中国东部地区地震活动与构造应力场关系的有限元数值模拟

运用有限元数值模拟方法结合板块构造边界条件和板内构造分布特征对中国大陆东部地区的基本构造应力场进行数值模拟,根据研究区受周边板块作用的情况分析板块边界作用力的变化对内部应力场的影响。对比有限元数值模拟结果解释了中国大陆东部地区地震活动空间分布的特点。     

数值模拟方法在应力场演化及地震科学中的研究进展

本文对数值模拟方法(主要针对有限单元法)在应力场演化及地震科学中的应用和发展做了回顾与总结,主要包括构造应力场模拟、地震活动性模拟、地震危险性模拟等部分,并对数值模拟方法的发展趋势、方法的优势及其所存在的主要问题做了探讨.     

甘东南地区地壳形变动力学数值模拟

正针对甘东南地区构造活动强烈、地震活动频繁的背景和区域现今地震活动特征、强震孕育趋势及机制的现实需求,利用甘东南地区地质、地震、地球物理、大地测量等多源观测数据,构建了甘东南地区地壳形变三维数值模型,通过有限元模拟结果与实际速度场结果对比,验证了模型的合理性,反演了甘东南地区构造应力场和位移场,分析了构造应力场特征,为甘东南地区强震趋势及地点预测提供了依据。     

黄陵矿区2号煤层构造应力场分析

煤层构造应力场与煤与瓦斯突出和煤层裂隙分布带范围密切相关.黄陵矿区煤层中瓦斯含量较高,分布不均是矿井安全生产的重要隐患.基于该区地震、地质和测井数据,本文对三维地震数据体进行精细的构造解释,用反演法建立了地质力学模型,并确定岩石力学参数,运用有限元理论和弹性计算力学对矿区三维构造应力场进行了数值模拟,得到黄陵矿区2号煤层地质构造带应力场分布特征,模拟结果与井田宏观及微观构造信息一致.这对预测该区裂隙分布带,煤与瓦斯突出等具有重要的指导意义.     

静水压下矿物颗粒边界力学性质的数值模拟研究

随着地球科学研究的深入以及计算机技术的飞速发展,有限元数值模拟正成为地震机理研究中的一种强有力的技术方法。从震源物理力学过程、断层类型及力学机制、区域构造应力场、波速比及地下水位变化、温度效应与应力触发等方面模拟研究地震孕育机理取得了很大的进展。但是,目前的地震机理有限元模拟研究中尚存在一些关键的问题,如模型中块体之间的界面效应往往被忽视,参数（弹性模量、粘滞系数）的选取不确定。     

如何用有限元新模型研究地震触发和应力场连续演化

首先提出了一种考虑构造应力场影响的有限元新模型和地震触发因子C.新有限元模型可以用来研究地震序列中的地震触发和应力场演化.地震触发因子C定义为滑动面上的剪应力和摩擦强度的比值,它可以用来预测地震能否触发以及触发区的范围.然后利用这个有限元新方法和地震触发因子C研究了1976年唐山地震序列的余震触发情况.结果表明唐山地震的应力场和断层带的非均匀性对余震触发有重要影响.落入新有限元模型预测的地震触发区中的余震要明显多于落入地震位错理论预测的地震触发区中的余震.     

辽宁及邻区地壳构造应力场及其与地震活动关系的三维有限元数值模拟研究

依据最新的辽宁及其邻近地区地壳上地幔三维地震波速结构，并考虑地质构造、断裂以及地壳深部的构造环境等因素，建立研究区的三维地质模型；结合震源机制解与原地应力测量资料，分析区域现代地应力场特征，确定了研究区的边界约束和动力边界条件．在以上基础上，采用线弹性介质模型进行研究区三维构造应力场的有限元数值模拟，探讨研究区地壳应力场的基本特征．对比分析表明，本区地壳内应力场的三维有限元数值模拟结果与已发生的地震有着较好的对应关系，并指出了值得注意的有潜在发震可能的地震危险区．      

华北地区断层运动与三维构造应力场的演化

利用华北地区断层形变测量资料，通过三维有限元模型，数值模拟了华北地区三维构造应力场的演化过程，得到了1986～1997年以一年为时间尺度的演化图象，并分析了应力场的演化特征；结合华北地区该时间段内的地震活动性，初步探讨了应力场的演化过程与地震活动性的关系．      

数值模拟在地球动力学中的研究进展

本文主要针对有限单元法，对近10几年来数值模拟在地球动力学中的应用和发展作了回顾，分为构造应力场模拟；地幔热对流模拟；板块碰撞模拟；岩石圈流变学模拟；以及地震机制与预测模拟等部分.简单阐述了当前地球动力学数值模拟的发展趋势并论述了其面临的主要问题.     

构造应力场模拟-有限元理论、方法和研究进展

采用有限元数值模拟方法对构造地质问题进行描述和定量化求解是当前地质学领域的研究的一个热点,该方法近10年以来取得了重要进展,形成了比较完整的理论和技术体系,并在一些典型的地质构造带获得了重要的研究成果,已成为当前定量研究构造应力场的主要方法.文中以有限元数值模拟方法理论作为出发点,总结分析了国内外有限元数值模拟方法在构...     

波动方程的应力-速度有限元解耦交叠格式

本基于有限差分交叠格式和解耦有限元方法的基本概念,以应力－速度为变量,提出了求解波动的应力－速度有限元解耦交叠格式,这一格式不仅时空解耦,而且为显式,它适合于线性及非线性波动问题的数值模拟,已有的应力－速度有限元交叠格式（即格子法）为本的特例。通过解析解数值检验表明,本建议的方法具有较高的精度,而格子法计算精度较低。     

Application of the discontinuous spectral Galerkin method to groundwater flow

The discontinuous spectral Galerkin method uses a finite-element discretization of the groundwater flow domain with basis functions of arbitrary order in each element. The independent choice of the basis functions in each element permits discontinuities in transmissivity in the flow domain. This formulation is shown to be of high order accuracy and particularly suitable for accurately calculating the flow field in porous media. Simulations are presented in terms of streamlines in a bidimensional aquifer, and compared with the solution calculated with a standard finite-element method and a mixed finite-element method. Numerical simulations show that the discontinuous spectral Galerkin approximation is more efficient than the standard finite-element method (in computing fluxes and streamlines/pathlines) for a given accuracy, and it is more accurate on a given grid. On the other hand the mixed finite-element method ensures the continuity of the fluxes at the cell boundaries and it is particular efficient in representing complicated flow fields with few mesh points. Simulations show that the mixed finite-element method is superior to the discontinuous spectral Galerkin method producing accurate streamlines even if few computational nodes are used. The application of the discontinuous Galerkin method is thus of interest in groundwater problems only when high order and extremely accurate solutions are needed.     

三维地震断层动力破裂的显式并行有限元解法

本文在近场波动有限元的基础上,根据断层动力破裂的摩擦模型,详细地推导出了断层面节点在破裂的不同时刻的计算公式,提出了一种模拟断层动力破裂的显式并行有限元方法,利用此方法,可以模拟断层的破裂过程、地表破裂及由此产生的地面运动。     

Magnetotelluric responses of three-dimensional conductive and magnetic anisotropic anomalies

A magnetotelluric finite-element modelling algorithm is developed, which is capable of handling three-dimensional conductive and magnetic anisotropic anomalies. Different from earlier three-dimensional magnetotelluric anisotropic modelling methods, the algorithm we presented has taken the magnetic anisotropy into consideration. The variational equations are produced by the Galerkin method and the governing equations are solved using a hexahedral vector edge finite-element method. The accuracy of this algorithm is firstly validated by comparing its solutions with the results of finite-difference method for a three-dimensional conductive arbitrary anisotropic model, and then validated by comparing with analytical solutions for a one-dimensional magnetic model. The responses of four kinds of models under different conditions are studied, and some conclusions are obtained. It shows that for materials with a high magnetic permeability, its influence on magnetotelluric responses cannot be ignored in some circumstances. Especially, if the magnetic susceptibility is exceptionally high, it may really distort the apparent resistivities of lower resistive anomalies. These conclusions are also beneficial for magnetotelluric survey.     

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

The representation of a force or moment point source in a spectral finite-element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite-element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on one-dimensional elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in three dimensions on continuous mass-lumped tetrahedral elements show a similar error behaviour as in the one-dimensional case, although in three dimensions the loss of accuracy for the moment source is not a severe as a full order.     

Doubly asymptotic multi-directional transmitting boundary for dynamic unbounded medium-structure-interaction analysis

The novel doubly asymptotic multi-directional transmitting boundary combines the advantages of the doubly asymptotic and multi-directional formulations. It is rigorous for the low-frequency limit (static case) and the high-frequency limit in the wave-propagation direction perpendicular to the artificial boundary and at all the preselected angles corresponding to various apparent velocities. It is implemented straightforwardly in the finite-element method. The doubly asymptotic multi-directional transmitting boundary is temporally local and spatially either global or local depending on the implementation of the static-stiffness matrix. It leads to much higher accuracy than other transmitting boundaries with the same finite-element mesh.     

利用地质规则块体建模方法的频率域有限元弹性波速度反演

在频率域弹性波有限元正演方程的基础上,依据匹配函数（也就是观测数据和正演数据残差的二次范数）最小的准则,用矩阵压缩存储与LU分解技术来存储和求解频率域正演方程中的大型稀疏复系数矩阵、用可调阻尼因子的Levenberg Marquard方法求解反演方程组,直接求取地下介质的弹性波速度,导出了频率域弹性波有限元最小二乘反演算法. 为了利用地下地质体的分布规律,减少反演所求的未知数个数,本文又提出了规则地质块体建模方法引入到反演中来. 经数值模型验证,在噪声干扰很大（噪声达到50髎）或初始模型与真实模型相差很大的情况下,反演也能取得很满意的效果,证明本方法具有很好的抗噪性与“强壮性”.     

高面板坝地震动三维非一致输入的波函数组合法

提出三维问题的波函数组合法求解不规则河谷的散射问题,应用到高面板坝动力有限元计算的地震动输入中,可以满足非一致输入的要求,并回避人工边界对外行波的反射问题。重点介绍三维问题的波函数组合法的理论推导和程序的算例验证,并给出将该方法应用到高面板坝地震动输入的基本步骤。     

二维有限元大地电磁正演模拟在Matlab上的实现

Matlab高级语言开发平台对矩阵的计算简便快速,并且绘图输出文件方便。以这些特点为契机,在Matlab平台上,讨论利用有限单元法实现二维大地电磁正演的问题,推导出相应的公式,计算地表或海底视电阻率及相位,并与解析解以及主流方法结果对比,证实了本文方法的正确性。     

Dynamic-stiffness matrix in time domain of unbounded medium by infinitesimal finite element cell method

To calculate the dynamic-stiffness matrix in the time domain (unit-impulse response functions) of the unbounded medium, the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed. As in the cloning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell. The derivation can be performed exclusively in the time domain, or alternatively in the frequency domain. At each time station a linear system of equations is solved. The consistent-boundary method to analyse a layered medium in the frequency domain and the viscous-dashpot boundary method are special cases of the infinitesimal finite element cell method. The error is governed by the finite element discretization in the circumferential direction, as the width of the finite-element cell in the radial direction is infinitesimal. The infinitesimal finite element cell method is thus ‘exact in the finite-element sense’. This method leads to highly accurate results for a vast class of problems, ranging from a one-dimensional spherical cavity to a rectangular foundation embedded in a half-plane.