Meshing scheme in the computation of spontaneous fault rupture process

The choice of spatial grid size has been being a crucial issue in all kinds of numerical algorithms. By using BIEM (Boundary Integral Equation Method) to calculate the rupture process of a planar fault embedded in an isotropic and homogeneous full space with simple discretization scheme,this paper focuses on what grid size should be applied to control the error as well as maintaining the computing efficiency for different parameter combinations of (Dc,Te),where Dc is the critical slip-weakening dis-tance and Te is the initial stress on the fault plane. We have preliminarily found the way of properly choosing the spatial grid size,which is of great significance in the computation of seismic source rup-ture process with BIEM.     

计算断层自发破裂过程的离散网格划分研究

离散化网格的空间步长选取在各种数值算法中都是一个很受关注的问题,在全空间均匀介质模型和简单离散化方案下,利用边界积分方程方法研究在自发破裂求解过程中动力学参数组合Dc和Te (Dc为临界滑动弱化位移,Te为有效的断层破裂面上的初始应力)对计算网格划分的影响,初步得到了Dc和Te参数空间中的有效计算网格的选取规律,对合理、有效地运用边界积分方程方法计算地震震源的破裂过程具有重要的指导意义.      

基于边界积分方程方法的弯折断层破裂传播过程控制因素分析

本文利用边界积分方程方法,以基于三角形网格的全空间格林函数及离散积分核计算为基础,进行了最常见的弯折断层的破裂传播过程模拟.为了去除边界积分方程方法中格林函数计算存在的高度奇异性,研究采用分部积分等方法对动力学方程进行了重整化和离散化处理.地震力学过程可以被视为断层由静摩擦转为动摩擦的过程,对于震源破裂过程的动力学模拟,摩擦准则起着重要作用,本研究采用常用的滑动弱化摩擦准则.计算引入Courant-Friedrich-Lewy比值来表达场点的影响,并控制计算的收敛性和稳定性.通过与典型算例的比对,检验了方法的正确性和有效性.地震破裂能否穿越断层弯折部位继续传播是震源动力学研究的重要内容,基于此,本文建立了多种理论弯折断层模型,模拟了断层弯折对地震破裂传播的控制作用,并通过改变断层周边初始应力场、断层弯折角度大小以及滑动弱化距离大小等来分析各个因素对破裂传播的影响.模拟结果表明:断层面上初始破裂区域内外的应力越高,破裂越容易越过断层弯折部位继续传播;初始破裂区域半径越大,或滑动弱化距离越小,破裂也越容易发生,并越过弯折部位继续传播.同样的初始条件,断层弯折角度越大,断层弯折作为障碍体,对破裂传播的阻碍作用越显著.小的弯折角,其破裂传播过程与平面断层差别不明显,基本仍以椭圆方式对称向两侧传播.     

断层几何形态和自发破裂的动力学参数对地震波场的影响

断层的自发破裂及其产生的地震波场是地震学研究的重要内容.断层几何形态和自发破裂过程中的动力学参数不同,往往会导致不同的震源破裂过程,进而对地震波场产生显著的影响.本文基于不同几何形态的断层上的自发破裂过程,通过计算研究其产生的地震波场的特征.针对弯折和分叉的断层系统,我们考察了初始成核区位置以及超剪切破裂对于地震波场的影响.结果显示,对于弯折断层,随着弯折角的增大,地震波场的峰值分布沿着弯折方向产生变化,过大的弯折角会对地震波场起抑制作用;在断层上破裂距离越长,积累的能量越大,引起的地震波场峰值也越大.对于分叉断层,角度更小的分支面具有更大的破裂优势,破裂强度更大,会引起更大的地震波场峰值.超剪切破裂将使得地震波场振幅更大,激发高频成分,在波形上能观察到明显的脉冲,同时增大永久位移.通过研究动力学破裂产生的地震波场的行为,有助于增进对地震波场特征产生原因的认识,为进一步的动力学参数反演奠定了基础.

     

基于时间域半空间Green函数建立的边界积分方程及其在动态破裂模拟中的应用

研究地震断层的自发破裂传播可以为通过震源过程了解地球介质应力状态提供理论基础,有助于理解震源破裂的机理和规律,在震源动力学研究中具有重要的地位.边界积分方程方法是研究地震断层破裂传播问题的常用方法之一,在处理复杂断层系统方面具有优势.本文从半无限空间Green函数的时间域积分形式解出发,推导出离散化的边界积分方程积分核,并将其分别应用到平面断层和弯折断层两种断层模型的动力学破裂过程的模拟中.模拟结果表明,当破裂传播到自由表面处时,会产生反射震相,反射震相与直达震相的耦合效应会导致自由表面处的破裂传播速率明显加快,同时这种耦合效应也可以促进破裂在断层弯折部位的传播.对于断层有一定埋深的情况,自由表面对破裂过程的影响较小,因而自由表面的效应仅在断层直接与地表相交或者断层上沿距离地表很近时需要纳入考虑范围.本文将自由表面的影响加入到断层的自发破裂传播研究中,有助于更真实地了解复杂断层系统中的动力学破裂过程.

     

基于非结构化网格的边界积分方程方法的断层自发破裂模拟

地震自发破裂模拟是震源动力学研究的重要内容,了解复杂的断层动力学破裂过程对深入认识震源特征和解释运动学反演结果具有重要意义.基于边界积分方程方法的破裂模拟已经被广泛使用,大多采用的是平面断层模型的结构化网格划分.由于实际的断层往往具有较为复杂的几何特征,为了更为灵活地刻画断层几何复杂性,我们建立断层模型的三角形网格离散方案,通过精确的解析解形式来计算断层各个单元之间的应力格林函数,联立滑动弱化摩擦准则和非奇异边界积分方程,对断层的自发破裂过程进行了模拟.在简单的平面断层模型下,将计算结果与前人的结果进行了对比,验证了方法的正确性与有效性.对于几种常见的复杂断层模型,例如弯折、阶跃、含障碍体断层等,我们模拟了其破裂过程并对计算结果进行了比较与分析.模拟结果表明,非结构化网格划分的边界积分方程方法能够很好地模拟平面矩形断层或由其组成的规则断层,同时也能成功地模拟具有复杂几何形状的不规则断层上的动力学破裂过程.本研究的结果显示了边界积分方程方法在模拟复杂断层系统的动力学破裂问题上具有较广阔的应用前景.

     

Equivalent formulae of stress Green's functions for a constant slip rate on a triangular fault

We present an equivalent form of the expressions first obtained by Tada(Geophys J Int 164:653–669,2006. doi:10.1111/j.1365-246 X.2006.03868.x), which represents the transient stress response of an infinite, homogeneous and isotropic medium to a constant slip rate on a triangular fault that continues perpetually after the slip onset. Our results are simpler than Tada's, and the corresponding codes have a higher running speed.     

The discrete wave number formulation of boundary integral equations and boundary element methods: A review with applications to the simulation of seismic wave propagation in complex geological structures

We review the application of the discrete wave number method to problems of scattering of seismic waves formulated in terms of boundary integral equation and boundary element methods. The approach is based on the representation of the diffracting surfaces and interfaces of the medium by surface distributions of sources or by boundary source elements, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green's functions are evaluated by the discrete wave number method, and the boundary conditions yield a linear system of equations. The inversion of this system allows the calculation of the full wave field in the medium. We investigate the accuracy of the method and we present applications to the simulation of surface seismic surveys, to the diffraction of elastic waves by fractures, to regional crustal wave propagation and to topographic scattering.     

断层自发破裂传播的数值模拟:速率状态摩擦定律本构参数的影响

地震往往受控于滑动面的摩擦性质,这种摩擦性质可以由速率状态摩擦定律较好地描述.速率状态摩擦定律中的本构参数a和b与动态摩擦系数相关,从而影响着同震位移与剪切应力的时空演化.本文在前人工作的基础上,采用三维边界积分方程法模拟速率状态摩擦定律控制下均匀全空间中平面断层的自发破裂传播过程,并详细讨论了a和b对滑动速率、剪切应力和破裂传播速度的影响.数值结果表明a和b的不同取值将导致不同的破裂行为,b－a的值越大,断层越不稳定,这种不稳定性有利于裂纹的产生与扩展.但滑动速率的时空分布不只依赖b－a,而且还与a和b的具体取值有关,断层面上滑动速率峰值与剪切破裂强度均随着a的减小而增大,随着b的增大而增大.相关结果有助于加深对断层自发破裂传播的认识.     

Seismotectonics of the Median Tectonic Line in southwest Japan: Implications for coupling among major fault systems

The relationship between the slip activity and occurrence of historical earthquakes along the Median Tectonic Line (MTL), together with that of the fault systems extending eastward has been examined. The MTL is divided into three segments, each containing diagnostic active faults. No historical earthquakes have been recorded along the central segment, although the segment has faster Quaternary slip rates compared with the other segments that have generated historical earthquakes. This discrepancy between earthquake generation and slip rate can be explained by a microplate model of southwest Japan. The microplate model also provides spatial and temporal coupling of slip on adjacent fault systems. In the context of this model, slip on adjacent faults reduces the normal stress on the MTL. Historical data and paleoseismic evidence indicate that slip on this segment occurs without significant strong ground motion. We interpret this as indicating anomalously slow seismic slip or aseismic slip. Slip on the central segment of the MTL creates transpressional regions at the eastern and western segments where historical earthquakes were recorded. Alternatively, the earthquakes at the eastern and western segments were triggered and concentrated shear stress at the edge of the segments resulted in postseismic slip along the central segment. The sequence of historical events suggests that the MTL characteristically does not produce great earthquakes. The microplate model also provides a tectonic framework for coupling of events among the MTL, the adjacent fault systems and the Nankai trough.     

Effect of source parameters on forward-directivity velocity pulse for vertical strike slip fault in half space

It has been found that the large velocity pulse is one of the most important characteristics of near-fault strong ground motions. Some statistical relationships between pulse period and the moment magnitude for near-fault strong ground motions have been established by Somerville （1998）; Alavi and Krawinkler （2000）; and Mavroeidis and Papageorgiou （2003）, where no variety of rupture velocity, fault depth, and fault distance, etc. were considered. Since near-fault ground motions are significantly influenced by the rupture process and source parameters, the effects of some source parameters on the amplitude and the period ofa forward-directivity velocity pulse in a half space are analyzed by the finite difference method combined with the kinematic source model in this paper. The study shows that the rupture velocity, fault depth, position of the initial rupture point and distribution of asperities are the most important parameters to the velocity pulse. Generally, the pulse period decreases and the pulse amplitude increases as the rupture velocity increases for shallow crustal earthquakes. In a definite region besides the fault trace, the pulse period increases as the fault depth increases. For a uniform strike slip fault, rupture initiating from one end of a fault and propagating to the other always generates a higher pulse amplitude and longer pulse period than in other cases.     

断层横向构造在逆冲型地震破裂中的作用——以汶川地震小鱼洞断层为例

大地震破裂大多由横向构造(如阶区、弯曲和分叉)所分割的多个段落组成.2008年5·12汶川地震破裂沿北东走向上穿过了多个横向构造部位,特别在震中北东45 km的位置,小鱼洞断层、北川断层和彭灌断层三者之间呈现复杂的断裂切割相交关系.复杂断层几何结构对破裂的扩展是有抑制还是促进的作用？在相交的断裂段之间是否存在最优的破裂顺序？本文以库仑应力分析为手段,探讨在汶川同震破裂初始30 s内,破裂在多分支断裂中选择扩展路径时的可能应力相互作用.库仑应力分析显示:如果北川断层先发生破裂,其滑动对小鱼洞断层和彭灌断层均产生强烈负应力的抑制作用,而彭灌断层的滑动却反而对小鱼洞断层和北川断层浅部有强烈正应力的促进作用.因此,从准静态应力分析角度,彭灌断层先于北川断层发生破裂的可能性较大,这一破裂顺序与小鱼洞断层参与同震破裂过程的事实相符.此外,小鱼洞断层在链接北川和彭灌断层的同震位移中可能起到桥梁作用,但非静态应力的影响.横向构造在逆冲型地震破裂扩展过程中起到的牵引作用使得逆冲型地震破裂能够比走滑型地震跨越更宽的阶区.横向构造是逆冲断裂带内广泛发育的构成单元,因此在地震危险性分析的最大潜在震级测算中应该考虑其作用.     

走滑断层地震地表破裂带分布影响因素数值模拟研究——以1973年炉霍MS7.6地震为例

地震后在断层两侧的强变形与破裂带是地震灾害最严重的区域.为系统、定量研究同震地表变形带特征及其影响因素,本研究建立了走滑断层的三维有限元模型,分别探讨了断层位错量、断层倾角、错动方式、上覆松散层厚度、沉积层土性等因素的影响规律.模拟结果显示：走滑断层同震地表变形表现为以断层为中心的近似对称单峰分布,强地表变形集中在断层两侧各50 m宽度范围,地表变形量峰值随位错量增加而增大,破裂带宽度也随位错量增加而增大,但增量逐渐减小,并趋于一个渐近值;断层倾角对地表变形与破裂带宽度影响表现为随倾角减小变形量峰值点向上盘小距离偏移;走滑兼正断位错引起的变形量峰值最大,但地表破裂带宽度最小,走滑兼逆断引起的变形量峰值最小,但地表破裂带宽度最大,直立纯走滑断层的两参量都居中;走滑断层地表变形量峰值随上覆松散层厚度增大而减小,但随厚度减小的速率逐渐变小,松散层厚度从5 m增加到20 m时,破裂带宽度随厚度增加而缓慢增加,但自厚度大于20 m时,破裂带宽度开始随厚度增加而逐渐下降;当不同土性覆盖层（粗砂、粉砂、黏土）厚度相同时,地震引起的地表变形量峰值自粗砂、粉砂、黏土逐次增大,当粗砂厚度为60 m以上时,3.6 m的同震水平位错已不能形成地表破裂,而粉砂的厚度为70 m以上,黏土的厚度则为75 m以上.