious surface in the rupture zone is given such that the interpolated stress on the fault is equal to the frictional stress. Within the area which does not rupture, stress on the fictitious surface is given a condition of no discontinuity of the velocity (or displacement). Fault normal displacement (or velocity) is given such that the normal stress on the fault is continuous across the fault. Artificial viscous damping is introduced on the fault to avoid vibration caused by onset of the slip. Our implementation has five advantages over previous versions: (1) No leakage of the slip prior to rupture and (2) a zero thickness fault, (3) stress on the fault is reliably calculated, (4) our implementation is suitable for the study of fault constitutive laws, as slip is defined as the difference between displacement on the plane of z = + 0 and that of z = − 0, and (5) cessation of slip is achieved correctly.     

动态应力与地震图像变化的相关性初探

列举11个大地震震例研究了发震断层面剪切运动方向与地震活动特征的相关性,提出由震后地震活动条带判断发震断层面走向的方法,结果表明,动态法判定的发震断层面与其它方法判定的发震断层面非常一致。探讨了动态应力场范围、传播和对基本应力场的加强作用,以及动态应力场展布范围与大面积宏观前兆等问题。     

地震断裂和应力场

本文讨论了地震断裂和构造应力之间的关系。首先综述了地震机制研究的结果,指出断层面解可以给出较好的断层面的取向,而得不到确切的应力场;认为地震是一个复杂的破裂过程,而P波初动只反映了破裂开始的状态。应用了库仑准则对地震断裂进行了讨论,得出在各向同性介质中,最大主应力与断层面的夹角α≤45°,断层面解只是它的一个特例,μ=0,即没有内摩擦,或相当于围压很高的岩石试验结果;在软弱面存在的情况下,断裂面与最大主应力的夹角可以分布在更大的范围内,可以大于45°,也可以小于45°,这范围取决于破裂参数S_w,μ_w以及中等主应力σ_2。讨论了震前应力变化的过程,指出了五种基本可能引起地震的过程     

2014年鲁甸6.5级地震成因、破裂特征和余震分布特征的库仑应力作用

根据2014年鲁甸M_S6.5地震的区域构造和余震共轭分布特征,本文首先计算了1733年小江断裂带北段M7.75地震,1850年则木河断裂带M7.5地震和1974年马边M_S7.1地震对鲁甸M_S6.5地震震源机制解两个节面的黏弹性库仑应力作用,结果显示NNW向发生主破裂的包谷垴-小河断裂受到这3次地震,尤其是1850年M7.5地震明显的库仑应力作用,我们认为则木河断裂的高速左旋走滑运动以及7级以上强震的重复发生对于包谷垴-小河断裂的强震孕育和断裂演化方面具有促进作用;然后分析了鲁甸6.5级地震的共轭破裂与余震分布特征,并分别计算了两个共轭破裂面单独破裂对另一破裂面的库仑应力作用,结果显示NEE向破裂促进NNW向破裂的发生,而NNW向破裂后则阻碍了NEE向破裂的进一步发展,最终发展成以NNW向破裂为主的共轭破裂事件;最后计算了共轭破裂产生的库仑应力变化对余震的影响,认为位于NEE向破裂面西侧的余震集中分布主要是由于应力触发作用而形成.     

龙门山断裂带南段横波分裂分析

基于2009年1月—2015年4月芦山地震震源区 (龙门山断裂带南段) 大量地震的双差重定位结果,对固定台站 (BAX, MDS, TQU) 和流动台站 (L131, L132, L134, L135) 周围处于横波分裂窗内的地震记录进行了横波分裂分析.研究结果表明:除台站TQU外,其它台站的快波偏振优势方向与龙门山断裂带的走向基本一致;台站TQU处于前山断裂与一条SE向断裂的交汇处,其偏振方向具有一定的方位性,表明SE向断裂可能是导致台站TQU快波偏振优势方向偏离的原因之一.各台站位于1角区 (入射射线与裂隙面夹角为15°—45°的双叶区域) 和2角区 (入射射线与裂隙面夹角为0°—15°的区域) 的归一化时间延迟结果显示,除台站L135由于缺少震后持续数据外,其余6个台站在1角区内的归一化时间延迟在芦山地震主震后均逐渐减小.另外,从BAX, MDS, L134, L131这几个台站的玫瑰图中可见,芦山地震后快波偏振矢量发生了90°翻转现象,说明各向异性孔隙弹性 (APE) 理论在该研究区的适用性,即该理论可用于监测研究区的区域应力场变化.      

Effect of Injected Water on Hydraulic Fracturing Deduced from Acoustic Emission Monitoring

—In order to investigate the effects of injected water in hydraulic fracturing, experiments were conducted on cubic granite specimens, comparing fracturings induced by conventional water injection with those induced by pressurization of a urethane sleeve, thereby realizing "hydraulic fracturing" without the use of fracturing fluid. In both experiments, a shear type mechanism was found to be dominant in fault plane solutions of AE events. However, in the case of water injection, cracks extended rapidly with large drops in hole water pressure and bursts of AE, whereas in pressurization by the urethane sleeve, cracks extended stepwise with no such large drops in hole pressure and no bursts of AE. The difference in crack extension in the two experiments can be analyzed by comparing relations between crack length and stress intensity factor of mode I at a crack tip. The observation and analysis indicate that existence of fracturing fluid like water helps initiated cracks to extend rapidly and widely in hydraulic fracturing in actual HDR fields. Received September 12, 1996, accepted January 24, 1997     

In situ stress measurements in a borehole close to the Nojima Fault

Abstract In situ stress was measured close to the fault associated with the 1995 Kobe Earthquake (Hyogo-ken Nanbu earthquake; January 1995; M 7.2) using the hydraulic fracturing method. The measurements were made approximately 2 years after the earthquake. The measured points were approximately 40 m from the fault plane at depths of about 1500 m. The maximum and the minimum horizontal compressive stresses were 45 MPa and 31 MPa, respectively. The maximum compressive stress and the maximum shear stress are very small in comparison with those of other seismically active areas. The azimuth of the maximum horizontal compressive stress was estimated from the observed azimuths of well bore breakouts at depths between 1400 m and 1600 m and was found to be N135° (clockwise). The maximum stress axis is perpendicular to the fault strike, N45°. These features are interpreted in terms of a small frictional coefficient of the fault. The shear stress on the fault was released and dropped almost to zero during the earthquake and it has not yet recovered. Zero shear stress on the fault plane resulted from the perpendicular orientation of one of the principal stress to the fault plane.     

潮汐应力与大震关系研究

选用1976—2009年全球震源深度小于70 km, M_W≥7.0的地震为研究对象, 利用震源机制解资料, 对每个地震的发震断层面进行了判断, 得到233个地震的发震断层面解。 据此, 本文讨论了发震时断层面上的地球固体潮汐剪应力方向与滑动方向的关系以及潮汐正应力在发震时所处的相位, 发震时断层面的库仑应力值。 结果表明, 当潮汐剪应力方向与滑动方向一致时触发作用最为明显, 逆断层地震与潮汐的关系最为密切; 而当潮汐剪应力方向与滑动方向相反时, 地震较少发生。     

澄江5.2级地震的震源机制、震源应力场和震源断层

利用地震波资料对澄江5．2级地震序列的震源机制、震源应力场和震源断层作了分析研究。结果表明，整个序列发展中，震源区及附近、构造应力场以南东东方向、水平作用为主的压应力场为主。其次还有南南东向、水平作用为主的压应力场的作用。由序列震源机制解分析，主震发震断层是走向北北东、倾角较陡的断层面，在南南东－南东向，接近水平的压应力场作用下，该断层面具有以左旋走滑为主的错动性质。该断层面是序列的主破裂面。在序列发展过程中，北西西－北西向断层也参与了活动。有的余震，虽然发生在与主破裂面一致或接近的断层面上，但破裂错动的旋性发生了变化，出现了相对主破裂事件的反向错动。极少数余震破裂错动性质呈现以倾向滑动为主的特征。在序列发展过程中，破裂面及其错动性质显地复杂。由于强震的发生，主破裂的错动，使得震源区局部应力场状态错综复杂。     

论地震序列的一种可能的重要成因

本文在Asperity模式和Barrier模式的基础上,提出了另外一种不均匀体模式——障碍体模式,并对该模式进行了数值模拟的研究。结果除证实了我们以前做过的单轴压力下模拟障碍体的实验结果以外,还表明在含有障碍体的断层面上,破裂的扩展与破裂的传播速度、始破裂区域的大小、裂纹的类型以及障碍体所在断层的介质有关。在有围压的情况下,破裂可以先越过或绕过强度较高或尺度较大的障碍体,经一段时间的应力积累过程后,再使障碍体发生破坏。本文通过对震源区中障碍体的性质和影响的研究,解释了海城和邢台两个地震序列形成和发展的可能原因,得到一些较为合理的结果。     

位错模型的有限单元公式

本文讨论了弹性和粘弹介质中用劈节点技术离散的结构面与非均匀位错面的等价原理,并由此证明有限单元位错公式表示的位移场与沃尔特拉位错公式表示的位移场等价,从而获得求解断层面错动产生的位移场与应力场的统一理论和方法,即用Volterra(沃尔特拉)位错公式和地面位移观测资料,反演断层面上的位移或位移速率,再用位错的有限单元公式和反演的断层位错,正演计算位移场和应力场。     

障碍体和凹凸体对地震矩的影响

本文利用具有非均匀剪切应力分布的圆盘状裂缝问题的解,定量计算了障碍体和凹凸体对地震矩的影响.我们发现,除非障碍体的尺寸很小或很接近于整个断层的尺寸,含有障碍体的断层的地震矩,大致为具有均匀应力降的等面积断层的地震矩的40%.由此可以推知,在障碍体的这种尺寸范围内,视应力降大致也是△Af=SA-f的40%.这里SA是远场应力,f是残余摩擦应力.另外,已存在滑动带对于凹凸体破坏的地震矩有明显的放大作用,这种作用在凹凸体尺寸较小时特别显著.例如,当凹凸体半径是整个断层半径的2/10时,凹凸体上的矩被放大7倍多;当其半径为整个断层半径的1/10时,凹凸体的矩将被放大约30倍. 文中还比较了三维效应和二维效应的差异.我们发现,Mx0/M0c在三维情形对障碍体尺寸的变化并不敏感,这是与二维情形很不相同的.这里,Mx0是具有障碍体的断层破裂所产生的地震矩,M0c是相应的均匀断层破裂的矩.所以,二维分析不适用于具有障碍体的三维断层.然而,在分析已存在滑动带对凹凸体破裂的矩的影响时,平面应变结果与三维结果差异并不很大.      

地震破裂过程的研究

研究震源力学模型的一个新方向是用动态扩展的剪切裂纹模拟地震破裂过程。本文利用裂端有塑性区薄层且断层面上有摩擦力的平面剪切裂纹错动模式来表示地震破裂过程,对运动方程和边界条件进行拉氏变换和傅氏变换,利用维纳-霍普（Wiener-Hopf）方法和卡格尼阿（Cagniard）方法得到了断层面上的位移和应力表达式。根据裂端附近的能量平衡条件,计算了地震破裂的平均速度和塑性区尺度,还讨论了断层面上的位错分布函数,并对某些前震地震波高频成分增多的现象提出了解释。在本文假定的参数条件下,地震破裂的平均速度c=0.72β,β是介质的剪切波速。塑性区尺度约为地震新断层总长度（包括塑性区）的12％。按本文的结果,由于破裂速度的增加,前震的震波初动半周期减小的异常幅度不会超过39％。     

Seismic swarms, fault plane solutions, and stress tensors for S?o Miguel Island central region (Azores)

The central region of S?o Miguel Island is one of the most seismically active areas of the Azores archipelago. A revised analysis of the seismicity distribution at this region has, for the first time, shown that the seismicity is clustered in two distinct areas: the area around Fogo Volcano (Fogo) and the area around Congro maar (Congro), with each area having a highly localized swarm activity. From a total of about 15,000 events in the period from 2002 to 2010, 78 best located events were selected to make fault plane solutions using P-wave polarities and amplitude ratios. This set of fault plane solutions, and another six subsets derived from it, were inverted for the best fitting stress tensor. The stress tensor using all the 78 fault plane solutions is characterized by a subhorizontal ??1 striking WNW-ESE and a ??3 striking NNE-SSW, consistent with the regional stress field for this region. A similar result, using only the fault plane solutions located in the Fogo area, was obtained. On the other hand, for the Congro area, a local stress field seems to be superimposed on the regional field: subhorizontal ??3, striking NNE-SSW, and a near-vertical ??1. The same stress regime persists in the first 5?km depth, probably related to the upwelling of thermal fluids. The rising fluids generate horizontal extension at shallow depths, which favour the opening of cracks and the circulation and ascension of hydrothermal fluids. The stress regime deeper than 5?km is more uncertain; however, it is indicative of a compressional regime. Thus, it can be conclude that the smaller Fogo area appears to be dominated by the normal regional stress field while the high active Congro area seems to have a different, highly heterogeneous stress field dominated by local conditions.     

2008年汶川Ms8.0地震在2013年芦山Ms7.0地震和2014年康定Ms6.3地震破裂区引起的库仑破裂应力

2008年5月12日四川汶川发生M_S8.0地震发生之后, 先后于2013年4月20日和2014年11月22日分别在汶川M_S8.0地震震中西南约80 km的芦山县和约178 km的康定县发生了M_S7.0和M_S6.3地震。 芦山地震位于龙门山前主边界处, 康定地震位于鲜水河断裂带上。 芦山地震发生前有几位作者先后计算了汶川M_S8.0地震引起的库仑破裂应力, 分析了其对周围断层的影响。 本文对这些研究结果进行了简要回顾, 并根据芦山地震和康定地震的实际发震断层面参数, 计算了汶川M_S8.0地震在芦山地震和康定地震震源深度处的水平面上以及其发震断层面上产生的库仑破裂应力, 还给出了其震中处库仑破裂应力随深度的变化。 结果表明, 汶川M_S8.0地震发生使芦山地震震源断层面上有利于其错动发震的应力大面积增加而使康定地震震源断层面上有利于其错动发震的应力大面积减小。 在芦山地震初始破裂点处引起的库仑破裂应力达0.245 MPa, 在康定地震初始破裂点处引起的库仑破裂应力为-0.00063 MPa。 因此, 汶川M_S8.0地震的发生对芦山地震具有明显的促进作用, 而对康定地震的作用不明显。 在目标断层面参数已知的情况下, 根据库仑破裂应力在目标断层面上的分布, 可能为未来地震发生的地点提供线索, 进而对地震发生的危险性进行预测。 若一次地震的发生使目标断层面上有利于其错动发震的应力大面积显著增加, 这种情况下库仑破裂应力对未来地震具有预测意义。     

STUDY ON THE SEISMOGENIC FAULT AND DYNAMICS PARAME-TERS OF THE 2014 MS6.6 JINGGU EARTHQUAKE IN YUNNAN

On October 17, 2014, a M_S6.6 earthquake occurred in Jinggu, Yunnan. The epicenter was located in the western branch of Wuliang Mountain, the northwest extension line of Puwen Fault. There are 2 faults in the surrounding area, one is a sinistral strike-slip and the other is the dextral. Two faults have mutual intersection with conjugate joints property to form a checkerboard faulting structure. The structure of the area of the focal region is complex. The present-day tectonic movement is strong, and the aftershock distribution indicates the faulting surface trending NNW. There is no obvious surface rupture related to the known fault in the epicenter, and there is a certain distance from the surface of the Puwen fault zone. Regional seismic activity is strong. In 1941, there were two over magnitude 7.0 earthquakes in the south of the epicenter of Jinggu County and Mengzhe Town. In 1988, two mainshock-aftershock type earthquakes occurred in Canglan-Gengma Counties, the principal stress axes of the whole seismic area is in the direction of NNE. Geological method can be adopted to clarify the distribution of surficial fracture caused by active faults, and high-precision seismic positioning and spatial distribution characteristics of seismic sequences can contribute to understand deep seismogenic faults and geometric features. Thus, we can better analyze the three-dimensional spatial distribution characteristics of seismotectonics and the deep and shallow tectonic relationship. The focal mechanism reveals the property and faulting process to a certain extent, which can help us understand not only the active property of faults, but also the important basis for deep tectonic stress and seismogenic mechanism. In order to study the fault characteristic of the Jinggu earthquake, the stress field characteristics of the source area and the geometric parameters of the fault plane, this paper firstly uses the 15 days aftershock data of the Jingsuo M_S6.6 earthquake, to precisely locate the main shock and aftershock sequences using double-difference location method. The results show that the aftershock sequences have clustering characteristics along the NW direction, with a depth mainly of 5~15km. Based on the precise location, calculations are made to the focal mechanisms of a total of 46 earthquakes including the main shock and aftershocks with M_L ≥ 3.0 of the Jinggu earthquake. The double-couple(DC)component of the focal mechanism of the main shock shows that nodal plane Ⅰ:The strike is 239°, the dip 81°, and the rake -22°; nodal plane Ⅱ, the strike is 333°, the dip 68°, and the rake -170.31°. According to focal mechanism solutions, there are 42 earthquakes with a focal mechanism of strike-slip type, accounting for 91.3%. According to the distribution of the aftershock sequence, it can be inferred that the nodal plane Ⅱ is the seismogenic fault. The obtained focal mechanism is used to invert the stress field in the source region. The distribution of horizontal maximum principal stress orienation is concentrated. The main features of the regional tectonic stress field are under the NNE-SSW compression(P axis)and the NW-SE extension(T axis)and are also affected by NNW direction stress fields in the central region of Yunnan, which indicates that Jinggu earthquake fault, like Gengma earthquake, is a new NW-trending fault which is under domination of large-scale tectonic stress and effected by local tectonic stress environment. In order to define more accurately the occurrence of the fault plane of the Jinggu earthquake, with the precise location results and the stress field in the source region, the global optimal solution of the fault plane parameters and its error are obtained by using both global searching simulated annealing algorithm and local searching Gauss-Newton method. Since the parameters of the fault plane fitting process use the stress parameters obtained by the focal mechanism inversion, the data obtained by the fault plane fitting is more representative of the rupture plane, that is, the strike 332.75°, the dip 89.53°, and the rake -167.12°. The buried depth of the rupture plane is 2.746km, indicating that the source fault has not cut through the surface. Based on the stress field characteristics and the inversion results of the fault plane, it is preliminarily believed that the seismogenic structure of the Jinggu earthquake is a newly generated nearly vertical right-lateral strike-slip fault with normal component. The rupture plane length is about 17.2km, which does not extend to the Puwen fault zone. Jinggu earthquake occurred in Simao-Puer seismic region in the south of Sichuan-Yunnan plate. Its focal mechanism solution is similar to that of the three sub-events of the Gengma earthquake in November 1988. The seismogenic structure of both of them is NW-trending and the principal stress is NE-SW. The rupture plane of the Jinggu main shock(NW direction)is significantly different from the known near NS direction Lancang Fault and the near NE direction Jinggu Fault in the study area. It is preliminarily inferred that the seismogenic structure of this earthquake has a neogenetic feature.