基于面向对象思想的正演反演统一框架结构

运用面向对象思想分析地球物理正演与反演问题,提出了一种基于有限单元正演与正则化非线性最小二乘反演的统一框架结构.该框架采用稀疏线性系统求解作为正演的基础类;分别建立一维、二维、三维的几何模型类,用于完成模型的剖分与有限单元钢度矩阵的生成,其中与单元物质属性相关的计算采用纯虚函数的形式,在具体解问题中实现;以正则化非线性最小二乘最优化算法作为反演基础类,反演中有关模型的正演数据计算及Fréchet矩阵求解等采用纯虚函数的形式,在具体问题中进行计算.框架结构的建立提高了代码的重用性与程序开发速度;对地质单元采用统一的空间剖分,有利于开展联合反演程序设计.     

有限单元法非均匀剖分对数值模拟影响研究

本文研究了有限单元法非均匀剖分对直流电阻率法数值模拟结果的影响.通过非均匀剖分对半空间地质体的视电阻率异常与均匀剖分的视电阻率对比,分析这种模拟方法的可行性,研究计算结果差异产生的原因.通过相邻单元的不同边长比例剖分的对比,研究在误差允许范围内非均匀剖分的单元边长比例极限.计算结果表明,测线方向非均匀剖分是误差产生的主要原因,XYZ三方向非均匀剖分所带来的误差总和是各方向非均匀剖分产生误差之和;当测线方向剖分单元不均匀剖分比例小于0.49∶0.01时,由于非均匀剖分产生的误差在容许范围内.     

基于波前最小走时单元的三角网射线追踪全局算法

为克服矩形网速度间断面及边界描述精度差的缺点,本文提出了一种基于波前最小走时单元的三角网射线追踪算法.该算法用三角单元剖分速度模型,把与波前面相邻、处于振动状态的三角单元称为波前单元,从源点所在单元开始构造由波前单元组成的波前单元域;1)选域中最小走时三角单元为当前单元;2)它先与相邻三角单元振动传递,再进行相邻单元各自内部节点的传递、并将处于振动状态的相邻单元扩展为波前单元;3)然后确认当前单元的振动状态、决定其在波前单元域中的去留,以此三步循环进行波前单元域的扩展及节点的最小走时和次级源搜索,直至波前单元域在剖分区域的消亡;最后利用各节点最小走时和次级源,通过最小走时搜索,拾取从接收点到源点的射线路径.数值模拟表明,该算法的模型剖分灵活性强,对速度间断面的描述准确,追踪结果精度高.     

三维直流电阻率自然单元-无限元耦合数值模拟

直流电阻率数值模拟对于实测电阻率数据反演、解释地下真实电阻率结构具有重要意义.为解决复杂地电模型剖分以及处理截断边界时面临的困难, 本文提出一种新的三维自然单元-无限元耦合法.该算法在自然单元区域灵活布设自然节点以填充复杂模型, 并引入无限单元替代截断边界条件以促使刚度矩阵与电源位置无关.首先推导了稳定电流场基本方程; 然后介绍了二、三维自然单元法及其形函数的构建过程; 再引入三维多向映射无限单元并实现自然单元-无限元的有效耦合; 最后通过4个数值模型, 结合传统有限单元法、有限元-无限元耦合法以及COMSOL Multiphysics软件的计算结果, 验证了算法的正确性及有效性.数值结果表明, 本文所提算法满足精度要求, 能有效减小计算区域, 无需二次更新刚度矩阵, 对复杂模型适应性强.

     

耦合有限单元法扩边的直流电阻率勘探无单元Galerkin法正演

本文分析了目前直流电阻率正演模拟中的无单元Galerkin法（EFGM）和有限单元法（FEM）的优缺点,针对采用第一类边界条件需要足够大的计算域时EFGM计算成本高的问题,在计算域外围区域采用FEM扩边,提出了直流电阻率的无单元Galerkin-有限单元耦合法（EFG-FE）.采用具有Kronecker delta函数性质的径向基点插值法（RPIM）构造EFGM形函数,在外围区域将EFGM与FEM直接耦合,无需其他处理手段,消除了传统EFGM与FEM耦合中存在的界面耦合困难.EFG-FE将模型计算域分割为EFGM区域和FEM区域,模型核心区域采用EFGM计算,发挥EFGM灵活性、适应性强和高精度的优点,使得模型建立简单方便,对任意复杂地电模型适应性强,同时获得高精度模拟结果.在模型计算域外围采用快速扩展的FEM单元网格进行剖分,利用其数值稳定性和高效性,使用少量FEM节点和单元网格将计算域大范围扩大满足第一类边界条件,同时不大幅增加计算成本,进而提高计算效率.最后,通过不同正演方法的模型算例的模拟结果对比,验证了本文提出的EFG-FE有效可行,其模拟结果具有很高的模拟精度,且相比于采用第三类边界条件的EFGM提高了计算效率,具有更好的模拟性能.

     

复杂地形三维直流电阻率有限元数值模拟

系统地论述了用有限单元法研究复杂地形条件下三维直流电阻率的正演计算技术.首先给出了三维构造中点源电场的边值问题以及相应的变分问题;然后利用有限单元法求解变分问题,采用四面体单元对研究区域进行剖分,在单元中进行三线性函数插值,将变分方程化为线性代数方程组;最后,考虑到节约计算时间,利用对称超松弛顸条件共轭梯度迭代算法求解大型线性方程组,得到了各节点的电位值,进而计算出地表的视电阻率.通过理论模型的计算检验了算法的可行性之后,给出了几种常见纯地形异常的数值模拟结果和一个组合模型的计算结果,其研究工作为研究三维直流电阻率反演奠定了基础.     

大地电磁二次函数插值的有限元法正演模拟

在矩形网格剖分情况下,讨论单元内采用二次函数插值的大地电磁二维有限元正演问题,推导出相应的计算公式,在解线性方程组求取各节点处的场值后,计算地表的电阻率和阻抗相位.通过与理论解析解及线性插值有限元法的计算结果的对比,证实了本文方法在网格剖分稀疏时,仍有高的计算精度,与线性插值法相比,采用放稀一倍的网格仍具有较高的计算精度,而两者的计算时间相差不多.     

大地电磁二次函数插值的有限元法正演模拟

在矩形网格剖分情况下,讨论单元内采用二次函数插值的大地电磁二维有限元正演问题,推导出相应的计算公式,在解线性方程组求取各节点处的场值后,计算地表的电阻率和阻抗相位.通过与理论解析解及线性插值有限元法的计算结果的对比,证实了本文方法在网格剖分稀疏时,仍有高的计算精度,与线性插值法相比,采用放稀一倍的网格仍具有较高的计算精度,而两者的计算时间相差不多.     

三维地形直流电阻率有限元法模拟

基于稳定电流场的基本方程、三维区域满足的边值问题以及相应的变分问题,研究了三维起伏地形条件下电阻率的有限单元数值模拟算法. 离散积分区域时,以三棱柱为最小研究单元,推导了含有地形特征信息的三线性插值型函数以及单元刚度矩阵. 采用变带宽、一维数组方式只存储稀疏刚度矩阵中非零元素,能够节约内存. 利用Cholesky分解法只分解一次大型稀疏矩阵,通过回代可以求出方程组的全部解,当求解有多个供电点的测深问题时可以缩短计算时间. 模型计算表明,在水平层状介质模型上,三维计算结果与解析解或二维数值解十分吻合,计算精度满足误差要求. 在二维山脊上的二极剖面或三维山谷上的中间梯度剖面上,其三维计算结果与相应模型的土槽实验结果或边界元法计算结果也非常接近.     

基于TrueGrid的起伏界面精准剖分及地震动模拟

利用谱元法的规则六面体单元进行网格剖分时,界面起伏较大处会出现阶梯状网格而导致模拟时产生数值散射。为消除阶梯状网格对起伏界面地震动模拟计算的影响,本文基于TrueGrid软件编写了应用程序,提出了起伏界面处六面体单元网格剖分方式,通过该程序可快速建立起伏界面处均匀的六面体网格模型。本文采取了删除四纵列拐角单元、删除一纵列拐角单元以及构造单元过渡环3种剖分方式,解决两个方向上（x-z与y-z方向）单元二合一过渡后拐角处产生扭曲单元的问题。将阶梯状网格经二合一处理后变为斜面网格,并投影至起伏界面,使得网格完全贴合起伏界面,改善了用台阶状网格近似描绘起伏界面的问题。将3种模型通过谱元法进行数值模拟计算验证了该剖分方式的正确性,对比结果发现删除拐角处一纵列单元方式与设置过渡环的方式均可使用,删除四纵列拐角单元方式不推荐使用,本文提出的方案有助于提高谱元法处理起伏界面问题的灵活性。     

Trace element behavior in hydrothermal experiments: Implications for fluid processes at shallow depths in subduction zones

Chemical evaluation of fluids affected during progressive water-sediment interactions provides critical information regarding the role of slab dehydration and/or crustal recycling in subduction zones. To place some constraints on geochemical processes during sediment subduction, reactions between décollement sediments and synthetic NaCl-CaCl₂ solutions at 25–350°C and 800 bar were monitored in laboratory hydrothermal experiments using an autoclave apparatus. This is the first attempt in a single set of experiments to investigate the relative mobilities of many subduction zone volatiles and trace elements but, because of difficulties in conducting hydrothermal experiments on sediments at high P-T conditions, the experiments could only be designed for a shallow ( 10 km) depth. The experimental results demonstrate mobilization of volatiles (B and NH₄) and incompatible elements (As, Be, Cs, Li, Pb, Rb) in hydrothermal fluids at relatively low temperatures ( 300°C). In addition, a limited fractionation of light from heavy rare earth elements (REEs) occurs under hydrothermal conditions. On the other hand, the high field strength elements (HFSEs) Cr, Hf, Nb, Ta, Ti, and Zr are not mobile in the reacted fluids. The observed behavior of volatiles and trace elements in hydrothermal fluids is similar to the observed enrichment in As, B, Cs, Li, Pb, Rb, and light REEs and depletion in HFSEs in arc magmas relative to magmas derived directly from the upper mantle. Thus, our work suggests a link between relative mobilities of trace elements in hydrothermal fluids and deep arc magma generation in subduction zones. The experimental results are highly consistent with the proposal that the addition of subduction zone hydrous fluids to the subarc mantle, which has been depleted by previous melting events, can produce the unique characteristics of arc magmas. Moreover, the results suggest that deeply subducted sediments may no longer have the composition necessary to generate the other distinct characteristics, such as the B-δ¹¹ B and B-¹⁰Be systematics, of arc lavas. Finally, the mobilization of B, Cs, Pb, and light REEs relative to heavy REEs in the hydrothermal fluids fractionate the ratios of B/Be, B/Nb, Cs/Rb, Pb/Ce, La/Ba and LREE/HREE, which behave conservatively during normal magmatic processes. These results demonstrate that the composition of slab-derived fluids has great implications for the recycling of elements; not only in arc magmas but also in mantle plumes.     

A comparative study of concentrated plasticity models in dynamic analysis of building structures

Concentrated plasticity (CP) models are frequently used in static and dynamic building analysis and have been implemented in available commercial software. This investigation deals with three different CP‐models, a simplified macroelement model (SEM) for a complete building story, a frame element with elasto‐plastic interaction hinges (PH), and a frame element with fiber hinges (FB). The objectives of this work are to evaluate the quality of the earthquake responses predicted by these models and to identify important aspects of their implementation and limitations for their use in dynamic analysis. The three elements are tested in a single‐story asymmetric plan building and in a three‐story steel building. Results show that base shear and global response values are usually computed with better accuracy than interstory deformations and local responses. Besides, the main limitation of elasto‐plastic CP models is to control the displacement offsets that result from perfect elasto‐plastic behavior. On the other hand, calibration of the SEM‐model shows that global responses in steel structures may be computed within 20% error in the mean at a computational cost two orders of magnitude smaller than that of the other CP elements considered. However, the three element models considered lead to increasing levels of accuracy in the dynamic response and their use depends on the refinement of the analysis performed. Copyright © 2005 John Wiley & Sons, Ltd.     

磁力测深公式的推导及应用

本文从地球物理场出发，通过严密的数学物理推导，提出了磁力测深公式，并导出了著名的重力测深公式的更一般表达式。为了得到更为精确的解，本文又提出了应用最优化理论的空间域迭代算法，并根据地球物理模型对于高斯优化法进行了改进，在算法上有所创新，使其在计算机上实现时算法简单，计算速度快。文中还列举了一些模型的实验结果，对磁力测深公式及迭代算法的有效性及可靠性进行了论证。用本文方法对实际资料的处理结果是令人满意的，证明该方法有一定的实用性。     

A Finite Element Algorithm of a Nonlinear Diffusive Climate Energy Balance Model

We present a finite element algorithm of a climate diagnostic model that takes as a climate indicator the atmospheric sea-level temperature. This model belongs to the category of energy balance models introduced independently by the climatologists M.I. Budyko and W.D. Sellers in 1969 to study the influence of certain geophysical mechanisms on the Earth climate. The energy balance model we are dealing with consists of a two-dimensional nonlinear parabolic problem on the 2-sphere with the albedo terms formulated according to Budyko as a bounded maximal monotone graph in The numerical model combines the first-order Euler implicit time discretization scheme with linear finite elements for space discretization, the latter is carried out for the special case of a spherical Earth and uses quasi-uniform spherical triangles as finite elements. The numerical formulation yields a nonlinear problem that is solved by an iterative procedure. We performed different numerical simulations starting with an initial datum consisting of a monthly average temperature field, calculated from the temperature field obtained from 50 years of simulations, corresponding to the period 1950–2000, carried out by the Atmosphere General Circulation Model HIRLAM.     

Trace element partitioning between amphibole and hydrous silicate glasses at 0.6–2.6 GPa

Partitioning behavior between amphibole and silicate glass of thirty-three minor and trace elements(Sc,Ti, V, Cr, Co, Rb, Sr, P, Y, Zr, Nb, Cs, Ba, K, La, Ce, Pr,Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, Pb,Th, and U) have been determined experimentally. Products of crystallization of hydrous basalt melts from 0.6 GPa/860 °C up to 2.6 GPa/970 °C were obtained in a multianvil apparatus. Major and trace element compositions of amphibole and glass were determined with a combination of electron microprobe and laser ablation inductively coupled plasma mass spectrometry. The main mineral phase is calcic amphibole, and the coexisting glass compositions are tonalite, granodiorite, and granite. The compatibility of rare earth elements increase at 915 °C and then decrease at 970 °C, but the compatibility of most of these elements shows a continued, significant increase with increasing pressure. For high-field strength elements, large ion lithophile elements, actinide compatibility decrease with increasing temperature or pressure, but transition metals show a continued increase in compatibility within the temperature–pressure conditions. From mathematical and graphical fitting, we determined best-fit values for the ideal ionic radius(r_0, 1.01–1.04 ?), the strain-free partitioncoefficient(D_0, 1.18–1.58), and apparent Young's modulus(E, 142–370 GPa) for the M4 site in amphibole according to the lattice strain model. The D_0^M4 for rare earth elements rises at 915 °C and then drops at 970 °C at 0.6 GPa.However, the D_0^M4 values are positively proportional to the pressure for rare earth elements in the amphibole-glass pairs at 0.6–2.6 GPa and 970 °C. Furthermore, the derived best-fit values for r_0^M4 and E^M4 are almost constant and trend to increase with rising temperature and pressure,respectively. The partition coefficient is distinctly different for different melt compositions. The rare earth elements become more enriched in amphibole if the quenched glass is granodiorite or granite compared to the tonalitic glasses.     

基于Midas/GTS的FLAC3D边坡建模技术及工程应用

探讨了如何基于Midas/GTS来实现用FLAC3D建立复杂边坡模型。首先在Midas/GTS中建立几何模型和划分网格,然后根据两种软件的网格数据形式进行转换,把Midas/GTS的网格模型导入FLAC3D中。对于二维边坡问题,认为采用四边形单元比三角形单元的计算精度更高,在模型较为复杂的情况下建议在Midas/GTS中采用四边形+三角形的方式生成混合网格,然后导入FLAC3D中形成brick+wedge形式的混合网格进行分析,以保证计算精度。最后将上述建模方法应用于某边坡工程的稳定性分析,验证了该建模方法的可行性和实用性。     

我国地球形状及重力场研究的进展

本文总结了我国解放三十年来重力学上的成就。首先叙述了我国普遍重力测量工作。此外,围绕天文大地测量网的天文点周围进行了十分密集的重力测量,以保证天文重力水准计算的精度。还进行了作为地球物理勘探及其他科学研究昕用的重力测量。由天文重力水准所得的天文大地高程异常图已经完成,空间异常及布格异常图正在编制之中。在理论研究方面,也进行了不少的工作。