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.     

最小能量准则用于1995年河北沙城ML 4.1地震序列破裂性质的探讨

运用变分原理,我们得到了最小地震波辐射能量约束准则并用于研究震源的物理过程.通过研究1995年M_L4.1河北沙城地震序列主震和余震的动力学过程,可知主震和余震震源的动态破裂过程明显不同;M_L4.1主震的破裂速度与瑞利波速相近,约为剪切波速度的0.89倍;而28个余震的破裂速度远远小于剪切波速度,大约是剪切波速度的0.05到0.55倍.根据裂纹扩展模型,计算得到其余震的地震波辐射效率多在10％以下,这也说明了余震的地震效率较低.我们认为余震震源的动态破裂过程应与断层内部新生裂纹的扩展有关,而非简单的岩体间的相对滑动.余震震源的动态破裂传播与破裂能占主导地位的小地震有关.这些小震所带来的破裂能也导致了断层的进一步扩展.在对该地震序列的研究中,我们发现主震与余震的震源破裂过程在能量分配上有着本质的区别.因此当地震断层尺度相当小时,破裂能的贡献不能忽略,它的大小将显著地影响地震波辐射能的大小.     

最小能量准则用于1995年河北沙城ML 4.1地震序列破裂性质的探讨

运用变分原理,我们得到了最小地震波辐射能量约束准则并用于研究震源的物理过程.通过研究1995年ML4.1河北沙城地震序列主震和余震的动力学过程,可知主震和余震震源的动态破裂过程明显不同;ML4.1主震的破裂速度与瑞利波速相近,约为剪切波速度的0.89倍;而28个余震的破裂速度远远小于剪切波速度,大约是剪切波速度的0.05到0.55倍.根据裂纹扩展模型,计算得到其余震的地震波辐射效率多在10%以下,这也说明了余震的地震效率较低.我们认为余震震源的动态破裂过程应与断层内部新生裂纹的扩展有关,而非简单的岩体间的相对滑动.余震震源的动态破裂传播与破裂能占主导地位的小地震有关.这些小震所带来的破裂能也导致了断层的进一步扩展.在对该地震序列的研究中,我们发现主震与余震的震源破裂过程在能量分配上有着本质的区别.因此当地震断层尺度相当小时,破裂能的贡献不能忽略,它的大小将显著地影响地震波辐射能的大小.     

Laboratory investigations on fault plane induced tensile cracks

Summary Tensile cracks induced by stress concentration around a fault plane in physical models under uniaxial load were analyzed. The results characterizing the decisive role of the fault plane inclination to the the stress direction are presented. Two stages of tensile crack life were determined, i.e. the first, seismoactive stage, accompanied by seismic energy release and the second aseismic one characterized by low velocity of crack propagation. Results obtained seem to be relevant to a better understanding of the character and regime of actual seismoactive faults.     

构造应力方向与震源机制解

本文根据二维模型实验的结果,探讨了地震波辐射图型、震源机制解以及构造应力方向之间的关系.地震波辐射图型取决于地震时震源介质运动的方式.它不但与震前存在的应力有关,而且依赖于震源区的地质条件等因素.根据岩石力学实验和我们实验的结果,可以认为,构造应力的主压应力方向要比震源机制解推断的释放主压应力方向更偏近断层面一些.      

从断裂力学观点研究地震的破裂过程和地震预报

把断裂力学中的应变能释放率公式和裂纹错开位移公式运用到地震破裂中来,再用震级-能量公式logε_e=α₁M+α₂,对于走向滑动、倾向滑动和圆盘形剪切破裂找到了震源参数和地壳应力状态之间的内在联系,汇总在表2。对于走滑断层情形,关系式如下: （1） （2） （3） （4）应力降 （5）平均应力 （6）用M_o和L²W求区域应力公式式中,M为震级,L、W为断层长度和宽度,η为地震效率,τ₀为区域剪切应力,τ_y为剪切屈服强度,μ为刚性系数,v为泊松比,为平均位错,M₀为地震矩。 利用（6）式或（1）式,在实验室测出地壳状态下屈服强度τ_y,后,可用地震观测资料算出区域剪切应力τ₀。 上述关系式和目前流行的震源参数之间的关系式有很大的差别。原因是以往只考虑了破裂的初态和终态,没有考虑破裂过程。而断裂力学恰恰是考虑了破裂过程。     

Seismic events with non-shear component: I. Shallow earthquakes with a possible tensile source component

The concept of seismicity of fast tensile fracturing is introduced and supported by the results of shear and of combined shear and tensile displacements along a loaded stress concentrator. The seismicity of tensile fracturing is demonstrated by means of acoustic (elastic) signals obtained during tensile fracturing in physical models under load; the basic physical relations between the parameters characterizing the loaded medium, load conditions, shear and tensile displacements, and release of acoustic energy are presented. For determining the tensile-source component in earthquakes a procedure based on the construction of radiation patterns is suggested and submitted for discussion. The criteria for selecting earthquakes with possible shear-tensile source mechanisms are listed and discussed. The existence of such a combined seismic source is sought in two shallow earthquakes which occurred in southern Iran in March 1977. In general, the paper should be regarded as a proposal to utilize the radiation characteristics of a seismic source—with all their insufficiencies—as a quick and simple tool for seeking combined shear and tensile mechanisms of seismic energy release.     

An asperity model to simulate rupture along heterogeneous fault surfaces

A model has been developed to simulate the statistical and mechanical nature of rupture on a heterogeneous strike-slip fault. The model is based on the progressive failure of circular asperities of varying sizes and strengths along a fault plane subjected to a constant far-field shear displacement rate. The basis of the model is a deformation and stress intensity factory solution for a single circular asperity under a unidirectional shear stress. The individual asperities are unified through the fault stiffness and the far-field stress and displacement. During fault deformation asperities can fail and reheal, resulting in changes in the local stresses in the asperities, stress drops, and changes in the stiffness of the fault. Depending on how the stress is redistributed following asperity failure and on the strenghts of the neighboring asperities an earthquake event can be the failure of one or more asperities. Following an earthquake event seismic source parameters such as the stress drop, energy change, and moment magnitude are calculated. Results from the model show a very realistic pattern of earthquake rupture, with reasonable source parameters, the proper magnitude-frequency behavior, and the development of characteristic earthquakes. Also the progression ofb-values in the model gives some insight into the phenomenon of self-organized criticality.     

断层地震孕育和发生的不稳定性模型

在以前的工作中,考虑直立走滑型断层地震,假设断层面微元破裂强度遵循Weibull概率分布,由细观力学方法推导出断层面的宏观本构关系是一个非线性函数,表现为弹性-软化塑性特征,在此基础上用稳定性理论研究了地震稳定性问题.而实际断层大多是倾斜的,为此,本文首先建立了由围岩和倾斜断层构成的平面地震力学模型,采用宏观的断层载荷-变形的全过程曲线,详细讨论了倾斜断层地震的不稳定性问题.结果表明,远场一旦施加位移,断层也同时错动,这可能与实际情况不符合.为了更好的模拟断层的初始能量累计过程,进一步对断层本构模型进行改进.考虑断层面破裂强度,采用Coulomb破裂准则,则断层表现为刚塑性本构关系,只有当断层面剪应力达到一个临界值时,断层才开始错动.研究表明,对于倾斜断层地震,与直立走滑型断层地震一样,系统刚度比β（围岩切线刚度与断层刚度最大值之比）是决定地震失稳的重要参数,只有当β<1时才会出现地震失稳,且伴随应力突跳和围岩应变能释放.当β≥1时,仅仅是断层无震滑动,不会发生地震.在远场应施以位移形式边界条件,以致地震失稳发生在平衡路径的位移转向点并伴有应力突跳.     

A Seismic Model of Casing Failure in Oil Fields

—We develop a seismic model that characterises the sudden tensional failure of oil-well casings. The energy released by the rupture of a well casing is transformed into heat and seismic energy. The upper bound of the seismic efficiency of this process is estimated at about 3%. The static situation at the completion of a casing failure episode is modelled by calculating the static displacement field generated by two opposing forces separated by an arm. The azimuthal patterns of these displacements and the change in the strain and stress fields caused by the force couple are described. The dynamics of the failure episode are modelled as a dipole with a seismic moment equivalent to the product of the average drop in shear stress, the failure surface, and an arm. The radiated P and S waves have mean-square radiation pattern coefficients of 1/5 for P waves and 2/15 for S waves. The displacement field as a function of time during rupture and the spectral properties in the far field are derived. The most promising seismic parameters that can be used for distinguishing between casing failure events and other possible events are polarisation properties of S waves and S/P amplitude ratios. S-wave polarisation distinguishes between shear events and casing failure events. S/P amplitude ratios distin guish between tensile events and casing failure events.     

2014年鲁甸6.5级地震GPS同震位移及反演分析

本文综合GPS流动和连续观测结果,并利用最速下降法（SDM）反演方法,给出并分析了2014年鲁甸6.5级地震同震位移、断层面滑动位移分布特征.GPS同震位移结果表明：此次地震沿北西方向表现出左旋应变释放特征、沿北东向表现出拉张应变释放的同震特征,并且随着离开断裂带距离的增加,拉张变形衰减;受包谷垴—小河断裂控制的左旋剪切应变释放的位移在莲峰、昭通—鲁甸断裂附近较弱,说明该断裂可能没有完全切割昭通—鲁甸断裂,不属于该区域主干断裂;昭通—鲁甸断裂带有一定的右旋应变释放,而逆冲应变释放不明显,表明该断裂带处于受南东向挤压的强闭锁状态.SDM反演结果表明,鲁甸地震以左旋走滑为主并兼有拉张性质,地震矩震级为M_W6.3左右.综上所述,并结合其他研究成果,我们认为莲峰、昭通—鲁甸断裂带仍存在强震危险性.     

2001年8.1级昆仑山大震破裂过程及对2008年汶川8.0级大震孕育发生影响的研究

本文用三维流变非连续变形(块体边界)与有限元(块体内)相结合(DDA+FEM)的方法,在青藏高原及其东侧四川盆地,鄂尔多斯块体地区三维构造块体相互制约的大环境中,考虑了龙门山断裂带东西两侧地势、地壳厚度和分层的明显变化,及断裂带东侧四川盆地及鄂尔多斯块体坚硬地壳阻挡的影响,通过用GPS资料做位移速率边界约束和震源机制约...     

新疆伽师强震群区的横波分裂与应力场特征

利用在新疆伽师地区布设的流动台阵记录到的地方震波形数据,研究了伽师强震群附近各台站横波分裂现象,给出了相应的快波偏振方向的平面场分布. 发现在台阵的塔里木盆地一侧,波偏振方向为近SN向,与塔里木盆地的区域主压应力方向一致,但在塔里木盆地北部边缘的褶皱变形带内,快波偏振方向变为近EW向,特别是在柯坪断裂附近,快波偏振方向与阿图什地震的震源断层方向基本一致. 由于快波偏振方向平行于主压应力方向,给出的快波偏振方向反映了相应的主压应力场特征. 结果表明,伽师强震群的成因很可能是塔里木盆地北缘横向非均匀变形造成的局部张性剪切应变能的释放.     

Implications of stress-drop models of earthquakes for the inversion of stress drop from seismic observations

We discuss the inversion of stress drops from seismic observations on the basis of crack or stress-drop models of earthquake mechanism. Since a formal inverse problem cannot be posed at present we discuss implications of solutions to direct problems. We first discuss the static approximations used to obtain stress drop from seismic moment and source dimensions. We show that the geometrical effects are quite significant if only one source dimension has been retrieved from seismic observations. The effect of variable stress drop is discussed and we show that the inverted stress drop is not a simple average of the actual stress drops on the fault. We discuss the energy release during faulting and show that the apparent stress has a complicated relation to the stress drop on the fault. We also show that the static stress drops obtained by seismologists are a lower bound to the actual dynamic stress drops on the fault. This may in part explain disagreements with laboratory results. Finally, we discuss the inversion of source dimensions from the far-field radiation. We analyse two extreme, simple dynamical source models, a circular fault and a rectangular fault and show that geometry has a much more pronounced effect on radiation than is usually acknowledged.     

Simulation of Unstable Fault Slip in Granite Using a Bonded-particle Model

—?A bonded-particle model is used to simulate shear-type microseismic events induced by tunnel excavation in granite. The model represents a volume of granite by an assembly of 50,000 individual particles bonded together at points of contact. A plane of weakness is included in the model and this plane is subjected to increasing shear load while the normal load across the plane is held constant. As shear stress in the model increases, bonds begin to break and small acoustic emissions (AE) result. After enough bonds have broken, macro-slip occurs across the large portions of the fault in an unstable manner. Since the model is run dynamically, seismic source information can be calculated for the simulated AE and macro-slip events. This information is compared with actual results obtained from seismic monitoring around an underground excavation. Although the modelled events exhibit larger magnitudes than the actual recorded events, there are many similarities between the model and the actual results, namely the presence of foreshocks before the macro-slip events and the patterns of energy release during loading. In particular, the model provides the ability to examine the complexity of the slip events in detail.     

基于震源机制解分析邢台地震的发震构造

活动断层几何形状的确定为评估一个地区的地震危险性提供重要的理论依据,邢台老震区内构造背景复杂,前人对邢台地震的发震构造展开大量研究,取得丰富成果。通过震源机制节面聚类得到邢台地震发震断层的走向、倾角及其标准差,综合前人研究结果求取发震断层面的平均解;结合区域地壳应力张量,估计该断层的滑动方向及其误差,分析该区域的地震活动危险性。结果表明：邢台地震发震断层的走向为32.45°,倾角为79.44°,滑动角-153.96°,标准差为4.55°。该断层为走向NNE、倾向NWW的高倾角走滑型断层,而非正断性质的新河断裂。区域地壳应力场在断层面上产生的相对剪应力为0.83,相对正应力为0.59。该断层不是最大剪应力的断层面形状,但剪应力强度仍较大,表明该断层在地震能量积累和释放过程中仍起到必不可少的作用。     

分析地震波估算地壳内的应力值

本文讨论了利用破裂力学理论说明地震破裂的过程, 认为地震本质上是岩石在应力作用下的低应力破裂现象.它是岩石中的裂纹不断稳态扩展、最后进入失稳扩展的结果.分析了在扩展过程中应力和位移的变化, 发现任何将要破裂的那一点的应力都要由初始应力0升高到屈服应力y 以后才破裂, 破裂后裂纹面上的点的应力降到0.在破裂前和破裂后的位移, 都可由弹性力学方程给出.在破裂的一瞬间破裂的端点产生的非弹性位移, 则不能由弹性力学方程给出.它可以由断裂力学中的裂纹滑开位移公式近似给出.根据位错模式由于计算弹性波辐射场的位错量 D(, t), 正是破裂瞬间产生的非弹性位移, 所以用弹性位移公式来计算地震位错量是错误的.我们采用了裂纹滑开位移公式来计算地震位错量, 从而导出了较合理的计算地震释放总能量的公式 ET=yDS(y 为屈服强度;D为平均位错;S 为断层面积)以及估算初始应力值0的公式:0 =[Dmax/L4y/(1-) ]1/2(L 为断层长度).用它们计算了一些地震的 Er 和0, 分别列于表1和表2.这些结果比以往的结果要更合理一些。 结果表明:(1)地震多数是在低应力作用下(即低初始应力)发生的(约100——200巴);(2)地震释放的总能量约比地震波能量大一个数量级.      

Frequency-dependent rupture process,stress change,and seismogenic mechanism of the 25 April 2015 Nepal Gorkha <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> 7.8 earthquake

On 25 April 2015, an M _w 7.8 earthquake occurred on the Main Himalaya Thrust fault with a dip angle of ~ 7° about 77 km northwest of Kathmandu, Nepal. This Nepal Gorkha event is the largest one on the Himalayan thrust belt since 1950. Here we use the compressive sensing method in the frequency domain to track the seismic radiation and rupture process of this event using teleseismic P waves recorded by array stations in North America. We also compute the distribution of static shear stress changes on the fault plane from a coseismic slip model. Our results indicate a dominant east-southeastward unilateral rupture process from the epicenter with an average rupture speed of ~3 km s^?1. Coseismic radiation of this earthquake shows clear frequency-dependent features. The lower frequency (0.05–0.3 Hz) radiation mainly originates from large coseismic slip regions with negative coseismic shear stress changes. In comparison, higher frequency (0.3–0.6 Hz) radiation appears to be from the down-dip part around the margin of large slip areas, which has been loaded and presents positive coseismic shear stress changes. We propose an asperity model to interpret this Nepal earthquake sequence and compare the frequency-dependent coseismic radiation with that in subduction zones. Such frequency-dependent radiation indicates the depth-varying frictional properties on the plate interface of the Nepal section in the main Himalaya thrust system, similar to previous findings in oceanic subduction zones. Our findings provide further evidence of the spatial correlation between changes of static stress status on the fault plane and the observed frequency-dependent coseismic radiation during large earthquakes. Our results show that the frequency-dependent coseismic radiation is not only found for megathrust earthquakes in the oceanic subduction environment, but also holds true for thrust events in the continental collision zone.     

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％。     

Self-induced Deformation on the Fault Plane During an Earthquake Part II: Continuous Tangential Displacements

— This paper regards the on-fault displacement field generated by an earthquake on its own fault plane, with special attention to the tangential displacement vector. It is the continuation and the completion of a previous paper (Armigliato et al., 2003) concerning the analysis of the normal on-fault displacement component. It is here recognised that in addition to the discontinuous shear displacement, which is the main contribution to the seismic dislocation on the fault, there is a tangential displacement contribution that is continuous across the fault. The continuous tangential displacement is exclusively produced by the presence of the free earth's surface. The tangential displacement vector has non-vanishing components in both directions, parallel as well as perpendicular to the imposed uniform shear slip, the first being predominant on the second. We perform a set of computations aimed at evaluating the dependence of the tangential displacement magnitude on the relevant fault parameters for basic cases of rectangular faults embedded in a homogeneous half-space.