震源动力学破裂过程数值模拟研究

首先阐述了震源动力学过程研究的重要意义, 在此基础上, 研究了复杂的断层几何形态及介质模型对动力学破裂过程的影响, 并对常用的有限元方法、 离散元方法、 有限差分方法和边界积分方程方法等进行了相应介绍. 讨论了这些数值模拟方法各自的优缺点, 建议在方法的选择上应视具体问题及计算的精度而定. 最后对动力学数值模拟的关键部分, 滑动摩擦准则进行了论述. 常用的滑动摩擦准则有滑动弱化准则、 速率弱化准则和速率-状态依赖摩擦准则. 在单纯考虑某个地震的动力学破裂传播过程时, 滑动弱化准则较为常用, 其中滑动弱化距离的选取至关重要. 但若考虑整个地震循环, 速率-状态依赖摩擦准则更为合适.      

震源破裂过程反演方法研究现状及展望

介绍了震源破裂过程反演方法研究的必要性及意义,简要回顾了震源破裂过程反演研究的历史,详细阐述了现在几种主要的震源破裂过程反演方法,分析了它们各自的优势和不足。展望了震源破裂反演的发展方向,指出地震波数据同其他多类数据尤其是大地测量数据(InSAR和GPS)联合进行反演是未来震源破裂过程反演的发展趋势。     

大地震震源破裂模型:从快速响应到联合反演的技术进展及展望

解析大地震的破裂模型是研究地震成因、破裂动力学机制和探究活动断层结构等研究方向的基础.在地震防灾、应急响应和危险性评估等实际问题中发挥着重要的作用.文章对近年来在大地震破裂模型反演的方法及应用上取得的进展进行综述和分析,结合北京大学地球物理专业相关研究人员在大地震破裂模型的快速反演、震源反投影、大地测量、地震波与形变观测数据的联合反演、复杂地球模型中破裂过程的反演及强地面运动模拟等方面的工作,分析不同研究方法的特长以及不足.提出从短期快速响应到长期科学问题的系统化研究思路,并对从震源模型反演到强地面运动预测的一体化自动应急系统,以及全动力学反演方法进行了分析和展望.     

1978和2005年宫城近海地震的动力学震源模拟:破裂能解释

对1978和2005年发生在同一板块边界而震级不同的日本宫城近海地震建立了自发动力破裂模型,再现了由运动学震源模型所预测的滑动和破裂速度。对这两次地震的动力学震源参数进行比较,可使我们看到同一断层上不同震源过程的破裂动力学特征。特别是,我们比较了应力降和破裂能,在这两次地震中,二者可以进行稳定的评估。在整个断层面上和两次地震破裂的凹凸体上,两个模型中应力降的最大值和平均值几乎相同。另外,1978年地震的震级比2005年的大,它的破裂能值不仅是在整个断层面上,而且在多次破裂的凹凸体上也比2005年的大。这些结果与先前用地震矩所做的破裂能标度的研究结果一致。我们还将破裂能值与以前研究中所估算的其他内陆地震的能值进行了对比,我们得到的宫城近海地震的值较小。造成这种不一致的原因可能是内陆浅源地震和俯冲带深源地震在构造背景上的差异。     

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.     

基岩地震动的一个相干函数模型--倾滑断层情形

本文研究了基岩随机地震动的空间变化规律，考虑了震源破裂速度、子源个数、震源深度和介质传播速度等因素的影响。对应于每个样本，用数值模拟方法计算了采用震源位错模型的弹性半空间近场地震动场，最后通过统计方法给出了一个倾滑断层情形下的近场基岩地震动的相干函数模型。这一方法可以补充常用的统计方法因观测资料有限而导致的欠缺。     

红河断裂带的震源机制与现代构造应力场

利用震源机制解对红河断裂带的现代构造应力场和震源破裂进行分析,结果表明沿断裂带震源机制、应力场和震源破裂存在着主体类型、优势作用和主要特征,同时也存在着复杂性特征,断裂带北、中、南段存在差异,反映了断裂带各段构造活动的差异。     

三维破裂及其在地震和断层研究中的应用（综述）

文中提出若干断层破裂和震源过程的重要问题,包括断层分布的形态、震源多重事件的非共面性、震源迁移和动力来源等,这些问题用目前二维力学模型无法回答,只有用三维模型才有可能。综述了三维岩石断裂力学的实验和Ｇｒｉｆｉｔｈ－Ｉｒｗｉｎ理论研究的进展情况,指出三维破裂研究既包括三维裂纹的破裂,也包括无初始裂纹的Ｈｅｒｔｚ接触引起的破裂。总结了岩石三维破裂的特征,并简述了三维破裂在震源过程和断层形成问题研究中的一些证据和研究前景,认为一些地震前兆机理问题有可能在三维模型中得到解答。同时也讨论了三维震源与断层模型简化为常用的二维模型的条件。     

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.      

1986年8月26日门源6.4级地震破裂过程研究

本文根据我国基准台基式仪P波记录,利用终止相和地震波谱综合研究了1986年8月26日青海省门源6.4级地震的震源过程,并求出相应的震源动力学参数。结果表明,门源地震的发震构造为北东50°走向,它朝北东方向单侧破裂,破裂长度为20公里,平均破裂速度为1.83公里/秒。     

A study on low strain integrity testing of platform-pile system using staggered grid finite difference method

To study the three-dimensional characteristics of wave propagation in platform-pile system, a three-dimensional computation model for transient vibration of platform-pile-soil system is established. Based on initial and boundary conditions, the numerical solution of this model is obtained. A MATLAB program is compiled through using staggered grid finite difference method. The dynamic response of the integrate pile in platform-pile-soil system is got under vertical impact force, and the reliability and feasibility of the numerical simulation are corroborated by comparing calculation result with measured data of low strain integrity testing of platform-pile system. The optimal sensor location at platform top is studied. The results show the position distancing the pile center 0.5R~0.6R (R is pile radius) is the optimal sensor location, which the line between sensor location and pile center parallels the short side. It plays a certain role in reducing three-dimensional interference through increasing shear wave velocity of surrounding soil and appropriately increasing the ratio of characteristic wavelength to pile radius. In addition, contact area has less influence on low strain integrity testing of platform-pile system.     

时域瞬变电磁法三维有限差分正演技术研究

瞬变电磁法应用广泛,三维数值模拟是研究复杂地质模型异常响应规律的重要技术手段之一,也是反演的基础.目前瞬变电磁数值模拟的不足主要有两个方面:第一,场源是在地表水平、浅层介质均匀的条件下计算的,限制了应用范围;第二,地下边界采用Dirichlet边界条件,导致计算空间很大,耗时较长.针对上述问题,在三维正演时,场源采用有限长细导线模型,在Maxwell有源差分方程中直接加入电流密度进行计算.在地表面加入空气层,避免了复杂的向上延拓计算,也可以对地形影响下的响应规律进行分析.在空气边界和地下边界均采用CPML吸收边界条件,并改进了CPML的参数分布,能够吸收空气介质和大地介质中的低频电磁波而反射误差极小,在满足计算精度的条件下可以有效减小节点数量.对循环迭代方法进行优化,将计算域、CPML区域和场源的空间循环统一转化为矩阵方式,加快了计算速度,但是空间消耗增大了约4~5倍.采用三维有限差分正演算法对均匀半空间模型、层状模型和地形模型进行了计算,并与解析解进行了对比验证.     

THE APPLICATION OF PML BOUNDARY CODITIONS IN THE SIMULATION OF SEISMIC WAVE BY THE HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCES AT THE TRANSVERSELY ISOTROPIC MEDIA

In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research.     

求解波动方程的任意差分精细积分法

在地震偏移成像技术中，常常要反向外推波场，因此涉及到波动方程的数值求解问题。本文提出了一种求解偏微分方程的新的半解析方法——任意差分精细积分(ADPI)法。其大体思路是：空间域上作坐标离散，但不采用古典差分法的等分离散方式，而是一种相对自由的、任意的离散法；时间域上则采用子域精细积分的方法，既保留了精细积分法的高精度，又克服了工作量大、占用存储大等缺点。该方法具有精度高、带宽小、稳定性好等多项突出优点，并且可以灵括处理各类边界条件。本文从简单一维、较普遍一维、以及二维3种情形讨论该方法对波动方程的具体应用，结合实际的算例，详细分析了各种算法的可行性和精度特点。     

徐淮地区煤矿井筒破裂原因初探

本用震源力学理论和方法研究了徐淮地区从１９７０年以来构造应力场的方向和强度的时空变化过程。结果表明：以唐山地震为分界线，本区的应力场Ｐ轴取向由震前平均６１．８°变为震后平均７７．７°。如果将本区以宿北断裂为界分为南区和北区两个部分，则北区的Ｐ轴取向从６８．１°变７１．２°，而南区的Ｐ轴取向由６２．５°变到８３．６°，南区的变化明显于北区。     

Arbitrary Difference Precise Integration Method for Solving the Seismic Wave Equation

Wave equation migration is often applied to solve seismic imaging problems. Usually, the finite difference method is used to obtain the numerical solution of the wave equation. In this paper, the arbitrary difference precise integration (ADPI) method is discussed and applied in seismic migration. The ADPI method has its own distinctive idea. When dispersing coordinates in the space domain, it employs a relatively unrestrained form instead of the one used by the conventional finite difference method. Moreover, in the time domain it adopts the sub-domain precise integration method. As a result, it not only takes the merits of high precision and narrow bandwidth, but also can process various boundary conditions and describe the feature of an inhomogeneous medium better. Numerical results show the benefit of the presented algorithm using the ADPI method.     

Numerical approximation of head and flux covariances in three dimensions using mixed finite elements

A numerical method is developed for accurately approximating head and flux covariances and cross-covariances in finite two- and three-dimensional domains using the mixed finite element method. The method is useful for determining head and flux covariances for non-stationary flow fields, for example those induced by injection or extraction wells, impermeable subsurface barriers, or non-stationary hydraulic conductivity fields. Because the numerical approximations to the flux covariances are obtained directly from the solution to the coupled problem rather than having to differentiate head covariances, the approximations are in general more accurate than those obtained from conventional finite difference or finite element methods. Results for uniform flow example problems are consistent with results from previously published finite domain analyses and demonstrate that head variances and covariances are quite sensitive to boundary conditions and the size of the bounded domain. Flux variances and covariances are less sensitive to boundary conditions and domain size. Results comparing approximations from lower-order Raviart–Thomas–Nedelec and higher order Brezzi–Douglas–Marini[9] finite element spaces indicate that higher order element space improve the estimate of the flux covariances, but do not significantly affect the estimate of the head covariances.     

2维和2.5维起伏地表直流电法有限差分数值模拟

起伏地表直流电场数值模拟现多采用有限元法,主要是因为其有灵活的处理曲边界的能力,然而有限元法比有限差分法要复杂,如果让有限差分法也同样具有较好的处理曲边界的能力,那数值模拟将变得更为简单.本文通过在非正则内点处采用不等距差分,在起伏地表点处直接实现边界条件,克服转移法人为改变地表形状的弊端,使得基于笛卡尔网格的有限差分...     

大地电磁有限差分数值解对比

基于网格精度、形成系统方程的方式、边界条件以及预条件线性算子等,文中对大地电磁（MT）有限差分数值解作了对比.对不同网格剖分方式下的三个均匀半空间模型的一维MT响应对比显示,在降低首层厚度的同时保持层间厚度变化在合理范围可以同时提高主场和辅助场的精度.在利用正常中心网格法（主场和辅助场都定义在单元顶面的中心）计算二维（2-D）TM模式响应时,应该从Maxwell一次差分方程开始组建二次差分方程,这样可以更充分考虑模型电阻率的变化.在对边界值如何影响数值解的测试表明,仅仅提高一维（1-D）边界值的精度对提高2-D MT有限差分数值解的精度是有限的.线性算子对提高MT解的效率十分重要,简单的对比进一步表明合适的预条件再配合好的线性算子（如文中求解2-D MT时所采用的DILU-BICGSTAB方法）不仅可以加速收敛,而且可以降低迭代次数.     

弹性半空间位错内源的数值解

本文首先将一般剪切位错点源表示成四种基本点位错的组合,断层面倾角和滑动系数仅与组合系数有关.利用将三维动力学问题化为两维的处理方法,将每一基本点源问题化成求解位移函数的轴对称问题,最后将人工透射边界的处理方法同有限差分结合起来,提出一种简便、节省的计算理论地震图的方法.利用这种方法获得了四种基本点位错源的典型近场理论地震图,并初步讨论了近场地面运动的若干特征,表明浅源地震近场地面位移中震相不能分离,且点位错源在近场产生大小相当的水平与垂直位移.本文的方法可用于研究复杂的近场地震波传播问题.