Numerical modeling of block structure dynamics: dependence of a synthetic earthquake flow on the structure separateness and boundary movements

A seismically active region is modelled as a system of absolutely rigid blocks separated by infinitely thin plane faults. The interaction of the blocks along the fault planes and with the underlying medium is viscous-elastic. The system of blocks moves as a consequence of prescribed motion of the boundary blocks and of the underlying medium. When for some part of a fault plane the ratio of the stress to the pressure exceeds a certain strength level a stress-drop (a failure) occurs (in accordance with the dry friction model), and it can cause a failure in other parts of the fault planes. In the model the failures represent earthquakes. As a result of the numerical simulation a synthetic earthquake catalog is produced. The numerical modelling was carried out for three types of structures with increasing of the structure separateness inside of each type and for two types of boundary movements. A synthetic earthquake flow is characterised by several features including the frequency-magnitude relation (the Gutenberg-Richter curve). When the structure separateness increases the slope of the curve changes monotonously in the same direction for all considered types of structures if the boundary movement is the same. The directions of changing of the slope are opposite for two considered boundary movements.     

Modeling the dynamics of the block structure and seismicity of the Caucasus

Based on the morphostructural zoning scheme of the Caucasus, the block structure reflecting the real fault geometry and the block formation of the region is constructed. Several dozens of numerical experiments are conducted for simulating the dynamics of the block structure and the arising seismicity. The modeling relies on the following principles. It is assumed that the structure is composed of perfectly rigid blocks separated by infinitely thin fault planes. On the fault planes and on the blocks' bottoms, the blocks viscoelastically interact with each other and with the underlying medium. At each time instant, the translational displacements and rotations of the blocks are calculated from the condition of the quasi-static equilibrium of the entire block structure. The earthquakes occur in accordance with the dry friction model at the time instants when within a certain segment of the fault the stress-to-pressure ratio exceeds the given threshold. The modeling yields the synthetic catalog of the Caucasian earthquakes the spatial distribution of which reflects a set of characteristic features of the real seismicity. The similarity is observed in the magnitude–frequency diagrams of the synthetic and real seismicity. The comparison of the positions of the epicenters of the strong synthetic earthquakes with the results of recognizing the highly seismically active areas in the Caucasus demonstrates the presence of such epicenters in a few highly active areas where, according to the observations, strong earthquakes have not occurred to date.     

由地震分布丛集性给出断层参数的一种新方法

由于大范围内地质构造的复杂性和介质的非均匀性,发震断层面的几何形态一般十分复杂.如果大地震的破裂过程涉及多个断层的活动,则发震断层并非是单一断层平面,而是多个断层面的组合.利用地震空间位置分布丛集性,即震源点成丛位于断层面附近的假设,结合稳健扩充算法和主成分分析给出一种可以重构活断层网络三维空间结构的新方法.该方法每次从震源点集中处开始,利用假设检验扩充子断层面,并得到多个子断层面.接着按震源点属于最近断层面的准则把各子断层面内的震源点进行竞争,并根据一定假设合并和删除一些子断层面,最后用主成分分析确定每个子断层面参数.于是可根据地震事件目录给出一组矩形区域来描述断层面网络结构,其中每个矩形断层面由其位置、走向和倾角确定.通过计算机模拟发现,新方法可成功地重建模拟地震目录的断层面,最后用于南加州1992年6月28日发生的Landers地震部分余震目录中,得到各个子断层面参数与已知地质破裂或隐伏断层相当一致.     

Modelling of Block-structure Dynamics: Parametric Study for Vrancea

—The dependence of synthetic earthquake catalog obtained by numerical modelling of block-structure dynamics for the Vrancea (Romania) seismoactive region on values of the model parameters is studied. The features of the synthetic seismicity, such as the spatial distribution of epicentres, the level of seismic activity, the relative activity of the different faults, are considered as functions of the directions of motions of the different blocks of the structure. The likelihood of the features of the synthetic and of the real seismicity could be used as criterion for the reconstruction of the direction of the tectonic motions.     

Simulation of Seismicity in the Block-structure Model of Italy and its Surroundings

The numerical block-model of the lithosphere dynamics is used to simulate seismicity in Italy and its surroundings, based on the available structural and geodynamics information. The purpose of the study is to understand which are the tectonic processes that control the main features of the observed seismicity and the kinematics of the region. The influence of the rheology of the fault systems is studied as well. The model we use differs from other modeling approaches in that it simulates earthquakes and hence it possibly relates to seismicity and geodynamics. The model provides an effective capability to include the set of documented constraints supplied by widely available earthquake catalogs. This is done by means of the comparison of the GR relation, of the focal mechanisms and of the space distribution for observed and computed seismicity. The region is modeled as a system of perfectly rigid blocks, separated by infinitely thin fault planes, in viscoelastic interaction between themselves and with the underlying medium. The movement of the boundary blocks and of the underlying medium determines the motion of the blocks. The synthetic seismicity obtained with the defined block-model is similar to the observed one for the most seismically active areas. A linear frequency-magnitude (FM) relation (Gutenberg-Richter law) is obtained for synthetic earthquakes; the slope (b-value) of the FM plot appears larger for the synthetic seismicity than for the observed one. Nevertheless, the b-value is essentially larger in northern and central Italy than that in southern Italy, both in the model and in the observations. The analysis of the source mechanisms of the synthetic earthquakes shows a good agreement with the observations. In the model normal faulting is typical for the Apennines, the eastern edge of Sicily and the Calabrian arc, while reverse faulting takes place at the northwestern boundary of the Adriatic Sea, in the southern Alps and along the eastern edge of the Adria, along the Dinarides. The model correctly reproduces the extension zone along the Apennines and the contraction zone along the northwestern boundary of the Adriatic Sea; the counter-clockwise rotation of the Adria is mimed. The resulting movements of the blocks are in overall agreement with GPS (Global Positioning System) observations. The results of the modeling experiments suggest that the main features of dynamics and seismicity in the central Mediterranean region cannot be satisfactorily explained as a consequence of Africa and Eurasia convergence only; the passive subduction in the Calabrian arc and the different rheology of faults are essential as well.     

Aftershock sequence simulations using synthetic earthquakes and rate-state seismicity formulation

We use an efficient earthquake simulator that incorporates rate-state constitutive properties and uses boundary element method to discretize the fault surfaces, to generate the synthetic earthquakes in the fault system. Rate-and-state seismicity equation is subsequently employed to calculate the seismicity rate in a region of interest using the Coulomb stress transfer from the main shocks in the fault system. The Coulomb stress transfer is obtained by resolving the induced stresses due to the fault patch slips onto the optimal-oriented fault planes. The example results show that immediately after a main shock the aftershocks are concentrated in the vicinity of the rupture area due to positive stress transfers and then disperse away into the surrounding region toward the background rate distribution. The number of aftershocks near the rupture region is found to decay with time as Omori aftershock decay law predicts. The example results demonstrate that the rate-and-state fault system earthquake simulator and the seismicity equations based on the rate-state friction nucleation of earthquake are well posited to characterize the aftershock distribution in regional assessments of earthquake probabilities.     

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.     

Preliminary analysis of earthquake probability based on the synthetic seismic catalog

The analysis of seismic hazards relies on the statistical analysis of historical seismic data and the instrumental seismic catalog to obtain the regional earthquake recurrence interval and earthquake probability. The accuracy of analysis thus depends strongly on the completeness of the seismic data used. However, available seismic catalogs are too short or incomplete for the reliable analysis of the statistical characteristics of earthquakes. If a long-term synthetic seismic catalog can be generated using a physics-based numerical simulation, and the simulation results match the crustal deformation, seismicity, and other observations,then such a synthetic catalog helps us to further understand the characteristics of seismic activity and analyze the regional seismic hazard. In this paper, taking the northeastern Tibetan Plateau as a case study, we establish a three-dimensional visco-elastoplastic finite-element model to simulate earthquake cycles and the spatiotemporal evolution of earthquakes on the model fault system and obtain a seismic catalog on a time scale of tens of thousands of years. On the basis that the model satisfies the regional geodynamics of the northeastern Tibetan Plateau, we analyze seismicity on the northeastern Tibetan Plateau using the simulated synthetic earthquake catalog. The characteristics of earthquake recurrence at different locations and different magnitudes, and the long-term average probability of earthquake occurrence within the fault system on the northeastern Tibetan plateau are studied. The results are a reference for regional seismic hazard assessment and provide a basis for the physics-based numerical prediction of earthquakes.     

用滑动方向拟合法反演唐山余震区的平均应力场

将每个震源机制解的两个节面交替取作尝试的断层面,使计算的断层面上的剪切力方向与观测的断层面的滑动方向夹角最小,从而根据29个震源机制解结果反演了唐山余震区三个分区的平均主应力方向和中等主应力相对大小。本文结果说明,唐山余震区的最大主应力轴水平,取近东西方向,较之1976年唐山大震前的方向可能水平地顺时针转动了大约30。对同样地区用平均P,B,T轴推断主应力方向的结果与用上述方法所得结果基本一致。所作的数值试验说明,在特定情况下,用平均P,B,T轴推断构造应力主轴方向时有可能出现系统偏差。      

Application of fuzzy clustering method to determining sub-fault planes of earthquake from aftershocks sequence

Earthquake rupture process generally involves several faults activities instead of a single fault. A new method using both fuzzy clustering and principal component analysis makes it possible to reconstruct three dimensional structure of involved faults in earthquake if the aftershocks around the active fault planes distribute uniformly. When seismic events are given, the optimal faults structures can be determined by our new method. Each of sub-fault planes is fully characterized by its central location, length, width, strike and dip. The resolution determines the number of fault segments needed to describe the earthquake catalog. The higher the resolution, the finer the structure of the reconstructed fault segments. The new method successfully reconstructs the fault segments using synthetic earthquake catalogs. By taking the 28 June 1992 Landers earthquake occured in southern California as an example, the reconstructed fault segments are consistent with the faults already known on geological maps or blind faults that appeared quite frequently in longer-term catalogs.     

由余震分布确定大地震子断层及其参数的模糊聚类方法

大地震的破裂过程一般涉及多个断层的活动, 发震断层并非是单一断层平面, 而是由多个断层平面组合而成． 利用成丛小震发生在断层面附近的原则, 假定震源点围绕子断层面中心服从三维正态分布, 使用GK模糊聚类方法结合主成分分析给出了一种可以重构活动断层网络三维空间结构的新方法.该方法首先对全部震源点目录使用GK模糊聚类方法得到它的划分矩阵, 再利用划分矩阵及合适的阈值, 剔除离群震源点, 提取出平面型分布的子类, 最后对每个子类在三维正态分布的假设下确定断层面分布的95%置信矩形断层区域位置、 走向角和倾向角参数.当给定地震目录事件后, 可以给出符合假设的一系列最优断层面区域, 每个子断层由它的中心位置、 长度、 宽度、 走向角和倾角所刻画.为检验新方法的性能, 先进行计算机仿真, 结果显示算法可成功地重建模拟地震目录的断层部分.最后将新方法用于南加州兰德斯(Landers)地震部分余震精确定位数据中, 得到的重建结果与已知的研究结果比较吻合, 说明了新方法的有效性.      

Focusing patterns of seismicity with relocation and collapsing

Seismicity is generally concentrated on faults or in fault zones of varying, sometimes complex geometry. An earthquake catalog, compiled over time, contains useful information about this geometry, which can help understanding the tectonics of a region. Interpreting the geometrical distribution of events in a catalog is often complicated by the diffuseness of the earthquake locations. Here, we explore a number of strategies to reduce this diffuseness and hence simplify the seismicity pattern of an earthquake catalog. These strategies utilize information about event locations contained in their overall catalog distribution. They apply this distribution as an a priori constraint on relocations of the events, or as an attractor for each individual event in a collapsing scheme, and thereby focus the locations. The latter strategy is not a relocation strategy in a strict sense, although event foci are moved, because the movements are not driven by data misfit. Both strategies simplify the seismicity pattern of the catalog and may help to interpret it. A synthetic example and a real-data example from an aftershock sequence in south west Iceland are presented to demonstrate application of the strategies. Entropy is used to quantify their effect.     

汶川8.0级地震前地震空间相关长度变化特征

分析了汶川8.0级地震前的地震空间长度的时空演变。在计算空间相关长度过程中采用长轴与孕震区主要断裂走向一致的椭圆型空间窗,并设计了优化程序。在本次特大地震前观测到了增长的地震空间相关长度。利用合成地震目录对结果进行了显著性检验,结果否定了零假设,表明观察到的模型不是由随机数据干扰造成的,这一观点的置信水平被证实为93.9%。     

Fault plane parameters of Sanhe-Pinggu M8 earthquake in 1679 determined using present-day small earthquakes

The great Sanhe-Pinggu M8 earthquake occurred in 1679 was the largest surface rupture event recorded in history in the northern part of North China plain. This study determines the fault geometry of this earthquake by inverting seismological data of present-day moderate-small earthquakes in the focal area. We relocated those earthquakes with the double-difference method. Based on the assumption that clustered small earthquakes often occur in the vicinity of fault plane of large earthquake, and referring to the morphology of the long axis of the isoseismal line obtained by the predecessors, we selected a strip-shaped zone from the relocated earthquake catalog in the period from 1980 to 2009 to invert fault plane parameters of this earthquake. The inversion results are as follows: the strike is 38.23°, the dip angle is 82.54°, the slip angle is -156.08°, the fault length is about 80 km, the lower-boundary depth is about 23 km and the buried depth of upper boundary is about 3 km. This shows that the seismogenic fault is a NNE-trending normal dip-slip fault, southeast wall downward and northwest wall uplift, with the right-lateral strike-slip component. Moreover, the surface rupture zone, intensity distribution of the earthquake and seismic-wave velocity profile in the focal area all verified our study result.     

2022年1月8日青海门源MS6.9地震序列重定位和震源机制解研究

2022年1月8日青海省海北州门源县发生M_S6.9地震,震后产生了长约22 km的地表破裂带,青海、甘肃和宁夏等多地震感强烈。本文基于区域地震台网资料,通过多阶段定位方法对门源M_S6.9地震早期序列（2022年1月8日至12日）进行了重定位,并利用gCAP方法反演了主震和M_S≥3.4余震的震源机制和震源矩心深度,计算了现今应力场体系在门源M_S6.9地震震源机制两个节面产生的相对剪应力和正应力。结果表明:门源M_S6.9地震的初始破裂深度为7.8 km,震源矩心深度为4 km,地震序列的优势初始破裂深度主要介于7—8 km之间,而M_S≥3.4余震的震源矩心深度为3—7 km;该地震序列的震源深度剖面显示震后24个小时内的地震序列长度约为25 km,与地表破裂带的长度大体一致,整体地震序列长度约为30 km,其中1月8日M_S6.9主震和M_S5.1余震位于余震区西段,1月12日M_S5.2余震位于余震区东段。2022年1月8日门源M_S6.9主震的震源机制解节面Ⅰ为走向290°、倾角81°、滑动角16°,节面Ⅱ为走向197°、倾角74°、滑动角171°,根据余震展布的总体趋势估计断层面走向为290°,表明此次地震为近乎直立断层面上的一次左旋走滑型事件;M_S≥3.4余震的震源机制解显示这些地震主要为走滑型地震,P轴走向从余震区西段到东段之间大体呈现NE向到EW向的变化。现今应力场体系在门源M_S6.9主震震源机制解节面Ⅰ上产生的相对剪应力为0.638,而在节面Ⅱ上的相对剪应力为0.522,表明这两个节面均非构造应力场的最大释放节面,这与2016年门源M_S6.4地震逆冲型震源机制为构造应力场的最优释放节面有着明显差异。结合地质构造、震源机制和余震展布,2022年1月8日门源M_S6.9主震的发震构造可能为冷龙岭断裂西段,其地震断层错动方式为左旋走滑。根据重定位结果、震级-破裂关系以及剪应力结果,本文认为门源地区存在一定的应力积累且应力未得到充分释放,该地区仍存在发生强震的危险。      

Numerical Simulation of Displacement and Stress Fields Associated with the 1993 Kushiro-oki, Japan, Earthquake

—We constructed a three-dimensional finite element model to simulate coseismic and postseismic displacement and stress fields associated with the 1993 Kushiro-oki earthquake, which was a very large intermediate-depth earthquake that occurred within the subducted Pacific plate at a depth of 107 km beneath the southeastern part of Hokkaido, Japan. Taking the configuration of the subducted Pacific plate into account, we constructed a realistic model with lateral heterogeneity of viscoelastic structure. We assigned a variable slip distribution to the fault plane, which was obtained from inversion analysis of near-field seismic waveforms. The result shows that elastic deformation associated with the faulting reflects the assigned inhomogeneous slip distribution on the fault plane near the fault region, while it does not reflect the distribution on the free surface of the model. The calculated postseismic deformation does not reflect the slip distribution, but shows symmetric spatial patterns concerning the dipping direction of the fault both near the fault region and on the model surface. For the next 20 years following the earthquake, the amount of the calculated deformation is a fraction of the coseismic deformation. The calculated coeseismic deformation is large just above and below the fault plane, reaching 1 m, while the postseismic deformation is dominant near the upper and lower material boundaries between the subducted plate and the surrounding asthenosphere. The spatial distribution of maximum shear stress near the fault plane corresponds to the assigned slip distribution, amounting to 32 MPa. The directions of principal stress-change axes represent reverse fault type in the SSE region of the fault, whereas normal fault type is dominant in the NNW region with the exception of some asymmetrical spatial patterns of the principal stress-change axes on the fault due to the inhomogeneous slip distribution. Time variations both in the amount and the directions of stresses are minor, suggesting that the coseismic state of the stress would remain unchanged for two decades after the event.     

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。     

Application of mechanical and statistical models to the study of seismicity of synthetic earthquakes and the prediction of natural ones

Based on a cellular automata model, which obeys rules produced by a spring-damper-slider model of fault network, a synthetic earthquake catalog of deterministic chaos can be produced. It is a challenge to inverse the model parameters and predict the synthetic earthquakes from the synthetic catalog. We apply an improved statistical model of coupled stress release to the synthetic catalog, it does successfully inverse the stress evolution of the system, but effectively prediction of the earthquakes from the stresses remains a problem. This research is partially supported by the Chinese Joint Seismological Science Foundation and Asian 2000 Foundation of New Zealand.     

A physics-based earthquake simulator and its application to seismic hazard assessment in Calabria (Southern Italy) region

The use of a newly developed earthquake simulator has allowed the production of catalogs lasting 100 kyr and containing more than 100,000 events of magnitudes ≥4.5. The model of the fault system upon which we applied the simulator code was obtained from the DISS 3.2.0 database, selecting all the faults that are recognized on the Calabria region, for a total of 22 fault segments. The application of our simulation algorithm provides typical features in time, space and magnitude behavior of the seismicity, which can be compared with those of the real observations. The results of the physics-based simulator algorithm were compared with those obtained by an alternative method using a slip-rate balanced technique. Finally, as an example of a possible use of synthetic catalogs, an attenuation law has been applied to all the events reported in the synthetic catalog for the production of maps showing the exceedance probability of given values of PGA on the territory under investigation.     

汶川小断裂带地震机理与监测建议

龙门山断裂带全长约560 km,宽30~50 km,面积约20 000 km2,深度在40 km左右,本文将其定义为小断裂带,它是由3条主干断裂和若干个狭小断裂块体组成的小规模断裂带群。单个块体具有刚体特征,其内部缝隙、孔隙可以忽略,在挤压剪切破碎时将其假设为剪切面,块体剪切破碎或者块体间错位滑动,从而引发地震。当应力释放时,整体表现为下沉稳定,同时,与其邻近大块体接触面因卸荷而出现上、下、左、右相对滑动,从而引发余震。本文针对龙门山小断裂带卸荷前后各块体运动特征,提出监测建议。