2.5-D modeling in electromagnetic methods of geophysics

Understanding, using, or eliminating three-dimensional (3-D) effects in electromagnetic methods of geophysics are critical requirements. Numerous achievements in 3-D modeling sometimes give the impression that they are widely available today in geophysical practice. This is not necessarily true. Existing 3-D modeling packages prove that we know how to perform 3-D modeling. However, the computer resources and costs involved make the practical application of 3-D EM modeling in geophysical applications very limited.A practical compromise, or even alternative, is represented by 2.5-D modeling characterized by the use of a 3-D source in a 2-D medium. This combination allows one to mathematically describe the related boundary value problem as a sequence of independent two-dimensional problems. The typical technique leading to such a split formulation is Fourier analysis. That is why the individual terms of a split solution are often referred to as harmonics.Although each independent problem is two-dimensional, the algorithmic implementation of finite differences or integral equations for the higher harmonics has some specific features not present in the classical 2-D cases. In this paper, a hybrid scheme consisting of a combination of the finite difference technique with the integral equation approach for transient fields is described. Evaluation of algorithm accuracy is presented and a transient logging technique application is considered. The algorithm is fast and easily implemented on a personal computer     

用边界单元法模拟二维地形对大地电磁场的影响

本文用边界单元法模拟二维地形对大地电磁场的影响.首先用格林公式将二维大地电磁的边值问题转变成积分方程,然后用边界单元法解积分方程,得到地形上的大地电磁场和它的法向导数,由此可计算电阻率.与有限单元法相比,本方法剖分后的地形与实际地形的拟合程度高,向计算机输入原始数据的工作简单,可以在微机上计算地形引起的视电阻率.本方法适合于在野外生产现场进行大地电磁法的地形改正.计算表明,地形对H_x型波的影响比对E_x型波严重得多;随着周期的增长,地形对H_x型波的影响变得稳定.     

复杂地形条件下四面体剖分电阻率三维有限元数值模拟

地形起伏对电阻率影响非常大,复杂地形条件下的电阻率异常解释一直受到很多的关注.本文提出了一种四面体网格交叉剖分方法,剖分的网格相互交错,使剖分的网格具有多样性,能较好地模拟复杂地形情况下的地电模型.同时,从点电源场满足的方程出发,本文推导了三维复杂地形条件下有限元数值模拟算法,并编制了计算程序.算例表明,本方法行之有效,计算精度高.     

Effect of Near-fault Terrain upon Dislocation Modeling

—Coseismic surface deformation provides important information needed to determine source rupture geometry and slip distribution as well as to estimate seismic moment. In this study, numerical experiments were designed to analyze and classify how free-surface topography affects surface deformation. The investigation was performed by 3-D finite element modeling. Results of this study show that crustal deformation induced by near-fault terrain is significant and can be measured with present geodetic survey techniques. The characteristics of the terrain effects show that a hill structure produces more crustal deformation than a half-space model, and that the crustal deformation of a basin structure is less than that of the half-space model. The topographic correction is in the order of five percent of the fault dislocation. On the basis of the relationship between fault offset and earthquake magnitude, it is suggested that the terrain effects on the coseismic crustal deformation of shallow earthquakes with a magnitude greater than 5.6 should be considered as one of the major errors in coseismic deformation modeling which ignored the surface topography on the order of 300 meters.     

三维重磁交互解释及区域与局部异常的分离

探讨了三维重磁交互解释的方法技术，提出构制任意形状三维物体模型的用于计算机的橡皮膜技术．针对通常分离区域与局部异常所存在的问题，提出在异常交互解释过程中同时进行异常分离的方法，并提出相应的算法．最后介绍一个应用实例．     

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.     

Real-time 3-D space numerical shake prediction for earthquake early warning

In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake prediction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.     

高密度电阻率法成像

介绍在地质大学电法科研组“高密度电阻率法正、反演软件”的基础上,研制高密度电阻率法2.5维电阻率成像系统;讨论不平地形条件下高密度电阻率法2.5维电阻率成像的算法和软件,可用于九种常用电极装置观测结果的电阻率成像。对理论和实测数据的成像结果表明,该成像系统程序运行稳定,成像效果很好。     

大地电磁Hx型波二维地形改正的方法与效果

用边界无法计算大地电磁H_x型波二维地形影响，并用有限元法计算了起伏地形下水平层状介质的大地电磁响应，用边界元法的结果对畸变后的大地电磁响应进行地形改正，基本恢复了水平地形下层状介质的大地电磁响应的特点．本文给出了物理意义明确、形式简单的视电阻车和阻抗相位地形改正公式．     

CDP RAY MODELING IN THE PRESENCE OF 3-D PLANE ISOVELOCITY LAYERS OF VARYING DIP AND STRIKE*

Various Dix-type formulae are derived, which are useful to approximate travel time functions that can be observed while modeling the common depth point (CDP) technique for 3-D isovelocity layers of varying dip and strike. All formulae can be used to compute interval velocities and recover the depth model from surface measurements. They are established by making use of the concept of wavefront curvature. Many similarities with known formulae valid for the 2-D plane isovelocity layer case exist.     

考虑海底地形的三维频率域可控源电磁响应有限体积法模拟

为了提高海洋可控源电磁的地形响应模拟精度,探讨了三维交错网格剖分有限体积法求解频率域电磁场解的数值方法.在似稳场近似条件下,推导了有限差分法和有限体积法低频电磁场控制方程的离散表达式.通过对离散表达式的分析比较表明,有限体积法较之有限差分具有更高的计算精度,同时也具有与有限差分相当的计算效率.对含地形界面网格单元电导率采用加权平均处理,通过与二维有限元程序的计算结果对比,验证了该方法可以有效提高有限体积法对地形变化的模拟精度.应用有限体积法计算了一个三维带地形储层模型的可控源电磁响应,分析表明地形变化对电场分量影响明显,磁场分量对地形变化不敏感.     

Global SH-wavefield calculation for a two-dimensional whole-Earth model with the parallel hybrid PSM/FDM algorithm

We present a parallel hybrid algorithm based on pseudospectral method (PSM) and finite difference method (FDM) for two-dimensional (2-D) global SH-wavefield simulation. The whole-Earth model is taken as a cross section of spherical Earth, and corresponding wave equations are defined in 2-D cylindrical coordinates. Spatial derivatives in the wave equations are approximated with efficient and high accuracy PSM in the lateral and high-order FDM in the radial direction on staggered grids. This algorithm allows us to divide the whole-Earth into sub-domains in radial direction and implement efficient parallel computing on PC cluster, while retains high accuracy and efficiency of PSM in lateral direction. A transformation of moment tensor between 3-D spherical Earth and our 2-D model was proposed to give corresponding moment tensor components used in 2-D modeling. Comparison of modeling results with those obtained by direct solution method shows very good accuracy of our algorithm. We also demonstrate its feasibility with a lateral heterogeneous whole-Earth model with localized velocity perturbation.     

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.     

地壳三维构造反演和速度层析成像

本文给出利用空间深地震测深反射资料重建地壳三维构造和速度分布的方法，适用于任意分层并且每层可由若干断块组成的地壳模型。通过采用适当的反演方法获得地壳界面的三维构造，并在此结果基础之上，进一步将剩余走时残差归因于地壳速度的不均匀性，采用东分块的反演方法，重建地壳三维速度分布，数值模拟的结果表明算法是有效的。     

Three-Dimensional Magnetotelluric Inversion: An Introductory Guide for Developers and Users

In the last few decades, the demand for three-dimensional (3-D) inversions for magnetotelluric data has significantly driven the progress of 3-D codes. There are currently a lot of new 3-D inversion and forward modeling codes. Some, such as the WSINV3DMT code of the author, are available to the academic community. The goal of this paper is to summarize all the important issues involving 3-D inversions. It aims to show how inversion works and how to use it properly. In this paper, I start by describing several good reasons for doing 3-D inversion instead of 2-D inversion. The main algorithms for 3-D inversion are reviewed along with some comparisons of their advantages and disadvantages. These algorithms are the classical Occam’s inversion, the data space Occam’s inversion, the Gauss–Newton method, the Gauss–Newton with the conjugate gradient method, the non-linear conjugate gradient method, and the quasi-Newton method. Other variants are based on these main algorithms. Forward modeling, sensitivity calculations, model covariance and its parallel implementation are all necessary components of inversions and are reviewed here. Rules of thumb for performing 3-D inversion are proposed for the benefit of the 3-D inversion novice. Problems regarding 3-D inversions are discussed along with suggested topics for future research for the developers of the next decades.     

基于非结构化网格的2.5-D直流电阻率自适应有限元数值模拟

2.5-D直流电阻率有限元数值模拟中,模型的剖分及加密主要通过手动实现.另外,采用的单元类型比较规则如矩形单元等,不易实现复杂模型的模拟.为解决上述问题,文中提出了一种自适应有限元算法.算法中采用稳健的后验误差估计来自动预测下一次网格的单元尺寸,直到设定的迭代条件满足为止.另外,采用非结构化三角形单元实现了任意复杂模型的灵活剖分.基于此,利用垂直接触面模型分析和对比了不同自适应策略的效率.通过对比发现,点源附近的单元得到了加密以消除源的奇异性.另外,对于任意一种策略,有限元结果均能最终收敛到精确解.最后,模拟了两个模型：2-D单个异常体模型和2-D地形模型.     

带地形的大地电磁各向异性二维模拟及实例对比分析

带地形的大地电磁二维正演数值模拟多数基于电性各向同性理论,由于地球内部电性各向异性现象的普遍存在,基于电性各向异性理论研究地形起伏情况下大地电磁二维正演数值模拟就显得非常迫切.本文首先由麦克斯韦方程出发,引入张量电导率,求得一组关于平行走向的电场分量Ex和磁场分量Hx的二阶偏微分方程,使用有限差分法求解出Ex和Hx的近似解,并以此求得其他场分量;其次,引入地形因素,改变变量在网格节点中的排列方式,选择交错排列方式从而给有限差分系数矩阵的最大带宽分配合理的存储空间;最后,使用Weaver的方法解决TM模式下,在地-空分界面垂直于构造走向的一些区域存在不同电导率的问题.通过对带地形的二维电性各向异性结构做正演模拟,研究地形因素对大地电磁响应的影响;以电性各向异性理论为基础,将地形因素引入对实测大地电磁资料的处理中,通过做二维正演拟合和未引入地形因素的结果做对比,说明电性各向异性现象的普遍存在,认识地形因素对观测大地电磁场的影响,为今后分析解释实测大地电磁资料包含地形因素和电性各向异性情况提供理论基础和技术指导.     

固定点源测深激电异常研究

电阻率法三维有限元数值模拟方法的实现, 给研究形状复杂的地质体的电性异常提供了有力工具.本文利用该数值模拟程序,通过先模拟计算模型的视电阻率,然后利用视电阻率和视极化率的转换公式转换,从而实现对激电异常的数值模拟.文章计算并分析了固定点源测深法在各种1\|D、2\|D、3\|D模型下的激电异常规律及定量解释结果,力求使人们从空间不同角度了解该方法的IP异常规律,从而指导野外生产实践,提高解释效率和精度.     

电导率连续变化的三维电阻率测深有限元模拟

针对地下岩矿石的物性参数常常是连续变化的情况,给出了电导率分块连续变化的三维地电断面电阻率测深的有限元数值模拟方法. 首先列出了三维地电断面点源电场的变分问题;然后利用有限单元法解变分问题,采用六面体单元对研究区域进行剖分,对电导率及电位均用三线性函数进行插值;并对2例模型进行了计算,将其结果与二维有限单元法的情况进行了对比,提高了精度.