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传统的高阶有限差分波动方程数值模拟方法采用高阶差分算子近似空间偏导数,能有效抑制空间频散.然而,传统的有限差分法仅采用二阶差分算子近似时间偏导数,这使得地震波场沿时间外推的精度较低.当采用较大的时间采样间隔,传统的有限差分法模拟波场会出现明显的时间频散,甚至不稳定.本文基于新的差分结构和中心网格剖分,发展了一种空间任意偶数阶精度、时间四阶和六阶精度的时空域有限差分方法.基于对离散后的频散关系进行泰勒展开,本文推导了时空域高阶有限差分算子的差分系数.相速度分析表明时间四阶、六阶精度的差分方法能显著地减小传统时间二阶精度差分方法的时间频散.在相同的精度下与传统差分法比较,本文发展的时间四阶、六阶有限差分方法的计算效率比传统方法高.均匀和非匀均介质中的波场数值模拟实验进一步证实本文研究的时空高阶有限差分方法的优越性. 相似文献
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基于曲线网格有限差分方法研究了垂直走滑断层在不同山体地形情况下的动力学破裂传播,分析并讨论了局部山体地形对断层破裂过程及相应地面地震动的影响,得到了各模型断层面的动力学破裂过程及相应的地表峰值速度特征。研究结果表明,山体地形尺度（山体高度及底部延展距离等）对断层动力学破裂过程影响较大,进而影响到相应的地面地震动分布。当山体地形处于自由地表上亚剪切向超剪切转换的位置附近时,山体地形会阻碍断层面上自由地表超剪切的产生。一般而言,对于具有一定埋深的断层,当山体地形底部延展距离一定时,山体高度越高,其对自由地表超剪切的阻碍程度越大;当山体高度一定时,地形底部延展距离越大,越会阻碍自由地表超剪切的产生,这种破裂过程的变化会导致相应地面地震动呈现不同特征的分布。此外,还探讨了断层破裂过程及相应地震动对成核区外初始剪切应力变化的响应,结果显示,当初始剪切应力较高时,高应力降引起的超剪切破裂会对断层破裂及相应的地震动分布起主导作用。 相似文献
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地震断层几何形态的确定是研究断层震源破裂过程和地面运动的先决条件.其中断层的破裂深度和倾角是两个未知的关键参数.半无限空间的地震弹性位错理论公式表明,除纯走滑断层以外,对于断层破裂至地表的地震产生的地表变形,其上盘水平应变的零值点与破裂深度之间存在简单的对应关系,可由地表的零应变点直接推算断层深度.本文通过数值计算方法探讨了盲断层与非均匀介质情形下,利用地表零应变点推算断层破裂深度的可行性.结果显示,介质和应力场的非均匀性一定程度上影响了对应关系;对于盲断层,当埋深在~1 km以内时,对应关系近似成立.此外,根据地表水平变形还可估算断层倾角的范围.最后探讨了如何根据大地震后的孔径雷达干涉方法记录推算断层破裂深度的方法,并将此方法应用于2008年汶川大地震,获得了这次地震的断层破裂深度.这种利用地表变形观测确定断层几何参数的方法简便易行,没有余震的影响,可以为反演提供有价值的约束. 相似文献
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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. 相似文献
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基于曲线网格有限差分方法,针对震源动力学模型中的边界条件的问题,本文提出了一种改进的特征量方法,即将牵引力镜像方法和特征量方法相结合,在保守形式的方程中通过镜像操作完成单边导数的计算,然后有约束地调整边界处的速度和应力值,以此保证满足模型中的边界条件.改进的特征量方法可用于处理曲线网格当中一般的边界条件,从而也可用于构建曲线网格有限差分法的分裂节点模型.我们将改进的特征量方法分别用于自由表面和断层面,并分别与前人计算结果进行了比较.计算结果表明,在相同的网格划分的情况下,改进的特征量方法能够得到与其他方法相似的计算结果,但改进方法的异常震荡更小,从而证明了本文提出的改进的特征量方法用于曲线网格有限差分法分裂节点模型的可行性. 相似文献
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通过建立三维数值模型,对隐伏正断层在均匀错动和倾斜错动方式下土体的破裂过程进行研究。利用应力罗德参数和等效塑性应变分别对断层错动过程中上覆土体的应力状态和破坏形式进行分析,并提出土体破裂的判别方法。通过对数值模拟结果的分析得到以下结论:① 在断层错动过程中,下盘一侧受断层错动影响的上覆土体的应力状态经压剪→纯剪→拉剪逐渐变化,而上盘一侧上覆土体的应力状态变化较为复杂,经压剪→纯剪→拉剪→纯剪→压剪重复变化;② 在断层均匀错动过程中,断层下盘一侧土体的破裂率先出现在地表拉剪区内,随错动量的增大,破裂带向两侧、向深部扩展;同时,下盘一侧土体的底部产生破坏,并斜向上扩展,逐渐与顶部破裂相连;③ 在断层倾斜错动过程中,地表破裂出现的位置和上覆土体的厚度有关。对于厚度较大的土体,正断层倾斜错动能够在地表形成与断层走向有一定夹角、且与断层长度相比长度很短的地表破裂或地裂缝,而数值模拟可对正断层错动导致的地表破裂的模式加以补充,为研究地裂缝的形成机理和分布形式提供依据。 相似文献
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波动方程有限差分法是一种使用广泛的地震波数值模拟方法.但是有限差分法本身固有存在着数值频散问题,会降低地震波场模拟的精度与分辨率.为了克服常规有限差分算子的数值频散,本文针对VTI介质地震波数值模拟问题,构造了频率-空间域qP波波动方程高精度有限差分优化算子,根据最优化理论中高斯-牛顿法确定了高精度有限差分算子的优化系数.利用常规差分算子和高精度优化差分算子对归一化相速度的频散关系精度进行了对比分析,并对均匀各向同性介质和均匀VTI介质中的qP波地震波场进行了有限差分数值模拟,通过频散关系精度分析和波场数值模拟结果表明：有限差分优化算子具有较高的波场数值模拟精度,有效压制了传统有限差分算子数值模拟中的数值频散现象,提高了有限差分算子精度,为VTI介质频率-空间域qP波正演模拟奠定了基础. 相似文献
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非均匀介质一般为多尺度介质,对非均匀介质进行正演模拟需要多尺度的网格剖分.碳酸盐岩缝洞介质的尺度一般为厘米级甚至毫米级.使用有限差分方法对其进行精细模拟需要差分步长达到缝洞介质的尺度.为了提高有限差分数值模拟方法的精度和效率,使之可以应用于非均匀介质的正演模拟,本文推导了基于PML边界的空间和时间步长同时变化的高倍数可变网格差分格式,步长变化倍数可以达到百倍以上.并且在一般意义的变网格算法的基础上,改进了变网格算法的网格剖分方式,进一步减小了精细尺度模型数值模拟的内存消耗.数值试验表明,该方法可以精细描述毫米尺度的地质体,提高有限差分方法模拟精度,同时也节约了内存,提高了模拟效率. 相似文献
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提出一种新的三维空间不规则网格有限差分方法,模拟具有地形构造的非均匀各向异性介质中弹性波传播过程. 该方法通过具有二阶时间精度和四阶空间精度的不规则交错网格差分算子来近似一阶弹性波动方程,与多重网格不同,无需在精细网格和粗糙网格间进行插值,所有网格点上的计算在同一次空间迭代中完成. 针对具有复杂物性参数和复杂几何特征的地层结构,使用精细不规则网格处理粗糙界面、断层和空间界面等复杂几何构造, 理论分析和数值算例表明,该方法不但节省了大量计算机内存和计算时间,而且具有令人满意的稳定性和精度. 相似文献
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The rupture dimensions of earthquake faults are important parameters for characterizing earthquake ruptures and ground motions. Two key parameters to be determined are the rupture depth and dip angle of earthquake faults. Dislocation theory in an elastic half space indicates that if a seismic rupture directly runs up to the ground surface, there exist zero points of horizontal strain in the surface deformation, which correspond to the rupture depths, except for pure strike-slip faults. In this study, we use numerical simulations to investigate the possibility of inferring rupture depths from zero-strain points for cases of buried faults and heterogeneous media. The results show that the correspondence of zero-strain points to the rupture depths can be influenced by the heterogeneity of the underground media and the stress field. For buried faults, the correspondence relationship is approximately valid when the fault depth is <1 km. In addition, the range of earthquake fault dip angles can be estimated by horizontal displacements on the ground. We also study how to determine the rupture depths of faults from InSAR data after large earthquakes, and successfully apply the method to the 2008 Wenchuan earthquake. The method proposed here, which determines the parameters of fault geometry according to surface deformation, is simple and easy to perform. With independent of aftershocks, it can provide valuable constraints to kinematic inversions. 相似文献
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The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ‘staircase fashion‘causing spurious diffractions. It is the aim of this work to eliminate these non-physical diffractions by using curved grids that generally follow the interfaces. A further advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled. One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so-called multiblock strategy). The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space. The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods. 相似文献
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— We quantify the effects of complex fault geometry on low-frequency (<1 Hz) strong ground motion using numerical modeling of dynamic rupture. Our tests include the computation of synthetic seismograms for several simple rupture scenarios with planar and curved fault approximations of the 1994 Northridge earthquake. We use the boundary integral equation method (BIEM) to compute the dynamic rupture process, which includes the normal stress effects along the curved fault geometries. The wave propagation and computation of synthetic seismograms are modeled using a fourth-order finite-difference method (FDM). The near-field ground motion is significantly affected by the acceleration, deceleration and arrest of rupture due to the curvature of the faults, as well as the variation in directivity of the rupture. For example, a 6-km-long hanging-wall or footwall splay with a maximum offset of 1 km can change 1-Hz peak velocities by up to a factor of 2-3 near the fault. Our tests suggest that the differences in waveform are larger on the hanging wall compared to those on the footwall, although the differences in amplitude are larger in the forward rupture direction (footwall). The results imply that kinematic ground motion estimates may be biased by the omission of dynamic rupture effects and even relatively gentle variation in fault geometry, and even for long-period waves. 相似文献
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An optimized finite difference method based on a polar coordinate system for regional-scale irregular topography 
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下载免费PDF全文 The finite difference method (FDM) is an important numerical approach for simulating the propagation of seismic waves, and some FDMs can be used to study the impact of the Earth’s curvature and topography over large distances. To efficiently model the effects of the Earth’s irregular topography on the propagation of seismic waves, here we optimize a previously proposed grid mesh method and develop a novel two-dimensional boundary-conforming FDM based on a curvilinear polar coordinate system. This method efficiently simulates the propagation of seismic waves in an arc-shaped model with large variations in surface topography. Our method was benchmarked against other reported methods using several global-scale models. The consistency of the results confirms the validity of our proposed optimization strategy. Furthermore, our findings indicate that the proposed optimization strategy improves computational efficiency. 相似文献
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When applying the conventional Fourier pseudospectral method (FSM) on a Cartesian grid that has a sufficient size to propagate a pulse, spurious diffractions from the staircase representation of the curved interfaces appear in the wavefield. It is demonstrated that these non-physical diffractions can be eliminated by using curved grids that conform to all the interfaces of the subsurface. Methods for solving the 2D acoustic wave equation using such curved grids have been published previously by the authors. Here the extensions to the full 2D elastic wave equations are presented. The curved grids are generated by using the so-called multiblock strategy which is a well-known concept in computational fluid dynamics. In principle the sub-surface is divided into a number of contiguous subdomains. A separate grid is generated for each subdomain patching the grid lines across domain boundaries to obtain a globally continuous grid. Using this approach, even configurations with pinch outs can be handled. The curved grid is taken to constitute a generalized curvilinear coordinate system. Thus, the elastic equations have to be written in a curvilinear frame before applying the numerical scheme. The method implies that twice the number of spatial derivatives have to be evaluated compared to the conventional FSM on a Cartesian grid. However, it is demonstrated that the extra terms are more than compensated for by the fewer grid points needed in the curved approach. 相似文献
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基于交错网格伪谱法和高阶精度有限差分方法,发展了模拟非均匀介质地震波传播的三维伪谱和有限差分混合算法.该方法在两个水平方向利用交错网格伪谱算子计算空间微分,保留了该方法高效、高精度的优势,在垂直方向采用交错网格高阶精度有限差分算子实现空间微分计算．利用有限差分方法的局部性特征,将三维计算区域在垂直方向上划分为一系列子区域,并分配给不同的处理器,实现了在并行计算机集群上的三维并行计算．通过模拟算例,与离散波数法比较,检验了该算法的精度．为了检验该方法的实用性,在64个处理器上,对三维沉积盆地模型进行了67108864个网格点的并行计算,模拟的波场主频率为1.25Hz,讨论了沉积盆地深度对三维沉积盆地地面运动的影响． 相似文献
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云南活动性断裂带的结构变异与孕震体构造的空间关系 总被引：2，自引：1，他引：1
中国的强震主要发生在一些板内大型走滑断裂带上,地震的破裂基本上是以走滑型破裂为特征。在这些活动性的走滑断裂带上形成的孕震体构造与该走滑断裂结构在空间的变化有关,并且表现出几种主要的变异形式。结合西南地区地震构造的实例,本文剖析了这几种结构变异形式,阐明了孕震体构造存在的空间机制。本文从地震与构造丛集相关及其所具有的分维特征入手,展开了对孕震区断裂结构变异特征的识别和孕震体空间机制的探讨,表述了一条活动性大断裂必须由若干次级断裂和无数中小断裂的空间组合,才能形成孕震体的必要条件。 相似文献
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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. 相似文献
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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... 相似文献