Complex Earthquake Cycle Simulations Using a Two-Degree-of-Freedom Spring-Block Model with a Rate- and State-Friction Law

Numerical simulations of complex earthquake cycles are conducted using a two-degree-of-freedom spring-block model with a rate- and state-friction law, which has been supported by laboratory experiments. The model consisted of two blocks coupled to each other and connected by elastic springs to a constant-velocity, moving driver. By widely and systematically varying the model parameters, various slip patterns were obtained, including the periodic recurrence of seismic and aseismic slip events, and several types of chaotic behaviour. The transition in the slip pattern from periodic to chaotic is examined using bifurcation diagrams. The model system exhibits typical period-doubling sequences for some parameter ranges, and attains chaotic motion. Simple relationships are found in iteration maps of the recurrence intervals of simulated earthquakes, suggesting that the simulated slip behaviour is deterministic chaos. Time evolutions of the cumulative slip distance in chaotic slip patterns are well approximated by a time-predictable model. In some cases, both seismic and aseismic slip events occur at a block, and aseismic slip events complicate the earthquake recurrence patterns.     

断裂分段之间不同相互作用对断裂运动的影响

采用速度和状态摩擦本构控制的一维弹簧滑块模型研究断裂分段间相互作用对运动特征的影响,为研究东昆仑活动断裂带库赛湖段和西大滩段2个断裂分段之间的相互影响,采用由弹簧相连的2个滑块模拟断裂分段,通过弹簧滑块系统的动力学分析,将断裂运动性质的描述归结为一组微分方程,数值求解该微分方程组,最终得到断裂运动性质的参数,从而达到确定断裂未来强震复发周期的目的。通过位错模型计算、借鉴前人研究成果以及古地震资料确定模型相关参数。研究断裂分段在不同相互作用下的强震复发周期,模拟表明断裂间不同相互作用对地震复发周期和地震时断裂错动位移的大小没有规律性的影响;只是对地震发生时断裂错动的速度有明显的影响,作用强时,地震发生时断裂错动速度大;反之,地震发生时断裂错动速度小。     

Bounding of near-fault ground motion based on radiated seismic energy with a consideration of fault frictional mechanisms

The energy radiated as seismic waves strongly depends on the fault rupture process associated with rupture speed and dynamic frictional mechanisms involved in the fault slip motion.Following McGarr and Fletcher approach,we derived a physics-based relationship of the weighted average fault slip velocity vs apparent stress,rupture speed and static stress drop based on a dynamic circular fault model.The resultant function can be approximately used to bound near-fault ground motion and seismic energy associated with near-fault coseismic deformation.Fault frictional overshoot and undershoot mechanisms governed by a simple slip-weakening constitutive relation are included in our consideration by using dynamic rupture models named as M-and D-models and proposed by Madariaga(1976) and Boatwright.We applied the above function to the 2008 great Wenchuan earthquake and the 1999 Jiji(Chi-Chi) earthquake to infer the near-fault ground motion called slip weighted average particle velocity and obtained that such model-dependent prediction of weighted average ground velocities is consistent to the results derived from the near-fault strong motion observations.Moreover,we compared our results with the results by McGarr and Fletcher approach,and we found that the values of the weighted average particle velocities we obtained for these two earthquakes are generally smaller and closer to the values by direct integration of strong motion recordings of the near-fault particle velocity waveform data.In other words,if this result comes to be true,it would be a straightforward way used to constrain the near-fault ground motion or to estimate source parameters such as rupture speed,static and dynamic stress drops.     

基于速率-状态摩擦定律的地震二维准动力学数值模拟:浅层正应力变化对断层演化的影响

本文基于结合速率-状态摩擦定律（RSF）的二维准动力学数值模型,以半空间垂直走滑断层为研究对象,通过比较两种正应力随深度变化模型的模拟结果,研究了浅层正应力变化对断层演化参数、地震孕育过程、震后滑移传播等方面的影响.结果显示,我们的数值模型在给定模型参数和约束条件下,能够完整模拟出地震周期中震间、震前、同震以及震后多个特征阶段.常数正应力模型下,动态破裂在浅层速率强化区停止,而在浅层变化正应力模型下动态破裂可以传播至自由表面,导致浅层更高的最大滑移速率和同震滑移量.两种模型下的地震矩、地震周期、平均应力降和震后滑移传播等差别不明显.两种滑移模型的傅氏振幅谱与理论K^-2模型傅氏振幅谱均符合较好,且浅层变化正应力模型下的拐角波数值高于常数正应力模型,说明两种模型均符合地震同震滑移模型的运动学特征,并且浅层变化正应力模型下最终应该产生高于常数正应力模型的高频强地面运动水平.我们认为选用不同的模型参数对最终结果存在显著影响,应当根据具体问题来选择模型参数,这样才能在保证结果准确前提下有效提高计算效率.     

Stochastic earthquake source model for ground motion simulation

In the analysis and design of important structures with relatively long life spans, there is a need to generate strong motion data for possible large events. The source of an earthquake is characterized by the spatial distribution of slip on the fault plane. For future events, this is unknown. In this paper, a stochastic earthquake source model is developed to address this issue. Here, 1D and 2D stochastic models for slip distribution developed by Lavallée et al.(2006) are used. The random field associated with the slip distribution is heavy-tailed stable distribution which can be used for large events. Using 236 past rupture models, the spectral scaling parameter and the four stable or Levy's parameters against empirical relationship for known quantities like magnitude or fault length are developed. The model is validated with data from 411 stations of 1999 Chi-Chi earthquake. The simulated response spectrum showed good agreement to actual data. Further the proposed model is used to generate ground motion for the 1993 Killari Earthquake where strong motion data is not available. The simulated mean peak ground velocity was in turn related to the intensity(MSK) and compared against values in the literature.     

2013年7月22日甘肃岷县-漳县M_S6.6地震震源破裂过程

2013年7月22日,在甘肃岷县漳县交界处发生MS6.6地震,地震震中位置靠近临潭—宕昌断裂.本文通过构建有限断层模型,利用国家强震动台网中心提供的12条强地面运动三分量资料,通过波形反演方法来研究这次地震的震源破裂过程.结果显示这次地震是发生在甘东南地区岷县—宕昌断裂带东段附近的一次MW6.1级逆冲兼具左旋走滑破裂事件,最大滑动量约为80cm.发震断层走向及滑动性质与岷县—宕昌断裂吻合,推断本次地震与东昆仑断裂向北的扩展和推挤密切相关,是岷县—宕昌断裂进一步活动的结果.     

昆仑山口西MＳ＝8．1级地震的形变应变场研究

根据昆仑山口西8．1级地震前后GPS测点的位移速率，用弹性模型公式计算了地壳应变参数．应变参量的变化表明，震前在地震区附近以压应变为主，应变速率较大．位移速率矢量显示出震前的震中地区相对周围为活动性较弱的“稳定”地区．地壳的形变和应变揭示出孕震体在挤压状态下积累了较高的应变势能．8．1级地震的同时期由于地壳释放了巨大的应变能而应变速率变化显著．计算结果表明，地震所产生的应变达到4．5×10-6以上．发震断裂带的平均左旋走滑量是3．31m（89°E～96°E）．     

近场强地震动数值模拟的简化计算方法

近场强地震动除受场地条件的影响外,还受到震源破裂面上子源的空间分布特点、子源破裂先后顺序的强烈控制,基于数值格林函数法的近场强地震动数值模拟方法可以综合考虑震源、传播途径及局部场地条件的影响,对计算过程进行合理简化,分2步完成地震动模拟:第1步,在介质均匀区采用矩张量的解析解计算所有子源在盖层底面的位移,形成下一步有限元计算的输入场;第2步,在盖层介质不均匀区,结合局部人工透射边界技术,采用时、空解耦的波动显式有限元方法计算地表强地震动。在有限断层模型中,采用具有9个力偶的等效地震矩张量表达断层产状、滑动方向等的影响,采用Brune模型定义各子源的滑动时间函数,描述滑动的时、空不均匀分布特征,从而细化震源模型。通过对Northridge地震中4个基岩台站地表地震动的模拟结果和强震记录,验证了此简化计算方法的可行性     

Dynamic Rupture in a 3-D Particle-based Simulation of a Rough Planar Fault

An appreciation of the physical mechanisms which cause observed seismicity complexity is fundamental to the understanding of the temporal behaviour of faults and single slip events. Numerical simulation of fault slip can provide insights into fault processes by allowing exploration of parameter spaces which influence microscopic and macroscopic physics of processes which may lead towards an answer to those questions. Particle-based models such as the Lattice Solid Model have been used previously for the simulation of stick-slip dynamics of faults, although mainly in two dimensions. Recent increases in the power of computers and the ability to use the power of parallel computer systems have made it possible to extend particle-based fault simulations to three dimensions. In this paper a particle-based numerical model of a rough planar fault embedded between two elastic blocks in three dimensions is presented. A very simple friction law without any rate dependency and no spatial heterogeneity in the intrinsic coefficient of friction is used in the model. To simulate earthquake dynamics the model is sheared in a direction parallel to the fault plane with a constant velocity at the driving edges. Spontaneous slip occurs on the fault when the shear stress is large enough to overcome the frictional forces on the fault. Slip events with a wide range of event sizes are observed. Investigation of the temporal evolution and spatial distribution of slip during each event shows a high degree of variability between the events. In some of the larger events highly complex slip patterns are observed.     

基于Kelvin-Voigt黏弹性骨架的含非饱和流体孔隙介质BISQ模型(英文)

本文综合考虑了在波传播过程中孔隙介质的三种重要力学机制——"Biot流动机制一squirt流动机制-固体骨架黏弹性机制",借鉴等效介质思想,将含水饱和度引入波动力学控制方程,并考虑了不同波频率下孔隙流体分布模式对其等效体积模量的影响,给出了能处理含粘滞性非饱和流体孔隙介质中波传播问题的黏弹性Biot/squirt(BISQ)模型。推导了时间-空间域的波动力学方程组,由一组平面谐波解假设,给出频率-波数域黏弹性BISQ模型的相速度和衰减系数表达式。基于数值算例分析了含水饱和度、渗透率与频率对纵波速度和衰减的影响,并结合致密砂岩和碳酸盐岩的实测数据,对非饱和情况下的储层纵波速度进行了外推,碳酸盐岩储层中纵波速度对含气饱和度的敏感性明显低于砂岩储层。     

2013年四川芦山MS7.0地震近断层强地面运动模拟及烈度分布估计

2013年4月20日在我国四川省发生了芦山M_S7.0地震,地震给当地群众的生命财产安全带来了巨大的损失,其中最严重的破坏发生在震中附近的芦山、宝兴等地区.根据地震发生的快速反演结果,及发震断层面上滑动位移的分布情况,构建有限断层模型,对近断层区域的强地面运动进行初步计算,并基于强地面运动的模拟结果给出震区烈度分布的初步估计.模拟结果显示：模拟烈度图显示极震区的烈度在IX级左右,VI级烈度影响范围大致为16000 km²,该结果与中国地震局于4月27日给出的震区实测烈度图一致程度较高.强烈地震发生后,基于近断层强地面运动模拟计算的结果,可以给出相对合理的地震烈度分布情况估计,对震区震情判定及救灾工作具备较高的现实意义.     

COSEISMIC DISPLACEMENT FIELD OF THE WENCHUAN EARTHQUAKE DERIVED FROM STRONG MOTION RECORDS AND APPLICATION IN SLIP INVERSION

The development of high-rate GNSS seismology and seismic observation methods has provided technical support for acquiring the near-field real-time displacement time series during earthquake. But in practice, the limited number of GNSS continuous stations hardly meets the requirement of near-field quasi-real-time coseismic displacement observation, while the macroseismographs could be an important complement. Compared with high-rate GNSS, macroseismograph has better sensitivity, higher resolution(100~200Hz)and larger dynamic range, and the most importantly, lower cost. However, baseline drift exists in strong-motion data, which limits its widespread use. This paper aims to prove the feasibility and reliability of strong motion data in acquiring seismic displacement sequences, as a supplement to high-rate GNSS. In this study, we have analyzed the strong-motion data of Wenchuan M_S8.0 earthquake in Longmenshan fault zone, based on the automatic scheme for empirical baseline correction proposed by Wang et al., which fits the uncorrected displacement by polynomial to obtain the fitting parameters, and then the baseline correction is completed in the velocity sequence. Through correction processing and quadratic integration, the static coseismic displacement field and displacement time series are obtained. Comparison of the displacement time series from the strong motions with the result of high-rate GPS shows a good coincidence. We have worked out the coseismic displacement field in the large area of Wenchuan earthquake using GPS data and strong motion data. The coseismic displacement fields calculated from GPS and strong motions are consistent with each other in terms of magnitude, direction and distribution patterns. High-precision coseismic deformation can provide better data constraint for fault slip inversion. To verify the influence of strong-motion data on slip distribution in Wenchuan earthquake, we used strong motion, GPS and InSAR data to estimate the stress drop, moment magnitude and coseismic slip model, and our results agreed with those of the previous studies. In addition, the inversion results of different data are different and complementary to some extent. The use of strong-motion data supplements the slip of the fault in the 180km segment and the 270~300km segment, thus making the inversion results of fault slip more comprehensive. From this result, we can draw the following conclusions:1)Based on the robust baseline correction method, the use of strong motion data, as an important complement to high-rate GNSS, can obtain reliable surface displacement after the earthquake. 2)The strong motion data provide an effective method to study the coseismic displacement sequence, the surface rupture process and quick seismogenic parameters acquisition. 3)The combination of multiple data can significantly improve the data coverage and give play to the advantages of different data. Therefore, it is suggested to combine multiple data(GPS, strong motion, InSAR, etc.)for joint inversion to improve the stability of fault slip model.     

远场地震波辐射能计算以及对近断层地面运动的约束

从圆盘断层模型出发,根据地震波能量表象定理推导出了滑移弱化过程中远场S-波辐射能量表达式,并同已有的动力学模型作了比较.结果表明,得到的模型能量值或视应力的取值强烈地依赖于断层上的动态、静态应力降和破裂传播速度,而破裂速度则对应了断层带模型中断层破坏过程所耗散的能量.动摩擦应力上调和应力下调力学机制在能量求解中得到了充...     

Earthquake ground motion modeling of induced seismicity in the Groningen gas field

A physics‐based numerical approach is used to characterize earthquake ground motion due to induced seismicity in the Groningen gas field and to improve empirical ground motion models for seismic hazard and risk assessment. To this end, a large‐scale (20 km × 20 km) heterogeneous 3D seismic wave propagation model for the Groningen area is constructed, based on the significant bulk of available geological, geophysical, geotechnical, and seismological data. Results of physics‐based numerical simulations are validated against the ground motion recordings of the January 8, 2018, M_L 3.4 Zeerijp earthquake. Taking advantage of suitable models of slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found to reproduce accurately the observed features of ground motions at epicentral distances less than 10 km, in a broad frequency range, up to about 8 Hz. A sensitivity analysis is also addressed to discuss the impact of 3D underground geological features, the stochastic variability of seismic velocities and the frequency dependence of the quality factor. Amongst others, results point out some key features related to 3D seismic wave propagation, such as the magnitude and distance dependence of site amplification functions, that may be relevant to the improvement of the empirical models for earthquake ground motion prediction.     

A compact representation of spatio-temporal slip distribution on a rupturing fault

We propose a mathematical representation to qualitatively describe the spatio-temporal slip evolution during earthquake rupture in an efficient and easy-to-use manner for numerical simulations of strong ground motion. It is based on three basis functions and associated expansion coefficients. It is an extension of the approach of Ide and Takeo, (J Geophys Res, 102:27379–27391, 1997). We compare our approach and theirs using simple kinematic source models to illustrate differences between the two approaches, and show that our approach more accurately represents the spatio-temporal slip evolution. We also propose a technique based on our representation for extracting a spatio-temporal slip velocity function from a kinematic source model obtained by the conventional source inversion. We then demonstrate the feasibility of our procedure with application to an inverted source model of the 26 March 1997 Northwestern Kagoshima, Japan, earthquake (M _W6.1). In the simulations for actual earthquakes, source models obtained from kinematic source inversions are commonly employed. Our scheme could be used as an interpolation method of slip time functions from relatively coarse finite-source models obtained by conventional kinematic source inversions.     

中国及邻区现代地块运动的数值模拟

本文利用板块几何学的方法研究中国及邻区地块间的相对运动,用数值方法计算了地块运动的角速度及边界断层的滑动速率。计算结果与活断层数据相当吻合,本文还利用地块运动速度讨论了我国现代构造活动     

Interplate Earthquake Fault Slip During Periodic Earthquake Cycles in a Viscoelastic Medium at a Subduction Zone

--A 2-D finite-element-method (FEM) numerical experiment of earthquake cycles at a subduction zone is performed to investigate the effect of viscoelasticity of the earth on great interplate earthquake fault slip. We construct a 2-D viscoelastic FEM model of northeast Japan, which consists of an elastic upper crust and a viscoelastic mantle wedge under gravitation overlying the subducting elastic Pacific plate. Instead of the dislocation model prescribing an amount of slip on a plate interface, we define an earthquake cycle, in which the plate interface down to a depth is locked during an interseismic period and unlocked during coseismic and postseismic periods by changing the friction on the boundary with the master-slave method. This earthquake cycle with steady plate subduction is periodically repeated to calculate the resultant earthquake fault slip.¶As simulated in a previous study (Wang, 1995), the amount of fault slip at the first earthquake cycle is smaller than the total relative plate motion. This small amount of fault slip in the viscoelastic medium was considered to be one factor explaining the small seismic coupling observed at several subduction zones. Our simulation, however, shows that the fault slip grows with an increasing number of repeated earthquake cycles and reaches an amount comparable to the total relative plate motion after more than ten earthquake cycles. This new finding indicates that the viscoelasticity of the earth is not the main factor in explaining the observed small seismic coupling. In comparison with a simple one-degree-of-freedom experiment, we demonstrate that the increase of the fault slip occurs in the transient state from the relaxed initial state to the stressed equilibrium state due to the intermittent plate loading in a viscoelastic medium.     

Determination of Euler parameters of Philippine Sea plate and the inferences

Euler vectors of 12 plates, including Philippine Sea plate (PH), relative to a randomly fixed Pacific plate(PA) were determined by inverting the 1122 data from NUVEL-1 global plate motion model, earthquake slip vectors along Philippine Sea plate boundary, and GPS observed velocities. Euler vectors of Philippine Sea plate relative to adjacent plates are also gained. Our results are well consistent with observed data and can satisfy the geological and geophysical constraints along the Caroline(CR)-PH and PA-CR boundaries. Deformation of Philippine Sea plate is also discussed by using the plate motion Euler parameters.     

中国大陆及周边地区的水平应变场

推导并建立了块体的两种弹性运动方程：块体的整体旋转与均匀应变方程和块体的整体旋转与线性应变方程. 应用统计学原理,使用西域、青藏和华北块体上的GPS站速度数据,对这两种弹性运动方程与刚体运动方程模拟块体站速度的无偏性和有效性进行了统计检验. 检验结果表明,块体的整体旋转与线性应变方程是描述块体运动的最优模型. 将中国大陆划分为10个块体,应用块体的整体旋转与线性应变方程和块体上的GPS站速度估计了各个块体上的旋转与应变参数,按照1°×1°的间距计算了中国大陆及周边地区上1005个点的应变参数,分析了中国大陆及周边地区应变场的基本特征. 用本文方法得到的主压应变方向与地质学方法和测震学方法得到的主压应力轴方向具有很好的一致性(华南块体除外).     

Simulation of accelerograms from simplified deterministic approach for the 23rd October 2004 Niigata-ken Chuetsu,Japan earthquake

A simple hybrid approach for the simulation of strong ground motion is presented in this paper. This approach is based on the deterministic modelling of rupture plane initially started by Midorikawa, Tectonophysics 218:287–295, (1993) and further modified by Joshi, Pure Appl Geophys (PAGEOPH) 8:161, (2004). In this technique, the finite rupture plane of the target event is divided into several subfaults, which satisfy scaling relationship. In this paper, simulation of strong ground motion due to a rupture buried in a earth medium consisting of several layers of different velocities and thicknesses is made by considering (1) transmission of energy at each layer; (2) frequency filtering properties of medium and earthquake source; (3) correction factor for slip of large and small magnitude earthquakes and (4) site amplification ratio at various stations. To test the efficacy of the developed technique, strong motion records were simulated at different stations that have recorded the 2004 Niigata-ken Chuetsu, Japan earthquake (M _s 7.0). Comparison is made between the simulated and observed velocity and acceleration records and their response spectra. Distribution of peak ground acceleration, velocity and displacement surrounding the rupture plane is prepared from simulated and observed records and are compared with each other. The comparison of synthetic with the observed records over wide range of frequencies shows that the present technique is effective to predict various strong motion parameters from simple deterministic model which is based on simple regression relations and modelling parameters.